Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₃×F₅

Direct product G=N×Q with N=C₂³ and Q=C₃×F₅

		d	ρ	Label	ID
F₅×C₂²×C₆		120		F5xC2^2xC6	480,1205

Semidirect products G=N:Q with N=C₂³ and Q=C₃×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊(C₃×F₅) = C₃×C₂³⋊F₅	φ: C₃×F₅/C₁₅ → C₄ ⊆ Aut C₂³	120	4	C2^3:(C3xF5)	480,291
C₂³⋊₂(C₃×F₅) = C₂×A₄×F₅	φ: C₃×F₅/F₅ → C₃ ⊆ Aut C₂³	30	12+	C2^3:2(C3xF5)	480,1192
C₂³⋊₃(C₃×F₅) = C₆×C₂²⋊F₅	φ: C₃×F₅/C₃×D₅ → C₂ ⊆ Aut C₂³	120		C2^3:3(C3xF5)	480,1059

Non-split extensions G=N.Q with N=C₂³ and Q=C₃×F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.(C₃×F₅) = C₃×C₂³.F₅	φ: C₃×F₅/C₁₅ → C₄ ⊆ Aut C₂³	120	4	C2^3.(C3xF5)	480,293
C₂³.₂(C₃×F₅) = A₄×C₅⋊C₈	φ: C₃×F₅/F₅ → C₃ ⊆ Aut C₂³	120	12-	C2^3.2(C3xF5)	480,966
C₂³.₃(C₃×F₅) = C₃×C₂³.₂F₅	φ: C₃×F₅/C₃×D₅ → C₂ ⊆ Aut C₂³	240		C2^3.3(C3xF5)	480,292
C₂³.₄(C₃×F₅) = C₆×C₂².F₅	φ: C₃×F₅/C₃×D₅ → C₂ ⊆ Aut C₂³	240		C2^3.4(C3xF5)	480,1058
C₂³.₅(C₃×F₅) = C₂×C₆×C₅⋊C₈	central extension (φ=1)	480		C2^3.5(C3xF5)	480,1057

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