Extensions 1→N→G→Q→1 with N=D₁₀ and Q=C₂³

Direct product G=N×Q with N=D₁₀ and Q=C₂³

		d	ρ	Label	ID
D₅×C₂⁴		80		D5xC2^4	160,237

Semidirect products G=N:Q with N=D₁₀ and Q=C₂³

extension	φ:Q→Out N	d	ρ	Label	ID
D₁₀⋊₁C₂³ = C₂²×D₂₀	φ: C₂³/C₂² → C₂ ⊆ Out D₁₀	80		D10:1C2^3	160,215
D₁₀⋊₂C₂³ = C₂×D₄×D₅	φ: C₂³/C₂² → C₂ ⊆ Out D₁₀	40		D10:2C2^3	160,217
D₁₀⋊₃C₂³ = C₂²×C₅⋊D₄	φ: C₂³/C₂² → C₂ ⊆ Out D₁₀	80		D10:3C2^3	160,227

Non-split extensions G=N.Q with N=D₁₀ and Q=C₂³

extension	φ:Q→Out N	d	ρ	Label	ID
D₁₀.₁C₂³ = C₂×C₄○D₂₀	φ: C₂³/C₂² → C₂ ⊆ Out D₁₀	80		D10.1C2^3	160,216
D₁₀.₂C₂³ = C₂×D₄⋊₂D₅	φ: C₂³/C₂² → C₂ ⊆ Out D₁₀	80		D10.2C2^3	160,218
D₁₀.₃C₂³ = D₄⋊₆D₁₀	φ: C₂³/C₂² → C₂ ⊆ Out D₁₀	40	4	D10.3C2^3	160,219
D₁₀.₄C₂³ = C₂×Q₈⋊₂D₅	φ: C₂³/C₂² → C₂ ⊆ Out D₁₀	80		D10.4C2^3	160,221
D₁₀.₅C₂³ = Q₈.₁₀D₁₀	φ: C₂³/C₂² → C₂ ⊆ Out D₁₀	80	4	D10.5C2^3	160,222
D₁₀.₆C₂³ = D₅×C₄○D₄	φ: C₂³/C₂² → C₂ ⊆ Out D₁₀	40	4	D10.6C2^3	160,223
D₁₀.₇C₂³ = D₄⋊₈D₁₀	φ: C₂³/C₂² → C₂ ⊆ Out D₁₀	40	4+	D10.7C2^3	160,224
D₁₀.₈C₂³ = D₄.₁₀D₁₀	φ: C₂³/C₂² → C₂ ⊆ Out D₁₀	80	4-	D10.8C2^3	160,225
D₁₀.₉C₂³ = C₂×C₄×F₅	φ: C₂³/C₂² → C₂ ⊆ Out D₁₀	40		D10.9C2^3	160,203
D₁₀.₁₀C₂³ = C₂×C₄⋊F₅	φ: C₂³/C₂² → C₂ ⊆ Out D₁₀	40		D10.10C2^3	160,204
D₁₀.₁₁C₂³ = D₁₀.C₂³	φ: C₂³/C₂² → C₂ ⊆ Out D₁₀	40	4	D10.11C2^3	160,205
D₁₀.₁₂C₂³ = D₄×F₅	φ: C₂³/C₂² → C₂ ⊆ Out D₁₀	20	8+	D10.12C2^3	160,207
D₁₀.₁₃C₂³ = Q₈×F₅	φ: C₂³/C₂² → C₂ ⊆ Out D₁₀	40	8-	D10.13C2^3	160,209
D₁₀.₁₄C₂³ = C₂×C₂²⋊F₅	φ: C₂³/C₂² → C₂ ⊆ Out D₁₀	40		D10.14C2^3	160,212
D₁₀.₁₅C₂³ = C₂³×F₅	φ: C₂³/C₂² → C₂ ⊆ Out D₁₀	40		D10.15C2^3	160,236
D₁₀.₁₆C₂³ = D₅×C₂²×C₄	φ: trivial image	80		D10.16C2^3	160,214
D₁₀.₁₇C₂³ = C₂×Q₈×D₅	φ: trivial image	80		D10.17C2^3	160,220

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁