Extensions 1→N→G→Q→1 with N=C₂×C₄ and Q=F₅

Direct product G=N×Q with N=C₂×C₄ and Q=F₅

		d	ρ	Label	ID
C₂×C₄×F₅		40		C2xC4xF5	160,203

Semidirect products G=N:Q with N=C₂×C₄ and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄)⋊F₅ = D₁₀.D₄	φ: F₅/C₅ → C₄ ⊆ Aut C₂×C₄	40	4+	(C2xC4):F5	160,74
(C₂×C₄)⋊₂F₅ = D₁₀.₃Q₈	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₄	40		(C2xC4):2F5	160,81
(C₂×C₄)⋊₃F₅ = C₂×C₄⋊F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₄	40		(C2xC4):3F5	160,204
(C₂×C₄)⋊₄F₅ = D₁₀.C₂³	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₄	40	4	(C2xC4):4F5	160,205

Non-split extensions G=N.Q with N=C₂×C₄ and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₄).F₅ = Dic₅.D₄	φ: F₅/C₅ → C₄ ⊆ Aut C₂×C₄	80	4-	(C2xC4).F5	160,80
(C₂×C₄).₂F₅ = C₁₀.C₄²	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₄	160		(C2xC4).2F5	160,77
(C₂×C₄).₃F₅ = D₁₀⋊C₈	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₄	80		(C2xC4).3F5	160,78
(C₂×C₄).₄F₅ = Dic₅⋊C₈	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₄	160		(C2xC4).4F5	160,79
(C₂×C₄).₅F₅ = C₂₀.C₈	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₄	80	4	(C2xC4).5F5	160,73
(C₂×C₄).₆F₅ = C₂₀⋊C₈	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₄	160		(C2xC4).6F5	160,76
(C₂×C₄).₇F₅ = C₂×C₄.F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₄	80		(C2xC4).7F5	160,201
(C₂×C₄).₈F₅ = D₅⋊M₄(2)	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₄	40	4	(C2xC4).8F5	160,202
(C₂×C₄).₉F₅ = C₂×C₅⋊C₁₆	central extension (φ=1)	160		(C2xC4).9F5	160,72
(C₂×C₄).₁₀F₅ = C₄×C₅⋊C₈	central extension (φ=1)	160		(C2xC4).10F5	160,75
(C₂×C₄).₁₁F₅ = C₂×D₅⋊C₈	central extension (φ=1)	80		(C2xC4).11F5	160,200

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁