Extensions 1→N→G→Q→1 with N=C₂×C₁₀ and Q=C₈

Direct product G=N×Q with N=C₂×C₁₀ and Q=C₈

		d	ρ	Label	ID
C₂²×C₄₀		160		C2^2xC40	160,190

Semidirect products G=N:Q with N=C₂×C₁₀ and Q=C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₁₀)⋊₁C₈ = C₂³.₂F₅	φ: C₈/C₂ → C₄ ⊆ Aut C₂×C₁₀	80		(C2xC10):1C8	160,87
(C₂×C₁₀)⋊₂C₈ = C₂²×C₅⋊C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₂×C₁₀	160		(C2xC10):2C8	160,210
(C₂×C₁₀)⋊₃C₈ = C₅×C₂²⋊C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₂×C₁₀	80		(C2xC10):3C8	160,48
(C₂×C₁₀)⋊₄C₈ = C₂₀.₅₅D₄	φ: C₈/C₄ → C₂ ⊆ Aut C₂×C₁₀	80		(C2xC10):4C8	160,37
(C₂×C₁₀)⋊₅C₈ = C₂²×C₅⋊₂C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₂×C₁₀	160		(C2xC10):5C8	160,141

Non-split extensions G=N.Q with N=C₂×C₁₀ and Q=C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₁₀).₁C₈ = C₂×C₅⋊C₁₆	φ: C₈/C₂ → C₄ ⊆ Aut C₂×C₁₀	160		(C2xC10).1C8	160,72
(C₂×C₁₀).₂C₈ = C₂₀.C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₂×C₁₀	80	4	(C2xC10).2C8	160,73
(C₂×C₁₀).₃C₈ = C₅×M₅(2)	φ: C₈/C₄ → C₂ ⊆ Aut C₂×C₁₀	80	2	(C2xC10).3C8	160,60
(C₂×C₁₀).₄C₈ = C₂×C₅⋊₂C₁₆	φ: C₈/C₄ → C₂ ⊆ Aut C₂×C₁₀	160		(C2xC10).4C8	160,18
(C₂×C₁₀).₅C₈ = C₂₀.₄C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₂×C₁₀	80	2	(C2xC10).5C8	160,19

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁