Extensions 1→N→G→Q→1 with N=C₅ and Q=C₂×C₄×C₁₂

Direct product G=N×Q with N=C₅ and Q=C₂×C₄×C₁₂

		d	ρ	Label	ID
C₂×C₄×C₆₀		480		C2xC4xC60	480,919

Semidirect products G=N:Q with N=C₅ and Q=C₂×C₄×C₁₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅⋊(C₂×C₄×C₁₂) = F₅×C₂×C₁₂	φ: C₂×C₄×C₁₂/C₂×C₁₂ → C₄ ⊆ Aut C₅	120		C5:(C2xC4xC12)	480,1050
C₅⋊₂(C₂×C₄×C₁₂) = D₅×C₄×C₁₂	φ: C₂×C₄×C₁₂/C₄×C₁₂ → C₂ ⊆ Aut C₅	240		C5:2(C2xC4xC12)	480,664
C₅⋊₃(C₂×C₄×C₁₂) = Dic₅×C₂×C₁₂	φ: C₂×C₄×C₁₂/C₂²×C₁₂ → C₂ ⊆ Aut C₅	480		C5:3(C2xC4xC12)	480,715

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁