# Extensions 1→N→G→Q→1 with N=C2×C20 and Q=S3

Direct product G=N×Q with N=C2×C20 and Q=S3
dρLabelID
S3×C2×C20120S3xC2xC20240,166

Semidirect products G=N:Q with N=C2×C20 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C2×C20)⋊1S3 = C5×D6⋊C4φ: S3/C3C2 ⊆ Aut C2×C20120(C2xC20):1S3240,59
(C2×C20)⋊2S3 = D303C4φ: S3/C3C2 ⊆ Aut C2×C20120(C2xC20):2S3240,75
(C2×C20)⋊3S3 = C2×D60φ: S3/C3C2 ⊆ Aut C2×C20120(C2xC20):3S3240,177
(C2×C20)⋊4S3 = D6011C2φ: S3/C3C2 ⊆ Aut C2×C201202(C2xC20):4S3240,178
(C2×C20)⋊5S3 = C2×C4×D15φ: S3/C3C2 ⊆ Aut C2×C20120(C2xC20):5S3240,176
(C2×C20)⋊6S3 = C10×D12φ: S3/C3C2 ⊆ Aut C2×C20120(C2xC20):6S3240,167
(C2×C20)⋊7S3 = C5×C4○D12φ: S3/C3C2 ⊆ Aut C2×C201202(C2xC20):7S3240,168

Non-split extensions G=N.Q with N=C2×C20 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C2×C20).1S3 = C5×Dic3⋊C4φ: S3/C3C2 ⊆ Aut C2×C20240(C2xC20).1S3240,57
(C2×C20).2S3 = C30.4Q8φ: S3/C3C2 ⊆ Aut C2×C20240(C2xC20).2S3240,73
(C2×C20).3S3 = C605C4φ: S3/C3C2 ⊆ Aut C2×C20240(C2xC20).3S3240,74
(C2×C20).4S3 = C2×Dic30φ: S3/C3C2 ⊆ Aut C2×C20240(C2xC20).4S3240,175
(C2×C20).5S3 = C60.7C4φ: S3/C3C2 ⊆ Aut C2×C201202(C2xC20).5S3240,71
(C2×C20).6S3 = C2×C153C8φ: S3/C3C2 ⊆ Aut C2×C20240(C2xC20).6S3240,70
(C2×C20).7S3 = C4×Dic15φ: S3/C3C2 ⊆ Aut C2×C20240(C2xC20).7S3240,72
(C2×C20).8S3 = C5×C4.Dic3φ: S3/C3C2 ⊆ Aut C2×C201202(C2xC20).8S3240,55
(C2×C20).9S3 = C5×C4⋊Dic3φ: S3/C3C2 ⊆ Aut C2×C20240(C2xC20).9S3240,58
(C2×C20).10S3 = C10×Dic6φ: S3/C3C2 ⊆ Aut C2×C20240(C2xC20).10S3240,165
(C2×C20).11S3 = C10×C3⋊C8central extension (φ=1)240(C2xC20).11S3240,54
(C2×C20).12S3 = Dic3×C20central extension (φ=1)240(C2xC20).12S3240,56

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