Extensions 1→N→G→Q→1 with N=C₅×Q₈ and Q=S₃

Direct product G=N×Q with N=C₅×Q₈ and Q=S₃

		d	ρ	Label	ID
C₅×S₃×Q₈		120	4	C5xS3xQ8	240,171

Semidirect products G=N:Q with N=C₅×Q₈ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×Q₈)⋊₁S₃ = Q₈⋊D₁₅	φ: S₃/C₁ → S₃ ⊆ Out C₅×Q₈	40	4+	(C5xQ8):1S3	240,106
(C₅×Q₈)⋊₂S₃ = C₅×GL₂(𝔽₃)	φ: S₃/C₁ → S₃ ⊆ Out C₅×Q₈	40	2	(C5xQ8):2S3	240,103
(C₅×Q₈)⋊₃S₃ = Q₈⋊₂D₁₅	φ: S₃/C₃ → C₂ ⊆ Out C₅×Q₈	120	4+	(C5xQ8):3S3	240,78
(C₅×Q₈)⋊₄S₃ = Q₈×D₁₅	φ: S₃/C₃ → C₂ ⊆ Out C₅×Q₈	120	4-	(C5xQ8):4S3	240,181
(C₅×Q₈)⋊₅S₃ = Q₈⋊₃D₁₅	φ: S₃/C₃ → C₂ ⊆ Out C₅×Q₈	120	4+	(C5xQ8):5S3	240,182
(C₅×Q₈)⋊₆S₃ = C₅×Q₈⋊₂S₃	φ: S₃/C₃ → C₂ ⊆ Out C₅×Q₈	120	4	(C5xQ8):6S3	240,62
(C₅×Q₈)⋊₇S₃ = C₅×Q₈⋊₃S₃	φ: trivial image	120	4	(C5xQ8):7S3	240,172

Non-split extensions G=N.Q with N=C₅×Q₈ and Q=S₃

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×Q₈).₁S₃ = Q₈.D₁₅	φ: S₃/C₁ → S₃ ⊆ Out C₅×Q₈	80	4-	(C5xQ8).1S3	240,105
(C₅×Q₈).₂S₃ = C₅×CSU₂(𝔽₃)	φ: S₃/C₁ → S₃ ⊆ Out C₅×Q₈	80	2	(C5xQ8).2S3	240,102
(C₅×Q₈).₃S₃ = C₁₅⋊₇Q₁₆	φ: S₃/C₃ → C₂ ⊆ Out C₅×Q₈	240	4-	(C5xQ8).3S3	240,79
(C₅×Q₈).₄S₃ = C₅×C₃⋊Q₁₆	φ: S₃/C₃ → C₂ ⊆ Out C₅×Q₈	240	4	(C5xQ8).4S3	240,63

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