Extensions 1→N→G→Q→1 with N=C₂²×C₁₀ and Q=Dic₃

Direct product G=N×Q with N=C₂²×C₁₀ and Q=Dic₃

		d	ρ	Label	ID
Dic₃×C₂²×C₁₀		480		Dic3xC2^2xC10	480,1163

Semidirect products G=N:Q with N=C₂²×C₁₀ and Q=Dic₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₁₀)⋊Dic₃ = C₂×A₄⋊F₅	φ: Dic₃/C₁ → Dic₃ ⊆ Aut C₂²×C₁₀	30	12+	(C2^2xC10):Dic3	480,1191
(C₂²×C₁₀)⋊₂Dic₃ = C₁₀×A₄⋊C₄	φ: Dic₃/C₂ → S₃ ⊆ Aut C₂²×C₁₀	120		(C2^2xC10):2Dic3	480,1022
(C₂²×C₁₀)⋊₃Dic₃ = C₂×A₄⋊Dic₅	φ: Dic₃/C₂ → S₃ ⊆ Aut C₂²×C₁₀	120		(C2^2xC10):3Dic3	480,1033
(C₂²×C₁₀)⋊₄Dic₃ = C₅×C₂³.₇D₆	φ: Dic₃/C₃ → C₄ ⊆ Aut C₂²×C₁₀	120	4	(C2^2xC10):4Dic3	480,153
(C₂²×C₁₀)⋊₅Dic₃ = C₂³.₇D₃₀	φ: Dic₃/C₃ → C₄ ⊆ Aut C₂²×C₁₀	120	4	(C2^2xC10):5Dic3	480,194
(C₂²×C₁₀)⋊₆Dic₃ = C₃⋊(C₂³⋊F₅)	φ: Dic₃/C₃ → C₄ ⊆ Aut C₂²×C₁₀	120	4	(C2^2xC10):6Dic3	480,316
(C₂²×C₁₀)⋊₇Dic₃ = C₂×D₁₀.D₆	φ: Dic₃/C₃ → C₄ ⊆ Aut C₂²×C₁₀	120		(C2^2xC10):7Dic3	480,1072
(C₂²×C₁₀)⋊₈Dic₃ = C₂³×C₃⋊F₅	φ: Dic₃/C₃ → C₄ ⊆ Aut C₂²×C₁₀	120		(C2^2xC10):8Dic3	480,1206
(C₂²×C₁₀)⋊₉Dic₃ = C₁₀×C₆.D₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₁₀	240		(C2^2xC10):9Dic3	480,831
(C₂²×C₁₀)⋊₁₀Dic₃ = C₂×C₃₀.₃₈D₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₁₀	240		(C2^2xC10):10Dic3	480,917
(C₂²×C₁₀)⋊₁₁Dic₃ = C₂³×Dic₁₅	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₁₀	480		(C2^2xC10):11Dic3	480,1178

Non-split extensions G=N.Q with N=C₂²×C₁₀ and Q=Dic₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂²×C₁₀).Dic₃ = Dic₅.S₄	φ: Dic₃/C₁ → Dic₃ ⊆ Aut C₂²×C₁₀	120	12-	(C2^2xC10).Dic3	480,963
(C₂²×C₁₀).₂Dic₃ = C₅×A₄⋊C₈	φ: Dic₃/C₂ → S₃ ⊆ Aut C₂²×C₁₀	120	3	(C2^2xC10).2Dic3	480,255
(C₂²×C₁₀).₃Dic₃ = C₂₀.S₄	φ: Dic₃/C₂ → S₃ ⊆ Aut C₂²×C₁₀	120	6	(C2^2xC10).3Dic3	480,259
(C₂²×C₁₀).₄Dic₃ = C₅×C₁₂.D₄	φ: Dic₃/C₃ → C₄ ⊆ Aut C₂²×C₁₀	120	4	(C2^2xC10).4Dic3	480,152
(C₂²×C₁₀).₅Dic₃ = C₆₀.₈D₄	φ: Dic₃/C₃ → C₄ ⊆ Aut C₂²×C₁₀	120	4	(C2^2xC10).5Dic3	480,193
(C₂²×C₁₀).₆Dic₃ = C₃₀.₂₂M₄(2)	φ: Dic₃/C₃ → C₄ ⊆ Aut C₂²×C₁₀	240		(C2^2xC10).6Dic3	480,317
(C₂²×C₁₀).₇Dic₃ = C₅⋊(C₁₂.D₄)	φ: Dic₃/C₃ → C₄ ⊆ Aut C₂²×C₁₀	120	4	(C2^2xC10).7Dic3	480,318
(C₂²×C₁₀).₈Dic₃ = C₂²×C₁₅⋊C₈	φ: Dic₃/C₃ → C₄ ⊆ Aut C₂²×C₁₀	480		(C2^2xC10).8Dic3	480,1070
(C₂²×C₁₀).₉Dic₃ = C₂×C₁₅⋊₈M₄(2)	φ: Dic₃/C₃ → C₄ ⊆ Aut C₂²×C₁₀	240		(C2^2xC10).9Dic3	480,1071
(C₂²×C₁₀).₁₀Dic₃ = C₅×C₁₂.₅₅D₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₁₀	240		(C2^2xC10).10Dic3	480,149
(C₂²×C₁₀).₁₁Dic₃ = C₁₀×C₄.Dic₃	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₁₀	240		(C2^2xC10).11Dic3	480,800
(C₂²×C₁₀).₁₂Dic₃ = C₆₀.₂₁₂D₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₁₀	240		(C2^2xC10).12Dic3	480,190
(C₂²×C₁₀).₁₃Dic₃ = C₂²×C₁₅⋊₃C₈	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₁₀	480		(C2^2xC10).13Dic3	480,885
(C₂²×C₁₀).₁₄Dic₃ = C₂×C₆₀.₇C₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₂²×C₁₀	240		(C2^2xC10).14Dic3	480,886
(C₂²×C₁₀).₁₅Dic₃ = C₂×C₁₀×C₃⋊C₈	central extension (φ=1)	480		(C2^2xC10).15Dic3	480,799

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