Extensions 1→N→G→Q→1 with N=C₂₀ and Q=S₃

Direct product G=NxQ with N=C₂₀ and Q=S₃

		d	ρ	Label	ID
S₃xC₂₀		60	2	S3xC20	120,22

Semidirect products G=N:Q with N=C₂₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀:₁S₃ = D₆₀	φ: S₃/C₃ → C₂ ⊆ Aut C₂₀	60	2+	C20:1S3	120,28
C₂₀:₂S₃ = C₄xD₁₅	φ: S₃/C₃ → C₂ ⊆ Aut C₂₀	60	2	C20:2S3	120,27
C₂₀:₃S₃ = C₅xD₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₂₀	60	2	C20:3S3	120,23

Non-split extensions G=N.Q with N=C₂₀ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂₀.₁S₃ = Dic₃₀	φ: S₃/C₃ → C₂ ⊆ Aut C₂₀	120	2-	C20.1S3	120,26
C₂₀.₂S₃ = C₁₅:₃C₈	φ: S₃/C₃ → C₂ ⊆ Aut C₂₀	120	2	C20.2S3	120,3
C₂₀.₃S₃ = C₅xDic₆	φ: S₃/C₃ → C₂ ⊆ Aut C₂₀	120	2	C20.3S3	120,21
C₂₀.₄S₃ = C₅xC₃:C₈	central extension (φ=1)	120	2	C20.4S3	120,1

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