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

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

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

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

extension	φ:Q→Out N	d	ρ	Label	ID
(C₄×F₅)⋊₁C₂ = D₄⋊F₅	φ: C₂/C₁ → C₂ ⊆ Out C₄×F₅	40	8-	(C4xF5):1C2	160,83
(C₄×F₅)⋊₂C₂ = Q₈⋊₂F₅	φ: C₂/C₁ → C₂ ⊆ Out C₄×F₅	40	8+	(C4xF5):2C2	160,85
(C₄×F₅)⋊₃C₂ = D₄×F₅	φ: C₂/C₁ → C₂ ⊆ Out C₄×F₅	20	8+	(C4xF5):3C2	160,207
(C₄×F₅)⋊₄C₂ = D₁₀.C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄×F₅	40	4	(C4xF5):4C2	160,205

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

extension	φ:Q→Out N	d	ρ	Label	ID
(C₄×F₅).₁C₂ = Q₈×F₅	φ: C₂/C₁ → C₂ ⊆ Out C₄×F₅	40	8-	(C4xF5).1C2	160,209
(C₄×F₅).₂C₂ = C₈⋊F₅	φ: C₂/C₁ → C₂ ⊆ Out C₄×F₅	40	4	(C4xF5).2C2	160,67
(C₄×F₅).₃C₂ = C₈×F₅	φ: trivial image	40	4	(C4xF5).3C2	160,66

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁