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Extensions 1→N→G→Q→1 with N=C2×C40 and Q=S3

Direct product G=N×Q with N=C2×C40 and Q=S3
dρLabelID
S3×C2×C40240S3xC2xC40480,778

Semidirect products G=N:Q with N=C2×C40 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C2×C40)⋊1S3 = C5×D6⋊C8φ: S3/C3 → C2 ⊆ Aut C2×C40240(C2xC40):1S3480,139
(C2×C40)⋊2S3 = C5×C2.D24φ: S3/C3 → C2 ⊆ Aut C2×C40240(C2xC40):2S3480,140
(C2×C40)⋊3S3 = D30⋊3C8φ: S3/C3 → C2 ⊆ Aut C2×C40240(C2xC40):3S3480,180
(C2×C40)⋊4S3 = D60⋊8C4φ: S3/C3 → C2 ⊆ Aut C2×C40240(C2xC40):4S3480,181
(C2×C40)⋊5S3 = C2×D120φ: S3/C3 → C2 ⊆ Aut C2×C40240(C2xC40):5S3480,868
(C2×C40)⋊6S3 = C40.69D6φ: S3/C3 → C2 ⊆ Aut C2×C402402(C2xC40):6S3480,869
(C2×C40)⋊7S3 = C2×C24⋊D5φ: S3/C3 → C2 ⊆ Aut C2×C40240(C2xC40):7S3480,867
(C2×C40)⋊8S3 = C2×C8×D15φ: S3/C3 → C2 ⊆ Aut C2×C40240(C2xC40):8S3480,864
(C2×C40)⋊9S3 = C2×C40⋊S3φ: S3/C3 → C2 ⊆ Aut C2×C40240(C2xC40):9S3480,865
(C2×C40)⋊10S3 = D60.6C4φ: S3/C3 → C2 ⊆ Aut C2×C402402(C2xC40):10S3480,866
(C2×C40)⋊11S3 = C10×D24φ: S3/C3 → C2 ⊆ Aut C2×C40240(C2xC40):11S3480,782
(C2×C40)⋊12S3 = C5×C4○D24φ: S3/C3 → C2 ⊆ Aut C2×C402402(C2xC40):12S3480,783
(C2×C40)⋊13S3 = C10×C24⋊C2φ: S3/C3 → C2 ⊆ Aut C2×C40240(C2xC40):13S3480,781
(C2×C40)⋊14S3 = C10×C8⋊S3φ: S3/C3 → C2 ⊆ Aut C2×C40240(C2xC40):14S3480,779
(C2×C40)⋊15S3 = C5×C8○D12φ: S3/C3 → C2 ⊆ Aut C2×C402402(C2xC40):15S3480,780

Non-split extensions G=N.Q with N=C2×C40 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C2×C40).1S3 = C5×Dic3⋊C8φ: S3/C3 → C2 ⊆ Aut C2×C40480(C2xC40).1S3480,133
(C2×C40).2S3 = C5×C2.Dic12φ: S3/C3 → C2 ⊆ Aut C2×C40480(C2xC40).2S3480,135
(C2×C40).3S3 = C60.26Q8φ: S3/C3 → C2 ⊆ Aut C2×C40480(C2xC40).3S3480,174
(C2×C40).4S3 = Dic30⋊8C4φ: S3/C3 → C2 ⊆ Aut C2×C40480(C2xC40).4S3480,176
(C2×C40).5S3 = C120⋊9C4φ: S3/C3 → C2 ⊆ Aut C2×C40480(C2xC40).5S3480,178
(C2×C40).6S3 = C2×Dic60φ: S3/C3 → C2 ⊆ Aut C2×C40480(C2xC40).6S3480,870
(C2×C40).7S3 = C4.18D60φ: S3/C3 → C2 ⊆ Aut C2×C402402(C2xC40).7S3480,179
(C2×C40).8S3 = C120⋊10C4φ: S3/C3 → C2 ⊆ Aut C2×C40480(C2xC40).8S3480,177
(C2×C40).9S3 = C2×C15⋊3C16φ: S3/C3 → C2 ⊆ Aut C2×C40480(C2xC40).9S3480,171
(C2×C40).10S3 = C60.7C8φ: S3/C3 → C2 ⊆ Aut C2×C402402(C2xC40).10S3480,172
(C2×C40).11S3 = C8×Dic15φ: S3/C3 → C2 ⊆ Aut C2×C40480(C2xC40).11S3480,173
(C2×C40).12S3 = C120⋊13C4φ: S3/C3 → C2 ⊆ Aut C2×C40480(C2xC40).12S3480,175
(C2×C40).13S3 = C5×C24⋊1C4φ: S3/C3 → C2 ⊆ Aut C2×C40480(C2xC40).13S3480,137
(C2×C40).14S3 = C10×Dic12φ: S3/C3 → C2 ⊆ Aut C2×C40480(C2xC40).14S3480,784
(C2×C40).15S3 = C5×C24.C4φ: S3/C3 → C2 ⊆ Aut C2×C402402(C2xC40).15S3480,138
(C2×C40).16S3 = C5×C8⋊Dic3φ: S3/C3 → C2 ⊆ Aut C2×C40480(C2xC40).16S3480,136
(C2×C40).17S3 = C5×C12.C8φ: S3/C3 → C2 ⊆ Aut C2×C402402(C2xC40).17S3480,131
(C2×C40).18S3 = C5×C24⋊C4φ: S3/C3 → C2 ⊆ Aut C2×C40480(C2xC40).18S3480,134
(C2×C40).19S3 = C10×C3⋊C16central extension (φ=1)480(C2xC40).19S3480,130
(C2×C40).20S3 = Dic3×C40central extension (φ=1)480(C2xC40).20S3480,132

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