Extensions 1→N→G→Q→1 with N=C₂xC₁₀ and Q=F₅

Direct product G=NxQ with N=C₂xC₁₀ and Q=F₅

		d	ρ	Label	ID
F₅xC₂xC₁₀		80		F5xC2xC10	400,214

Semidirect products G=N:Q with N=C₂xC₁₀ and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂xC₁₀):₁F₅ = C₁₀²:C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₂xC₁₀	100		(C2xC10):1F5	400,155
(C₂xC₁₀):₂F₅ = C₁₀²:₄C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₂xC₁₀	20	4+	(C2xC10):2F5	400,162
(C₂xC₁₀):₃F₅ = C₂²xC₅:F₅	φ: F₅/C₅ → C₄ ⊆ Aut C₂xC₁₀	100		(C2xC10):3F5	400,216
(C₂xC₁₀):₄F₅ = C₂²xC₅²:C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₂xC₁₀	40		(C2xC10):4F5	400,217
(C₂xC₁₀):₅F₅ = C₅xC₂²:F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂xC₁₀	40	4	(C2xC10):5F5	400,141
(C₂xC₁₀):₆F₅ = D₁₀.D₁₀	φ: F₅/D₅ → C₂ ⊆ Aut C₂xC₁₀	40	4	(C2xC10):6F5	400,148
(C₂xC₁₀):₇F₅ = C₂²xD₅.D₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂xC₁₀	80		(C2xC10):7F5	400,215

Non-split extensions G=N.Q with N=C₂xC₁₀ and Q=F₅

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂xC₁₀).₁F₅ = C₂xC₂₅:C₈	φ: F₅/C₅ → C₄ ⊆ Aut C₂xC₁₀	400		(C2xC10).1F5	400,32
(C₂xC₁₀).₂F₅ = C₂₅:M₄(2)	φ: F₅/C₅ → C₄ ⊆ Aut C₂xC₁₀	200	4-	(C2xC10).2F5	400,33
(C₂xC₁₀).₃F₅ = D₂₅.D₄	φ: F₅/C₅ → C₄ ⊆ Aut C₂xC₁₀	100	4+	(C2xC10).3F5	400,34
(C₂xC₁₀).₄F₅ = C₂²xC₂₅:C₄	φ: F₅/C₅ → C₄ ⊆ Aut C₂xC₁₀	100		(C2xC10).4F5	400,53
(C₂xC₁₀).₅F₅ = C₂xC₅²:₄C₈	φ: F₅/C₅ → C₄ ⊆ Aut C₂xC₁₀	400		(C2xC10).5F5	400,153
(C₂xC₁₀).₆F₅ = C₅²:₁₃M₄(2)	φ: F₅/C₅ → C₄ ⊆ Aut C₂xC₁₀	200		(C2xC10).6F5	400,154
(C₂xC₁₀).₇F₅ = C₂xC₅²:₅C₈	φ: F₅/C₅ → C₄ ⊆ Aut C₂xC₁₀	80		(C2xC10).7F5	400,160
(C₂xC₁₀).₈F₅ = C₅²:₁₄M₄(2)	φ: F₅/C₅ → C₄ ⊆ Aut C₂xC₁₀	40	4-	(C2xC10).8F5	400,161
(C₂xC₁₀).₉F₅ = C₅xC₂².F₅	φ: F₅/D₅ → C₂ ⊆ Aut C₂xC₁₀	40	4	(C2xC10).9F5	400,140
(C₂xC₁₀).₁₀F₅ = C₂xC₅²:₃C₈	φ: F₅/D₅ → C₂ ⊆ Aut C₂xC₁₀	80		(C2xC10).10F5	400,146
(C₂xC₁₀).₁₁F₅ = C₁₀².C₄	φ: F₅/D₅ → C₂ ⊆ Aut C₂xC₁₀	40	4	(C2xC10).11F5	400,147
(C₂xC₁₀).₁₂F₅ = C₁₀xC₅:C₈	central extension (φ=1)	80		(C2xC10).12F5	400,139

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