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Extensions 1→N→G→Q→1 with N=C20 and Q=C4×S3

Direct product G=N×Q with N=C20 and Q=C4×S3
dρLabelID
S3×C4×C20240S3xC4xC20480,750

Semidirect products G=N:Q with N=C20 and Q=C4×S3
extensionφ:Q→Aut NdρLabelID
C20⋊1(C4×S3) = F5×D12φ: C4×S3/C3 → C2×C4 ⊆ Aut C20608+C20:1(C4xS3)480,995
C20⋊2(C4×S3) = D60⋊3C4φ: C4×S3/C3 → C2×C4 ⊆ Aut C20608+C20:2(C4xS3)480,997
C20⋊3(C4×S3) = S3×C4⋊F5φ: C4×S3/S3 → C4 ⊆ Aut C20608C20:3(C4xS3)480,996
C20⋊4(C4×S3) = C4×S3×F5φ: C4×S3/S3 → C4 ⊆ Aut C20608C20:4(C4xS3)480,994
C20⋊5(C4×S3) = Dic5×D12φ: C4×S3/C6 → C22 ⊆ Aut C20240C20:5(C4xS3)480,491
C20⋊6(C4×S3) = D60⋊17C4φ: C4×S3/C6 → C22 ⊆ Aut C20240C20:6(C4xS3)480,494
C20⋊7(C4×S3) = Dic15⋊8D4φ: C4×S3/C6 → C22 ⊆ Aut C20240C20:7(C4xS3)480,511
C20⋊8(C4×S3) = D30.2Q8φ: C4×S3/C6 → C22 ⊆ Aut C20240C20:8(C4xS3)480,513
C20⋊9(C4×S3) = C4⋊C4×D15φ: C4×S3/C6 → C22 ⊆ Aut C20240C20:9(C4xS3)480,856
C20⋊10(C4×S3) = D60⋊11C4φ: C4×S3/C6 → C22 ⊆ Aut C20240C20:10(C4xS3)480,858
C20⋊11(C4×S3) = D60⋊14C4φ: C4×S3/Dic3 → C2 ⊆ Aut C20240C20:11(C4xS3)480,504
C20⋊12(C4×S3) = C4×D30.C2φ: C4×S3/Dic3 → C2 ⊆ Aut C20240C20:12(C4xS3)480,477
C20⋊13(C4×S3) = C5×Dic3⋊5D4φ: C4×S3/Dic3 → C2 ⊆ Aut C20240C20:13(C4xS3)480,772
C20⋊14(C4×S3) = C4×D60φ: C4×S3/C12 → C2 ⊆ Aut C20240C20:14(C4xS3)480,838
C20⋊15(C4×S3) = C42×D15φ: C4×S3/C12 → C2 ⊆ Aut C20240C20:15(C4xS3)480,836
C20⋊16(C4×S3) = C20×D12φ: C4×S3/C12 → C2 ⊆ Aut C20240C20:16(C4xS3)480,752
C20⋊17(C4×S3) = S3×C4⋊Dic5φ: C4×S3/D6 → C2 ⊆ Aut C20240C20:17(C4xS3)480,502
C20⋊18(C4×S3) = C4×S3×Dic5φ: C4×S3/D6 → C2 ⊆ Aut C20240C20:18(C4xS3)480,473
C20⋊19(C4×S3) = C5×S3×C4⋊C4φ: C4×S3/D6 → C2 ⊆ Aut C20240C20:19(C4xS3)480,770

Non-split extensions G=N.Q with N=C20 and Q=C4×S3
extensionφ:Q→Aut NdρLabelID
C20.1(C4×S3) = D60⋊C4φ: C4×S3/C3 → C2×C4 ⊆ Aut C201208+C20.1(C4xS3)480,227
C20.2(C4×S3) = D12⋊F5φ: C4×S3/C3 → C2×C4 ⊆ Aut C201208+C20.2(C4xS3)480,228
C20.3(C4×S3) = Dic6⋊F5φ: C4×S3/C3 → C2×C4 ⊆ Aut C201208-C20.3(C4xS3)480,229
C20.4(C4×S3) = Dic30⋊C4φ: C4×S3/C3 → C2×C4 ⊆ Aut C201208-C20.4(C4xS3)480,230
C20.5(C4×S3) = D12⋊4F5φ: C4×S3/C3 → C2×C4 ⊆ Aut C201208-C20.5(C4xS3)480,231
C20.6(C4×S3) = D12⋊2F5φ: C4×S3/C3 → C2×C4 ⊆ Aut C201208-C20.6(C4xS3)480,232
C20.7(C4×S3) = D60⋊2C4φ: C4×S3/C3 → C2×C4 ⊆ Aut C201208+C20.7(C4xS3)480,233
C20.8(C4×S3) = D60⋊5C4φ: C4×S3/C3 → C2×C4 ⊆ Aut C201208+C20.8(C4xS3)480,234
C20.9(C4×S3) = F5×Dic6φ: C4×S3/C3 → C2×C4 ⊆ Aut C201208-C20.9(C4xS3)480,982
C20.10(C4×S3) = Dic6⋊5F5φ: C4×S3/C3 → C2×C4 ⊆ Aut C201208-C20.10(C4xS3)480,984
C20.11(C4×S3) = D12.2F5φ: C4×S3/C3 → C2×C4 ⊆ Aut C202408-C20.11(C4xS3)480,987
C20.12(C4×S3) = D12.F5φ: C4×S3/C3 → C2×C4 ⊆ Aut C202408-C20.12(C4xS3)480,989
C20.13(C4×S3) = D60.C4φ: C4×S3/C3 → C2×C4 ⊆ Aut C202408+C20.13(C4xS3)480,990
C20.14(C4×S3) = Dic6.F5φ: C4×S3/C3 → C2×C4 ⊆ Aut C202408+C20.14(C4xS3)480,992
C20.15(C4×S3) = Dic5.Dic6φ: C4×S3/S3 → C4 ⊆ Aut C201208C20.15(C4xS3)480,235
C20.16(C4×S3) = Dic5.4Dic6φ: C4×S3/S3 → C4 ⊆ Aut C201208C20.16(C4xS3)480,236
C20.17(C4×S3) = D10.Dic6φ: C4×S3/S3 → C4 ⊆ Aut C202408C20.17(C4xS3)480,237
C20.18(C4×S3) = D10.2Dic6φ: C4×S3/S3 → C4 ⊆ Aut C202408C20.18(C4xS3)480,238
C20.19(C4×S3) = C4⋊F5⋊3S3φ: C4×S3/S3 → C4 ⊆ Aut C201208C20.19(C4xS3)480,983
C20.20(C4×S3) = S3×C4.F5φ: C4×S3/S3 → C4 ⊆ Aut C201208C20.20(C4xS3)480,988
C20.21(C4×S3) = D15⋊M4(2)φ: C4×S3/S3 → C4 ⊆ Aut C201208C20.21(C4xS3)480,991
C20.22(C4×S3) = F5×C3⋊C8φ: C4×S3/S3 → C4 ⊆ Aut C201208C20.22(C4xS3)480,223
C20.23(C4×S3) = C30.C42φ: C4×S3/S3 → C4 ⊆ Aut C201208C20.23(C4xS3)480,224
C20.24(C4×S3) = C30.3C42φ: C4×S3/S3 → C4 ⊆ Aut C201208C20.24(C4xS3)480,225
C20.25(C4×S3) = C30.4C42φ: C4×S3/S3 → C4 ⊆ Aut C201208C20.25(C4xS3)480,226
C20.26(C4×S3) = S3×C5⋊C16φ: C4×S3/S3 → C4 ⊆ Aut C202408C20.26(C4xS3)480,239
C20.27(C4×S3) = D15⋊C16φ: C4×S3/S3 → C4 ⊆ Aut C202408C20.27(C4xS3)480,240
C20.28(C4×S3) = C15⋊M5(2)φ: C4×S3/S3 → C4 ⊆ Aut C202408C20.28(C4xS3)480,241
C20.29(C4×S3) = D30.C8φ: C4×S3/S3 → C4 ⊆ Aut C202408C20.29(C4xS3)480,242
C20.30(C4×S3) = (C4×S3)⋊F5φ: C4×S3/S3 → C4 ⊆ Aut C201208C20.30(C4xS3)480,985
C20.31(C4×S3) = S3×D5⋊C8φ: C4×S3/S3 → C4 ⊆ Aut C201208C20.31(C4xS3)480,986
C20.32(C4×S3) = C5⋊C8⋊D6φ: C4×S3/S3 → C4 ⊆ Aut C201208C20.32(C4xS3)480,993
C20.33(C4×S3) = D12⋊Dic5φ: C4×S3/C6 → C22 ⊆ Aut C20240C20.33(C4xS3)480,42
C20.34(C4×S3) = C10.D24φ: C4×S3/C6 → C22 ⊆ Aut C20240C20.34(C4xS3)480,43
C20.35(C4×S3) = D60⋊15C4φ: C4×S3/C6 → C22 ⊆ Aut C20240C20.35(C4xS3)480,45
C20.36(C4×S3) = Dic6⋊Dic5φ: C4×S3/C6 → C22 ⊆ Aut C20480C20.36(C4xS3)480,48
C20.37(C4×S3) = C10.Dic12φ: C4×S3/C6 → C22 ⊆ Aut C20480C20.37(C4xS3)480,49
C20.38(C4×S3) = Dic30⋊15C4φ: C4×S3/C6 → C22 ⊆ Aut C20480C20.38(C4xS3)480,51
C20.39(C4×S3) = C60.98D4φ: C4×S3/C6 → C22 ⊆ Aut C201204C20.39(C4xS3)480,54
C20.40(C4×S3) = C60.99D4φ: C4×S3/C6 → C22 ⊆ Aut C201204C20.40(C4xS3)480,55
C20.41(C4×S3) = D60⋊16C4φ: C4×S3/C6 → C22 ⊆ Aut C201204C20.41(C4xS3)480,57
C20.42(C4×S3) = C30.SD16φ: C4×S3/C6 → C22 ⊆ Aut C20480C20.42(C4xS3)480,62
C20.43(C4×S3) = C30.20D8φ: C4×S3/C6 → C22 ⊆ Aut C20480C20.43(C4xS3)480,65
C20.44(C4×S3) = C60.D4φ: C4×S3/C6 → C22 ⊆ Aut C202404C20.44(C4xS3)480,68
C20.45(C4×S3) = C60.1Q8φ: C4×S3/C6 → C22 ⊆ Aut C20480C20.45(C4xS3)480,167
C20.46(C4×S3) = C60.2Q8φ: C4×S3/C6 → C22 ⊆ Aut C20480C20.46(C4xS3)480,168
C20.47(C4×S3) = D60⋊9C4φ: C4×S3/C6 → C22 ⊆ Aut C20240C20.47(C4xS3)480,169
C20.48(C4×S3) = Dic30⋊9C4φ: C4×S3/C6 → C22 ⊆ Aut C20480C20.48(C4xS3)480,170
C20.49(C4×S3) = C60.210D4φ: C4×S3/C6 → C22 ⊆ Aut C202404C20.49(C4xS3)480,182
C20.50(C4×S3) = D60⋊10C4φ: C4×S3/C6 → C22 ⊆ Aut C201204C20.50(C4xS3)480,185
C20.51(C4×S3) = D12.2Dic5φ: C4×S3/C6 → C22 ⊆ Aut C202404C20.51(C4xS3)480,362
C20.52(C4×S3) = D12.Dic5φ: C4×S3/C6 → C22 ⊆ Aut C202404C20.52(C4xS3)480,364
C20.53(C4×S3) = D60.5C4φ: C4×S3/C6 → C22 ⊆ Aut C202404C20.53(C4xS3)480,366
C20.54(C4×S3) = D15⋊4M4(2)φ: C4×S3/C6 → C22 ⊆ Aut C201204C20.54(C4xS3)480,368
C20.55(C4×S3) = Dic5×Dic6φ: C4×S3/C6 → C22 ⊆ Aut C20480C20.55(C4xS3)480,408
C20.56(C4×S3) = Dic30⋊17C4φ: C4×S3/C6 → C22 ⊆ Aut C20480C20.56(C4xS3)480,409
C20.57(C4×S3) = Dic15⋊7Q8φ: C4×S3/C6 → C22 ⊆ Aut C20480C20.57(C4xS3)480,420
C20.58(C4×S3) = (C4×D15)⋊8C4φ: C4×S3/C6 → C22 ⊆ Aut C20240C20.58(C4xS3)480,423
C20.59(C4×S3) = Dic15⋊10Q8φ: C4×S3/C6 → C22 ⊆ Aut C20480C20.59(C4xS3)480,852
C20.60(C4×S3) = C4⋊C4⋊7D15φ: C4×S3/C6 → C22 ⊆ Aut C20240C20.60(C4xS3)480,857
C20.61(C4×S3) = M4(2)×D15φ: C4×S3/C6 → C22 ⊆ Aut C201204C20.61(C4xS3)480,871
C20.62(C4×S3) = D60.3C4φ: C4×S3/C6 → C22 ⊆ Aut C202404C20.62(C4xS3)480,872
C20.63(C4×S3) = D60⋊12C4φ: C4×S3/Dic3 → C2 ⊆ Aut C20240C20.63(C4xS3)480,44
C20.64(C4×S3) = Dic30⋊12C4φ: C4×S3/Dic3 → C2 ⊆ Aut C20480C20.64(C4xS3)480,50
C20.65(C4×S3) = D60⋊13C4φ: C4×S3/Dic3 → C2 ⊆ Aut C201204C20.65(C4xS3)480,56
C20.66(C4×S3) = D60.4C4φ: C4×S3/Dic3 → C2 ⊆ Aut C202404C20.66(C4xS3)480,367
C20.67(C4×S3) = Dic30⋊14C4φ: C4×S3/Dic3 → C2 ⊆ Aut C20480C20.67(C4xS3)480,416
C20.68(C4×S3) = D15⋊2C16φ: C4×S3/Dic3 → C2 ⊆ Aut C202404C20.68(C4xS3)480,9
C20.69(C4×S3) = D30.5C8φ: C4×S3/Dic3 → C2 ⊆ Aut C202404C20.69(C4xS3)480,12
C20.70(C4×S3) = Dic5×C3⋊C8φ: C4×S3/Dic3 → C2 ⊆ Aut C20480C20.70(C4xS3)480,25
C20.71(C4×S3) = Dic3×C5⋊2C8φ: C4×S3/Dic3 → C2 ⊆ Aut C20480C20.71(C4xS3)480,26
C20.72(C4×S3) = C30.22C42φ: C4×S3/Dic3 → C2 ⊆ Aut C20480C20.72(C4xS3)480,29
C20.73(C4×S3) = C2×D15⋊2C8φ: C4×S3/Dic3 → C2 ⊆ Aut C20240C20.73(C4xS3)480,365
C20.74(C4×S3) = C2×D30.5C4φ: C4×S3/Dic3 → C2 ⊆ Aut C20240C20.74(C4xS3)480,371
C20.75(C4×S3) = (C4×D15)⋊10C4φ: C4×S3/Dic3 → C2 ⊆ Aut C20240C20.75(C4xS3)480,462
C20.76(C4×S3) = C5×C6.D8φ: C4×S3/Dic3 → C2 ⊆ Aut C20240C20.76(C4xS3)480,128
C20.77(C4×S3) = C5×C6.SD16φ: C4×S3/Dic3 → C2 ⊆ Aut C20480C20.77(C4xS3)480,129
C20.78(C4×S3) = C5×D12⋊C4φ: C4×S3/Dic3 → C2 ⊆ Aut C201204C20.78(C4xS3)480,144
C20.79(C4×S3) = C5×Dic6⋊C4φ: C4×S3/Dic3 → C2 ⊆ Aut C20480C20.79(C4xS3)480,766
C20.80(C4×S3) = C5×D12.C4φ: C4×S3/Dic3 → C2 ⊆ Aut C202404C20.80(C4xS3)480,786
C20.81(C4×S3) = D60⋊7C4φ: C4×S3/C12 → C2 ⊆ Aut C201202C20.81(C4xS3)480,165
C20.82(C4×S3) = Dic30⋊8C4φ: C4×S3/C12 → C2 ⊆ Aut C20480C20.82(C4xS3)480,176
C20.83(C4×S3) = D60⋊8C4φ: C4×S3/C12 → C2 ⊆ Aut C20240C20.83(C4xS3)480,181
C20.84(C4×S3) = C4×Dic30φ: C4×S3/C12 → C2 ⊆ Aut C20480C20.84(C4xS3)480,833
C20.85(C4×S3) = D60.6C4φ: C4×S3/C12 → C2 ⊆ Aut C202402C20.85(C4xS3)480,866
C20.86(C4×S3) = C16×D15φ: C4×S3/C12 → C2 ⊆ Aut C202402C20.86(C4xS3)480,157
C20.87(C4×S3) = C80⋊S3φ: C4×S3/C12 → C2 ⊆ Aut C202402C20.87(C4xS3)480,158
C20.88(C4×S3) = C4×C15⋊3C8φ: C4×S3/C12 → C2 ⊆ Aut C20480C20.88(C4xS3)480,162
C20.89(C4×S3) = C42.D15φ: C4×S3/C12 → C2 ⊆ Aut C20480C20.89(C4xS3)480,163
C20.90(C4×S3) = C8×Dic15φ: C4×S3/C12 → C2 ⊆ Aut C20480C20.90(C4xS3)480,173
C20.91(C4×S3) = C120⋊13C4φ: C4×S3/C12 → C2 ⊆ Aut C20480C20.91(C4xS3)480,175
C20.92(C4×S3) = C42⋊2D15φ: C4×S3/C12 → C2 ⊆ Aut C20240C20.92(C4xS3)480,837
C20.93(C4×S3) = C2×C8×D15φ: C4×S3/C12 → C2 ⊆ Aut C20240C20.93(C4xS3)480,864
C20.94(C4×S3) = C2×C40⋊S3φ: C4×S3/C12 → C2 ⊆ Aut C20240C20.94(C4xS3)480,865
C20.95(C4×S3) = C5×C42⋊4S3φ: C4×S3/C12 → C2 ⊆ Aut C201202C20.95(C4xS3)480,124
C20.96(C4×S3) = C5×C2.Dic12φ: C4×S3/C12 → C2 ⊆ Aut C20480C20.96(C4xS3)480,135
C20.97(C4×S3) = C5×C2.D24φ: C4×S3/C12 → C2 ⊆ Aut C20240C20.97(C4xS3)480,140
C20.98(C4×S3) = C20×Dic6φ: C4×S3/C12 → C2 ⊆ Aut C20480C20.98(C4xS3)480,747
C20.99(C4×S3) = C5×C8○D12φ: C4×S3/C12 → C2 ⊆ Aut C202402C20.99(C4xS3)480,780
C20.100(C4×S3) = C60.Q8φ: C4×S3/D6 → C2 ⊆ Aut C20480C20.100(C4xS3)480,63
C20.101(C4×S3) = C60.5Q8φ: C4×S3/D6 → C2 ⊆ Aut C20480C20.101(C4xS3)480,66
C20.102(C4×S3) = C12.59D20φ: C4×S3/D6 → C2 ⊆ Aut C202404C20.102(C4xS3)480,69
C20.103(C4×S3) = S3×C4.Dic5φ: C4×S3/D6 → C2 ⊆ Aut C201204C20.103(C4xS3)480,363
C20.104(C4×S3) = (S3×C20)⋊5C4φ: C4×S3/D6 → C2 ⊆ Aut C20240C20.104(C4xS3)480,414
C20.105(C4×S3) = S3×C5⋊2C16φ: C4×S3/D6 → C2 ⊆ Aut C202404C20.105(C4xS3)480,8
C20.106(C4×S3) = C40.52D6φ: C4×S3/D6 → C2 ⊆ Aut C202404C20.106(C4xS3)480,11
C20.107(C4×S3) = Dic15⋊4C8φ: C4×S3/D6 → C2 ⊆ Aut C20480C20.107(C4xS3)480,27
C20.108(C4×S3) = C30.21C42φ: C4×S3/D6 → C2 ⊆ Aut C20480C20.108(C4xS3)480,28
C20.109(C4×S3) = C30.23C42φ: C4×S3/D6 → C2 ⊆ Aut C20480C20.109(C4xS3)480,30
C20.110(C4×S3) = C2×S3×C5⋊2C8φ: C4×S3/D6 → C2 ⊆ Aut C20240C20.110(C4xS3)480,361
C20.111(C4×S3) = C2×D6.Dic5φ: C4×S3/D6 → C2 ⊆ Aut C20240C20.111(C4xS3)480,370
C20.112(C4×S3) = (S3×C20)⋊7C4φ: C4×S3/D6 → C2 ⊆ Aut C20240C20.112(C4xS3)480,447
C20.113(C4×S3) = C5×C6.Q16φ: C4×S3/D6 → C2 ⊆ Aut C20480C20.113(C4xS3)480,126
C20.114(C4×S3) = C5×C12.Q8φ: C4×S3/D6 → C2 ⊆ Aut C20480C20.114(C4xS3)480,127
C20.115(C4×S3) = C5×C12.53D4φ: C4×S3/D6 → C2 ⊆ Aut C202404C20.115(C4xS3)480,141
C20.116(C4×S3) = C5×C4⋊C4⋊7S3φ: C4×S3/D6 → C2 ⊆ Aut C20240C20.116(C4xS3)480,771
C20.117(C4×S3) = C5×S3×M4(2)φ: C4×S3/D6 → C2 ⊆ Aut C201204C20.117(C4xS3)480,785
C20.118(C4×S3) = S3×C80central extension (φ=1)2402C20.118(C4xS3)480,116
C20.119(C4×S3) = C5×D6.C8central extension (φ=1)2402C20.119(C4xS3)480,117
C20.120(C4×S3) = C20×C3⋊C8central extension (φ=1)480C20.120(C4xS3)480,121
C20.121(C4×S3) = C5×C42.S3central extension (φ=1)480C20.121(C4xS3)480,122
C20.122(C4×S3) = Dic3×C40central extension (φ=1)480C20.122(C4xS3)480,132
C20.123(C4×S3) = C5×C24⋊C4central extension (φ=1)480C20.123(C4xS3)480,134
C20.124(C4×S3) = C5×C42⋊2S3central extension (φ=1)240C20.124(C4xS3)480,751
C20.125(C4×S3) = S3×C2×C40central extension (φ=1)240C20.125(C4xS3)480,778
C20.126(C4×S3) = C10×C8⋊S3central extension (φ=1)240C20.126(C4xS3)480,779

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