Extensions 1→N→G→Q→1 with N=C₄○D₄ and Q=D₁₅

Direct product G=N×Q with N=C₄○D₄ and Q=D₁₅

		d	ρ	Label	ID
C₄○D₄×D₁₅		120	4	C4oD4xD15	480,1175

Semidirect products G=N:Q with N=C₄○D₄ and Q=D₁₅

extension	φ:Q→Out N	d	ρ	Label	ID
C₄○D₄⋊₁D₁₅ = C₂₀.₆S₄	φ: D₁₅/C₅ → S₃ ⊆ Out C₄○D₄	80	4	C4oD4:1D15	480,1031
C₄○D₄⋊₂D₁₅ = C₂₀.₃S₄	φ: D₁₅/C₅ → S₃ ⊆ Out C₄○D₄	80	4+	C4oD4:2D15	480,1032
C₄○D₄⋊₃D₁₅ = D₄⋊D₃₀	φ: D₁₅/C₁₅ → C₂ ⊆ Out C₄○D₄	120	4+	C4oD4:3D15	480,914
C₄○D₄⋊₄D₁₅ = D₄.₈D₃₀	φ: D₁₅/C₁₅ → C₂ ⊆ Out C₄○D₄	240	4	C4oD4:4D15	480,915
C₄○D₄⋊₅D₁₅ = D₄⋊₈D₃₀	φ: D₁₅/C₁₅ → C₂ ⊆ Out C₄○D₄	120	4+	C4oD4:5D15	480,1176
C₄○D₄⋊₆D₁₅ = D₄.₁₀D₃₀	φ: D₁₅/C₁₅ → C₂ ⊆ Out C₄○D₄	240	4-	C4oD4:6D15	480,1177

Non-split extensions G=N.Q with N=C₄○D₄ and Q=D₁₅

extension	φ:Q→Out N	d	ρ	Label	ID
C₄○D₄.₁D₁₅ = C₅⋊₂U₂(𝔽₃)	φ: D₁₅/C₅ → S₃ ⊆ Out C₄○D₄	120	4	C4oD4.1D15	480,261
C₄○D₄.₂D₁₅ = C₂₀.₂S₄	φ: D₁₅/C₅ → S₃ ⊆ Out C₄○D₄	160	4-	C4oD4.2D15	480,1030
C₄○D₄.₃D₁₅ = Q₈⋊₃Dic₁₅	φ: D₁₅/C₁₅ → C₂ ⊆ Out C₄○D₄	120	4	C4oD4.3D15	480,197
C₄○D₄.₄D₁₅ = D₄.₉D₃₀	φ: D₁₅/C₁₅ → C₂ ⊆ Out C₄○D₄	240	4-	C4oD4.4D15	480,916
C₄○D₄.₅D₁₅ = D₄.Dic₁₅	φ: trivial image	240	4	C4oD4.5D15	480,913

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁