Extensions 1→N→G→Q→1 with N=C₄×C₂₀ and Q=C₂

Direct product G=N×Q with N=C₄×C₂₀ and Q=C₂

		d	ρ	Label	ID
C₂×C₄×C₂₀		160		C2xC4xC20	160,175

Semidirect products G=N:Q with N=C₄×C₂₀ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₄×C₂₀)⋊₁C₂ = C₄²⋊₂D₅	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	80		(C4xC20):1C2	160,97
(C₄×C₂₀)⋊₂C₂ = C₅×C₄²⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	80		(C4xC20):2C2	160,178
(C₄×C₂₀)⋊₃C₂ = C₅×C₄²⋊₂C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	80		(C4xC20):3C2	160,187
(C₄×C₂₀)⋊₄C₂ = C₂₀⋊₄D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	80		(C4xC20):4C2	160,95
(C₄×C₂₀)⋊₅C₂ = C₄.D₂₀	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	80		(C4xC20):5C2	160,96
(C₄×C₂₀)⋊₆C₂ = D₂₀⋊₄C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	40	2	(C4xC20):6C2	160,12
(C₄×C₂₀)⋊₇C₂ = C₄×D₂₀	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	80		(C4xC20):7C2	160,94
(C₄×C₂₀)⋊₈C₂ = D₅×C₄²	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	80		(C4xC20):8C2	160,92
(C₄×C₂₀)⋊₉C₂ = C₄²⋊D₅	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	80		(C4xC20):9C2	160,93
(C₄×C₂₀)⋊₁₀C₂ = C₅×C₄≀C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	40	2	(C4xC20):10C2	160,54
(C₄×C₂₀)⋊₁₁C₂ = D₄×C₂₀	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	80		(C4xC20):11C2	160,179
(C₄×C₂₀)⋊₁₂C₂ = C₅×C₄.₄D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	80		(C4xC20):12C2	160,185
(C₄×C₂₀)⋊₁₃C₂ = C₅×C₄⋊₁D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	80		(C4xC20):13C2	160,188

Non-split extensions G=N.Q with N=C₄×C₂₀ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₄×C₂₀).₁C₂ = C₅×C₈⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	160		(C4xC20).1C2	160,47
(C₄×C₂₀).₂C₂ = C₂₀⋊₂Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	160		(C4xC20).2C2	160,90
(C₄×C₂₀).₃C₂ = C₂₀.₆Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	160		(C4xC20).3C2	160,91
(C₄×C₂₀).₄C₂ = C₂₀⋊₃C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	160		(C4xC20).4C2	160,11
(C₄×C₂₀).₅C₂ = C₄×Dic₁₀	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	160		(C4xC20).5C2	160,89
(C₄×C₂₀).₆C₂ = C₄×C₅⋊₂C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	160		(C4xC20).6C2	160,9
(C₄×C₂₀).₇C₂ = C₄².D₅	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	160		(C4xC20).7C2	160,10
(C₄×C₂₀).₈C₂ = C₅×C₄⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	160		(C4xC20).8C2	160,55
(C₄×C₂₀).₉C₂ = Q₈×C₂₀	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	160		(C4xC20).9C2	160,180
(C₄×C₂₀).₁₀C₂ = C₅×C₄².C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	160		(C4xC20).10C2	160,186
(C₄×C₂₀).₁₁C₂ = C₅×C₄⋊Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₄×C₂₀	160		(C4xC20).11C2	160,189

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