Extensions 1→N→G→Q→1 with N=C₅×M₅(2) and Q=C₂

Direct product G=N×Q with N=C₅×M₅(2) and Q=C₂

		d	ρ	Label	ID
C₁₀×M₅(2)		160		C10xM5(2)	320,1004

Semidirect products G=N:Q with N=C₅×M₅(2) and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×M₅(2))⋊₁C₂ = D₈₀⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	80	4+	(C5xM5(2)):1C2	320,535
(C₅×M₅(2))⋊₂C₂ = C₁₆.D₁₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	160	4-	(C5xM5(2)):2C2	320,536
(C₅×M₅(2))⋊₃C₂ = C₅×C₁₆⋊C₂²	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	80	4	(C5xM5(2)):3C2	320,1010
(C₅×M₅(2))⋊₄C₂ = C₅×Q₃₂⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	160	4	(C5xM5(2)):4C2	320,1011
(C₅×M₅(2))⋊₅C₂ = D₅×M₅(2)	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	80	4	(C5xM5(2)):5C2	320,533
(C₅×M₅(2))⋊₆C₂ = D₂₀.₅C₈	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	160	4	(C5xM5(2)):6C2	320,534
(C₅×M₅(2))⋊₇C₂ = C₈.₂₅D₂₀	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	80	4	(C5xM5(2)):7C2	320,72
(C₅×M₅(2))⋊₈C₂ = D₂₀.₄C₈	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	160	4	(C5xM5(2)):8C2	320,73
(C₅×M₅(2))⋊₉C₂ = D₄₀.₄C₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	80	4+	(C5xM5(2)):9C2	320,74
(C₅×M₅(2))⋊₁₀C₂ = D₄₀⋊₈C₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	80	4	(C5xM5(2)):10C2	320,76
(C₅×M₅(2))⋊₁₁C₂ = C₅×C₂³.C₈	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	80	4	(C5xM5(2)):11C2	320,154
(C₅×M₅(2))⋊₁₂C₂ = C₅×D₄.C₈	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	160	2	(C5xM5(2)):12C2	320,155
(C₅×M₅(2))⋊₁₃C₂ = C₅×D₈⋊₂C₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	80	4	(C5xM5(2)):13C2	320,165
(C₅×M₅(2))⋊₁₄C₂ = C₅×M₅(2)⋊C₂	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	80	4	(C5xM5(2)):14C2	320,166
(C₅×M₅(2))⋊₁₅C₂ = C₅×D₄○C₁₆	φ: trivial image	160	2	(C5xM5(2)):15C2	320,1005

Non-split extensions G=N.Q with N=C₅×M₅(2) and Q=C₂

extension	φ:Q→Out N	d	ρ	Label	ID
(C₅×M₅(2)).₁C₂ = C₄₀.Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	80	4	(C5xM5(2)).1C2	320,71
(C₅×M₅(2)).₂C₂ = C₈₀⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	80	4	(C5xM5(2)).2C2	320,70
(C₅×M₅(2)).₃C₂ = C₅×C₈.Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	80	4	(C5xM5(2)).3C2	320,170
(C₅×M₅(2)).₄C₂ = C₄₀.₉Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	80	4	(C5xM5(2)).4C2	320,69
(C₅×M₅(2)).₅C₂ = C₂₀.₄D₈	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	160	4-	(C5xM5(2)).5C2	320,75
(C₅×M₅(2)).₆C₂ = C₅×C₁₆⋊C₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	80	4	(C5xM5(2)).6C2	320,152
(C₅×M₅(2)).₇C₂ = C₅×C₈.₁₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	160	4	(C5xM5(2)).7C2	320,167
(C₅×M₅(2)).₈C₂ = C₅×C₈.C₈	φ: C₂/C₁ → C₂ ⊆ Out C₅×M₅(2)	80	2	(C5xM5(2)).8C2	320,169

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