Extensions 1→N→G→Q→1 with N=C₄xC₂₀ and Q=S₃

Direct product G=NxQ with N=C₄xC₂₀ and Q=S₃

		d	ρ	Label	ID
S₃xC₄xC₂₀		240		S3xC4xC20	480,750

Semidirect products G=N:Q with N=C₄xC₂₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₄xC₂₀):₁S₃ = C₄²:D₁₅	φ: S₃/C₁ → S₃ ⊆ Aut C₄xC₂₀	60	6+	(C4xC20):1S3	480,258
(C₄xC₂₀):₂S₃ = C₅xC₄²:S₃	φ: S₃/C₁ → S₃ ⊆ Aut C₄xC₂₀	60	3	(C4xC20):2S3	480,254
(C₄xC₂₀):₃S₃ = C₅xC₄²:₂S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	240		(C4xC20):3S3	480,751
(C₄xC₂₀):₄S₃ = C₅xC₄²:₃S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	240		(C4xC20):4S3	480,755
(C₄xC₂₀):₅S₃ = C₄²:₃D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	240		(C4xC20):5S3	480,841
(C₄xC₂₀):₆S₃ = C₄²:₆D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	240		(C4xC20):6S3	480,839
(C₄xC₂₀):₇S₃ = C₄²:₇D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	240		(C4xC20):7S3	480,840
(C₄xC₂₀):₈S₃ = D₆₀:₇C₄	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	120	2	(C4xC20):8S3	480,165
(C₄xC₂₀):₉S₃ = C₄xD₆₀	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	240		(C4xC20):9S3	480,838
(C₄xC₂₀):₁₀S₃ = C₄²xD₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	240		(C4xC20):10S3	480,836
(C₄xC₂₀):₁₁S₃ = C₄²:₂D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	240		(C4xC20):11S3	480,837
(C₄xC₂₀):₁₂S₃ = C₅xC₄²:₄S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	120	2	(C4xC20):12S3	480,124
(C₄xC₂₀):₁₃S₃ = C₂₀xD₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	240		(C4xC20):13S3	480,752
(C₄xC₂₀):₁₄S₃ = C₅xC₄:D₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	240		(C4xC20):14S3	480,753
(C₄xC₂₀):₁₅S₃ = C₅xC₄²:₇S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	240		(C4xC20):15S3	480,754

Non-split extensions G=N.Q with N=C₄xC₂₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₄xC₂₀).₁S₃ = C₅xC₄².S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	480		(C4xC20).1S3	480,122
(C₄xC₂₀).₂S₃ = C₆₀:₈Q₈	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	480		(C4xC20).2S3	480,834
(C₄xC₂₀).₃S₃ = C₆₀.₂₄Q₈	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	480		(C4xC20).3S3	480,835
(C₄xC₂₀).₄S₃ = C₆₀:₅C₈	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	480		(C4xC20).4S3	480,164
(C₄xC₂₀).₅S₃ = C₄xDic₃₀	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	480		(C4xC20).5S3	480,833
(C₄xC₂₀).₆S₃ = C₄xC₁₅:₃C₈	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	480		(C4xC20).6S3	480,162
(C₄xC₂₀).₇S₃ = C₄².D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	480		(C4xC20).7S3	480,163
(C₄xC₂₀).₈S₃ = C₅xC₁₂:C₈	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	480		(C4xC20).8S3	480,123
(C₄xC₂₀).₉S₃ = C₂₀xDic₆	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	480		(C4xC20).9S3	480,747
(C₄xC₂₀).₁₀S₃ = C₅xC₁₂:₂Q₈	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	480		(C4xC20).10S3	480,748
(C₄xC₂₀).₁₁S₃ = C₅xC₁₂.₆Q₈	φ: S₃/C₃ → C₂ ⊆ Aut C₄xC₂₀	480		(C4xC20).11S3	480,749
(C₄xC₂₀).₁₂S₃ = C₂₀xC₃:C₈	central extension (φ=1)	480		(C4xC20).12S3	480,121

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