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Extensions 1→N→G→Q→1 with N=C10 and Q=D4⋊S3

Direct product G=N×Q with N=C10 and Q=D4⋊S3
dρLabelID
C10×D4⋊S3240C10xD4:S3480,810

Semidirect products G=N:Q with N=C10 and Q=D4⋊S3
extensionφ:Q→Aut NdρLabelID
C10⋊1(D4⋊S3) = C2×C3⋊D40φ: D4⋊S3/C3⋊C8 → C2 ⊆ Aut C10240C10:1(D4:S3)480,376
C10⋊2(D4⋊S3) = C2×C15⋊D8φ: D4⋊S3/D12 → C2 ⊆ Aut C10240C10:2(D4:S3)480,372
C10⋊3(D4⋊S3) = C2×D4⋊D15φ: D4⋊S3/C3×D4 → C2 ⊆ Aut C10240C10:3(D4:S3)480,896

Non-split extensions G=N.Q with N=C10 and Q=D4⋊S3
extensionφ:Q→Aut NdρLabelID
C10.1(D4⋊S3) = C3⋊D80φ: D4⋊S3/C3⋊C8 → C2 ⊆ Aut C102404+C10.1(D4:S3)480,14
C10.2(D4⋊S3) = D40.S3φ: D4⋊S3/C3⋊C8 → C2 ⊆ Aut C102404-C10.2(D4:S3)480,18
C10.3(D4⋊S3) = C24.D10φ: D4⋊S3/C3⋊C8 → C2 ⊆ Aut C102404+C10.3(D4:S3)480,19
C10.4(D4⋊S3) = C3⋊Dic40φ: D4⋊S3/C3⋊C8 → C2 ⊆ Aut C104804-C10.4(D4:S3)480,23
C10.5(D4⋊S3) = C6.D40φ: D4⋊S3/C3⋊C8 → C2 ⊆ Aut C10240C10.5(D4:S3)480,41
C10.6(D4⋊S3) = D60⋊12C4φ: D4⋊S3/C3⋊C8 → C2 ⊆ Aut C10240C10.6(D4:S3)480,44
C10.7(D4⋊S3) = C60.5Q8φ: D4⋊S3/C3⋊C8 → C2 ⊆ Aut C10480C10.7(D4:S3)480,66
C10.8(D4⋊S3) = C15⋊D16φ: D4⋊S3/D12 → C2 ⊆ Aut C102404C10.8(D4:S3)480,13
C10.9(D4⋊S3) = C40.D6φ: D4⋊S3/D12 → C2 ⊆ Aut C102404C10.9(D4:S3)480,16
C10.10(D4⋊S3) = C15⋊SD32φ: D4⋊S3/D12 → C2 ⊆ Aut C102404C10.10(D4:S3)480,17
C10.11(D4⋊S3) = C15⋊Q32φ: D4⋊S3/D12 → C2 ⊆ Aut C104804C10.11(D4:S3)480,22
C10.12(D4⋊S3) = C30.D8φ: D4⋊S3/D12 → C2 ⊆ Aut C10240C10.12(D4:S3)480,40
C10.13(D4⋊S3) = D12⋊Dic5φ: D4⋊S3/D12 → C2 ⊆ Aut C10240C10.13(D4:S3)480,42
C10.14(D4⋊S3) = C30.20D8φ: D4⋊S3/D12 → C2 ⊆ Aut C10480C10.14(D4:S3)480,65
C10.15(D4⋊S3) = C60.1Q8φ: D4⋊S3/C3×D4 → C2 ⊆ Aut C10480C10.15(D4:S3)480,167
C10.16(D4⋊S3) = D60⋊9C4φ: D4⋊S3/C3×D4 → C2 ⊆ Aut C10240C10.16(D4:S3)480,169
C10.17(D4⋊S3) = C15⋊7D16φ: D4⋊S3/C3×D4 → C2 ⊆ Aut C102404+C10.17(D4:S3)480,186
C10.18(D4⋊S3) = D8.D15φ: D4⋊S3/C3×D4 → C2 ⊆ Aut C102404-C10.18(D4:S3)480,187
C10.19(D4⋊S3) = C8.6D30φ: D4⋊S3/C3×D4 → C2 ⊆ Aut C102404+C10.19(D4:S3)480,188
C10.20(D4⋊S3) = C15⋊7Q32φ: D4⋊S3/C3×D4 → C2 ⊆ Aut C104804-C10.20(D4:S3)480,189
C10.21(D4⋊S3) = D4⋊Dic15φ: D4⋊S3/C3×D4 → C2 ⊆ Aut C10240C10.21(D4:S3)480,192
C10.22(D4⋊S3) = C5×C6.Q16central extension (φ=1)480C10.22(D4:S3)480,126
C10.23(D4⋊S3) = C5×C6.D8central extension (φ=1)240C10.23(D4:S3)480,128
C10.24(D4⋊S3) = C5×C3⋊D16central extension (φ=1)2404C10.24(D4:S3)480,145
C10.25(D4⋊S3) = C5×D8.S3central extension (φ=1)2404C10.25(D4:S3)480,146
C10.26(D4⋊S3) = C5×C8.6D6central extension (φ=1)2404C10.26(D4:S3)480,147
C10.27(D4⋊S3) = C5×C3⋊Q32central extension (φ=1)4804C10.27(D4:S3)480,148
C10.28(D4⋊S3) = C5×D4⋊Dic3central extension (φ=1)240C10.28(D4:S3)480,151

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