Extensions 1→N→G→Q→1 with N=D₄ and Q=C₂×C₁₀

Direct product G=N×Q with N=D₄ and Q=C₂×C₁₀

		d	ρ	Label	ID
D₄×C₂×C₁₀		80		D4xC2xC10	160,229

Semidirect products G=N:Q with N=D₄ and Q=C₂×C₁₀

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊₁(C₂×C₁₀) = C₁₀×D₈	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out D₄	80		D4:1(C2xC10)	160,193
D₄⋊₂(C₂×C₁₀) = C₅×C₈⋊C₂²	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out D₄	40	4	D4:2(C2xC10)	160,197
D₄⋊₃(C₂×C₁₀) = C₁₀×C₄○D₄	φ: trivial image	80		D4:3(C2xC10)	160,231
D₄⋊₄(C₂×C₁₀) = C₅×2₊¹⁺⁴	φ: trivial image	40	4	D4:4(C2xC10)	160,232

Non-split extensions G=N.Q with N=D₄ and Q=C₂×C₁₀

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.₁(C₂×C₁₀) = C₁₀×SD₁₆	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out D₄	80		D4.1(C2xC10)	160,194
D₄.₂(C₂×C₁₀) = C₅×C₄○D₈	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out D₄	80	2	D4.2(C2xC10)	160,196
D₄.₃(C₂×C₁₀) = C₅×C₈.C₂²	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out D₄	80	4	D4.3(C2xC10)	160,198
D₄.₄(C₂×C₁₀) = C₅×2_-¹⁺⁴	φ: trivial image	80	4	D4.4(C2xC10)	160,233

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