Extensions 1→N→G→Q→1 with N=C₃ and Q=C₂×C₂²⋊F₅

Direct product G=N×Q with N=C₃ and Q=C₂×C₂²⋊F₅

		d	ρ	Label	ID
C₆×C₂²⋊F₅		120		C6xC2^2:F5	480,1059

Semidirect products G=N:Q with N=C₃ and Q=C₂×C₂²⋊F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₂×C₂²⋊F₅) = S₃×C₂²⋊F₅	φ: C₂×C₂²⋊F₅/C₂²⋊F₅ → C₂ ⊆ Aut C₃	60	8+	C3:1(C2xC2^2:F5)	480,1011
C₃⋊₂(C₂×C₂²⋊F₅) = C₂×D₆⋊F₅	φ: C₂×C₂²⋊F₅/C₂²×F₅ → C₂ ⊆ Aut C₃	120		C3:2(C2xC2^2:F5)	480,1000
C₃⋊₃(C₂×C₂²⋊F₅) = C₂×D₁₀.D₆	φ: C₂×C₂²⋊F₅/C₂³×D₅ → C₂ ⊆ Aut C₃	120		C3:3(C2xC2^2:F5)	480,1072

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