Extensions 1→N→G→Q→1 with N=C₅² and Q=F₅

Direct product G=N×Q with N=C₅² and Q=F₅

		d	ρ	Label	ID
F₅×C₅²		100		F5xC5^2	500,41

Semidirect products G=N:Q with N=C₅² and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅²⋊₁F₅ = C₅²⋊C₂₀	φ: F₅/C₁ → F₅ ⊆ Aut C₅²	25	20+	C5^2:1F5	500,17
C₅²⋊₂F₅ = He₅⋊C₄	φ: F₅/C₁ → F₅ ⊆ Aut C₅²	25	20+	C5^2:2F5	500,21
C₅²⋊₃F₅ = C₅²⋊F₅	φ: F₅/C₁ → F₅ ⊆ Aut C₅²	25	10+	C5^2:3F5	500,23
C₅²⋊₄F₅ = He₅⋊₄C₄	φ: F₅/C₁ → F₅ ⊆ Aut C₅²	25	5	C5^2:4F5	500,25
C₅²⋊₅F₅ = C₅×C₅⋊F₅	φ: F₅/C₅ → C₄ ⊆ Aut C₅²	100		C5^2:5F5	500,43
C₅²⋊₆F₅ = C₅×C₅²⋊C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₅²	20	4	C5^2:6F5	500,44
C₅²⋊₇F₅ = C₅³⋊₆C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₅²	20	4	C5^2:7F5	500,46
C₅²⋊₈F₅ = C₅³⋊₇C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₅²	100		C5^2:8F5	500,47
C₅²⋊₉F₅ = C₅³⋊₈C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₅²	125		C5^2:9F5	500,48
C₅²⋊₁₀F₅ = C₅³⋊₉C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₅²	50		C5^2:10F5	500,49
C₅²⋊₁₁F₅ = C₅×D₅.D₅	φ: F₅/D₅ → C₂ ⊆ Aut C₅²	20	4	C5^2:11F5	500,42
C₅²⋊₁₂F₅ = C₅³⋊C₄	φ: F₅/D₅ → C₂ ⊆ Aut C₅²	100		C5^2:12F5	500,45

Non-split extensions G=N.Q with N=C₅² and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅².F₅ = C₂₅⋊C₂₀	φ: F₅/C₁ → F₅ ⊆ Aut C₅²	25	20+	C5^2.F5	500,18
C₅².₂F₅ = C₅×C₂₅⋊C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₅²	100	4	C5^2.2F5	500,16
C₅².₃F₅ = D₂₅.D₅	φ: F₅/C₅ → C₄ ⊆ Aut C₅²	100	4	C5^2.3F5	500,20
C₅².₄F₅ = C₂₅⋊F₅	φ: F₅/C₅ → C₄ ⊆ Aut C₅²	125		C5^2.4F5	500,22
C₅².₅F₅ = C₂₅⋊₂F₅	φ: F₅/C₅ → C₄ ⊆ Aut C₅²	50	4+	C5^2.5F5	500,24

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