C_n D_n S_n A_n ...

Extensions 1→N→G→Q→1 with N=Q₁₆ and Q=C₂×C₁₀

Direct product G=N×Q with N=Q₁₆ and Q=C₂×C₁₀

		d	ρ	Label	ID
Q₁₆×C₂×C₁₀		320		Q16xC2xC10	320,1573

Semidirect products G=N:Q with N=Q₁₆ and Q=C₂×C₁₀

extension	φ:Q→Out N	d	ρ	Label	ID
Q₁₆⋊₁(C₂×C₁₀) = C₁₀×SD₃₂	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Q₁₆	160		Q16:1(C2xC10)	320,1007
Q₁₆⋊₂(C₂×C₁₀) = C₅×C₁₆⋊C₂²	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Q₁₆	80	4	Q16:2(C2xC10)	320,1010
Q₁₆⋊₃(C₂×C₁₀) = C₁₀×C₈.C₂²	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Q₁₆	160		Q16:3(C2xC10)	320,1576
Q₁₆⋊₄(C₂×C₁₀) = C₅×D₈⋊C₂²	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Q₁₆	80	4	Q16:4(C2xC10)	320,1577
Q₁₆⋊₅(C₂×C₁₀) = C₅×D₄○SD₁₆	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Q₁₆	80	4	Q16:5(C2xC10)	320,1579
Q₁₆⋊₆(C₂×C₁₀) = C₁₀×C₄○D₈	φ: trivial image	160		Q16:6(C2xC10)	320,1574
Q₁₆⋊₇(C₂×C₁₀) = C₅×D₄○D₈	φ: trivial image	80	4	Q16:7(C2xC10)	320,1578

Non-split extensions G=N.Q with N=Q₁₆ and Q=C₂×C₁₀

extension	φ:Q→Out N	d	ρ	Label	ID
Q₁₆.₁(C₂×C₁₀) = C₁₀×Q₃₂	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Q₁₆	320		Q16.1(C2xC10)	320,1008
Q₁₆.₂(C₂×C₁₀) = C₅×C₄○D₁₆	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Q₁₆	160	2	Q16.2(C2xC10)	320,1009
Q₁₆.₃(C₂×C₁₀) = C₅×Q₃₂⋊C₂	φ: C₂×C₁₀/C₁₀ → C₂ ⊆ Out Q₁₆	160	4	Q16.3(C2xC10)	320,1011
Q₁₆.₄(C₂×C₁₀) = C₅×Q₈○D₈	φ: trivial image	160	4	Q16.4(C2xC10)	320,1580

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