Extensions 1→N→G→Q→1 with N=D₄ and Q=D₃₀

Direct product G=N×Q with N=D₄ and Q=D₃₀

		d	ρ	Label	ID
C₂×D₄×D₁₅		120		C2xD4xD15	480,1169

Semidirect products G=N:Q with N=D₄ and Q=D₃₀

extension	φ:Q→Out N	d	ρ	Label	ID
D₄⋊₁D₃₀ = D₈×D₁₅	φ: D₃₀/D₁₅ → C₂ ⊆ Out D₄	120	4+	D4:1D30	480,875
D₄⋊₂D₃₀ = D₈⋊D₁₅	φ: D₃₀/D₁₅ → C₂ ⊆ Out D₄	120	4	D4:2D30	480,876
D₄⋊₃D₃₀ = C₂×D₄⋊D₁₅	φ: D₃₀/C₃₀ → C₂ ⊆ Out D₄	240		D4:3D30	480,896
D₄⋊₄D₃₀ = D₄⋊D₃₀	φ: D₃₀/C₃₀ → C₂ ⊆ Out D₄	120	4+	D4:4D30	480,914
D₄⋊₅D₃₀ = C₂×D₄⋊₂D₁₅	φ: trivial image	240		D4:5D30	480,1170
D₄⋊₆D₃₀ = D₄⋊₆D₃₀	φ: trivial image	120	4	D4:6D30	480,1171
D₄⋊₇D₃₀ = C₄○D₄×D₁₅	φ: trivial image	120	4	D4:7D30	480,1175
D₄⋊₈D₃₀ = D₄⋊₈D₃₀	φ: trivial image	120	4+	D4:8D30	480,1176

Non-split extensions G=N.Q with N=D₄ and Q=D₃₀

extension	φ:Q→Out N	d	ρ	Label	ID
D₄.₁D₃₀ = D₈⋊₃D₁₅	φ: D₃₀/D₁₅ → C₂ ⊆ Out D₄	240	4-	D4.1D30	480,877
D₄.₂D₃₀ = SD₁₆×D₁₅	φ: D₃₀/D₁₅ → C₂ ⊆ Out D₄	120	4	D4.2D30	480,878
D₄.₃D₃₀ = Q₈⋊₃D₃₀	φ: D₃₀/D₁₅ → C₂ ⊆ Out D₄	120	4+	D4.3D30	480,879
D₄.₄D₃₀ = SD₁₆⋊D₁₅	φ: D₃₀/D₁₅ → C₂ ⊆ Out D₄	240	4-	D4.4D30	480,880
D₄.₅D₃₀ = D₄.₅D₃₀	φ: D₃₀/D₁₅ → C₂ ⊆ Out D₄	240	4	D4.5D30	480,881
D₄.₆D₃₀ = D₄.D₃₀	φ: D₃₀/C₃₀ → C₂ ⊆ Out D₄	120	4	D4.6D30	480,897
D₄.₇D₃₀ = C₂×D₄.D₁₅	φ: D₃₀/C₃₀ → C₂ ⊆ Out D₄	240		D4.7D30	480,898
D₄.₈D₃₀ = D₄.₈D₃₀	φ: D₃₀/C₃₀ → C₂ ⊆ Out D₄	240	4	D4.8D30	480,915
D₄.₉D₃₀ = D₄.₉D₃₀	φ: D₃₀/C₃₀ → C₂ ⊆ Out D₄	240	4-	D4.9D30	480,916
D₄.₁₀D₃₀ = D₄.₁₀D₃₀	φ: trivial image	240	4-	D4.10D30	480,1177

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁