Extensions 1→N→G→Q→1 with N=C10×C3⋊S3 and Q=C2

Direct product G=N×Q with N=C10×C3⋊S3 and Q=C2
dρLabelID
C3⋊S3×C2×C10180C3:S3xC2xC10360,160

Semidirect products G=N:Q with N=C10×C3⋊S3 and Q=C2
extensionφ:Q→Out NdρLabelID
(C10×C3⋊S3)⋊1C2 = C30.12D6φ: C2/C1C2 ⊆ Out C10×C3⋊S3180(C10xC3:S3):1C2360,68
(C10×C3⋊S3)⋊2C2 = C15⋊D12φ: C2/C1C2 ⊆ Out C10×C3⋊S3180(C10xC3:S3):2C2360,70
(C10×C3⋊S3)⋊3C2 = D30⋊S3φ: C2/C1C2 ⊆ Out C10×C3⋊S3604(C10xC3:S3):3C2360,86
(C10×C3⋊S3)⋊4C2 = C2×D5×C3⋊S3φ: C2/C1C2 ⊆ Out C10×C3⋊S390(C10xC3:S3):4C2360,152
(C10×C3⋊S3)⋊5C2 = C2×D15⋊S3φ: C2/C1C2 ⊆ Out C10×C3⋊S3604(C10xC3:S3):5C2360,155
(C10×C3⋊S3)⋊6C2 = C5×C3⋊D12φ: C2/C1C2 ⊆ Out C10×C3⋊S3604(C10xC3:S3):6C2360,75
(C10×C3⋊S3)⋊7C2 = C5×C12⋊S3φ: C2/C1C2 ⊆ Out C10×C3⋊S3180(C10xC3:S3):7C2360,107
(C10×C3⋊S3)⋊8C2 = C5×C327D4φ: C2/C1C2 ⊆ Out C10×C3⋊S3180(C10xC3:S3):8C2360,109
(C10×C3⋊S3)⋊9C2 = S32×C10φ: C2/C1C2 ⊆ Out C10×C3⋊S3604(C10xC3:S3):9C2360,153

Non-split extensions G=N.Q with N=C10×C3⋊S3 and Q=C2
extensionφ:Q→Out NdρLabelID
(C10×C3⋊S3).1C2 = C3⋊S3×Dic5φ: C2/C1C2 ⊆ Out C10×C3⋊S3180(C10xC3:S3).1C2360,66
(C10×C3⋊S3).2C2 = Dic15⋊S3φ: C2/C1C2 ⊆ Out C10×C3⋊S3604(C10xC3:S3).2C2360,85
(C10×C3⋊S3).3C2 = C5×C6.D6φ: C2/C1C2 ⊆ Out C10×C3⋊S3604(C10xC3:S3).3C2360,73
(C10×C3⋊S3).4C2 = C10×C32⋊C4φ: C2/C1C2 ⊆ Out C10×C3⋊S3604(C10xC3:S3).4C2360,148
(C10×C3⋊S3).5C2 = C2×C32⋊Dic5φ: C2/C1C2 ⊆ Out C10×C3⋊S3604(C10xC3:S3).5C2360,149
(C10×C3⋊S3).6C2 = C3⋊S3×C20φ: trivial image180(C10xC3:S3).6C2360,106

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