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Extensions 1→N→G→Q→1 with N=C10 and Q=C8⋊S3

Direct product G=N×Q with N=C10 and Q=C8⋊S3
dρLabelID
C10×C8⋊S3240C10xC8:S3480,779

Semidirect products G=N:Q with N=C10 and Q=C8⋊S3
extensionφ:Q→Aut NdρLabelID
C10⋊1(C8⋊S3) = C2×Dic3.F5φ: C8⋊S3/Dic3 → C4 ⊆ Aut C10240C10:1(C8:S3)480,1009
C10⋊2(C8⋊S3) = C2×D6.F5φ: C8⋊S3/D6 → C4 ⊆ Aut C10240C10:2(C8:S3)480,1008
C10⋊3(C8⋊S3) = C2×D30.5C4φ: C8⋊S3/C3⋊C8 → C2 ⊆ Aut C10240C10:3(C8:S3)480,371
C10⋊4(C8⋊S3) = C2×C40⋊S3φ: C8⋊S3/C24 → C2 ⊆ Aut C10240C10:4(C8:S3)480,865
C10⋊5(C8⋊S3) = C2×D6.Dic5φ: C8⋊S3/C4×S3 → C2 ⊆ Aut C10240C10:5(C8:S3)480,370

Non-split extensions G=N.Q with N=C10 and Q=C8⋊S3
extensionφ:Q→Aut NdρLabelID
C10.1(C8⋊S3) = C30.M4(2)φ: C8⋊S3/Dic3 → C4 ⊆ Aut C10480C10.1(C8:S3)480,245
C10.2(C8⋊S3) = D30⋊C8φ: C8⋊S3/Dic3 → C4 ⊆ Aut C10240C10.2(C8:S3)480,247
C10.3(C8⋊S3) = C30.4M4(2)φ: C8⋊S3/Dic3 → C4 ⊆ Aut C10480C10.3(C8:S3)480,252
C10.4(C8⋊S3) = Dic5.22D12φ: C8⋊S3/D6 → C4 ⊆ Aut C10240C10.4(C8:S3)480,246
C10.5(C8⋊S3) = Dic15⋊C8φ: C8⋊S3/D6 → C4 ⊆ Aut C10480C10.5(C8:S3)480,253
C10.6(C8⋊S3) = C30.23C42φ: C8⋊S3/C3⋊C8 → C2 ⊆ Aut C10480C10.6(C8:S3)480,30
C10.7(C8⋊S3) = D30⋊4C8φ: C8⋊S3/C3⋊C8 → C2 ⊆ Aut C10240C10.7(C8:S3)480,33
C10.8(C8⋊S3) = C60.14Q8φ: C8⋊S3/C3⋊C8 → C2 ⊆ Aut C10480C10.8(C8:S3)480,59
C10.9(C8⋊S3) = C60.26Q8φ: C8⋊S3/C24 → C2 ⊆ Aut C10480C10.9(C8:S3)480,174
C10.10(C8⋊S3) = C120⋊13C4φ: C8⋊S3/C24 → C2 ⊆ Aut C10480C10.10(C8:S3)480,175
C10.11(C8⋊S3) = D30⋊3C8φ: C8⋊S3/C24 → C2 ⊆ Aut C10240C10.11(C8:S3)480,180
C10.12(C8⋊S3) = C30.22C42φ: C8⋊S3/C4×S3 → C2 ⊆ Aut C10480C10.12(C8:S3)480,29
C10.13(C8⋊S3) = C60.94D4φ: C8⋊S3/C4×S3 → C2 ⊆ Aut C10240C10.13(C8:S3)480,32
C10.14(C8⋊S3) = C60.15Q8φ: C8⋊S3/C4×S3 → C2 ⊆ Aut C10480C10.14(C8:S3)480,60
C10.15(C8⋊S3) = C5×Dic3⋊C8central extension (φ=1)480C10.15(C8:S3)480,133
C10.16(C8⋊S3) = C5×C24⋊C4central extension (φ=1)480C10.16(C8:S3)480,134
C10.17(C8⋊S3) = C5×D6⋊C8central extension (φ=1)240C10.17(C8:S3)480,139

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