Extensions 1→N→G→Q→1 with N=C₄×C₂₀ and Q=S₃

Direct product G=N×Q with N=C₄×C₂₀ and Q=S₃

		d	ρ	Label	ID
S₃×C₄×C₂₀		240		S3xC4xC20	480,750

Semidirect products G=N:Q with N=C₄×C₂₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₄×C₂₀)⋊₁S₃ = C₄²⋊D₁₅	φ: S₃/C₁ → S₃ ⊆ Aut C₄×C₂₀	60	6+	(C4xC20):1S3	480,258
(C₄×C₂₀)⋊₂S₃ = C₅×C₄²⋊S₃	φ: S₃/C₁ → S₃ ⊆ Aut C₄×C₂₀	60	3	(C4xC20):2S3	480,254
(C₄×C₂₀)⋊₃S₃ = C₅×C₄²⋊₂S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):3S3	480,751
(C₄×C₂₀)⋊₄S₃ = C₅×C₄²⋊₃S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):4S3	480,755
(C₄×C₂₀)⋊₅S₃ = C₄²⋊₃D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):5S3	480,841
(C₄×C₂₀)⋊₆S₃ = C₄²⋊₆D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):6S3	480,839
(C₄×C₂₀)⋊₇S₃ = C₄²⋊₇D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):7S3	480,840
(C₄×C₂₀)⋊₈S₃ = D₆₀⋊₇C₄	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	120	2	(C4xC20):8S3	480,165
(C₄×C₂₀)⋊₉S₃ = C₄×D₆₀	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):9S3	480,838
(C₄×C₂₀)⋊₁₀S₃ = C₄²×D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):10S3	480,836
(C₄×C₂₀)⋊₁₁S₃ = C₄²⋊₂D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):11S3	480,837
(C₄×C₂₀)⋊₁₂S₃ = C₅×C₄²⋊₄S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	120	2	(C4xC20):12S3	480,124
(C₄×C₂₀)⋊₁₃S₃ = C₂₀×D₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):13S3	480,752
(C₄×C₂₀)⋊₁₄S₃ = C₅×C₄⋊D₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):14S3	480,753
(C₄×C₂₀)⋊₁₅S₃ = C₅×C₄²⋊₇S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	240		(C4xC20):15S3	480,754

Non-split extensions G=N.Q with N=C₄×C₂₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₄×C₂₀).₁S₃ = C₅×C₄².S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).1S3	480,122
(C₄×C₂₀).₂S₃ = C₆₀⋊₈Q₈	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).2S3	480,834
(C₄×C₂₀).₃S₃ = C₆₀.₂₄Q₈	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).3S3	480,835
(C₄×C₂₀).₄S₃ = C₆₀⋊₅C₈	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).4S3	480,164
(C₄×C₂₀).₅S₃ = C₄×Dic₃₀	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).5S3	480,833
(C₄×C₂₀).₆S₃ = C₄×C₁₅⋊₃C₈	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).6S3	480,162
(C₄×C₂₀).₇S₃ = C₄².D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).7S3	480,163
(C₄×C₂₀).₈S₃ = C₅×C₁₂⋊C₈	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).8S3	480,123
(C₄×C₂₀).₉S₃ = C₂₀×Dic₆	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).9S3	480,747
(C₄×C₂₀).₁₀S₃ = C₅×C₁₂⋊₂Q₈	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).10S3	480,748
(C₄×C₂₀).₁₁S₃ = C₅×C₁₂.₆Q₈	φ: S₃/C₃ → C₂ ⊆ Aut C₄×C₂₀	480		(C4xC20).11S3	480,749
(C₄×C₂₀).₁₂S₃ = C₂₀×C₃⋊C₈	central extension (φ=1)	480		(C4xC20).12S3	480,121

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