Extensions 1→N→G→Q→1 with N=C₄.Dic₅ and Q=S₃

Direct product G=N×Q with N=C₄.Dic₅ and Q=S₃

		d	ρ	Label	ID
S₃×C₄.Dic₅		120	4	S3xC4.Dic5	480,363

Semidirect products G=N:Q with N=C₄.Dic₅ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₄.Dic₅⋊₁S₃ = D₆₀⋊₁₃C₄	φ: S₃/C₃ → C₂ ⊆ Out C₄.Dic₅	120	4	C4.Dic5:1S3	480,56
C₄.Dic₅⋊₂S₃ = C₂₀.₅D₁₂	φ: S₃/C₃ → C₂ ⊆ Out C₄.Dic₅	120	4	C4.Dic5:2S3	480,35
C₄.Dic₅⋊₃S₃ = C₆₀.₂₉D₄	φ: S₃/C₃ → C₂ ⊆ Out C₄.Dic₅	120	4+	C4.Dic5:3S3	480,36
C₄.Dic₅⋊₄S₃ = C₆₀.₉₈D₄	φ: S₃/C₃ → C₂ ⊆ Out C₄.Dic₅	120	4	C4.Dic5:4S3	480,54
C₄.Dic₅⋊₅S₃ = D₁₂.Dic₅	φ: S₃/C₃ → C₂ ⊆ Out C₄.Dic₅	240	4	C4.Dic5:5S3	480,364
C₄.Dic₅⋊₆S₃ = D₁₅⋊₄M₄(2)	φ: S₃/C₃ → C₂ ⊆ Out C₄.Dic₅	120	4	C4.Dic5:6S3	480,368
C₄.Dic₅⋊₇S₃ = D₆₀⋊₃₆C₂²	φ: S₃/C₃ → C₂ ⊆ Out C₄.Dic₅	120	4	C4.Dic5:7S3	480,380
C₄.Dic₅⋊₈S₃ = C₆₀.₃₈D₄	φ: S₃/C₃ → C₂ ⊆ Out C₄.Dic₅	120	4+	C4.Dic5:8S3	480,381
C₄.Dic₅⋊₉S₃ = C₂₀.D₁₂	φ: S₃/C₃ → C₂ ⊆ Out C₄.Dic₅	240	4	C4.Dic5:9S3	480,397
C₄.Dic₅⋊₁₀S₃ = D₁₂.₃₃D₁₀	φ: S₃/C₃ → C₂ ⊆ Out C₄.Dic₅	240	4-	C4.Dic5:10S3	480,398
C₄.Dic₅⋊₁₁S₃ = D₆₀.₄C₄	φ: trivial image	240	4	C4.Dic5:11S3	480,367

Non-split extensions G=N.Q with N=C₄.Dic₅ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
C₄.Dic₅.₁S₃ = C₁₂.₅₉D₂₀	φ: S₃/C₃ → C₂ ⊆ Out C₄.Dic₅	240	4	C4.Dic5.1S3	480,69
C₄.Dic₅.₂S₃ = C₆₀.₅₄D₄	φ: S₃/C₃ → C₂ ⊆ Out C₄.Dic₅	240	4	C4.Dic5.2S3	480,38
C₄.Dic₅.₃S₃ = C₆₀.₃₁D₄	φ: S₃/C₃ → C₂ ⊆ Out C₄.Dic₅	240	4-	C4.Dic5.3S3	480,39
C₄.Dic₅.₄S₃ = C₆₀.D₄	φ: S₃/C₃ → C₂ ⊆ Out C₄.Dic₅	240	4	C4.Dic5.4S3	480,68

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