Extensions 1→N→G→Q→1 with N=D₃₀ and Q=C₄

Direct product G=N×Q with N=D₃₀ and Q=C₄

		d	ρ	Label	ID
C₂×C₄×D₁₅		120		C2xC4xD15	240,176

Semidirect products G=N:Q with N=D₃₀ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
D₃₀⋊₁C₄ = D₆⋊F₅	φ: C₄/C₁ → C₄ ⊆ Out D₃₀	60	8+	D30:1C4	240,96
D₃₀⋊₂C₄ = C₂×S₃×F₅	φ: C₄/C₁ → C₄ ⊆ Out D₃₀	30	8+	D30:2C4	240,195
D₃₀⋊₃C₄ = D₃₀⋊₃C₄	φ: C₄/C₂ → C₂ ⊆ Out D₃₀	120		D30:3C4	240,75
D₃₀⋊₄C₄ = D₃₀⋊₄C₄	φ: C₄/C₂ → C₂ ⊆ Out D₃₀	120		D30:4C4	240,28
D₃₀⋊₅C₄ = C₂×D₃₀.C₂	φ: C₄/C₂ → C₂ ⊆ Out D₃₀	120		D30:5C4	240,144

Non-split extensions G=N.Q with N=D₃₀ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
D₃₀.₁C₄ = D₁₅⋊C₈	φ: C₄/C₁ → C₄ ⊆ Out D₃₀	120	8+	D30.1C4	240,99
D₃₀.₂C₄ = Dic₃.F₅	φ: C₄/C₁ → C₄ ⊆ Out D₃₀	120	8+	D30.2C4	240,101
D₃₀.₃C₄ = C₄₀⋊S₃	φ: C₄/C₂ → C₂ ⊆ Out D₃₀	120	2	D30.3C4	240,66
D₃₀.₄C₄ = D₁₅⋊₂C₈	φ: C₄/C₂ → C₂ ⊆ Out D₃₀	120	4	D30.4C4	240,9
D₃₀.₅C₄ = D₃₀.₅C₄	φ: C₄/C₂ → C₂ ⊆ Out D₃₀	120	4	D30.5C4	240,12
D₃₀.₆C₄ = C₈×D₁₅	φ: trivial image	120	2	D30.6C4	240,65

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁