Extensions 1→N→G→Q→1 with N=C₅×Q₈ and Q=C₂

Direct product G=N×Q with N=C₅×Q₈ and Q=C₂

		d	ρ	Label	ID
Q₈×C₁₀		80		Q8xC10	80,47

Semidirect products G=N:Q with N=C₅×Q₈ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×Q₈)⋊₁C₂ = Q₈⋊D₅	φ: C₂/C₁ → C₂ ⊆ Out C₅×Q₈	40	4+	(C5xQ8):1C2	80,17
(C₅×Q₈)⋊₂C₂ = Q₈×D₅	φ: C₂/C₁ → C₂ ⊆ Out C₅×Q₈	40	4-	(C5xQ8):2C2	80,41
(C₅×Q₈)⋊₃C₂ = Q₈⋊₂D₅	φ: C₂/C₁ → C₂ ⊆ Out C₅×Q₈	40	4+	(C5xQ8):3C2	80,42
(C₅×Q₈)⋊₄C₂ = C₅×SD₁₆	φ: C₂/C₁ → C₂ ⊆ Out C₅×Q₈	40	2	(C5xQ8):4C2	80,26
(C₅×Q₈)⋊₅C₂ = C₅×C₄○D₄	φ: trivial image	40	2	(C5xQ8):5C2	80,48

Non-split extensions G=N.Q with N=C₅×Q₈ and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×Q₈).₁C₂ = C₅⋊Q₁₆	φ: C₂/C₁ → C₂ ⊆ Out C₅×Q₈	80	4-	(C5xQ8).1C2	80,18
(C₅×Q₈).₂C₂ = C₅×Q₁₆	φ: C₂/C₁ → C₂ ⊆ Out C₅×Q₈	80	2	(C5xQ8).2C2	80,27

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁