Extensions 1→N→G→Q→1 with N=C₅×C₁₅ and Q=S₃

Direct product G=N×Q with N=C₅×C₁₅ and Q=S₃

		d	ρ	Label	ID
S₃×C₅×C₁₅		150		S3xC5xC15	450,28

Semidirect products G=N:Q with N=C₅×C₁₅ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₅×C₁₅)⋊₁S₃ = C₅²⋊(C₃⋊S₃)	φ: S₃/C₁ → S₃ ⊆ Aut C₅×C₁₅	45	6+	(C5xC15):1S3	450,21
(C₅×C₁₅)⋊₂S₃ = C₃×C₅²⋊S₃	φ: S₃/C₁ → S₃ ⊆ Aut C₅×C₁₅	45	3	(C5xC15):2S3	450,20
(C₅×C₁₅)⋊₃S₃ = C₁₅⋊D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₅×C₁₅	225		(C5xC15):3S3	450,33
(C₅×C₁₅)⋊₄S₃ = C₅×C₃⋊D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₅×C₁₅	90		(C5xC15):4S3	450,32
(C₅×C₁₅)⋊₅S₃ = C₁₅×D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₅×C₁₅	30	2	(C5xC15):5S3	450,29
(C₅×C₁₅)⋊₆S₃ = C₃×C₅⋊D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₅×C₁₅	150		(C5xC15):6S3	450,30
(C₅×C₁₅)⋊₇S₃ = C₃⋊S₃×C₅²	φ: S₃/C₃ → C₂ ⊆ Aut C₅×C₁₅	225		(C5xC15):7S3	450,31

Non-split extensions G=N.Q with N=C₅×C₁₅ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₅×C₁₅).S₃ = C₅²⋊D₉	φ: S₃/C₁ → S₃ ⊆ Aut C₅×C₁₅	45	6+	(C5xC15).S3	450,11
(C₅×C₁₅).₂S₃ = C₅⋊D₄₅	φ: S₃/C₃ → C₂ ⊆ Aut C₅×C₁₅	225		(C5xC15).2S3	450,18
(C₅×C₁₅).₃S₃ = C₅×D₄₅	φ: S₃/C₃ → C₂ ⊆ Aut C₅×C₁₅	90	2	(C5xC15).3S3	450,17
(C₅×C₁₅).₄S₃ = D₉×C₅²	φ: S₃/C₃ → C₂ ⊆ Aut C₅×C₁₅	225		(C5xC15).4S3	450,16

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