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

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

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

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

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₅×C₁₀)⋊C₈ = C₂×C₅²⋊C₈	φ: C₈/C₁ → C₈ ⊆ Aut C₅×C₁₀	20	8+	(C5xC10):C8	400,208
(C₅×C₁₀)⋊₂C₈ = C₁₀×C₅⋊C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₅×C₁₀	80		(C5xC10):2C8	400,139
(C₅×C₁₀)⋊₃C₈ = C₂×C₅²⋊₃C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₅×C₁₀	80		(C5xC10):3C8	400,146
(C₅×C₁₀)⋊₄C₈ = C₂×C₅²⋊₄C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₅×C₁₀	400		(C5xC10):4C8	400,153
(C₅×C₁₀)⋊₅C₈ = C₂×C₅²⋊₅C₈	φ: C₈/C₂ → C₄ ⊆ Aut C₅×C₁₀	80		(C5xC10):5C8	400,160
(C₅×C₁₀)⋊₆C₈ = C₁₀×C₅⋊₂C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₅×C₁₀	80		(C5xC10):6C8	400,81
(C₅×C₁₀)⋊₇C₈ = C₂×C₅²⋊₇C₈	φ: C₈/C₄ → C₂ ⊆ Aut C₅×C₁₀	400		(C5xC10):7C8	400,97

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

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₅×C₁₀).C₈ = C₅²⋊C₁₆	φ: C₈/C₁ → C₈ ⊆ Aut C₅×C₁₀	80	8-	(C5xC10).C8	400,116
(C₅×C₁₀).₂C₈ = C₅×C₅⋊C₁₆	φ: C₈/C₂ → C₄ ⊆ Aut C₅×C₁₀	80	4	(C5xC10).2C8	400,56
(C₅×C₁₀).₃C₈ = C₅²⋊₃C₁₆	φ: C₈/C₂ → C₄ ⊆ Aut C₅×C₁₀	80	4	(C5xC10).3C8	400,57
(C₅×C₁₀).₄C₈ = C₅²⋊₄C₁₆	φ: C₈/C₂ → C₄ ⊆ Aut C₅×C₁₀	400		(C5xC10).4C8	400,58
(C₅×C₁₀).₅C₈ = C₅²⋊₅C₁₆	φ: C₈/C₂ → C₄ ⊆ Aut C₅×C₁₀	80	4	(C5xC10).5C8	400,59
(C₅×C₁₀).₆C₈ = C₅×C₅⋊₂C₁₆	φ: C₈/C₄ → C₂ ⊆ Aut C₅×C₁₀	80	2	(C5xC10).6C8	400,49
(C₅×C₁₀).₇C₈ = C₅²⋊₇C₁₆	φ: C₈/C₄ → C₂ ⊆ Aut C₅×C₁₀	400		(C5xC10).7C8	400,50

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁