Extensions 1→N→G→Q→1 with N=D₁₀ and Q=F₅

Direct product G=N×Q with N=D₁₀ and Q=F₅

		d	ρ	Label	ID
C₂×D₅×F₅		40	8+	C2xD5xF5	400,209

Semidirect products G=N:Q with N=D₁₀ and Q=F₅

extension	φ:Q→Out N	d	ρ	Label	ID
D₁₀⋊₁F₅ = D₅.D₂₀	φ: F₅/D₅ → C₂ ⊆ Out D₁₀	40	8+	D10:1F5	400,118
D₁₀⋊₂F₅ = D₁₀⋊F₅	φ: F₅/D₅ → C₂ ⊆ Out D₁₀	20	8+	D10:2F5	400,125
D₁₀⋊₃F₅ = C₂×D₅⋊F₅	φ: F₅/D₅ → C₂ ⊆ Out D₁₀	20	8+	D10:3F5	400,210

Non-split extensions G=N.Q with N=D₁₀ and Q=F₅

extension	φ:Q→Out N	d	ρ	Label	ID
D₁₀.₁F₅ = D₁₀.F₅	φ: F₅/D₅ → C₂ ⊆ Out D₁₀	80	8-	D10.1F5	400,122
D₁₀.₂F₅ = D₁₀.₂F₅	φ: F₅/D₅ → C₂ ⊆ Out D₁₀	80	8-	D10.2F5	400,127
D₁₀.₃F₅ = C₅²⋊₄M₄(2)	φ: F₅/D₅ → C₂ ⊆ Out D₁₀	80	8-	D10.3F5	400,128
D₁₀.₄F₅ = D₅×C₅⋊C₈	φ: trivial image	80	8-	D10.4F5	400,120

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁