Extensions 1→N→G→Q→1 with N=C₅×C₄○D₄ and Q=S₃

Direct product G=N×Q with N=C₅×C₄○D₄ and Q=S₃

		d	ρ	Label	ID
C₅×S₃×C₄○D₄		120	4	C5xS3xC4oD4	480,1160

Semidirect products G=N:Q with N=C₅×C₄○D₄ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×C₄○D₄)⋊₁S₃ = C₂₀.₆S₄	φ: S₃/C₁ → S₃ ⊆ Out C₅×C₄○D₄	80	4	(C5xC4oD4):1S3	480,1031
(C₅×C₄○D₄)⋊₂S₃ = C₂₀.₃S₄	φ: S₃/C₁ → S₃ ⊆ Out C₅×C₄○D₄	80	4+	(C5xC4oD4):2S3	480,1032
(C₅×C₄○D₄)⋊₃S₃ = C₅×C₄.₆S₄	φ: S₃/C₁ → S₃ ⊆ Out C₅×C₄○D₄	80	2	(C5xC4oD4):3S3	480,1020
(C₅×C₄○D₄)⋊₄S₃ = C₅×C₄.₃S₄	φ: S₃/C₁ → S₃ ⊆ Out C₅×C₄○D₄	80	4	(C5xC4oD4):4S3	480,1021
(C₅×C₄○D₄)⋊₅S₃ = D₄⋊D₃₀	φ: S₃/C₃ → C₂ ⊆ Out C₅×C₄○D₄	120	4+	(C5xC4oD4):5S3	480,914
(C₅×C₄○D₄)⋊₆S₃ = D₄.₈D₃₀	φ: S₃/C₃ → C₂ ⊆ Out C₅×C₄○D₄	240	4	(C5xC4oD4):6S3	480,915
(C₅×C₄○D₄)⋊₇S₃ = C₄○D₄×D₁₅	φ: S₃/C₃ → C₂ ⊆ Out C₅×C₄○D₄	120	4	(C5xC4oD4):7S3	480,1175
(C₅×C₄○D₄)⋊₈S₃ = D₄⋊₈D₃₀	φ: S₃/C₃ → C₂ ⊆ Out C₅×C₄○D₄	120	4+	(C5xC4oD4):8S3	480,1176
(C₅×C₄○D₄)⋊₉S₃ = D₄.₁₀D₃₀	φ: S₃/C₃ → C₂ ⊆ Out C₅×C₄○D₄	240	4-	(C5xC4oD4):9S3	480,1177
(C₅×C₄○D₄)⋊₁₀S₃ = C₅×D₄⋊D₆	φ: S₃/C₃ → C₂ ⊆ Out C₅×C₄○D₄	120	4	(C5xC4oD4):10S3	480,828
(C₅×C₄○D₄)⋊₁₁S₃ = C₅×Q₈.₁₃D₆	φ: S₃/C₃ → C₂ ⊆ Out C₅×C₄○D₄	240	4	(C5xC4oD4):11S3	480,829
(C₅×C₄○D₄)⋊₁₂S₃ = C₅×D₄○D₁₂	φ: S₃/C₃ → C₂ ⊆ Out C₅×C₄○D₄	120	4	(C5xC4oD4):12S3	480,1161
(C₅×C₄○D₄)⋊₁₃S₃ = C₅×Q₈○D₁₂	φ: S₃/C₃ → C₂ ⊆ Out C₅×C₄○D₄	240	4	(C5xC4oD4):13S3	480,1162

Non-split extensions G=N.Q with N=C₅×C₄○D₄ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×C₄○D₄).₁S₃ = C₅⋊₂U₂(𝔽₃)	φ: S₃/C₁ → S₃ ⊆ Out C₅×C₄○D₄	120	4	(C5xC4oD4).1S3	480,261
(C₅×C₄○D₄).₂S₃ = C₂₀.₂S₄	φ: S₃/C₁ → S₃ ⊆ Out C₅×C₄○D₄	160	4-	(C5xC4oD4).2S3	480,1030
(C₅×C₄○D₄).₃S₃ = C₅×U₂(𝔽₃)	φ: S₃/C₁ → S₃ ⊆ Out C₅×C₄○D₄	120	2	(C5xC4oD4).3S3	480,257
(C₅×C₄○D₄).₄S₃ = C₅×C₄.S₄	φ: S₃/C₁ → S₃ ⊆ Out C₅×C₄○D₄	160	4	(C5xC4oD4).4S3	480,1019
(C₅×C₄○D₄).₅S₃ = Q₈⋊₃Dic₁₅	φ: S₃/C₃ → C₂ ⊆ Out C₅×C₄○D₄	120	4	(C5xC4oD4).5S3	480,197
(C₅×C₄○D₄).₆S₃ = D₄.Dic₁₅	φ: S₃/C₃ → C₂ ⊆ Out C₅×C₄○D₄	240	4	(C5xC4oD4).6S3	480,913
(C₅×C₄○D₄).₇S₃ = D₄.₉D₃₀	φ: S₃/C₃ → C₂ ⊆ Out C₅×C₄○D₄	240	4-	(C5xC4oD4).7S3	480,916
(C₅×C₄○D₄).₈S₃ = C₅×Q₈⋊₃Dic₃	φ: S₃/C₃ → C₂ ⊆ Out C₅×C₄○D₄	120	4	(C5xC4oD4).8S3	480,156
(C₅×C₄○D₄).₉S₃ = C₅×Q₈.₁₄D₆	φ: S₃/C₃ → C₂ ⊆ Out C₅×C₄○D₄	240	4	(C5xC4oD4).9S3	480,830
(C₅×C₄○D₄).₁₀S₃ = C₅×D₄.Dic₃	φ: trivial image	240	4	(C5xC4oD4).10S3	480,827

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁