Extensions 1→N→G→Q→1 with N=C₄×C₂₀ and Q=C₆

Direct product G=N×Q with N=C₄×C₂₀ and Q=C₆

		d	ρ	Label	ID
C₂×C₄×C₆₀		480		C2xC4xC60	480,919

Semidirect products G=N:Q with N=C₄×C₂₀ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₄×C₂₀)⋊₁C₆ = (C₄×C₂₀)⋊C₆	φ: C₆/C₁ → C₆ ⊆ Aut C₄×C₂₀	80	6	(C4xC20):1C6	480,263
(C₄×C₂₀)⋊₂C₆ = C₅×C₄²⋊C₆	φ: C₆/C₁ → C₆ ⊆ Aut C₄×C₂₀	80	6	(C4xC20):2C6	480,657
(C₄×C₂₀)⋊₃C₆ = C₂₀⋊₄D₄⋊C₃	φ: C₆/C₁ → C₆ ⊆ Aut C₄×C₂₀	60	6+	(C4xC20):3C6	480,262
(C₄×C₂₀)⋊₄C₆ = D₅×C₄²⋊C₃	φ: C₆/C₁ → C₆ ⊆ Aut C₄×C₂₀	60	6	(C4xC20):4C6	480,264
(C₄×C₂₀)⋊₅C₆ = C₅×C₂³.A₄	φ: C₆/C₁ → C₆ ⊆ Aut C₄×C₂₀	60	6	(C4xC20):5C6	480,658
(C₄×C₂₀)⋊₆C₆ = C₁₀×C₄²⋊C₃	φ: C₆/C₂ → C₃ ⊆ Aut C₄×C₂₀	60	3	(C4xC20):6C6	480,654
(C₄×C₂₀)⋊₇C₆ = C₃×C₄²⋊₂D₅	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):7C6	480,669
(C₄×C₂₀)⋊₈C₆ = C₁₅×C₄²⋊C₂	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):8C6	480,922
(C₄×C₂₀)⋊₉C₆ = C₁₅×C₄²⋊₂C₂	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):9C6	480,931
(C₄×C₂₀)⋊₁₀C₆ = C₃×C₂₀⋊₄D₄	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):10C6	480,667
(C₄×C₂₀)⋊₁₁C₆ = C₃×C₄.D₂₀	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):11C6	480,668
(C₄×C₂₀)⋊₁₂C₆ = C₃×D₂₀⋊₄C₄	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	120	2	(C4xC20):12C6	480,83
(C₄×C₂₀)⋊₁₃C₆ = C₁₂×D₂₀	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):13C6	480,666
(C₄×C₂₀)⋊₁₄C₆ = D₅×C₄×C₁₂	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):14C6	480,664
(C₄×C₂₀)⋊₁₅C₆ = C₃×C₄²⋊D₅	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):15C6	480,665
(C₄×C₂₀)⋊₁₆C₆ = C₁₅×C₄≀C₂	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	120	2	(C4xC20):16C6	480,207
(C₄×C₂₀)⋊₁₇C₆ = D₄×C₆₀	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):17C6	480,923
(C₄×C₂₀)⋊₁₈C₆ = C₁₅×C₄.₄D₄	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):18C6	480,929
(C₄×C₂₀)⋊₁₉C₆ = C₁₅×C₄⋊₁D₄	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):19C6	480,932

Non-split extensions G=N.Q with N=C₄×C₂₀ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₄×C₂₀).₁C₆ = C₁₅×C₈⋊C₄	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).1C6	480,200
(C₄×C₂₀).₂C₆ = C₃×C₂₀⋊₂Q₈	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).2C6	480,662
(C₄×C₂₀).₃C₆ = C₃×C₂₀.₆Q₈	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).3C6	480,663
(C₄×C₂₀).₄C₆ = C₃×C₂₀⋊₃C₈	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).4C6	480,82
(C₄×C₂₀).₅C₆ = C₁₂×Dic₁₀	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).5C6	480,661
(C₄×C₂₀).₆C₆ = C₁₂×C₅⋊₂C₈	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).6C6	480,80
(C₄×C₂₀).₇C₆ = C₃×C₄².D₅	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).7C6	480,81
(C₄×C₂₀).₈C₆ = C₁₅×C₄⋊C₈	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).8C6	480,208
(C₄×C₂₀).₉C₆ = Q₈×C₆₀	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).9C6	480,924
(C₄×C₂₀).₁₀C₆ = C₁₅×C₄².C₂	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).10C6	480,930
(C₄×C₂₀).₁₁C₆ = C₁₅×C₄⋊Q₈	φ: C₆/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).11C6	480,933

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