Extensions 1→N→G→Q→1 with N=C₅² and Q=D₁₀

Direct product G=N×Q with N=C₅² and Q=D₁₀

		d	ρ	Label	ID
D₅×C₅×C₁₀		100		D5xC5xC10	500,53

Semidirect products G=N:Q with N=C₅² and Q=D₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅²⋊D₁₀ = C₅²⋊D₁₀	φ: D₁₀/C₁ → D₁₀ ⊆ Aut C₅²	25	10+	C5^2:D10	500,27
C₅²⋊₂D₁₀ = C₂×C₅²⋊C₁₀	φ: D₁₀/C₂ → D₅ ⊆ Aut C₅²	50	10+	C5^2:2D10	500,30
C₅²⋊₃D₁₀ = C₂×He₅⋊C₂	φ: D₁₀/C₂ → D₅ ⊆ Aut C₅²	50	5	C5^2:3D10	500,33
C₅²⋊₄D₁₀ = D₅×C₅⋊D₅	φ: D₁₀/C₅ → C₂² ⊆ Aut C₅²	50		C5^2:4D10	500,51
C₅²⋊₅D₁₀ = C₅²⋊₅D₁₀	φ: D₁₀/C₅ → C₂² ⊆ Aut C₅²	20	4	C5^2:5D10	500,52
C₅²⋊₆D₁₀ = C₅×D₅²	φ: D₁₀/D₅ → C₂ ⊆ Aut C₅²	20	4	C5^2:6D10	500,50
C₅²⋊₇D₁₀ = C₁₀×C₅⋊D₅	φ: D₁₀/C₁₀ → C₂ ⊆ Aut C₅²	100		C5^2:7D10	500,54
C₅²⋊₈D₁₀ = C₂×C₅³⋊C₂	φ: D₁₀/C₁₀ → C₂ ⊆ Aut C₅²	250		C5^2:8D10	500,55

Non-split extensions G=N.Q with N=C₅² and Q=D₁₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅².D₁₀ = C₂×C₂₅⋊C₁₀	φ: D₁₀/C₂ → D₅ ⊆ Aut C₅²	50	10+	C5^2.D10	500,31
C₅².₂D₁₀ = D₅×D₂₅	φ: D₁₀/C₅ → C₂² ⊆ Aut C₅²	50	4+	C5^2.2D10	500,26
C₅².₃D₁₀ = C₁₀×D₂₅	φ: D₁₀/C₁₀ → C₂ ⊆ Aut C₅²	100	2	C5^2.3D10	500,28
C₅².₄D₁₀ = C₂×C₂₅⋊D₅	φ: D₁₀/C₁₀ → C₂ ⊆ Aut C₅²	250		C5^2.4D10	500,32

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