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Extensions 1→N→G→Q→1 with N=C2×C5⋊D4 and Q=S3

Direct product G=N×Q with N=C2×C5⋊D4 and Q=S3
dρLabelID
C2×S3×C5⋊D4120C2xS3xC5:D4480,1123

Semidirect products G=N:Q with N=C2×C5⋊D4 and Q=S3
extensionφ:Q→Out NdρLabelID
(C2×C5⋊D4)⋊1S3 = D30⋊6D4φ: S3/C3 → C2 ⊆ Out C2×C5⋊D4240(C2xC5:D4):1S3480,609
(C2×C5⋊D4)⋊2S3 = (C6×D5)⋊D4φ: S3/C3 → C2 ⊆ Out C2×C5⋊D4240(C2xC5:D4):2S3480,625
(C2×C5⋊D4)⋊3S3 = Dic15⋊3D4φ: S3/C3 → C2 ⊆ Out C2×C5⋊D4240(C2xC5:D4):3S3480,626
(C2×C5⋊D4)⋊4S3 = (S3×C10)⋊D4φ: S3/C3 → C2 ⊆ Out C2×C5⋊D4240(C2xC5:D4):4S3480,641
(C2×C5⋊D4)⋊5S3 = Dic15⋊5D4φ: S3/C3 → C2 ⊆ Out C2×C5⋊D4240(C2xC5:D4):5S3480,643
(C2×C5⋊D4)⋊6S3 = C15⋊C22≀C2φ: S3/C3 → C2 ⊆ Out C2×C5⋊D4120(C2xC5:D4):6S3480,644
(C2×C5⋊D4)⋊7S3 = (C2×C6)⋊D20φ: S3/C3 → C2 ⊆ Out C2×C5⋊D4240(C2xC5:D4):7S3480,645
(C2×C5⋊D4)⋊8S3 = Dic15⋊18D4φ: S3/C3 → C2 ⊆ Out C2×C5⋊D4240(C2xC5:D4):8S3480,647
(C2×C5⋊D4)⋊9S3 = D30⋊18D4φ: S3/C3 → C2 ⊆ Out C2×C5⋊D4120(C2xC5:D4):9S3480,648
(C2×C5⋊D4)⋊10S3 = D30⋊8D4φ: S3/C3 → C2 ⊆ Out C2×C5⋊D4120(C2xC5:D4):10S3480,653
(C2×C5⋊D4)⋊11S3 = C2×C30.C23φ: S3/C3 → C2 ⊆ Out C2×C5⋊D4240(C2xC5:D4):11S3480,1114
(C2×C5⋊D4)⋊12S3 = C2×D10⋊D6φ: S3/C3 → C2 ⊆ Out C2×C5⋊D4120(C2xC5:D4):12S3480,1124
(C2×C5⋊D4)⋊13S3 = C15⋊2+ 1+4φ: S3/C3 → C2 ⊆ Out C2×C5⋊D41204(C2xC5:D4):13S3480,1125
(C2×C5⋊D4)⋊14S3 = C2×Dic5.D6φ: trivial image240(C2xC5:D4):14S3480,1113

Non-split extensions G=N.Q with N=C2×C5⋊D4 and Q=S3
extensionφ:Q→Out NdρLabelID
(C2×C5⋊D4).1S3 = (C2×C6).D20φ: S3/C3 → C2 ⊆ Out C2×C5⋊D41204(C2xC5:D4).1S3480,71
(C2×C5⋊D4).2S3 = C6.(D4×D5)φ: S3/C3 → C2 ⊆ Out C2×C5⋊D4240(C2xC5:D4).2S3480,610
(C2×C5⋊D4).3S3 = (C2×C30).D4φ: S3/C3 → C2 ⊆ Out C2×C5⋊D4240(C2xC5:D4).3S3480,612
(C2×C5⋊D4).4S3 = C6.(C2×D20)φ: S3/C3 → C2 ⊆ Out C2×C5⋊D4240(C2xC5:D4).4S3480,613
(C2×C5⋊D4).5S3 = C23.17(S3×D5)φ: S3/C3 → C2 ⊆ Out C2×C5⋊D4240(C2xC5:D4).5S3480,624
(C2×C5⋊D4).6S3 = Dic15⋊16D4φ: S3/C3 → C2 ⊆ Out C2×C5⋊D4240(C2xC5:D4).6S3480,635
(C2×C5⋊D4).7S3 = C3⋊(C23⋊F5)φ: S3/C3 → C2 ⊆ Out C2×C5⋊D41204(C2xC5:D4).7S3480,316
(C2×C5⋊D4).8S3 = C5⋊(C12.D4)φ: S3/C3 → C2 ⊆ Out C2×C5⋊D41204(C2xC5:D4).8S3480,318
(C2×C5⋊D4).9S3 = Dic3×C5⋊D4φ: trivial image240(C2xC5:D4).9S3480,629

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