Extensions 1→N→G→Q→1 with N=C₅×C₈⋊C₂² and Q=C₂

Direct product G=N×Q with N=C₅×C₈⋊C₂² and Q=C₂

		d	ρ	Label	ID
C₁₀×C₈⋊C₂²		80		C10xC8:C2^2	320,1575

Semidirect products G=N:Q with N=C₅×C₈⋊C₂² and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×C₈⋊C₂²)⋊₁C₂ = D₅×C₈⋊C₂²	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₈⋊C₂²	40	8+	(C5xC8:C2^2):1C2	320,1444
(C₅×C₈⋊C₂²)⋊₂C₂ = SD₁₆⋊D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₈⋊C₂²	80	8-	(C5xC8:C2^2):2C2	320,1445
(C₅×C₈⋊C₂²)⋊₃C₂ = D₈⋊₅D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₈⋊C₂²	80	8+	(C5xC8:C2^2):3C2	320,1446
(C₅×C₈⋊C₂²)⋊₄C₂ = D₈⋊₆D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₈⋊C₂²	80	8-	(C5xC8:C2^2):4C2	320,1447
(C₅×C₈⋊C₂²)⋊₅C₂ = D₂₀⋊₁₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₈⋊C₂²	40	8+	(C5xC8:C2^2):5C2	320,825
(C₅×C₈⋊C₂²)⋊₆C₂ = M₄(2).D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₈⋊C₂²	80	8+	(C5xC8:C2^2):6C2	320,826
(C₅×C₈⋊C₂²)⋊₇C₂ = D₂₀.₃₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₈⋊C₂²	80	8-	(C5xC8:C2^2):7C2	320,828
(C₅×C₈⋊C₂²)⋊₈C₂ = C₅×D₄⋊₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₈⋊C₂²	40	4	(C5xC8:C2^2):8C2	320,954
(C₅×C₈⋊C₂²)⋊₉C₂ = C₅×D₄.₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₈⋊C₂²	80	4	(C5xC8:C2^2):9C2	320,955
(C₅×C₈⋊C₂²)⋊₁₀C₂ = C₅×D₄.₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₈⋊C₂²	80	4	(C5xC8:C2^2):10C2	320,973
(C₅×C₈⋊C₂²)⋊₁₁C₂ = C₅×D₄○D₈	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₈⋊C₂²	80	4	(C5xC8:C2^2):11C2	320,1578
(C₅×C₈⋊C₂²)⋊₁₂C₂ = C₅×D₄○SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₈⋊C₂²	80	4	(C5xC8:C2^2):12C2	320,1579
(C₅×C₈⋊C₂²)⋊₁₃C₂ = C₅×D₈⋊C₂²	φ: trivial image	80	4	(C5xC8:C2^2):13C2	320,1577

Non-split extensions G=N.Q with N=C₅×C₈⋊C₂² and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×C₈⋊C₂²).₁C₂ = M₄(2).₁₃D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₈⋊C₂²	80	8-	(C5xC8:C2^2).1C2	320,827
(C₅×C₈⋊C₂²).₂C₂ = C₅×D₄.₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×C₈⋊C₂²	80	4	(C5xC8:C2^2).2C2	320,972

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁