Extensions 1→N→G→Q→1 with N=C₂³xC₁₀ and Q=S₃

Direct product G=NxQ with N=C₂³xC₁₀ and Q=S₃

		d	ρ	Label	ID
S₃xC₂³xC₁₀		240		S3xC2^3xC10	480,1211

Semidirect products G=N:Q with N=C₂³xC₁₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂³xC₁₀):₁S₃ = C₅xA₄:D₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₁₀	60	6	(C2^3xC10):1S3	480,1023
(C₂³xC₁₀):₂S₃ = C₂xC₁₀xS₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₁₀	60		(C2^3xC10):2S3	480,1198
(C₂³xC₁₀):₃S₃ = C₅xC₂²:S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₁₀	40	6	(C2^3xC10):3S3	480,1200
(C₂³xC₁₀):₄S₃ = C₂⁴:₂D₁₅	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₁₀	60	6	(C2^3xC10):4S3	480,1034
(C₂³xC₁₀):₅S₃ = C₂²xC₅:S₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₁₀	60		(C2^3xC10):5S3	480,1199
(C₂³xC₁₀):₆S₃ = C₂⁴:₄D₁₅	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₁₀	40	6	(C2^3xC10):6S3	480,1201
(C₂³xC₁₀):₇S₃ = C₅xC₂⁴:₄S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₁₀	120		(C2^3xC10):7S3	480,832
(C₂³xC₁₀):₈S₃ = C₂xC₁₀xC₃:D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₁₀	240		(C2^3xC10):8S3	480,1164
(C₂³xC₁₀):₉S₃ = C₂⁴:₅D₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₁₀	120		(C2^3xC10):9S3	480,918
(C₂³xC₁₀):₁₀S₃ = C₂²xC₁₅:₇D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₁₀	240		(C2^3xC10):10S3	480,1179
(C₂³xC₁₀):₁₁S₃ = C₂⁴xD₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₁₀	240		(C2^3xC10):11S3	480,1212

Non-split extensions G=N.Q with N=C₂³xC₁₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₂³xC₁₀).₁S₃ = C₁₀xA₄:C₄	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₁₀	120		(C2^3xC10).1S3	480,1022
(C₂³xC₁₀).₂S₃ = C₂xA₄:Dic₅	φ: S₃/C₁ → S₃ ⊆ Aut C₂³xC₁₀	120		(C2^3xC10).2S3	480,1033
(C₂³xC₁₀).₃S₃ = C₁₀xC₆.D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₁₀	240		(C2^3xC10).3S3	480,831
(C₂³xC₁₀).₄S₃ = C₂xC₃₀.₃₈D₄	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₁₀	240		(C2^3xC10).4S3	480,917
(C₂³xC₁₀).₅S₃ = C₂³xDic₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₂³xC₁₀	480		(C2^3xC10).5S3	480,1178
(C₂³xC₁₀).₆S₃ = Dic₃xC₂²xC₁₀	central extension (φ=1)	480		(C2^3xC10).6S3	480,1163

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