Extensions 1→N→G→Q→1 with N=C₄² and Q=C₃₀

Direct product G=N×Q with N=C₄² and Q=C₃₀

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

Semidirect products G=N:Q with N=C₄² and Q=C₃₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄²⋊₁C₃₀ = C₅×C₄²⋊C₆	φ: C₃₀/C₅ → C₆ ⊆ Aut C₄²	80	6	C4^2:1C30	480,657
C₄²⋊₂C₃₀ = C₅×C₂³.A₄	φ: C₃₀/C₅ → C₆ ⊆ Aut C₄²	60	6	C4^2:2C30	480,658
C₄²⋊₃C₃₀ = C₁₀×C₄²⋊C₃	φ: C₃₀/C₁₀ → C₃ ⊆ Aut C₄²	60	3	C4^2:3C30	480,654
C₄²⋊₄C₃₀ = C₁₅×C₄²⋊C₂	φ: C₃₀/C₁₅ → C₂ ⊆ Aut C₄²	240		C4^2:4C30	480,922
C₄²⋊₅C₃₀ = C₁₅×C₄²⋊₂C₂	φ: C₃₀/C₁₅ → C₂ ⊆ Aut C₄²	240		C4^2:5C30	480,931
C₄²⋊₆C₃₀ = C₁₅×C₄≀C₂	φ: C₃₀/C₁₅ → C₂ ⊆ Aut C₄²	120	2	C4^2:6C30	480,207
C₄²⋊₇C₃₀ = D₄×C₆₀	φ: C₃₀/C₁₅ → C₂ ⊆ Aut C₄²	240		C4^2:7C30	480,923
C₄²⋊₈C₃₀ = C₁₅×C₄.₄D₄	φ: C₃₀/C₁₅ → C₂ ⊆ Aut C₄²	240		C4^2:8C30	480,929
C₄²⋊₉C₃₀ = C₁₅×C₄⋊₁D₄	φ: C₃₀/C₁₅ → C₂ ⊆ Aut C₄²	240		C4^2:9C30	480,932

Non-split extensions G=N.Q with N=C₄² and Q=C₃₀

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄².₁C₃₀ = C₁₅×C₈⋊C₄	φ: C₃₀/C₁₅ → C₂ ⊆ Aut C₄²	480		C4^2.1C30	480,200
C₄².₂C₃₀ = C₁₅×C₄⋊C₈	φ: C₃₀/C₁₅ → C₂ ⊆ Aut C₄²	480		C4^2.2C30	480,208
C₄².₃C₃₀ = Q₈×C₆₀	φ: C₃₀/C₁₅ → C₂ ⊆ Aut C₄²	480		C4^2.3C30	480,924
C₄².₄C₃₀ = C₁₅×C₄².C₂	φ: C₃₀/C₁₅ → C₂ ⊆ Aut C₄²	480		C4^2.4C30	480,930
C₄².₅C₃₀ = C₁₅×C₄⋊Q₈	φ: C₃₀/C₁₅ → C₂ ⊆ Aut C₄²	480		C4^2.5C30	480,933

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