Extensions 1→N→G→Q→1 with N=C₂×C₁₀ and Q=F₅

Direct product G=N×Q with N=C₂×C₁₀ and Q=F₅

		d	ρ	Label	ID
F₅×C₂×C₁₀		80		F5xC2xC10	400,214

Semidirect products G=N:Q with N=C₂×C₁₀ and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₁₀)⋊₁F₅ = C₁₀²⋊C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₂×C₁₀	100		(C2xC10):1F5	400,155
(C₂×C₁₀)⋊₂F₅ = C₁₀²⋊₄C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₂×C₁₀	20	4+	(C2xC10):2F5	400,162
(C₂×C₁₀)⋊₃F₅ = C₂²×C₅⋊F₅	φ: F₅/C₅ → C₄ ⊆ Aut C₂×C₁₀	100		(C2xC10):3F5	400,216
(C₂×C₁₀)⋊₄F₅ = C₂²×C₅²⋊C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₂×C₁₀	40		(C2xC10):4F5	400,217
(C₂×C₁₀)⋊₅F₅ = C₅×C₂²⋊F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₁₀	40	4	(C2xC10):5F5	400,141
(C₂×C₁₀)⋊₆F₅ = D₁₀.D₁₀	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₁₀	40	4	(C2xC10):6F5	400,148
(C₂×C₁₀)⋊₇F₅ = C₂²×D₅.D₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₁₀	80		(C2xC10):7F5	400,215

Non-split extensions G=N.Q with N=C₂×C₁₀ and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂×C₁₀).₁F₅ = C₂×C₂₅⋊C₈	φ: F₅/C₅ → C₄ ⊆ Aut C₂×C₁₀	400		(C2xC10).1F5	400,32
(C₂×C₁₀).₂F₅ = C₂₅⋊M₄(2)	φ: F₅/C₅ → C₄ ⊆ Aut C₂×C₁₀	200	4-	(C2xC10).2F5	400,33
(C₂×C₁₀).₃F₅ = D₂₅.D₄	φ: F₅/C₅ → C₄ ⊆ Aut C₂×C₁₀	100	4+	(C2xC10).3F5	400,34
(C₂×C₁₀).₄F₅ = C₂²×C₂₅⋊C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₂×C₁₀	100		(C2xC10).4F5	400,53
(C₂×C₁₀).₅F₅ = C₂×C₅²⋊₄C₈	φ: F₅/C₅ → C₄ ⊆ Aut C₂×C₁₀	400		(C2xC10).5F5	400,153
(C₂×C₁₀).₆F₅ = C₅²⋊₁₃M₄(2)	φ: F₅/C₅ → C₄ ⊆ Aut C₂×C₁₀	200		(C2xC10).6F5	400,154
(C₂×C₁₀).₇F₅ = C₂×C₅²⋊₅C₈	φ: F₅/C₅ → C₄ ⊆ Aut C₂×C₁₀	80		(C2xC10).7F5	400,160
(C₂×C₁₀).₈F₅ = C₅²⋊₁₄M₄(2)	φ: F₅/C₅ → C₄ ⊆ Aut C₂×C₁₀	40	4-	(C2xC10).8F5	400,161
(C₂×C₁₀).₉F₅ = C₅×C₂².F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₁₀	40	4	(C2xC10).9F5	400,140
(C₂×C₁₀).₁₀F₅ = C₂×C₅²⋊₃C₈	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₁₀	80		(C2xC10).10F5	400,146
(C₂×C₁₀).₁₁F₅ = C₁₀².C₄	φ: F₅/D₅ → C₂ ⊆ Aut C₂×C₁₀	40	4	(C2xC10).11F5	400,147
(C₂×C₁₀).₁₂F₅ = C₁₀×C₅⋊C₈	central extension (φ=1)	80		(C2xC10).12F5	400,139

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