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Extensions 1→N→G→Q→1 with N=C5×C4⋊C4 and Q=S3

Direct product G=N×Q with N=C5×C4⋊C4 and Q=S3
dρLabelID
C5×S3×C4⋊C4240C5xS3xC4:C4480,770

Semidirect products G=N:Q with N=C5×C4⋊C4 and Q=S3
extensionφ:Q→Out NdρLabelID
(C5×C4⋊C4)⋊1S3 = D60⋊9C4φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4240(C5xC4:C4):1S3480,169
(C5×C4⋊C4)⋊2S3 = C4⋊C4×D15φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4240(C5xC4:C4):2S3480,856
(C5×C4⋊C4)⋊3S3 = C4⋊C4⋊7D15φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4240(C5xC4:C4):3S3480,857
(C5×C4⋊C4)⋊4S3 = D60⋊11C4φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4240(C5xC4:C4):4S3480,858
(C5×C4⋊C4)⋊5S3 = D30.29D4φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4240(C5xC4:C4):5S3480,859
(C5×C4⋊C4)⋊6S3 = C4⋊D60φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4240(C5xC4:C4):6S3480,860
(C5×C4⋊C4)⋊7S3 = D30⋊5Q8φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4240(C5xC4:C4):7S3480,861
(C5×C4⋊C4)⋊8S3 = D30⋊6Q8φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4240(C5xC4:C4):8S3480,862
(C5×C4⋊C4)⋊9S3 = C4⋊C4⋊D15φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4240(C5xC4:C4):9S3480,863
(C5×C4⋊C4)⋊10S3 = C5×C6.D8φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4240(C5xC4:C4):10S3480,128
(C5×C4⋊C4)⋊11S3 = C5×D6.D4φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4240(C5xC4:C4):11S3480,773
(C5×C4⋊C4)⋊12S3 = C5×C12⋊D4φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4240(C5xC4:C4):12S3480,774
(C5×C4⋊C4)⋊13S3 = C5×D6⋊Q8φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4240(C5xC4:C4):13S3480,775
(C5×C4⋊C4)⋊14S3 = C5×C4.D12φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4240(C5xC4:C4):14S3480,776
(C5×C4⋊C4)⋊15S3 = C5×C4⋊C4⋊S3φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4240(C5xC4:C4):15S3480,777
(C5×C4⋊C4)⋊16S3 = C5×C4⋊C4⋊7S3φ: trivial image240(C5xC4:C4):16S3480,771
(C5×C4⋊C4)⋊17S3 = C5×Dic3⋊5D4φ: trivial image240(C5xC4:C4):17S3480,772

Non-split extensions G=N.Q with N=C5×C4⋊C4 and Q=S3
extensionφ:Q→Out NdρLabelID
(C5×C4⋊C4).1S3 = C60.1Q8φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4480(C5xC4:C4).1S3480,167
(C5×C4⋊C4).2S3 = C60.2Q8φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4480(C5xC4:C4).2S3480,168
(C5×C4⋊C4).3S3 = Dic30⋊9C4φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4480(C5xC4:C4).3S3480,170
(C5×C4⋊C4).4S3 = Dic15⋊10Q8φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4480(C5xC4:C4).4S3480,852
(C5×C4⋊C4).5S3 = C4⋊Dic30φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4480(C5xC4:C4).5S3480,853
(C5×C4⋊C4).6S3 = Dic15.3Q8φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4480(C5xC4:C4).6S3480,854
(C5×C4⋊C4).7S3 = C4.Dic30φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4480(C5xC4:C4).7S3480,855
(C5×C4⋊C4).8S3 = C5×C6.Q16φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4480(C5xC4:C4).8S3480,126
(C5×C4⋊C4).9S3 = C5×C12.Q8φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4480(C5xC4:C4).9S3480,127
(C5×C4⋊C4).10S3 = C5×C6.SD16φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4480(C5xC4:C4).10S3480,129
(C5×C4⋊C4).11S3 = C5×C12⋊Q8φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4480(C5xC4:C4).11S3480,767
(C5×C4⋊C4).12S3 = C5×Dic3.Q8φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4480(C5xC4:C4).12S3480,768
(C5×C4⋊C4).13S3 = C5×C4.Dic6φ: S3/C3 → C2 ⊆ Out C5×C4⋊C4480(C5xC4:C4).13S3480,769
(C5×C4⋊C4).14S3 = C5×Dic6⋊C4φ: trivial image480(C5xC4:C4).14S3480,766

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