Non-monomial groups

See monomial groups.

Groups of order 24

		d	ρ	Label	ID
SL₂(𝔽₃)	Special linear group on 𝔽₃²; = Q₈ ⋊C₃ = 2T = <2,3,3> = 1^st non-monomial group	8	2-	SL(2,3)	24,3

Groups of order 48

		d	ρ	Label	ID
GL₂(𝔽₃)	General linear group on 𝔽₃²; = Q₈ ⋊S₃ = Aut(C₃²)	8	2	GL(2,3)	48,29
CSU₂(𝔽₃)	Conformal special unitary group on 𝔽₃²; = Q₈ .S₃ = 2O = <2,3,4>	16	2-	CSU(2,3)	48,28
C₄.A₄	The central extension by C₄ of A₄	16	2	C4.A4	48,33
C₂×SL₂(𝔽₃)	Direct product of C₂ and SL₂(𝔽₃)	16		C2xSL(2,3)	48,32

Groups of order 60

		d	ρ	Label	ID
A₅	Alternating group on 5 letters; = SL₂(𝔽₄) = L₂(5) = L₂(4) = icosahedron/dodecahedron rotations; 1^st non-abelian simple	5	3+	A5	60,5

Groups of order 72

		d	ρ	Label	ID
Q₈⋊C₉	The semidirect product of Q₈ and C₉ acting via C₉/C₃=C₃	72	2	Q8:C9	72,3
C₃×SL₂(𝔽₃)	Direct product of C₃ and SL₂(𝔽₃)	24	2	C3xSL(2,3)	72,25

Groups of order 96

		d	ρ	Label	ID
U₂(𝔽₃)	Unitary group on 𝔽₃²; = SL₂(𝔽₃)⋊₂ C₄	24	2	U(2,3)	96,67
Q₈⋊A₄	1^st semidirect product of Q₈ and A₄ acting via A₄/C₂²=C₃	24	6-	Q8:A4	96,203
Q₈⋊Dic₃	The semidirect product of Q₈ and Dic₃ acting via Dic₃/C₂=S₃	32		Q8:Dic3	96,66
C₂³.₃A₄	1^st non-split extension by C₂³ of A₄ acting via A₄/C₂²=C₃	12	6+	C2^3.3A4	96,3
D₄.A₄	The non-split extension by D₄ of A₄ acting through Inn(D₄)	16	4-	D4.A4	96,202
C₄.₆S₄	3^rd central extension by C₄ of S₄	16	2	C4.6S4	96,192
C₄.₃S₄	3^rd non-split extension by C₄ of S₄ acting via S₄/A₄=C₂	16	4+	C4.3S4	96,193
Q₈.D₆	2^nd non-split extension by Q₈ of D₆ acting via D₆/C₂=S₃	16	4-	Q8.D6	96,190
Q₈.A₄	The non-split extension by Q₈ of A₄ acting through Inn(Q₈)	24	4+	Q8.A4	96,201
C₈.A₄	The central extension by C₈ of A₄	32	2	C8.A4	96,74
C₄.S₄	2^nd non-split extension by C₄ of S₄ acting via S₄/A₄=C₂	32	4-	C4.S4	96,191
C₂×GL₂(𝔽₃)	Direct product of C₂ and GL₂(𝔽₃)	16		C2xGL(2,3)	96,189
C₄×SL₂(𝔽₃)	Direct product of C₄ and SL₂(𝔽₃)	32		C4xSL(2,3)	96,69
C₂×CSU₂(𝔽₃)	Direct product of C₂ and CSU₂(𝔽₃)	32		C2xCSU(2,3)	96,188
C₂²×SL₂(𝔽₃)	Direct product of C₂² and SL₂(𝔽₃)	32		C2^2xSL(2,3)	96,198
C₂×C₄.A₄	Direct product of C₂ and C₄.A₄	32		C2xC4.A4	96,200

Groups of order 108

		d	ρ	Label	ID
He₃⋊C₄	The semidirect product of He₃ and C₄ acting faithfully	18	3	He3:C4	108,15

Groups of order 120

		d	ρ	Label	ID
S₅	Symmetric group on 5 letters; = PGL₂(𝔽₅) = Aut(A₅) = 5-cell symmetries; almost simple	5	4+	S5	120,34
SL₂(𝔽₅)	Special linear group on 𝔽₅²; = C₂ .A₅ = 2I = <2,3,5>	24	2-	SL(2,5)	120,5
C₂×A₅	Direct product of C₂ and A₅; = icosahedron/dodecahedron symmetries	10	3+	C2xA5	120,35
C₅×SL₂(𝔽₃)	Direct product of C₅ and SL₂(𝔽₃)	40	2	C5xSL(2,3)	120,15

Groups of order 144

		d	ρ	Label	ID
Q₈⋊D₉	The semidirect product of Q₈ and D₉ acting via D₉/C₃=S₃	72	4+	Q8:D9	144,32
C₆.₆S₄	6^th non-split extension by C₆ of S₄ acting via S₄/A₄=C₂	24	4+	C6.6S4	144,125
C₆.₅S₄	5^th non-split extension by C₆ of S₄ acting via S₄/A₄=C₂	48	4-	C6.5S4	144,124
Dic₃.A₄	The non-split extension by Dic₃ of A₄ acting through Inn(Dic₃)	48	4+	Dic3.A4	144,127
Q₈.C₁₈	The non-split extension by Q₈ of C₁₈ acting via C₁₈/C₆=C₃	72	2	Q8.C18	144,36
Q₈.D₉	The non-split extension by Q₈ of D₉ acting via D₉/C₃=S₃	144	4-	Q8.D9	144,31
C₃×GL₂(𝔽₃)	Direct product of C₃ and GL₂(𝔽₃)	24	2	C3xGL(2,3)	144,122
S₃×SL₂(𝔽₃)	Direct product of S₃ and SL₂(𝔽₃); = SL₂(ℤ/6ℤ)	24	4-	S3xSL(2,3)	144,128
C₆×SL₂(𝔽₃)	Direct product of C₆ and SL₂(𝔽₃)	48		C6xSL(2,3)	144,156
C₃×CSU₂(𝔽₃)	Direct product of C₃ and CSU₂(𝔽₃)	48	2	C3xCSU(2,3)	144,121
C₃×C₄.A₄	Direct product of C₃ and C₄.A₄	48	2	C3xC4.A4	144,157
C₂×Q₈⋊C₉	Direct product of C₂ and Q₈⋊C₉	144		C2xQ8:C9	144,35

Groups of order 160

		d	ρ	Label	ID
2_-¹⁺⁴⋊C₅	The semidirect product of 2_-¹⁺⁴ and C₅ acting faithfully	32	4-	ES-(2,2):C5	160,199

Groups of order 168

		d	ρ	Label	ID
GL₃(𝔽₂)	General linear group on 𝔽₂³; = Aut(C₂³) = L₃(2) = L₂(7); 2^nd non-abelian simple	7	3	GL(3,2)	168,42
C₁₄.A₄	The non-split extension by C₁₄ of A₄ acting via A₄/C₂²=C₃	56	6	C14.A4	168,23
C₇×SL₂(𝔽₃)	Direct product of C₇ and SL₂(𝔽₃)	56	2	C7xSL(2,3)	168,22

Groups of order 180

		d	ρ	Label	ID
C₃×A₅	Direct product of C₃ and A₅; = GL₂(𝔽₄)	15	3	C3xA5	180,19

Groups of order 192

		d	ρ	Label	ID
CU₂(𝔽₃)	Conformal unitary group on 𝔽₃²; = U₂(𝔽₃)⋊₇ C₂	32	2	CU(2,3)	192,963
Q₈⋊S₄	1^st semidirect product of Q₈ and S₄ acting via S₄/C₂²=S₃	24	6	Q8:S4	192,1490
Q₈⋊D₁₂	The semidirect product of Q₈ and D₁₂ acting via D₁₂/C₄=S₃	32		Q8:D12	192,952
U₂(𝔽₃)⋊C₂	6^th semidirect product of U₂(𝔽₃) and C₂ acting faithfully	32	4	U(2,3):C2	192,982
GL₂(𝔽₃)⋊C₄	1^st semidirect product of GL₂(𝔽₃) and C₄ acting via C₄/C₂=C₂	32		GL(2,3):C4	192,953
SL₂(𝔽₃)⋊D₄	2^nd semidirect product of SL₂(𝔽₃) and D₄ acting via D₄/C₂²=C₂	32		SL(2,3):D4	192,986
SL₂(𝔽₃)⋊₅D₄	1^st semidirect product of SL₂(𝔽₃) and D₄ acting through Inn(SL₂(𝔽₃))	32		SL(2,3):5D4	192,1003
2_-¹⁺⁴⋊₃C₆	2^nd semidirect product of 2_-¹⁺⁴ and C₆ acting via C₆/C₂=C₃	32	4	ES-(2,2):3C6	192,1504
GL₂(𝔽₃)⋊C₂²	3^rd semidirect product of GL₂(𝔽₃) and C₂² acting via C₂²/C₂=C₂	32	4	GL(2,3):C2^2	192,1482
Q₈⋊Dic₆	The semidirect product of Q₈ and Dic₆ acting via Dic₆/C₄=S₃	64		Q8:Dic6	192,945
Q₈⋊SL₂(𝔽₃)	The semidirect product of Q₈ and SL₂(𝔽₃) acting via SL₂(𝔽₃)/Q₈=C₃	64		Q8:SL(2,3)	192,1022
SL₂(𝔽₃)⋊Q₈	2^nd semidirect product of SL₂(𝔽₃) and Q₈ acting via Q₈/C₄=C₂	64		SL(2,3):Q8	192,950
SL₂(𝔽₃)⋊₆D₄	2^nd semidirect product of SL₂(𝔽₃) and D₄ acting through Inn(SL₂(𝔽₃))	64		SL(2,3):6D4	192,1005
SL₂(𝔽₃)⋊₃Q₈	The semidirect product of SL₂(𝔽₃) and Q₈ acting through Inn(SL₂(𝔽₃))	64		SL(2,3):3Q8	192,1006
CSU₂(𝔽₃)⋊C₄	1^st semidirect product of CSU₂(𝔽₃) and C₄ acting via C₄/C₂=C₂	64		CSU(2,3):C4	192,947
C₂³⋊₂D₄⋊C₃	The semidirect product of C₂³⋊₂D₄ and C₃ acting faithfully	12	6+	C2^3:2D4:C3	192,194
C₄○D₄⋊A₄	1^st semidirect product of C₄○D₄ and A₄ acting via A₄/C₂²=C₃	24	6	C4oD4:A4	192,1507
C₄²⋊₄C₄⋊C₃	The semidirect product of C₄²⋊₄C₄ and C₃ acting faithfully	24	6	C4^2:4C4:C3	192,190
(C₂×Q₈)⋊C₁₂	The semidirect product of C₂×Q₈ and C₁₂ acting via C₁₂/C₂=C₆	32		(C2xQ8):C12	192,998
C₄○D₄⋊C₁₂	The semidirect product of C₄○D₄ and C₁₂ acting via C₁₂/C₂=C₆	64		C4oD4:C12	192,999
C₄.A₄⋊C₄	4^th semidirect product of C₄.A₄ and C₄ acting via C₄/C₂=C₂	64		C4.A4:C4	192,983
C₂⁴.₂A₄	2^nd non-split extension by C₂⁴ of A₄ acting faithfully	12	6+	C2^4.2A4	192,197
D₄.₄S₄	1^st non-split extension by D₄ of S₄ acting through Inn(D₄)	16	4	D4.4S4	192,1485
C₂⁴.₇A₄	7^th non-split extension by C₂⁴ of A₄ acting faithfully	16		C2^4.7A4	192,1021
C₂³.SL₂(𝔽₃)	1^st non-split extension by C₂³ of SL₂(𝔽₃) acting via SL₂(𝔽₃)/C₂=A₄	16	4	C2^3.SL(2,3)	192,4
Q₈.₅S₄	3^rd non-split extension by Q₈ of S₄ acting via S₄/A₄=C₂	24	4+	Q8.5S4	192,988
C₂³.₇S₄	1^st non-split extension by C₂³ of S₄ acting via S₄/C₂²=S₃	24	6	C2^3.7S4	192,180
C₂³.₈S₄	2^nd non-split extension by C₂³ of S₄ acting via S₄/C₂²=S₃	24	6+	C2^3.8S4	192,181
C₂⁴.A₄	1^st non-split extension by C₂⁴ of A₄ acting faithfully	24	6	C2^4.A4	192,195
C₂⁴.₃A₄	3^rd non-split extension by C₂⁴ of A₄ acting faithfully	24	6	C2^4.3A4	192,198
D₈.A₄	The non-split extension by D₈ of A₄ acting through Inn(D₈)	32	4-	D8.A4	192,1019
C₈.₅S₄	5^th non-split extension by C₈ of S₄ acting via S₄/A₄=C₂	32	4	C8.5S4	192,964
C₈.₄S₄	4^th non-split extension by C₈ of S₄ acting via S₄/A₄=C₂	32	4	C8.4S4	192,965
C₈.₃S₄	3^rd non-split extension by C₈ of S₄ acting via S₄/A₄=C₂	32	4+	C8.3S4	192,966
D₄.S₄	2^nd non-split extension by D₄ of S₄ acting via S₄/A₄=C₂	32	4-	D4.S4	192,989
D₄.₃S₄	3^rd non-split extension by D₄ of S₄ acting via S₄/A₄=C₂	32	4	D4.3S4	192,990
D₄.₅S₄	2^nd non-split extension by D₄ of S₄ acting through Inn(D₄)	32	4-	D4.5S4	192,1486
SD₁₆.A₄	The non-split extension by SD₁₆ of A₄ acting through Inn(SD₁₆)	32	4	SD16.A4	192,1018
Q₈.₆S₄	1^st non-split extension by Q₈ of S₄ acting through Inn(Q₈)	32	4	Q8.6S4	192,1483
Q₈.₇S₄	2^nd non-split extension by Q₈ of S₄ acting through Inn(Q₈)	32	4+	Q8.7S4	192,1484
Q₈.₂D₁₂	2^nd non-split extension by Q₈ of D₁₂ acting via D₁₂/C₄=S₃	32		Q8.2D12	192,954
M₄(2).A₄	The non-split extension by M₄(2) of A₄ acting through Inn(M₄(2))	32	4	M4(2).A4	192,1013
C₂³.₁₄S₄	1^st non-split extension by C₂³ of S₄ acting via S₄/A₄=C₂	32		C2^3.14S4	192,978
C₂³.₁₅S₄	2^nd non-split extension by C₂³ of S₄ acting via S₄/A₄=C₂	32		C2^3.15S4	192,979
C₂³.₁₆S₄	3^rd non-split extension by C₂³ of S₄ acting via S₄/A₄=C₂	32		C2^3.16S4	192,980
Q₁₆.A₄	The non-split extension by Q₁₆ of A₄ acting through Inn(Q₁₆)	48	4+	Q16.A4	192,1017
Q₈.₄S₄	2^nd non-split extension by Q₈ of S₄ acting via S₄/A₄=C₂	48	4	Q8.4S4	192,987
Q₈.₁S₄	1^st non-split extension by Q₈ of S₄ acting via S₄/C₂²=S₃	48	6-	Q8.1S4	192,1489
C₁₆.A₄	The central extension by C₁₆ of A₄	64	2	C16.A4	192,204
C₈.₇S₄	2^nd central extension by C₈ of S₄	64	2	C8.7S4	192,187
C₈.S₄	2^nd non-split extension by C₈ of S₄ acting via S₄/A₄=C₂	64	4-	C8.S4	192,962
C₂.U₂(𝔽₃)	The central extension by C₂ of U₂(𝔽₃)	64		C2.U(2,3)	192,183
Q₈.D₁₂	1^st non-split extension by Q₈ of D₁₂ acting via D₁₂/C₄=S₃	64		Q8.D12	192,949
Q₈.Dic₆	1^st non-split extension by Q₈ of Dic₆ acting via Dic₆/C₄=S₃	64		Q8.Dic6	192,948
SL₂(𝔽₃).D₄	2^nd non-split extension by SL₂(𝔽₃) of D₄ acting via D₄/C₂²=C₂	64		SL(2,3).D4	192,984
(C₂²×C₄).A₄	4^th non-split extension by C₂²×C₄ of A₄ acting faithfully	24	6-	(C2^2xC4).A4	192,196
C₂³.₁₉(C₂×A₄)	12^nd non-split extension by C₂³ of C₂×A₄ acting via C₂×A₄/C₂³=C₃	24	6	C2^3.19(C2xA4)	192,199
(C₂×C₄).S₄	15^th non-split extension by C₂×C₄ of S₄ acting via S₄/A₄=C₂	64		(C2xC4).S4	192,985
C₄×GL₂(𝔽₃)	Direct product of C₄ and GL₂(𝔽₃)	32		C4xGL(2,3)	192,951
D₄×SL₂(𝔽₃)	Direct product of D₄ and SL₂(𝔽₃)	32		D4xSL(2,3)	192,1004
C₂²×GL₂(𝔽₃)	Direct product of C₂² and GL₂(𝔽₃)	32		C2^2xGL(2,3)	192,1475
C₂×U₂(𝔽₃)	Direct product of C₂ and U₂(𝔽₃)	48		C2xU(2,3)	192,981
C₈×SL₂(𝔽₃)	Direct product of C₈ and SL₂(𝔽₃)	64		C8xSL(2,3)	192,200
Q₈×SL₂(𝔽₃)	Direct product of Q₈ and SL₂(𝔽₃)	64		Q8xSL(2,3)	192,1007
C₄×CSU₂(𝔽₃)	Direct product of C₄ and CSU₂(𝔽₃)	64		C4xCSU(2,3)	192,946
C₂³×SL₂(𝔽₃)	Direct product of C₂³ and SL₂(𝔽₃)	64		C2^3xSL(2,3)	192,1498
C₂²×CSU₂(𝔽₃)	Direct product of C₂² and CSU₂(𝔽₃)	64		C2^2xCSU(2,3)	192,1474
C₂×C₂³.₃A₄	Direct product of C₂ and C₂³.₃A₄	24		C2xC2^3.3A4	192,189
C₂×D₄.A₄	Direct product of C₂ and D₄.A₄	32		C2xD4.A4	192,1503
C₂×C₄.₆S₄	Direct product of C₂ and C₄.₆S₄	32		C2xC4.6S4	192,1480
C₂×C₄.₃S₄	Direct product of C₂ and C₄.₃S₄	32		C2xC4.3S4	192,1481
C₂×Q₈.D₆	Direct product of C₂ and Q₈.D₆	32		C2xQ8.D6	192,1476
C₂×Q₈⋊A₄	Direct product of C₂ and Q₈⋊A₄	48		C2xQ8:A4	192,1506
C₂×Q₈.A₄	Direct product of C₂ and Q₈.A₄	48		C2xQ8.A4	192,1502
C₄×C₄.A₄	Direct product of C₄ and C₄.A₄	64		C4xC4.A4	192,997
C₂×C₈.A₄	Direct product of C₂ and C₈.A₄	64		C2xC8.A4	192,1012
C₂×C₄.S₄	Direct product of C₂ and C₄.S₄	64		C2xC4.S4	192,1479
C₂×Q₈⋊Dic₃	Direct product of C₂ and Q₈⋊Dic₃	64		C2xQ8:Dic3	192,977
C₂²×C₄.A₄	Direct product of C₂² and C₄.A₄	64		C2^2xC4.A4	192,1500
C₂×C₄×SL₂(𝔽₃)	Direct product of C₂×C₄ and SL₂(𝔽₃)	64		C2xC4xSL(2,3)	192,996

Groups of order 216

		d	ρ	Label	ID
SU₃(𝔽₂)	Special unitary group on 𝔽₂³; = He₃ ⋊Q₈	27	3	SU(3,2)	216,88
ASL₂(𝔽₃)	Hessian group = Affine special linear group on 𝔽₃²; = PSU₃(𝔽₂)⋊C₃	9	8+	ASL(2,3)	216,153
He₃⋊D₄	The semidirect product of He₃ and D₄ acting faithfully	18	6+	He3:D4	216,87
He₃⋊C₈	The semidirect product of He₃ and C₈ acting faithfully	27	6+	He3:C8	216,86
Q₈⋊He₃	The semidirect product of Q₈ and He₃ acting via He₃/C₃²=C₃	72	6	Q8:He3	216,42
He₃⋊₂C₈	The semidirect product of He₃ and C₈ acting via C₈/C₂=C₄	72	3	He3:2C8	216,25
Q₈⋊3_-¹⁺²	The semidirect product of Q₈ and 3_-¹⁺² acting via 3_-¹⁺²/C₃²=C₃	72	6	Q8:ES-(3,1)	216,41
Q₈⋊C₂₇	The semidirect product of Q₈ and C₂₇ acting via C₂₇/C₉=C₃	216	2	Q8:C27	216,3
C₁₈.A₄	The non-split extension by C₁₈ of A₄ acting via A₄/C₂²=C₃	72	6	C18.A4	216,39
C₉×SL₂(𝔽₃)	Direct product of C₉ and SL₂(𝔽₃)	72	2	C9xSL(2,3)	216,38
C₃²×SL₂(𝔽₃)	Direct product of C₃² and SL₂(𝔽₃)	72		C3^2xSL(2,3)	216,134
C₂×He₃⋊C₄	Direct product of C₂ and He₃⋊C₄	36	3	C2xHe3:C4	216,100
C₃×Q₈⋊C₉	Direct product of C₃ and Q₈⋊C₉	216		C3xQ8:C9	216,40

Groups of order 240

		d	ρ	Label	ID
CSU₂(𝔽₅)	Conformal special unitary group on 𝔽₅²; = C₂ .₂ S₅	48	4-	CSU(2,5)	240,89
A₅⋊C₄	The semidirect product of A₅ and C₄ acting via C₄/C₂=C₂	12	4	A5:C4	240,91
Q₈⋊D₁₅	The semidirect product of Q₈ and D₁₅ acting via D₁₅/C₅=S₃	40	4+	Q8:D15	240,106
C₄.A₅	The central extension by C₄ of A₅	24	2	C4.A5	240,93
C₂.S₅	2^nd central stem extension by C₂ of S₅	40	4-	C2.S5	240,90
Q₈.D₁₅	The non-split extension by Q₈ of D₁₅ acting via D₁₅/C₅=S₃	80	4-	Q8.D15	240,105
Dic₅.A₄	The non-split extension by Dic₅ of A₄ acting through Inn(Dic₅)	80	4+	Dic5.A4	240,108
C₂×S₅	Direct product of C₂ and S₅; = O₃(𝔽₅)	10	4+	C2xS5	240,189
C₄×A₅	Direct product of C₄ and A₅	20	3	C4xA5	240,92
C₂²×A₅	Direct product of C₂² and A₅	20		C2^2xA5	240,190
C₅×GL₂(𝔽₃)	Direct product of C₅ and GL₂(𝔽₃)	40	2	C5xGL(2,3)	240,103
D₅×SL₂(𝔽₃)	Direct product of D₅ and SL₂(𝔽₃)	40	4-	D5xSL(2,3)	240,109
C₂×SL₂(𝔽₅)	Direct product of C₂ and SL₂(𝔽₅)	48		C2xSL(2,5)	240,94
C₅×CSU₂(𝔽₃)	Direct product of C₅ and CSU₂(𝔽₃)	80	2	C5xCSU(2,3)	240,102
C₁₀×SL₂(𝔽₃)	Direct product of C₁₀ and SL₂(𝔽₃)	80		C10xSL(2,3)	240,153
C₅×C₄.A₄	Direct product of C₅ and C₄.A₄	80	2	C5xC4.A4	240,154

Groups of order 264

		d	ρ	Label	ID
C₁₁×SL₂(𝔽₃)	Direct product of C₁₁ and SL₂(𝔽₃)	88	2	C11xSL(2,3)	264,12

Groups of order 288

		d	ρ	Label	ID
Ω₄⁺ (𝔽₃)	Omega group of + type on 𝔽₃⁴; = SL₂(𝔽₃)⋊A₄	24	4+	Omega+(4,3)	288,860
GL₂(𝔽₃)⋊S₃	1^st semidirect product of GL₂(𝔽₃) and S₃ acting via S₃/C₃=C₂	48	4+	GL(2,3):S3	288,847
C₃⋊U₂(𝔽₃)	The semidirect product of C₃ and U₂(𝔽₃) acting via U₂(𝔽₃)/C₄.A₄=C₂	72	4	C3:U(2,3)	288,404
2₊¹⁺⁴⋊C₉	1^st semidirect product of 2₊¹⁺⁴ and C₉ acting via C₉/C₃=C₃	72	4	ES+(2,2):C9	288,348
CSU₂(𝔽₃)⋊S₃	1^st semidirect product of CSU₂(𝔽₃) and S₃ acting via S₃/C₃=C₂	96	4	CSU(2,3):S3	288,844
2_-¹⁺⁴⋊C₉	The semidirect product of 2_-¹⁺⁴ and C₉ acting via C₉/C₃=C₃	144	4	ES-(2,2):C9	288,349
Q₈⋊Dic₉	The semidirect product of Q₈ and Dic₉ acting via Dic₉/C₆=S₃	288		Q8:Dic9	288,69
C₂²⋊(Q₈⋊C₉)	The semidirect product of C₂² and Q₈⋊C₉ acting via Q₈⋊C₉/C₃×Q₈=C₃	72	6	C2^2:(Q8:C9)	288,350
D₁₂.A₄	The non-split extension by D₁₂ of A₄ acting through Inn(D₁₂)	48	4-	D12.A4	288,926
C₁₂.₇S₄	7^th non-split extension by C₁₂ of S₄ acting via S₄/A₄=C₂	48	4+	C12.7S4	288,915
D₆.S₄	1^st non-split extension by D₆ of S₄ acting via S₄/A₄=C₂	48	4-	D6.S4	288,849
D₆.₂S₄	2^nd non-split extension by D₆ of S₄ acting via S₄/A₄=C₂	48	4	D6.2S4	288,850
C₁₂.₁₄S₄	14^th non-split extension by C₁₂ of S₄ acting via S₄/A₄=C₂	48	4	C12.14S4	288,914
Dic₃.₄S₄	1^st non-split extension by Dic₃ of S₄ acting through Inn(Dic₃)	48	4	Dic3.4S4	288,845
Dic₃.₅S₄	2^nd non-split extension by Dic₃ of S₄ acting through Inn(Dic₃)	48	4+	Dic3.5S4	288,846
SL₂(𝔽₃).D₆	2^nd non-split extension by SL₂(𝔽₃) of D₆ acting via D₆/C₆=C₂	48	4	SL(2,3).D6	288,912
SL₂(𝔽₃).₁₁D₆	1^st non-split extension by SL₂(𝔽₃) of D₆ acting through Inn(SL₂(𝔽₃))	48	4	SL(2,3).11D6	288,923
C₁₂.₉S₄	9^th non-split extension by C₁₂ of S₄ acting via S₄/A₄=C₂	72	4	C12.9S4	288,70
C₁₂.₄S₄	4^th non-split extension by C₁₂ of S₄ acting via S₄/A₄=C₂	72	4+	C12.4S4	288,340
Dic₆.A₄	The non-split extension by Dic₆ of A₄ acting through Inn(Dic₆)	72	4+	Dic6.A4	288,924
C₁₂.₆S₄	6^th non-split extension by C₁₂ of S₄ acting via S₄/A₄=C₂	96	4-	C12.6S4	288,913
C₆.GL₂(𝔽₃)	3^rd non-split extension by C₆ of GL₂(𝔽₃) acting via GL₂(𝔽₃)/SL₂(𝔽₃)=C₂	96		C6.GL(2,3)	288,403
SL₂(𝔽₃).Dic₃	The non-split extension by SL₂(𝔽₃) of Dic₃ acting through Inn(SL₂(𝔽₃))	96	4	SL(2,3).Dic3	288,410
Q₈.C₃₆	The non-split extension by Q₈ of C₃₆ acting via C₃₆/C₁₂=C₃	144	2	Q8.C36	288,77
C₁₂.₃S₄	3^rd non-split extension by C₁₂ of S₄ acting via S₄/A₄=C₂	144	4-	C12.3S4	288,338
C₁₂.₁₁S₄	11^st non-split extension by C₁₂ of S₄ acting via S₄/A₄=C₂	144	4	C12.11S4	288,339
Q₈.D₁₈	2^nd non-split extension by Q₈ of D₁₈ acting via D₁₈/C₆=S₃	144	4	Q8.D18	288,337
C₂.(C₄²⋊C₉)	The central stem extension by C₂ of C₄²⋊C₉	36	6	C2.(C4^2:C9)	288,3
S₃×GL₂(𝔽₃)	Direct product of S₃ and GL₂(𝔽₃); = GL₂(ℤ/6ℤ)	24	4	S3xGL(2,3)	288,851
A₄×SL₂(𝔽₃)	Direct product of A₄ and SL₂(𝔽₃)	24	6-	A4xSL(2,3)	288,859
C₆×GL₂(𝔽₃)	Direct product of C₆ and GL₂(𝔽₃)	48		C6xGL(2,3)	288,900
S₃×CSU₂(𝔽₃)	Direct product of S₃ and CSU₂(𝔽₃)	48	4-	S3xCSU(2,3)	288,848
C₃×U₂(𝔽₃)	Direct product of C₃ and U₂(𝔽₃)	72	2	C3xU(2,3)	288,400
C₁₂×SL₂(𝔽₃)	Direct product of C₁₂ and SL₂(𝔽₃)	96		C12xSL(2,3)	288,633
C₆×CSU₂(𝔽₃)	Direct product of C₆ and CSU₂(𝔽₃)	96		C6xCSU(2,3)	288,899
Dic₃×SL₂(𝔽₃)	Direct product of Dic₃ and SL₂(𝔽₃)	96		Dic3xSL(2,3)	288,409
C₃×C₂³.₃A₄	Direct product of C₃ and C₂³.₃A₄	36	6	C3xC2^3.3A4	288,230
S₃×C₄.A₄	Direct product of S₃ and C₄.A₄	48	4	S3xC4.A4	288,925
C₃×D₄.A₄	Direct product of C₃ and D₄.A₄	48	4	C3xD4.A4	288,985
C₃×C₄.₆S₄	Direct product of C₃ and C₄.₆S₄	48	2	C3xC4.6S4	288,903
C₃×C₄.₃S₄	Direct product of C₃ and C₄.₃S₄	48	4	C3xC4.3S4	288,904
C₂×C₆.₆S₄	Direct product of C₂ and C₆.₆S₄	48		C2xC6.6S4	288,911
C₃×Q₈.D₆	Direct product of C₃ and Q₈.D₆	48	4	C3xQ8.D6	288,901
C₂×S₃×SL₂(𝔽₃)	Direct product of C₂, S₃ and SL₂(𝔽₃)	48		C2xS3xSL(2,3)	288,922
C₃×Q₈⋊A₄	Direct product of C₃ and Q₈⋊A₄	72	6	C3xQ8:A4	288,986
C₃×Q₈.A₄	Direct product of C₃ and Q₈.A₄	72	4	C3xQ8.A4	288,984
C₃×C₈.A₄	Direct product of C₃ and C₈.A₄	96	2	C3xC8.A4	288,638
C₆×C₄.A₄	Direct product of C₆ and C₄.A₄	96		C6xC4.A4	288,983
C₃×C₄.S₄	Direct product of C₃ and C₄.S₄	96	4	C3xC4.S4	288,902
C₂×C₆.₅S₄	Direct product of C₂ and C₆.₅S₄	96		C2xC6.5S4	288,910
C₃×Q₈⋊Dic₃	Direct product of C₃ and Q₈⋊Dic₃	96		C3xQ8:Dic3	288,399
C₂×C₆×SL₂(𝔽₃)	Direct product of C₂×C₆ and SL₂(𝔽₃)	96		C2xC6xSL(2,3)	288,981
C₂×Dic₃.A₄	Direct product of C₂ and Dic₃.A₄	96		C2xDic3.A4	288,921
C₂×Q₈⋊D₉	Direct product of C₂ and Q₈⋊D₉	144		C2xQ8:D9	288,336
C₂×Q₈.C₁₈	Direct product of C₂ and Q₈.C₁₈	144		C2xQ8.C18	288,347
C₄×Q₈⋊C₉	Direct product of C₄ and Q₈⋊C₉	288		C4xQ8:C9	288,72
C₂×Q₈.D₉	Direct product of C₂ and Q₈.D₉	288		C2xQ8.D9	288,335
C₂²×Q₈⋊C₉	Direct product of C₂² and Q₈⋊C₉	288		C2^2xQ8:C9	288,345

Groups of order 300

		d	ρ	Label	ID
C₅×A₅	Direct product of C₅ and A₅; = U₂(𝔽₄)	25	3	C5xA5	300,22

Groups of order 312

		d	ρ	Label	ID
C₂₆.A₄	The non-split extension by C₂₆ of A₄ acting via A₄/C₂²=C₃	104	6	C26.A4	312,26
C₁₃×SL₂(𝔽₃)	Direct product of C₁₃ and SL₂(𝔽₃)	104	2	C13xSL(2,3)	312,25

Groups of order 320

		d	ρ	Label	ID
2_-¹⁺⁴⋊D₅	The semidirect product of 2_-¹⁺⁴ and D₅ acting faithfully	32	4	ES-(2,2):D5	320,1582
C₂².₅₈C₂⁴⋊C₅	The semidirect product of C₂².₅₈C₂⁴ and C₅ acting faithfully	64		C2^2.58C2^4:C5	320,1012
2_-¹⁺⁴.D₅	The non-split extension by 2_-¹⁺⁴ of D₅ acting faithfully	64	4-	ES-(2,2).D5	320,1581
2_-¹⁺⁴.C₁₀	The non-split extension by 2_-¹⁺⁴ of C₁₀ acting via C₁₀/C₂=C₅	64	4	ES-(2,2).C10	320,1586
C₂×2_-¹⁺⁴⋊C₅	Direct product of C₂ and 2_-¹⁺⁴⋊C₅	64		C2xES-(2,2):C5	320,1585

Groups of order 324

		d	ρ	Label	ID
He₃⋊₄Dic₃	The semidirect product of He₃ and Dic₃ acting via Dic₃/C₃=C₄	18	6	He3:4Dic3	324,113
He₃.₃C₁₂	The non-split extension by He₃ of C₁₂ acting via C₁₂/C₃=C₄	54	3	He3.3C12	324,111
C₃×He₃⋊C₄	Direct product of C₃ and He₃⋊C₄	54		C3xHe3:C4	324,110

Groups of order 336

		d	ρ	Label	ID
SL₂(𝔽₇)	Special linear group on 𝔽₇²; = C₂ .GL₃(𝔽₂)	16	4	SL(2,7)	336,114
PGL₂(𝔽₇)	Projective linear group on 𝔽₇²; = GL₃(𝔽₂)⋊C₂ = Aut(GL₃(𝔽₂)); almost simple	8	6+	PGL(2,7)	336,208
Q₈⋊F₇	The semidirect product of Q₈ and F₇ acting via F₇/D₇=C₃	56	12-	Q8:F7	336,135
Q₈⋊D₂₁	The semidirect product of Q₈ and D₂₁ acting via D₂₁/C₇=S₃	56	4+	Q8:D21	336,119
C₂₈.A₄	The non-split extension by C₂₈ of A₄ acting via A₄/C₂²=C₃	112	6	C28.A4	336,173
Q₈.F₇	The non-split extension by Q₈ of F₇ acting via F₇/D₇=C₃	112	12+	Q8.F7	336,134
Q₈.D₂₁	The non-split extension by Q₈ of D₂₁ acting via D₂₁/C₇=S₃	112	4-	Q8.D21	336,118
Dic₇.₂A₄	The non-split extension by Dic₇ of A₄ acting through Inn(Dic₇)	112	4+	Dic7.2A4	336,131
C₂×GL₃(𝔽₂)	Direct product of C₂ and GL₃(𝔽₂)	14	3	C2xGL(3,2)	336,209
C₇×GL₂(𝔽₃)	Direct product of C₇ and GL₂(𝔽₃)	56	2	C7xGL(2,3)	336,116
D₇×SL₂(𝔽₃)	Direct product of D₇ and SL₂(𝔽₃)	56	4-	D7xSL(2,3)	336,132
C₇×CSU₂(𝔽₃)	Direct product of C₇ and CSU₂(𝔽₃)	112	2	C7xCSU(2,3)	336,115
C₁₄×SL₂(𝔽₃)	Direct product of C₁₄ and SL₂(𝔽₃)	112		C14xSL(2,3)	336,169
C₇×C₄.A₄	Direct product of C₇ and C₄.A₄	112	2	C7xC4.A4	336,170
C₂×C₁₄.A₄	Direct product of C₂ and C₁₄.A₄	112		C2xC14.A4	336,172

Groups of order 360

		d	ρ	Label	ID
A₆	Alternating group on 6 letters; = PSL₂(𝔽₉) = L₂(9); 3^rd non-abelian simple	6	5+	A6	360,118
ΓL₂(𝔽₄)	Semilinear group on 𝔽₄²; = C₃ ⋊S₅	15	6	GammaL(2,4)	360,120
C₃×S₅	Direct product of C₃ and S₅	15	4	C3xS5	360,119
S₃×A₅	Direct product of S₃ and A₅	15	6+	S3xA5	360,121
C₆×A₅	Direct product of C₆ and A₅	30	3	C6xA5	360,122
C₃×SL₂(𝔽₅)	Direct product of C₃ and SL₂(𝔽₅)	72	2	C3xSL(2,5)	360,51
C₁₅×SL₂(𝔽₃)	Direct product of C₁₅ and SL₂(𝔽₃)	120	2	C15xSL(2,3)	360,89
C₅×Q₈⋊C₉	Direct product of C₅ and Q₈⋊C₉	360	2	C5xQ8:C9	360,14

Groups of order 375

		d	ρ	Label	ID
He₅⋊C₃	The semidirect product of He₅ and C₃ acting faithfully	75	5	He5:C3	375,2

Groups of order 408

		d	ρ	Label	ID
C₁₇×SL₂(𝔽₃)	Direct product of C₁₇ and SL₂(𝔽₃)	136	2	C17xSL(2,3)	408,14

Groups of order 420

		d	ρ	Label	ID
C₇×A₅	Direct product of C₇ and A₅	35	3	C7xA5	420,13

Groups of order 432

		d	ρ	Label	ID
AGL₂(𝔽₃)	Affine linear group on 𝔽₃²; = PSU₃(𝔽₂)⋊S₃ = Aut(C₃⋊S₃) = Hol(C₃²)	9	8+	AGL(2,3)	432,734
He₃⋊SD₁₆	The semidirect product of He₃ and SD₁₆ acting faithfully	27	6+	He3:SD16	432,520
He₃⋊D₈	The semidirect product of He₃ and D₈ acting via D₈/C₂=D₄	72	6+	He3:D8	432,235
He₃⋊₂SD₁₆	The semidirect product of He₃ and SD₁₆ acting via SD₁₆/C₂=D₄	72	6	He3:2SD16	432,234
He₃⋊₁M₄(2)	The semidirect product of He₃ and M₄(2) acting via M₄(2)/C₄=C₄	72	6	He3:1M4(2)	432,274
He₃⋊₄M₄(2)	The semidirect product of He₃ and M₄(2) acting via M₄(2)/C₂²=C₄	72	6	He3:4M4(2)	432,278
C₃²⋊₂GL₂(𝔽₃)	1^st semidirect product of C₃² and GL₂(𝔽₃) acting via GL₂(𝔽₃)/Q₈=S₃	72	12+	C3^2:2GL(2,3)	432,248
C₃²⋊₃GL₂(𝔽₃)	2^nd semidirect product of C₃² and GL₂(𝔽₃) acting via GL₂(𝔽₃)/Q₈=S₃	72	6	C3^2:3GL(2,3)	432,258
C₃²⋊₅GL₂(𝔽₃)	2^nd semidirect product of C₃² and GL₂(𝔽₃) acting via GL₂(𝔽₃)/SL₂(𝔽₃)=C₂	72		C3^2:5GL(2,3)	432,620
He₃⋊C₁₆	The semidirect product of He₃ and C₁₆ acting via C₁₆/C₂=C₈	144	6	He3:C16	432,233
He₃⋊Q₁₆	The semidirect product of He₃ and Q₁₆ acting via Q₁₆/C₂=D₄	144	6-	He3:Q16	432,236
He₃⋊₂C₁₆	The semidirect product of He₃ and C₁₆ acting via C₁₆/C₄=C₄	144	3	He3:2C16	432,57
C₃²⋊CSU₂(𝔽₃)	1^st semidirect product of C₃² and CSU₂(𝔽₃) acting via CSU₂(𝔽₃)/Q₈=S₃	144	12-	C3^2:CSU(2,3)	432,247
C₃²⋊₂CSU₂(𝔽₃)	2^nd semidirect product of C₃² and CSU₂(𝔽₃) acting via CSU₂(𝔽₃)/Q₈=S₃	144	6	C3^2:2CSU(2,3)	432,257
C₃²⋊₄CSU₂(𝔽₃)	2^nd semidirect product of C₃² and CSU₂(𝔽₃) acting via CSU₂(𝔽₃)/SL₂(𝔽₃)=C₂	144		C3^2:4CSU(2,3)	432,619
Q₈⋊D₂₇	The semidirect product of Q₈ and D₂₇ acting via D₂₇/C₉=S₃	216	4+	Q8:D27	432,38
C₃²⋊D₆⋊C₄	The semidirect product of C₃²⋊D₆ and C₄ acting via C₄/C₂=C₂	36	6	C3^2:D6:C4	432,238
C₂²⋊(He₃⋊C₄)	The semidirect product of C₂² and He₃⋊C₄ acting via He₃⋊C₄/He₃⋊C₂=C₂	36	6	C2^2:(He3:C4)	432,279
C₄○D₄⋊He₃	The semidirect product of C₄○D₄ and He₃ acting via He₃/C₃²=C₃	72	6	C4oD4:He3	432,339
C₄⋊(He₃⋊C₄)	The semidirect product of C₄ and He₃⋊C₄ acting via He₃⋊C₄/He₃⋊C₂=C₂	72	6	C4:(He3:C4)	432,276
Q₈⋊C₉⋊₄C₆	3^rd semidirect product of Q₈⋊C₉ and C₆ acting via C₆/C₂=C₃	72	6	Q8:C9:4C6	432,338
Q₈⋊He₃⋊C₂	4^th semidirect product of Q₈⋊He₃ and C₂ acting faithfully	72	12-	Q8:He3:C2	432,270
He₃⋊₂(C₂×C₈)	The semidirect product of He₃ and C₂×C₈ acting via C₂×C₈/C₄=C₄	72	3	He3:2(C2xC8)	432,273
Q₈⋊C₉⋊₃S₃	The semidirect product of Q₈⋊C₉ and S₃ acting through Inn(Q₈⋊C₉)	144	4	Q8:C9:3S3	432,267
D₁₈.A₄	The non-split extension by D₁₈ of A₄ acting via A₄/C₂²=C₃	72	12-	D18.A4	432,263
C₁₈.₆S₄	6^th non-split extension by C₁₈ of S₄ acting via S₄/A₄=C₂	72	4+	C18.6S4	432,253
C₂.SU₃(𝔽₂)	The central extension by C₂ of SU₃(𝔽₂)	72	3	C2.SU(3,2)	432,239
C₃².GL₂(𝔽₃)	The non-split extension by C₃² of GL₂(𝔽₃) acting via GL₂(𝔽₃)/Q₈=S₃	72	12+	C3^2.GL(2,3)	432,245
C₃₆.A₄	The non-split extension by C₃₆ of A₄ acting via A₄/C₂²=C₃	144	6	C36.A4	432,330
C₁₈.₅S₄	5^th non-split extension by C₁₈ of S₄ acting via S₄/A₄=C₂	144	4-	C18.5S4	432,252
Dic₉.A₄	The non-split extension by Dic₉ of A₄ acting via A₄/C₂²=C₃	144	12+	Dic9.A4	432,261
Dic₉.₂A₄	The non-split extension by Dic₉ of A₄ acting through Inn(Dic₉)	144	4+	Dic9.2A4	432,262
C₃².CSU₂(𝔽₃)	The non-split extension by C₃² of CSU₂(𝔽₃) acting via CSU₂(𝔽₃)/Q₈=S₃	144	12-	C3^2.CSU(2,3)	432,243
Q₈.C₅₄	The non-split extension by Q₈ of C₅₄ acting via C₅₄/C₁₈=C₃	216	2	Q8.C54	432,42
C₃².₃GL₂(𝔽₃)	2^nd non-split extension by C₃² of GL₂(𝔽₃) acting via GL₂(𝔽₃)/SL₂(𝔽₃)=C₂	216		C3^2.3GL(2,3)	432,256
Q₈.D₂₇	The non-split extension by Q₈ of D₂₇ acting via D₂₇/C₉=S₃	432	4-	Q8.D27	432,37
C₃².₃CSU₂(𝔽₃)	2^nd non-split extension by C₃² of CSU₂(𝔽₃) acting via CSU₂(𝔽₃)/SL₂(𝔽₃)=C₂	432		C3^2.3CSU(2,3)	432,255
C₆.S₃≀C₂	4^th non-split extension by C₆ of S₃≀C₂ acting via S₃≀C₂/C₃²⋊C₄=C₂	72	6-	C6.S3wrC2	432,237
C₆.(S₃×A₄)	7^th non-split extension by C₆ of S₃×A₄ acting via S₃×A₄/C₃×A₄=C₂	72	12+	C6.(S3xA4)	432,269
C₃⋊Dic₃.₂A₄	The non-split extension by C₃⋊Dic₃ of A₄ acting through Inn(C₃⋊Dic₃)	144		C3:Dic3.2A4	432,625
C₂×ASL₂(𝔽₃)	Direct product of C₂ and ASL₂(𝔽₃)	18	8+	C2xASL(2,3)	432,735
C₂×SU₃(𝔽₂)	Direct product of C₂ and SU₃(𝔽₂)	54	3	C2xSU(3,2)	432,531
C₉×GL₂(𝔽₃)	Direct product of C₉ and GL₂(𝔽₃)	72	2	C9xGL(2,3)	432,241
D₉×SL₂(𝔽₃)	Direct product of D₉ and SL₂(𝔽₃)	72	4-	D9xSL(2,3)	432,264
C₃²×GL₂(𝔽₃)	Direct product of C₃² and GL₂(𝔽₃)	72		C3^2xGL(2,3)	432,614
C₉×CSU₂(𝔽₃)	Direct product of C₉ and CSU₂(𝔽₃)	144	2	C9xCSU(2,3)	432,240
C₁₈×SL₂(𝔽₃)	Direct product of C₁₈ and SL₂(𝔽₃)	144		C18xSL(2,3)	432,327
C₃²×CSU₂(𝔽₃)	Direct product of C₃² and CSU₂(𝔽₃)	144		C3^2xCSU(2,3)	432,613
C₂×He₃⋊D₄	Direct product of C₂ and He₃⋊D₄	36	6+	C2xHe3:D4	432,530
C₃×C₆.₅S₄	Direct product of C₃ and C₆.₅S₄	48	4	C3xC6.5S4	432,616
C₃×C₆.₆S₄	Direct product of C₃ and C₆.₆S₄	48	4	C3xC6.6S4	432,617
C₃×S₃×SL₂(𝔽₃)	Direct product of C₃, S₃ and SL₂(𝔽₃)	48	4	C3xS3xSL(2,3)	432,623
C₃×Dic₃.A₄	Direct product of C₃ and Dic₃.A₄	48	4	C3xDic3.A4	432,622
C₂×He₃⋊C₈	Direct product of C₂ and He₃⋊C₈	54	6+	C2xHe3:C8	432,529
C₄×He₃⋊C₄	Direct product of C₄ and He₃⋊C₄	72	3	C4xHe3:C4	432,275
C₂²×He₃⋊C₄	Direct product of C₂² and He₃⋊C₄	72		C2^2xHe3:C4	432,543
C₃⋊S₃×SL₂(𝔽₃)	Direct product of C₃⋊S₃ and SL₂(𝔽₃)	72		C3:S3xSL(2,3)	432,626
S₃×Q₈⋊C₉	Direct product of S₃ and Q₈⋊C₉	144	4	S3xQ8:C9	432,268
C₉×C₄.A₄	Direct product of C₉ and C₄.A₄	144	2	C9xC4.A4	432,329
C₃×Q₈⋊D₉	Direct product of C₃ and Q₈⋊D₉	144	4	C3xQ8:D9	432,246
C₂×Q₈⋊He₃	Direct product of C₂ and Q₈⋊He₃	144		C2xQ8:He3	432,336
C₂×C₁₈.A₄	Direct product of C₂ and C₁₈.A₄	144		C2xC18.A4	432,328
C₃×Q₈.D₉	Direct product of C₃ and Q₈.D₉	144	4	C3xQ8.D9	432,244
C₂×He₃⋊₂C₈	Direct product of C₂ and He₃⋊₂C₈	144		C2xHe3:2C8	432,277
C₃²×C₄.A₄	Direct product of C₃² and C₄.A₄	144		C3^2xC4.A4	432,699
C₃×C₆×SL₂(𝔽₃)	Direct product of C₃×C₆ and SL₂(𝔽₃)	144		C3xC6xSL(2,3)	432,698
C₂×Q₈⋊3_-¹⁺²	Direct product of C₂ and Q₈⋊3_-¹⁺²	144		C2xQ8:ES-(3,1)	432,335
C₃×Q₈.C₁₈	Direct product of C₃ and Q₈.C₁₈	216		C3xQ8.C18	432,337
C₆×Q₈⋊C₉	Direct product of C₆ and Q₈⋊C₉	432		C6xQ8:C9	432,334
C₂×Q₈⋊C₂₇	Direct product of C₂ and Q₈⋊C₂₇	432		C2xQ8:C27	432,41

Groups of order 456

		d	ρ	Label	ID
C₃₈.A₄	The non-split extension by C₃₈ of A₄ acting via A₄/C₂²=C₃	152	6	C38.A4	456,23
C₁₉×SL₂(𝔽₃)	Direct product of C₁₉ and SL₂(𝔽₃)	152	2	C19xSL(2,3)	456,22

Groups of order 480

		d	ρ	Label	ID
GL₂(𝔽₅)	General linear group on 𝔽₅²; = SL₂(𝔽₅)⋊₁ C₄ = Aut(C₅²)	24	4	GL(2,5)	480,218
C₄⋊S₅	The semidirect product of C₄ and S₅ acting via S₅/A₅=C₂	20	6	C4:S5	480,944
C₂²⋊S₅	The semidirect product of C₂² and S₅ acting via S₅/A₅=C₂	20	6+	C2^2:S5	480,951
A₅⋊Q₈	The semidirect product of A₅ and Q₈ acting via Q₈/C₄=C₂	24	6	A5:Q8	480,945
A₅⋊C₈	The semidirect product of A₅ and C₈ acting via C₈/C₄=C₂	40	4	A5:C8	480,217
GL₂(𝔽₃)⋊D₅	1^st semidirect product of GL₂(𝔽₃) and D₅ acting via D₅/C₅=C₂	80	4+	GL(2,3):D5	480,970
C₅⋊U₂(𝔽₃)	The semidirect product of C₅ and U₂(𝔽₃) acting via U₂(𝔽₃)/SL₂(𝔽₃)=C₄	120	8+	C5:U(2,3)	480,961
C₅⋊₂U₂(𝔽₃)	The semidirect product of C₅ and U₂(𝔽₃) acting via U₂(𝔽₃)/C₄.A₄=C₂	120	4	C5:2U(2,3)	480,261
Q₈⋊Dic₁₅	The semidirect product of Q₈ and Dic₁₅ acting via Dic₁₅/C₁₀=S₃	160		Q8:Dic15	480,260
CSU₂(𝔽₃)⋊D₅	1^st semidirect product of CSU₂(𝔽₃) and D₅ acting via D₅/C₅=C₂	160	4	CSU(2,3):D5	480,967
C₄.₃S₅	3^rd non-split extension by C₄ of S₅ acting via S₅/A₅=C₂	40	4	C4.3S5	480,948
D₁₀.S₄	3^rd non-split extension by D₁₀ of S₄ acting via S₄/A₄=C₂	40	8-	D10.S4	480,962
C₈.A₅	The central extension by C₈ of A₅	48	2	C8.A5	480,221
D₄.A₅	The non-split extension by D₄ of A₅ acting through Inn(D₄)	48	4-	D4.A5	480,957
Q₈.A₅	The non-split extension by Q₈ of A₅ acting through Inn(Q₈)	48	4+	Q8.A5	480,959
C₄.₆S₅	3^rd central extension by C₄ of S₅	48	4	C4.6S5	480,946
C₄.S₅	2^nd non-split extension by C₄ of S₅ acting via S₅/A₅=C₂	48	4	C4.S5	480,947
C₂².S₅	The non-split extension by C₂² of S₅ acting via S₅/A₅=C₂	48	4-	C2^2.S5	480,953
D₂₀.A₄	The non-split extension by D₂₀ of A₄ acting through Inn(D₂₀)	80	4-	D20.A4	480,1043
C₂₀.₆S₄	6^th non-split extension by C₂₀ of S₄ acting via S₄/A₄=C₂	80	4	C20.6S4	480,1031
C₂₀.₃S₄	3^rd non-split extension by C₂₀ of S₄ acting via S₄/A₄=C₂	80	4+	C20.3S4	480,1032
D₁₀.₁S₄	1^st non-split extension by D₁₀ of S₄ acting via S₄/A₄=C₂	80	4-	D10.1S4	480,972
D₁₀.₂S₄	2^nd non-split extension by D₁₀ of S₄ acting via S₄/A₄=C₂	80	4	D10.2S4	480,973
Q₈.D₃₀	2^nd non-split extension by Q₈ of D₃₀ acting via D₃₀/C₁₀=S₃	80	4	Q8.D30	480,1029
Dic₅.₆S₄	1^st non-split extension by Dic₅ of S₄ acting through Inn(Dic₅)	80	4	Dic5.6S4	480,968
Dic₅.₇S₄	2^nd non-split extension by Dic₅ of S₄ acting through Inn(Dic₅)	80	4+	Dic5.7S4	480,969
SL₂(𝔽₃).₁₁D₁₀	1^st non-split extension by SL₂(𝔽₃) of D₁₀ acting through Inn(SL₂(𝔽₃))	80	4	SL(2,3).11D10	480,1040
C₂².₂S₅	1^st central extension by C₂² of S₅	96		C2^2.2S5	480,219
Dic₁₀.A₄	The non-split extension by Dic₁₀ of A₄ acting through Inn(Dic₁₀)	120	4+	Dic10.A4	480,1041
C₂₀.₂S₄	2^nd non-split extension by C₂₀ of S₄ acting via S₄/A₄=C₂	160	4-	C20.2S4	480,1030
SL₂(𝔽₃).F₅	The non-split extension by SL₂(𝔽₃) of F₅ acting through Inn(SL₂(𝔽₃))	160	8+	SL(2,3).F5	480,964
SL₂(𝔽₃).Dic₅	The non-split extension by SL₂(𝔽₃) of Dic₅ acting through Inn(SL₂(𝔽₃))	160	4	SL(2,3).Dic5	480,267
C₄×S₅	Direct product of C₄ and S₅; = CO₃(𝔽₅)	20	4	C4xS5	480,943
D₄×A₅	Direct product of D₄ and A₅	20	6+	D4xA5	480,956
C₂²×S₅	Direct product of C₂² and S₅	20		C2^2xS5	480,1186
C₈×A₅	Direct product of C₈ and A₅	40	3	C8xA5	480,220
Q₈×A₅	Direct product of Q₈ and A₅	40	6-	Q8xA5	480,958
C₂³×A₅	Direct product of C₂³ and A₅	40		C2^3xA5	480,1187
F₅×SL₂(𝔽₃)	Direct product of F₅ and SL₂(𝔽₃)	40	8-	F5xSL(2,3)	480,965
D₅×GL₂(𝔽₃)	Direct product of D₅ and GL₂(𝔽₃)	40	4	D5xGL(2,3)	480,974
D₅×CSU₂(𝔽₃)	Direct product of D₅ and CSU₂(𝔽₃)	80	4-	D5xCSU(2,3)	480,971
C₁₀×GL₂(𝔽₃)	Direct product of C₁₀ and GL₂(𝔽₃)	80		C10xGL(2,3)	480,1017
C₄×SL₂(𝔽₅)	Direct product of C₄ and SL₂(𝔽₅)	96		C4xSL(2,5)	480,222
C₂×CSU₂(𝔽₅)	Direct product of C₂ and CSU₂(𝔽₅)	96		C2xCSU(2,5)	480,949
C₂²×SL₂(𝔽₅)	Direct product of C₂² and SL₂(𝔽₅)	96		C2^2xSL(2,5)	480,960
C₅×U₂(𝔽₃)	Direct product of C₅ and U₂(𝔽₃)	120	2	C5xU(2,3)	480,257
C₂₀×SL₂(𝔽₃)	Direct product of C₂₀ and SL₂(𝔽₃)	160		C20xSL(2,3)	480,655
C₁₀×CSU₂(𝔽₃)	Direct product of C₁₀ and CSU₂(𝔽₃)	160		C10xCSU(2,3)	480,1016
Dic₅×SL₂(𝔽₃)	Direct product of Dic₅ and SL₂(𝔽₃)	160		Dic5xSL(2,3)	480,266
C₂×A₅⋊C₄	Direct product of C₂ and A₅⋊C₄	24		C2xA5:C4	480,952
C₂×C₄×A₅	Direct product of C₂×C₄ and A₅	40		C2xC4xA5	480,954
C₂×C₄.A₅	Direct product of C₂ and C₄.A₅	48		C2xC4.A5	480,955
C₅×C₂³.₃A₄	Direct product of C₅ and C₂³.₃A₄	60	6	C5xC2^3.3A4	480,74
D₅×C₄.A₄	Direct product of D₅ and C₄.A₄	80	4	D5xC4.A4	480,1042
C₂×C₂.S₅	Direct product of C₂ and C₂.S₅	80		C2xC2.S5	480,950
C₂×Q₈⋊D₁₅	Direct product of C₂ and Q₈⋊D₁₅	80		C2xQ8:D15	480,1028
C₅×D₄.A₄	Direct product of C₅ and D₄.A₄	80	4	C5xD4.A4	480,1132
C₅×C₄.₆S₄	Direct product of C₅ and C₄.₆S₄	80	2	C5xC4.6S4	480,1020
C₅×C₄.₃S₄	Direct product of C₅ and C₄.₃S₄	80	4	C5xC4.3S4	480,1021
C₅×Q₈.D₆	Direct product of C₅ and Q₈.D₆	80	4	C5xQ8.D6	480,1018
C₂×D₅×SL₂(𝔽₃)	Direct product of C₂, D₅ and SL₂(𝔽₃)	80		C2xD5xSL(2,3)	480,1039
C₃×2_-¹⁺⁴⋊C₅	Direct product of C₃ and 2_-¹⁺⁴⋊C₅	96	4	C3xES-(2,2):C5	480,1046
C₅×Q₈⋊A₄	Direct product of C₅ and Q₈⋊A₄	120	6	C5xQ8:A4	480,1133
C₅×Q₈.A₄	Direct product of C₅ and Q₈.A₄	120	4	C5xQ8.A4	480,1131
C₅×C₈.A₄	Direct product of C₅ and C₈.A₄	160	2	C5xC8.A4	480,660
C₁₀×C₄.A₄	Direct product of C₁₀ and C₄.A₄	160		C10xC4.A4	480,1130
C₅×C₄.S₄	Direct product of C₅ and C₄.S₄	160	4	C5xC4.S4	480,1019
C₅×Q₈⋊Dic₃	Direct product of C₅ and Q₈⋊Dic₃	160		C5xQ8:Dic3	480,256
C₂×Q₈.D₁₅	Direct product of C₂ and Q₈.D₁₅	160		C2xQ8.D15	480,1027
C₂×Dic₅.A₄	Direct product of C₂ and Dic₅.A₄	160		C2xDic5.A4	480,1038
C₂×C₁₀×SL₂(𝔽₃)	Direct product of C₂×C₁₀ and SL₂(𝔽₃)	160		C2xC10xSL(2,3)	480,1128

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