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

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

		d	ρ	Label	ID
C₁₀×C₄₀		400		C10xC40	400,111

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

extension	φ:Q→Aut N	d	Label	ID
C₈⋊₁(C₅×C₁₀) = D₈×C₅²	φ: C₅×C₁₀/C₅² → C₂ ⊆ Aut C₈	200	C8:1(C5xC10)	400,113
C₈⋊₂(C₅×C₁₀) = SD₁₆×C₅²	φ: C₅×C₁₀/C₅² → C₂ ⊆ Aut C₈	200	C8:2(C5xC10)	400,114
C₈⋊₃(C₅×C₁₀) = M₄(2)×C₅²	φ: C₅×C₁₀/C₅² → C₂ ⊆ Aut C₈	200	C8:3(C5xC10)	400,112

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈.(C₅×C₁₀) = Q₁₆×C₅²	φ: C₅×C₁₀/C₅² → C₂ ⊆ Aut C₈	400		C8.(C5xC10)	400,115

⋊

ℤ

𝔽

○

≀

ℚ

◁

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