Extensions 1→N→G→Q→1 with N=Q₈ and Q=D₁₀

Direct product G=N×Q with N=Q₈ and Q=D₁₀

		d	ρ	Label	ID
C₂×Q₈×D₅		80		C2xQ8xD5	160,220

Semidirect products G=N:Q with N=Q₈ and Q=D₁₀

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈⋊₁D₁₀ = D₅×SD₁₆	φ: D₁₀/D₅ → C₂ ⊆ Out Q₈	40	4	Q8:1D10	160,134
Q₈⋊₂D₁₀ = D₄₀⋊C₂	φ: D₁₀/D₅ → C₂ ⊆ Out Q₈	40	4+	Q8:2D10	160,135
Q₈⋊₃D₁₀ = C₂×Q₈⋊D₅	φ: D₁₀/C₁₀ → C₂ ⊆ Out Q₈	80		Q8:3D10	160,162
Q₈⋊₄D₁₀ = D₄⋊D₁₀	φ: D₁₀/C₁₀ → C₂ ⊆ Out Q₈	40	4+	Q8:4D10	160,170
Q₈⋊₅D₁₀ = C₂×Q₈⋊₂D₅	φ: trivial image	80		Q8:5D10	160,221
Q₈⋊₆D₁₀ = D₅×C₄○D₄	φ: trivial image	40	4	Q8:6D10	160,223
Q₈⋊₇D₁₀ = D₄⋊₈D₁₀	φ: trivial image	40	4+	Q8:7D10	160,224

Non-split extensions G=N.Q with N=Q₈ and Q=D₁₀

extension	φ:Q→Out N	d	ρ	Label	ID
Q₈.₁D₁₀ = SD₁₆⋊D₅	φ: D₁₀/D₅ → C₂ ⊆ Out Q₈	80	4-	Q8.1D10	160,136
Q₈.₂D₁₀ = SD₁₆⋊₃D₅	φ: D₁₀/D₅ → C₂ ⊆ Out Q₈	80	4	Q8.2D10	160,137
Q₈.₃D₁₀ = D₅×Q₁₆	φ: D₁₀/D₅ → C₂ ⊆ Out Q₈	80	4-	Q8.3D10	160,138
Q₈.₄D₁₀ = Q₁₆⋊D₅	φ: D₁₀/D₅ → C₂ ⊆ Out Q₈	80	4	Q8.4D10	160,139
Q₈.₅D₁₀ = Q₈.D₁₀	φ: D₁₀/D₅ → C₂ ⊆ Out Q₈	80	4+	Q8.5D10	160,140
Q₈.₆D₁₀ = C₂₀.C₂³	φ: D₁₀/C₁₀ → C₂ ⊆ Out Q₈	80	4	Q8.6D10	160,163
Q₈.₇D₁₀ = C₂×C₅⋊Q₁₆	φ: D₁₀/C₁₀ → C₂ ⊆ Out Q₈	160		Q8.7D10	160,164
Q₈.₈D₁₀ = D₄.₈D₁₀	φ: D₁₀/C₁₀ → C₂ ⊆ Out Q₈	80	4	Q8.8D10	160,171
Q₈.₉D₁₀ = D₄.₉D₁₀	φ: D₁₀/C₁₀ → C₂ ⊆ Out Q₈	80	4-	Q8.9D10	160,172
Q₈.₁₀D₁₀ = Q₈.₁₀D₁₀	φ: trivial image	80	4	Q8.10D10	160,222
Q₈.₁₁D₁₀ = D₄.₁₀D₁₀	φ: trivial image	80	4-	Q8.11D10	160,225

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁