Extensions 1→N→G→Q→1 with N=C₅×C₁₀ and Q=D₅

Direct product G=N×Q with N=C₅×C₁₀ and Q=D₅

		d	ρ	Label	ID
D₅×C₅×C₁₀		100		D5xC5xC10	500,53

Semidirect products G=N:Q with N=C₅×C₁₀ and Q=D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₅×C₁₀)⋊₁D₅ = C₂×C₅²⋊C₁₀	φ: D₅/C₁ → D₅ ⊆ Aut C₅×C₁₀	50	10+	(C5xC10):1D5	500,30
(C₅×C₁₀)⋊₂D₅ = C₂×He₅⋊C₂	φ: D₅/C₁ → D₅ ⊆ Aut C₅×C₁₀	50	5	(C5xC10):2D5	500,33
(C₅×C₁₀)⋊₃D₅ = C₁₀×C₅⋊D₅	φ: D₅/C₅ → C₂ ⊆ Aut C₅×C₁₀	100		(C5xC10):3D5	500,54
(C₅×C₁₀)⋊₄D₅ = C₂×C₅³⋊C₂	φ: D₅/C₅ → C₂ ⊆ Aut C₅×C₁₀	250		(C5xC10):4D5	500,55

Non-split extensions G=N.Q with N=C₅×C₁₀ and Q=D₅

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₅×C₁₀).₁D₅ = He₅⋊₅C₄	φ: D₅/C₁ → D₅ ⊆ Aut C₅×C₁₀	100	10-	(C5xC10).1D5	500,8
(C₅×C₁₀).₂D₅ = C₅₀.C₁₀	φ: D₅/C₁ → D₅ ⊆ Aut C₅×C₁₀	100	10-	(C5xC10).2D5	500,9
(C₅×C₁₀).₃D₅ = He₅⋊₆C₄	φ: D₅/C₁ → D₅ ⊆ Aut C₅×C₁₀	100	5	(C5xC10).3D5	500,11
(C₅×C₁₀).₄D₅ = C₂×C₂₅⋊C₁₀	φ: D₅/C₁ → D₅ ⊆ Aut C₅×C₁₀	50	10+	(C5xC10).4D5	500,31
(C₅×C₁₀).₅D₅ = C₅×Dic₂₅	φ: D₅/C₅ → C₂ ⊆ Aut C₅×C₁₀	100	2	(C5xC10).5D5	500,6
(C₅×C₁₀).₆D₅ = C₅₀.D₅	φ: D₅/C₅ → C₂ ⊆ Aut C₅×C₁₀	500		(C5xC10).6D5	500,10
(C₅×C₁₀).₇D₅ = C₁₀×D₂₅	φ: D₅/C₅ → C₂ ⊆ Aut C₅×C₁₀	100	2	(C5xC10).7D5	500,28
(C₅×C₁₀).₈D₅ = C₂×C₂₅⋊D₅	φ: D₅/C₅ → C₂ ⊆ Aut C₅×C₁₀	250		(C5xC10).8D5	500,32
(C₅×C₁₀).₉D₅ = C₅×C₅²⋊₆C₄	φ: D₅/C₅ → C₂ ⊆ Aut C₅×C₁₀	100		(C5xC10).9D5	500,38
(C₅×C₁₀).₁₀D₅ = C₅³⋊₁₂C₄	φ: D₅/C₅ → C₂ ⊆ Aut C₅×C₁₀	500		(C5xC10).10D5	500,39
(C₅×C₁₀).₁₁D₅ = Dic₅×C₅²	central extension (φ=1)	100		(C5xC10).11D5	500,37

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