Extensions 1→N→G→Q→1 with N=C₅⋊₂C₈ and Q=C₁₀

Direct product G=N×Q with N=C₅⋊₂C₈ and Q=C₁₀

		d	ρ	Label	ID
C₁₀×C₅⋊₂C₈		80		C10xC5:2C8	400,81

Semidirect products G=N:Q with N=C₅⋊₂C₈ and Q=C₁₀

extension	φ:Q→Out N	d	ρ	Label	ID
C₅⋊₂C₈⋊₁C₁₀ = C₅×D₄⋊D₅	φ: C₁₀/C₅ → C₂ ⊆ Out C₅⋊₂C₈	40	4	C5:2C8:1C10	400,87
C₅⋊₂C₈⋊₂C₁₀ = C₅×D₄.D₅	φ: C₁₀/C₅ → C₂ ⊆ Out C₅⋊₂C₈	40	4	C5:2C8:2C10	400,88
C₅⋊₂C₈⋊₃C₁₀ = C₅×Q₈⋊D₅	φ: C₁₀/C₅ → C₂ ⊆ Out C₅⋊₂C₈	80	4	C5:2C8:3C10	400,89
C₅⋊₂C₈⋊₄C₁₀ = C₅×C₈⋊D₅	φ: C₁₀/C₅ → C₂ ⊆ Out C₅⋊₂C₈	80	2	C5:2C8:4C10	400,77
C₅⋊₂C₈⋊₅C₁₀ = C₅×C₄.Dic₅	φ: C₁₀/C₅ → C₂ ⊆ Out C₅⋊₂C₈	40	2	C5:2C8:5C10	400,82
C₅⋊₂C₈⋊₆C₁₀ = D₅×C₄₀	φ: trivial image	80	2	C5:2C8:6C10	400,76

Non-split extensions G=N.Q with N=C₅⋊₂C₈ and Q=C₁₀

extension	φ:Q→Out N	d	ρ	Label	ID
C₅⋊₂C₈.₁C₁₀ = C₅×C₅⋊Q₁₆	φ: C₁₀/C₅ → C₂ ⊆ Out C₅⋊₂C₈	80	4	C5:2C8.1C10	400,90
C₅⋊₂C₈.₂C₁₀ = C₅×C₅⋊C₁₆	φ: C₁₀/C₅ → C₂ ⊆ Out C₅⋊₂C₈	80	4	C5:2C8.2C10	400,56

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁