Extensions 1→N→G→Q→1 with N=C₂×C₁₀ and Q=Q₈

Direct product G=N×Q with N=C₂×C₁₀ and Q=Q₈

		d	ρ	Label	ID
Q₈×C₂×C₁₀		160		Q8xC2xC10	160,230

Semidirect products G=N:Q with N=C₂×C₁₀ and Q=Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₁₀)⋊Q₈ = Dic₅.₁₄D₄	φ: Q₈/C₂ → C₂² ⊆ Aut C₂×C₁₀	80		(C2xC10):Q8	160,99
(C₂×C₁₀)⋊₂Q₈ = C₅×C₂²⋊Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₂×C₁₀	80		(C2xC10):2Q8	160,183
(C₂×C₁₀)⋊₃Q₈ = C₂₀.₄₈D₄	φ: Q₈/C₄ → C₂ ⊆ Aut C₂×C₁₀	80		(C2xC10):3Q8	160,145
(C₂×C₁₀)⋊₄Q₈ = C₂²×Dic₁₀	φ: Q₈/C₄ → C₂ ⊆ Aut C₂×C₁₀	160		(C2xC10):4Q8	160,213

Non-split extensions G=N.Q with N=C₂×C₁₀ and Q=Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₁₀).Q₈ = C₂₀.₅₃D₄	φ: Q₈/C₂ → C₂² ⊆ Aut C₂×C₁₀	80	4	(C2xC10).Q8	160,29
(C₂×C₁₀).₂Q₈ = C₅×C₈.C₄	φ: Q₈/C₄ → C₂ ⊆ Aut C₂×C₁₀	80	2	(C2xC10).2Q8	160,58
(C₂×C₁₀).₃Q₈ = C₄₀.₆C₄	φ: Q₈/C₄ → C₂ ⊆ Aut C₂×C₁₀	80	2	(C2xC10).3Q8	160,26
(C₂×C₁₀).₄Q₈ = C₁₀.₁₀C₄²	φ: Q₈/C₄ → C₂ ⊆ Aut C₂×C₁₀	160		(C2xC10).4Q8	160,38
(C₂×C₁₀).₅Q₈ = C₂×C₁₀.D₄	φ: Q₈/C₄ → C₂ ⊆ Aut C₂×C₁₀	160		(C2xC10).5Q8	160,144
(C₂×C₁₀).₆Q₈ = C₂×C₄⋊Dic₅	φ: Q₈/C₄ → C₂ ⊆ Aut C₂×C₁₀	160		(C2xC10).6Q8	160,146
(C₂×C₁₀).₇Q₈ = C₅×C₂.C₄²	central extension (φ=1)	160		(C2xC10).7Q8	160,45
(C₂×C₁₀).₈Q₈ = C₁₀×C₄⋊C₄	central extension (φ=1)	160		(C2xC10).8Q8	160,177

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁