Extensions 1→N→G→Q→1 with N=C₅ and Q=C₂²×F₅

Direct product G=N×Q with N=C₅ and Q=C₂²×F₅

		d	ρ	Label	ID
F₅×C₂×C₁₀		80		F5xC2xC10	400,214

Semidirect products G=N:Q with N=C₅ and Q=C₂²×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊₁(C₂²×F₅) = C₂×D₅⋊F₅	φ: C₂²×F₅/D₁₀ → C₄ ⊆ Aut C₅	20	8+	C5:1(C2^2xF5)	400,210
C₅⋊₂(C₂²×F₅) = C₂²×C₅⋊F₅	φ: C₂²×F₅/C₂×C₁₀ → C₄ ⊆ Aut C₅	100		C5:2(C2^2xF5)	400,216
C₅⋊₃(C₂²×F₅) = C₂²×C₅²⋊C₄	φ: C₂²×F₅/C₂×C₁₀ → C₄ ⊆ Aut C₅	40		C5:3(C2^2xF5)	400,217
C₅⋊₄(C₂²×F₅) = C₂×D₅×F₅	φ: C₂²×F₅/C₂×F₅ → C₂ ⊆ Aut C₅	40	8+	C5:4(C2^2xF5)	400,209
C₅⋊₅(C₂²×F₅) = C₂²×D₅.D₅	φ: C₂²×F₅/C₂²×D₅ → C₂ ⊆ Aut C₅	80		C5:5(C2^2xF5)	400,215

Non-split extensions G=N.Q with N=C₅ and Q=C₂²×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(C₂²×F₅) = C₂²×C₂₅⋊C₄	φ: C₂²×F₅/C₂×C₁₀ → C₄ ⊆ Aut C₅	100		C5.(C2^2xF5)	400,53

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