Extensions 1→N→G→Q→1 with N=D₄ and Q=C₂×C₂₀

Direct product G=N×Q with N=D₄ and Q=C₂×C₂₀

		d	ρ	Label	ID
D₄×C₂×C₂₀		160		D4xC2xC20	320,1517

Semidirect products G=N:Q with N=D₄ and Q=C₂×C₂₀

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊₁(C₂×C₂₀) = D₈×C₂₀	φ: C₂×C₂₀/C₂₀ → C₂ ⊆ Out D₄	160		D4:1(C2xC20)	320,938
D₄⋊₂(C₂×C₂₀) = C₅×D₈⋊C₄	φ: C₂×C₂₀/C₂₀ → C₂ ⊆ Out D₄	160		D4:2(C2xC20)	320,943
D₄⋊₃(C₂×C₂₀) = C₁₀×D₄⋊C₄	φ: C₂×C₂₀/C₂×C₁₀ → C₂ ⊆ Out D₄	160		D4:3(C2xC20)	320,915
D₄⋊₄(C₂×C₂₀) = C₅×C₂³.₃₆D₄	φ: C₂×C₂₀/C₂×C₁₀ → C₂ ⊆ Out D₄	160		D4:4(C2xC20)	320,918
D₄⋊₅(C₂×C₂₀) = C₁₀×C₄≀C₂	φ: C₂×C₂₀/C₂×C₁₀ → C₂ ⊆ Out D₄	80		D4:5(C2xC20)	320,921
D₄⋊₆(C₂×C₂₀) = C₄○D₄×C₂₀	φ: trivial image	160		D4:6(C2xC20)	320,1519
D₄⋊₇(C₂×C₂₀) = C₅×C₂².₁₁C₂⁴	φ: trivial image	80		D4:7(C2xC20)	320,1520
D₄⋊₈(C₂×C₂₀) = C₅×C₂³.₃₃C₂³	φ: trivial image	160		D4:8(C2xC20)	320,1522

Non-split extensions G=N.Q with N=D₄ and Q=C₂×C₂₀

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.₁(C₂×C₂₀) = SD₁₆×C₂₀	φ: C₂×C₂₀/C₂₀ → C₂ ⊆ Out D₄	160		D4.1(C2xC20)	320,939
D₄.₂(C₂×C₂₀) = C₅×SD₁₆⋊C₄	φ: C₂×C₂₀/C₂₀ → C₂ ⊆ Out D₄	160		D4.2(C2xC20)	320,941
D₄.₃(C₂×C₂₀) = C₅×C₈○D₈	φ: C₂×C₂₀/C₂₀ → C₂ ⊆ Out D₄	80	2	D4.3(C2xC20)	320,944
D₄.₄(C₂×C₂₀) = C₅×C₈.₂₆D₄	φ: C₂×C₂₀/C₂₀ → C₂ ⊆ Out D₄	80	4	D4.4(C2xC20)	320,945
D₄.₅(C₂×C₂₀) = C₅×C₂³.₂₄D₄	φ: C₂×C₂₀/C₂×C₁₀ → C₂ ⊆ Out D₄	160		D4.5(C2xC20)	320,917
D₄.₆(C₂×C₂₀) = C₅×C₂³.₃₇D₄	φ: C₂×C₂₀/C₂×C₁₀ → C₂ ⊆ Out D₄	80		D4.6(C2xC20)	320,919
D₄.₇(C₂×C₂₀) = C₅×C₄²⋊C₂²	φ: C₂×C₂₀/C₂×C₁₀ → C₂ ⊆ Out D₄	80	4	D4.7(C2xC20)	320,922
D₄.₈(C₂×C₂₀) = C₁₀×C₈○D₄	φ: trivial image	160		D4.8(C2xC20)	320,1569
D₄.₉(C₂×C₂₀) = C₅×Q₈○M₄(2)	φ: trivial image	80	4	D4.9(C2xC20)	320,1570

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