Extensions 1→N→G→Q→1 with N=C₅ and Q=C₂×C₄×D₅

Direct product G=N×Q with N=C₅ and Q=C₂×C₄×D₅

		d	ρ	Label	ID
D₅×C₂×C₂₀		80		D5xC2xC20	400,182

Semidirect products G=N:Q with N=C₅ and Q=C₂×C₄×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊(C₂×C₄×D₅) = C₂×D₅×F₅	φ: C₂×C₄×D₅/D₁₀ → C₄ ⊆ Aut C₅	40	8+	C5:(C2xC4xD5)	400,209
C₅⋊₂(C₂×C₄×D₅) = C₄×D₅²	φ: C₂×C₄×D₅/C₄×D₅ → C₂ ⊆ Aut C₅	40	4	C5:2(C2xC4xD5)	400,169
C₅⋊₃(C₂×C₄×D₅) = C₂×Dic₅⋊₂D₅	φ: C₂×C₄×D₅/C₂×Dic₅ → C₂ ⊆ Aut C₅	40		C5:3(C2xC4xD5)	400,175
C₅⋊₄(C₂×C₄×D₅) = C₂×C₄×C₅⋊D₅	φ: C₂×C₄×D₅/C₂×C₂₀ → C₂ ⊆ Aut C₅	200		C5:4(C2xC4xD5)	400,192
C₅⋊₅(C₂×C₄×D₅) = C₂×D₅×Dic₅	φ: C₂×C₄×D₅/C₂²×D₅ → C₂ ⊆ Aut C₅	80		C5:5(C2xC4xD5)	400,172

Non-split extensions G=N.Q with N=C₅ and Q=C₂×C₄×D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅.(C₂×C₄×D₅) = C₂×C₄×D₂₅	φ: C₂×C₄×D₅/C₂×C₂₀ → C₂ ⊆ Aut C₅	200		C5.(C2xC4xD5)	400,36

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