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Extensions 1→N→G→Q→1 with N=C12 and Q=C2×Dic5

Direct product G=N×Q with N=C12 and Q=C2×Dic5
dρLabelID
Dic5×C2×C12480Dic5xC2xC12480,715

Semidirect products G=N:Q with N=C12 and Q=C2×Dic5
extensionφ:Q→Aut NdρLabelID
C12⋊1(C2×Dic5) = S3×C4⋊Dic5φ: C2×Dic5/C10 → C22 ⊆ Aut C12240C12:1(C2xDic5)480,502
C12⋊2(C2×Dic5) = Dic15⋊8D4φ: C2×Dic5/C10 → C22 ⊆ Aut C12240C12:2(C2xDic5)480,511
C12⋊3(C2×Dic5) = D4×Dic15φ: C2×Dic5/C10 → C22 ⊆ Aut C12240C12:3(C2xDic5)480,899
C12⋊4(C2×Dic5) = Dic5×D12φ: C2×Dic5/Dic5 → C2 ⊆ Aut C12240C12:4(C2xDic5)480,491
C12⋊5(C2×Dic5) = C4×S3×Dic5φ: C2×Dic5/Dic5 → C2 ⊆ Aut C12240C12:5(C2xDic5)480,473
C12⋊6(C2×Dic5) = C3×D4×Dic5φ: C2×Dic5/Dic5 → C2 ⊆ Aut C12240C12:6(C2xDic5)480,727
C12⋊7(C2×Dic5) = C2×C60⋊5C4φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C12480C12:7(C2xDic5)480,890
C12⋊8(C2×Dic5) = C2×C4×Dic15φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C12480C12:8(C2xDic5)480,887
C12⋊9(C2×Dic5) = C6×C4⋊Dic5φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C12480C12:9(C2xDic5)480,718

Non-split extensions G=N.Q with N=C12 and Q=C2×Dic5
extensionφ:Q→Aut NdρLabelID
C12.1(C2×Dic5) = D12⋊Dic5φ: C2×Dic5/C10 → C22 ⊆ Aut C12240C12.1(C2xDic5)480,42
C12.2(C2×Dic5) = Dic6⋊Dic5φ: C2×Dic5/C10 → C22 ⊆ Aut C12480C12.2(C2xDic5)480,48
C12.3(C2×Dic5) = C60.98D4φ: C2×Dic5/C10 → C22 ⊆ Aut C121204C12.3(C2xDic5)480,54
C12.4(C2×Dic5) = C60.Q8φ: C2×Dic5/C10 → C22 ⊆ Aut C12480C12.4(C2xDic5)480,63
C12.5(C2×Dic5) = C60.5Q8φ: C2×Dic5/C10 → C22 ⊆ Aut C12480C12.5(C2xDic5)480,66
C12.6(C2×Dic5) = C12.59D20φ: C2×Dic5/C10 → C22 ⊆ Aut C122404C12.6(C2xDic5)480,69
C12.7(C2×Dic5) = D4⋊Dic15φ: C2×Dic5/C10 → C22 ⊆ Aut C12240C12.7(C2xDic5)480,192
C12.8(C2×Dic5) = Q8⋊2Dic15φ: C2×Dic5/C10 → C22 ⊆ Aut C12480C12.8(C2xDic5)480,195
C12.9(C2×Dic5) = Q8⋊3Dic15φ: C2×Dic5/C10 → C22 ⊆ Aut C121204C12.9(C2xDic5)480,197
C12.10(C2×Dic5) = S3×C4.Dic5φ: C2×Dic5/C10 → C22 ⊆ Aut C121204C12.10(C2xDic5)480,363
C12.11(C2×Dic5) = D12.Dic5φ: C2×Dic5/C10 → C22 ⊆ Aut C122404C12.11(C2xDic5)480,364
C12.12(C2×Dic5) = (S3×C20)⋊5C4φ: C2×Dic5/C10 → C22 ⊆ Aut C12240C12.12(C2xDic5)480,414
C12.13(C2×Dic5) = Dic15⋊7Q8φ: C2×Dic5/C10 → C22 ⊆ Aut C12480C12.13(C2xDic5)480,420
C12.14(C2×Dic5) = Q8×Dic15φ: C2×Dic5/C10 → C22 ⊆ Aut C12480C12.14(C2xDic5)480,910
C12.15(C2×Dic5) = D4.Dic15φ: C2×Dic5/C10 → C22 ⊆ Aut C122404C12.15(C2xDic5)480,913
C12.16(C2×Dic5) = C10.D24φ: C2×Dic5/Dic5 → C2 ⊆ Aut C12240C12.16(C2xDic5)480,43
C12.17(C2×Dic5) = C10.Dic12φ: C2×Dic5/Dic5 → C2 ⊆ Aut C12480C12.17(C2xDic5)480,49
C12.18(C2×Dic5) = C60.99D4φ: C2×Dic5/Dic5 → C2 ⊆ Aut C121204C12.18(C2xDic5)480,55
C12.19(C2×Dic5) = D12.2Dic5φ: C2×Dic5/Dic5 → C2 ⊆ Aut C122404C12.19(C2xDic5)480,362
C12.20(C2×Dic5) = Dic5×Dic6φ: C2×Dic5/Dic5 → C2 ⊆ Aut C12480C12.20(C2xDic5)480,408
C12.21(C2×Dic5) = S3×C5⋊2C16φ: C2×Dic5/Dic5 → C2 ⊆ Aut C122404C12.21(C2xDic5)480,8
C12.22(C2×Dic5) = C40.52D6φ: C2×Dic5/Dic5 → C2 ⊆ Aut C122404C12.22(C2xDic5)480,11
C12.23(C2×Dic5) = Dic5×C3⋊C8φ: C2×Dic5/Dic5 → C2 ⊆ Aut C12480C12.23(C2xDic5)480,25
C12.24(C2×Dic5) = Dic15⋊4C8φ: C2×Dic5/Dic5 → C2 ⊆ Aut C12480C12.24(C2xDic5)480,27
C12.25(C2×Dic5) = C30.21C42φ: C2×Dic5/Dic5 → C2 ⊆ Aut C12480C12.25(C2xDic5)480,28
C12.26(C2×Dic5) = C30.23C42φ: C2×Dic5/Dic5 → C2 ⊆ Aut C12480C12.26(C2xDic5)480,30
C12.27(C2×Dic5) = C2×S3×C5⋊2C8φ: C2×Dic5/Dic5 → C2 ⊆ Aut C12240C12.27(C2xDic5)480,361
C12.28(C2×Dic5) = C2×D6.Dic5φ: C2×Dic5/Dic5 → C2 ⊆ Aut C12240C12.28(C2xDic5)480,370
C12.29(C2×Dic5) = (S3×C20)⋊7C4φ: C2×Dic5/Dic5 → C2 ⊆ Aut C12240C12.29(C2xDic5)480,447
C12.30(C2×Dic5) = C3×D4⋊Dic5φ: C2×Dic5/Dic5 → C2 ⊆ Aut C12240C12.30(C2xDic5)480,110
C12.31(C2×Dic5) = C3×Q8⋊Dic5φ: C2×Dic5/Dic5 → C2 ⊆ Aut C12480C12.31(C2xDic5)480,113
C12.32(C2×Dic5) = C3×D4⋊2Dic5φ: C2×Dic5/Dic5 → C2 ⊆ Aut C121204C12.32(C2xDic5)480,115
C12.33(C2×Dic5) = C3×Q8×Dic5φ: C2×Dic5/Dic5 → C2 ⊆ Aut C12480C12.33(C2xDic5)480,738
C12.34(C2×Dic5) = C3×D4.Dic5φ: C2×Dic5/Dic5 → C2 ⊆ Aut C122404C12.34(C2xDic5)480,741
C12.35(C2×Dic5) = C120⋊10C4φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C12480C12.35(C2xDic5)480,177
C12.36(C2×Dic5) = C120⋊9C4φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C12480C12.36(C2xDic5)480,178
C12.37(C2×Dic5) = C4.18D60φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C122402C12.37(C2xDic5)480,179
C12.38(C2×Dic5) = C2×C60.7C4φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C12240C12.38(C2xDic5)480,886
C12.39(C2×Dic5) = C2×C15⋊3C16φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C12480C12.39(C2xDic5)480,171
C12.40(C2×Dic5) = C60.7C8φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C122402C12.40(C2xDic5)480,172
C12.41(C2×Dic5) = C8×Dic15φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C12480C12.41(C2xDic5)480,173
C12.42(C2×Dic5) = C120⋊13C4φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C12480C12.42(C2xDic5)480,175
C12.43(C2×Dic5) = C22×C15⋊3C8φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C12480C12.43(C2xDic5)480,885
C12.44(C2×Dic5) = C23.26D30φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C12240C12.44(C2xDic5)480,891
C12.45(C2×Dic5) = C3×C40⋊6C4φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C12480C12.45(C2xDic5)480,95
C12.46(C2×Dic5) = C3×C40⋊5C4φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C12480C12.46(C2xDic5)480,96
C12.47(C2×Dic5) = C3×C40.6C4φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C122402C12.47(C2xDic5)480,97
C12.48(C2×Dic5) = C6×C4.Dic5φ: C2×Dic5/C2×C10 → C2 ⊆ Aut C12240C12.48(C2xDic5)480,714
C12.49(C2×Dic5) = C6×C5⋊2C16central extension (φ=1)480C12.49(C2xDic5)480,89
C12.50(C2×Dic5) = C3×C20.4C8central extension (φ=1)2402C12.50(C2xDic5)480,90
C12.51(C2×Dic5) = Dic5×C24central extension (φ=1)480C12.51(C2xDic5)480,91
C12.52(C2×Dic5) = C3×C40⋊8C4central extension (φ=1)480C12.52(C2xDic5)480,93
C12.53(C2×Dic5) = C2×C6×C5⋊2C8central extension (φ=1)480C12.53(C2xDic5)480,713
C12.54(C2×Dic5) = C3×C23.21D10central extension (φ=1)240C12.54(C2xDic5)480,719

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