Extensions 1→N→G→Q→1 with N=C₅×2₊¹⁺⁴ and Q=C₂

Direct product G=N×Q with N=C₅×2₊¹⁺⁴ and Q=C₂

		d	ρ	Label	ID
C₁₀×2₊¹⁺⁴		80		C10xES+(2,2)	320,1632

Semidirect products G=N:Q with N=C₅×2₊¹⁺⁴ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×2₊¹⁺⁴)⋊₁C₂ = 2₊¹⁺⁴⋊D₅	φ: C₂/C₁ → C₂ ⊆ Out C₅×2₊¹⁺⁴	40	8+	(C5xES+(2,2)):1C2	320,868
(C₅×2₊¹⁺⁴)⋊₂C₂ = D₂₀.₃₂C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₅×2₊¹⁺⁴	80	8+	(C5xES+(2,2)):2C2	320,1507
(C₅×2₊¹⁺⁴)⋊₃C₂ = D₂₀.₃₃C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₅×2₊¹⁺⁴	80	8-	(C5xES+(2,2)):3C2	320,1508
(C₅×2₊¹⁺⁴)⋊₄C₂ = D₅×2₊¹⁺⁴	φ: C₂/C₁ → C₂ ⊆ Out C₅×2₊¹⁺⁴	40	8+	(C5xES+(2,2)):4C2	320,1622
(C₅×2₊¹⁺⁴)⋊₅C₂ = D₂₀.₃₇C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₅×2₊¹⁺⁴	80	8-	(C5xES+(2,2)):5C2	320,1623
(C₅×2₊¹⁺⁴)⋊₆C₂ = 2₊¹⁺⁴⋊₂D₅	φ: C₂/C₁ → C₂ ⊆ Out C₅×2₊¹⁺⁴	40	8+	(C5xES+(2,2)):6C2	320,871
(C₅×2₊¹⁺⁴)⋊₇C₂ = C₅×D₄⋊₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×2₊¹⁺⁴	40	4	(C5xES+(2,2)):7C2	320,954
(C₅×2₊¹⁺⁴)⋊₈C₂ = C₅×C₂≀C₂²	φ: C₂/C₁ → C₂ ⊆ Out C₅×2₊¹⁺⁴	40	4	(C5xES+(2,2)):8C2	320,958
(C₅×2₊¹⁺⁴)⋊₉C₂ = C₅×D₄○D₈	φ: C₂/C₁ → C₂ ⊆ Out C₅×2₊¹⁺⁴	80	4	(C5xES+(2,2)):9C2	320,1578
(C₅×2₊¹⁺⁴)⋊₁₀C₂ = C₅×D₄○SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out C₅×2₊¹⁺⁴	80	4	(C5xES+(2,2)):10C2	320,1579
(C₅×2₊¹⁺⁴)⋊₁₁C₂ = C₅×C₂.C₂⁵	φ: trivial image	80	4	(C5xES+(2,2)):11C2	320,1634

Non-split extensions G=N.Q with N=C₅×2₊¹⁺⁴ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×2₊¹⁺⁴).₁C₂ = 2₊¹⁺⁴.D₅	φ: C₂/C₁ → C₂ ⊆ Out C₅×2₊¹⁺⁴	80	8-	(C5xES+(2,2)).1C2	320,869
(C₅×2₊¹⁺⁴).₂C₂ = 2₊¹⁺⁴.₂D₅	φ: C₂/C₁ → C₂ ⊆ Out C₅×2₊¹⁺⁴	80	8-	(C5xES+(2,2)).2C2	320,870
(C₅×2₊¹⁺⁴).₃C₂ = C₅×D₄.₉D₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×2₊¹⁺⁴	80	4	(C5xES+(2,2)).3C2	320,956
(C₅×2₊¹⁺⁴).₄C₂ = C₅×C₂³.₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×2₊¹⁺⁴	80	4	(C5xES+(2,2)).4C2	320,959

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁