Extensions 1→N→G→Q→1 with N=C₂²⋊C₄ and Q=C₃₀

Direct product G=N×Q with N=C₂²⋊C₄ and Q=C₃₀

		d	ρ	Label	ID
C₂²⋊C₄×C₃₀		240		C2^2:C4xC30	480,920

Semidirect products G=N:Q with N=C₂²⋊C₄ and Q=C₃₀

extension	φ:Q→Out N	d	ρ	Label	ID
C₂²⋊C₄⋊₁C₃₀ = C₁₅×C₂³⋊C₄	φ: C₃₀/C₁₅ → C₂ ⊆ Out C₂²⋊C₄	120	4	C2^2:C4:1C30	480,202
C₂²⋊C₄⋊₂C₃₀ = C₁₅×C₂²≀C₂	φ: C₃₀/C₁₅ → C₂ ⊆ Out C₂²⋊C₄	120		C2^2:C4:2C30	480,925
C₂²⋊C₄⋊₃C₃₀ = C₁₅×C₄⋊D₄	φ: C₃₀/C₁₅ → C₂ ⊆ Out C₂²⋊C₄	240		C2^2:C4:3C30	480,926
C₂²⋊C₄⋊₄C₃₀ = C₁₅×C₂².D₄	φ: C₃₀/C₁₅ → C₂ ⊆ Out C₂²⋊C₄	240		C2^2:C4:4C30	480,928
C₂²⋊C₄⋊₅C₃₀ = C₁₅×C₄.₄D₄	φ: C₃₀/C₁₅ → C₂ ⊆ Out C₂²⋊C₄	240		C2^2:C4:5C30	480,929
C₂²⋊C₄⋊₆C₃₀ = D₄×C₆₀	φ: trivial image	240		C2^2:C4:6C30	480,923

Non-split extensions G=N.Q with N=C₂²⋊C₄ and Q=C₃₀

extension	φ:Q→Out N	d	ρ	Label	ID
C₂²⋊C₄.₁C₃₀ = C₁₅×C₂²⋊Q₈	φ: C₃₀/C₁₅ → C₂ ⊆ Out C₂²⋊C₄	240		C2^2:C4.1C30	480,927
C₂²⋊C₄.₂C₃₀ = C₁₅×C₄²⋊₂C₂	φ: C₃₀/C₁₅ → C₂ ⊆ Out C₂²⋊C₄	240		C2^2:C4.2C30	480,931
C₂²⋊C₄.₃C₃₀ = C₁₅×C₄²⋊C₂	φ: trivial image	240		C2^2:C4.3C30	480,922

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁