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Extensions 1→N→G→Q→1 with N=C30 and Q=C22:C4

Direct product G=NxQ with N=C30 and Q=C22:C4
dρLabelID
C22:C4xC30240C2^2:C4xC30480,920

Semidirect products G=N:Q with N=C30 and Q=C22:C4
extensionφ:Q→Aut NdρLabelID
C30:(C22:C4) = C2xD6:F5φ: C22:C4/C2 → C2xC4 ⊆ Aut C30120C30:(C2^2:C4)480,1000
C30:2(C22:C4) = C2xD10.D6φ: C22:C4/C22 → C4 ⊆ Aut C30120C30:2(C2^2:C4)480,1072
C30:3(C22:C4) = C6xC22:F5φ: C22:C4/C22 → C4 ⊆ Aut C30120C30:3(C2^2:C4)480,1059
C30:4(C22:C4) = C2xD10:Dic3φ: C22:C4/C22 → C22 ⊆ Aut C30240C30:4(C2^2:C4)480,611
C30:5(C22:C4) = C2xD6:Dic5φ: C22:C4/C22 → C22 ⊆ Aut C30240C30:5(C2^2:C4)480,614
C30:6(C22:C4) = C2xD30:4C4φ: C22:C4/C22 → C22 ⊆ Aut C30240C30:6(C2^2:C4)480,616
C30:7(C22:C4) = C2xD30:3C4φ: C22:C4/C2xC4 → C2 ⊆ Aut C30240C30:7(C2^2:C4)480,892
C30:8(C22:C4) = C6xD10:C4φ: C22:C4/C2xC4 → C2 ⊆ Aut C30240C30:8(C2^2:C4)480,720
C30:9(C22:C4) = C10xD6:C4φ: C22:C4/C2xC4 → C2 ⊆ Aut C30240C30:9(C2^2:C4)480,806
C30:10(C22:C4) = C2xC30.38D4φ: C22:C4/C23 → C2 ⊆ Aut C30240C30:10(C2^2:C4)480,917
C30:11(C22:C4) = C6xC23.D5φ: C22:C4/C23 → C2 ⊆ Aut C30240C30:11(C2^2:C4)480,745
C30:12(C22:C4) = C10xC6.D4φ: C22:C4/C23 → C2 ⊆ Aut C30240C30:12(C2^2:C4)480,831

Non-split extensions G=N.Q with N=C30 and Q=C22:C4
extensionφ:Q→Aut NdρLabelID
C30.1(C22:C4) = D60:C4φ: C22:C4/C2 → C2xC4 ⊆ Aut C301208+C30.1(C2^2:C4)480,227
C30.2(C22:C4) = D12:F5φ: C22:C4/C2 → C2xC4 ⊆ Aut C301208+C30.2(C2^2:C4)480,228
C30.3(C22:C4) = Dic6:F5φ: C22:C4/C2 → C2xC4 ⊆ Aut C301208-C30.3(C2^2:C4)480,229
C30.4(C22:C4) = Dic30:C4φ: C22:C4/C2 → C2xC4 ⊆ Aut C301208-C30.4(C2^2:C4)480,230
C30.5(C22:C4) = D12:4F5φ: C22:C4/C2 → C2xC4 ⊆ Aut C301208-C30.5(C2^2:C4)480,231
C30.6(C22:C4) = D12:2F5φ: C22:C4/C2 → C2xC4 ⊆ Aut C301208-C30.6(C2^2:C4)480,232
C30.7(C22:C4) = D60:2C4φ: C22:C4/C2 → C2xC4 ⊆ Aut C301208+C30.7(C2^2:C4)480,233
C30.8(C22:C4) = D60:5C4φ: C22:C4/C2 → C2xC4 ⊆ Aut C301208+C30.8(C2^2:C4)480,234
C30.9(C22:C4) = D10.20D12φ: C22:C4/C2 → C2xC4 ⊆ Aut C30120C30.9(C2^2:C4)480,243
C30.10(C22:C4) = Dic5.22D12φ: C22:C4/C2 → C2xC4 ⊆ Aut C30240C30.10(C2^2:C4)480,246
C30.11(C22:C4) = D30:C8φ: C22:C4/C2 → C2xC4 ⊆ Aut C30240C30.11(C2^2:C4)480,247
C30.12(C22:C4) = D10.D12φ: C22:C4/C2 → C2xC4 ⊆ Aut C301208-C30.12(C2^2:C4)480,248
C30.13(C22:C4) = D10.4D12φ: C22:C4/C2 → C2xC4 ⊆ Aut C301208+C30.13(C2^2:C4)480,249
C30.14(C22:C4) = Dic5.D12φ: C22:C4/C2 → C2xC4 ⊆ Aut C301208+C30.14(C2^2:C4)480,250
C30.15(C22:C4) = Dic5.4D12φ: C22:C4/C2 → C2xC4 ⊆ Aut C302408-C30.15(C2^2:C4)480,251
C30.16(C22:C4) = (C2xC60):C4φ: C22:C4/C22 → C4 ⊆ Aut C301204C30.16(C2^2:C4)480,304
C30.17(C22:C4) = C30.7M4(2)φ: C22:C4/C22 → C4 ⊆ Aut C30240C30.17(C2^2:C4)480,308
C30.18(C22:C4) = (C2xC60).C4φ: C22:C4/C22 → C4 ⊆ Aut C302404C30.18(C2^2:C4)480,310
C30.19(C22:C4) = D10.10D12φ: C22:C4/C22 → C4 ⊆ Aut C30120C30.19(C2^2:C4)480,311
C30.20(C22:C4) = D20:Dic3φ: C22:C4/C22 → C4 ⊆ Aut C301208C30.20(C2^2:C4)480,312
C30.21(C22:C4) = Dic10:Dic3φ: C22:C4/C22 → C4 ⊆ Aut C301208C30.21(C2^2:C4)480,313
C30.22(C22:C4) = Dic10:2Dic3φ: C22:C4/C22 → C4 ⊆ Aut C301208C30.22(C2^2:C4)480,314
C30.23(C22:C4) = D20:2Dic3φ: C22:C4/C22 → C4 ⊆ Aut C301208C30.23(C2^2:C4)480,315
C30.24(C22:C4) = C3:(C23:F5)φ: C22:C4/C22 → C4 ⊆ Aut C301204C30.24(C2^2:C4)480,316
C30.25(C22:C4) = C30.22M4(2)φ: C22:C4/C22 → C4 ⊆ Aut C30240C30.25(C2^2:C4)480,317
C30.26(C22:C4) = C5:(C12.D4)φ: C22:C4/C22 → C4 ⊆ Aut C301204C30.26(C2^2:C4)480,318
C30.27(C22:C4) = C3xD10.D4φ: C22:C4/C22 → C4 ⊆ Aut C301204C30.27(C2^2:C4)480,279
C30.28(C22:C4) = C3xD10:C8φ: C22:C4/C22 → C4 ⊆ Aut C30240C30.28(C2^2:C4)480,283
C30.29(C22:C4) = C3xDic5.D4φ: C22:C4/C22 → C4 ⊆ Aut C302404C30.29(C2^2:C4)480,285
C30.30(C22:C4) = C3xD10.3Q8φ: C22:C4/C22 → C4 ⊆ Aut C30120C30.30(C2^2:C4)480,286
C30.31(C22:C4) = C3xD20:C4φ: C22:C4/C22 → C4 ⊆ Aut C301208C30.31(C2^2:C4)480,287
C30.32(C22:C4) = C3xD4:F5φ: C22:C4/C22 → C4 ⊆ Aut C301208C30.32(C2^2:C4)480,288
C30.33(C22:C4) = C3xQ8:F5φ: C22:C4/C22 → C4 ⊆ Aut C301208C30.33(C2^2:C4)480,289
C30.34(C22:C4) = C3xQ8:2F5φ: C22:C4/C22 → C4 ⊆ Aut C301208C30.34(C2^2:C4)480,290
C30.35(C22:C4) = C3xC23:F5φ: C22:C4/C22 → C4 ⊆ Aut C301204C30.35(C2^2:C4)480,291
C30.36(C22:C4) = C3xC23.2F5φ: C22:C4/C22 → C4 ⊆ Aut C30240C30.36(C2^2:C4)480,292
C30.37(C22:C4) = C3xC23.F5φ: C22:C4/C22 → C4 ⊆ Aut C301204C30.37(C2^2:C4)480,293
C30.38(C22:C4) = C60.93D4φ: C22:C4/C22 → C22 ⊆ Aut C30240C30.38(C2^2:C4)480,31
C30.39(C22:C4) = C60.94D4φ: C22:C4/C22 → C22 ⊆ Aut C30240C30.39(C2^2:C4)480,32
C30.40(C22:C4) = D30:4C8φ: C22:C4/C22 → C22 ⊆ Aut C30240C30.40(C2^2:C4)480,33
C30.41(C22:C4) = C60.28D4φ: C22:C4/C22 → C22 ⊆ Aut C301204C30.41(C2^2:C4)480,34
C30.42(C22:C4) = C20.5D12φ: C22:C4/C22 → C22 ⊆ Aut C301204C30.42(C2^2:C4)480,35
C30.43(C22:C4) = C60.29D4φ: C22:C4/C22 → C22 ⊆ Aut C301204+C30.43(C2^2:C4)480,36
C30.44(C22:C4) = C12.6D20φ: C22:C4/C22 → C22 ⊆ Aut C302404C30.44(C2^2:C4)480,37
C30.45(C22:C4) = C60.54D4φ: C22:C4/C22 → C22 ⊆ Aut C302404C30.45(C2^2:C4)480,38
C30.46(C22:C4) = C60.31D4φ: C22:C4/C22 → C22 ⊆ Aut C302404-C30.46(C2^2:C4)480,39
C30.47(C22:C4) = C30.D8φ: C22:C4/C22 → C22 ⊆ Aut C30240C30.47(C2^2:C4)480,40
C30.48(C22:C4) = C6.D40φ: C22:C4/C22 → C22 ⊆ Aut C30240C30.48(C2^2:C4)480,41
C30.49(C22:C4) = D12:Dic5φ: C22:C4/C22 → C22 ⊆ Aut C30240C30.49(C2^2:C4)480,42
C30.50(C22:C4) = C10.D24φ: C22:C4/C22 → C22 ⊆ Aut C30240C30.50(C2^2:C4)480,43
C30.51(C22:C4) = D60:12C4φ: C22:C4/C22 → C22 ⊆ Aut C30240C30.51(C2^2:C4)480,44
C30.52(C22:C4) = D60:15C4φ: C22:C4/C22 → C22 ⊆ Aut C30240C30.52(C2^2:C4)480,45
C30.53(C22:C4) = C30.Q16φ: C22:C4/C22 → C22 ⊆ Aut C30480C30.53(C2^2:C4)480,46
C30.54(C22:C4) = C6.Dic20φ: C22:C4/C22 → C22 ⊆ Aut C30480C30.54(C2^2:C4)480,47
C30.55(C22:C4) = Dic6:Dic5φ: C22:C4/C22 → C22 ⊆ Aut C30480C30.55(C2^2:C4)480,48
C30.56(C22:C4) = C10.Dic12φ: C22:C4/C22 → C22 ⊆ Aut C30480C30.56(C2^2:C4)480,49
C30.57(C22:C4) = Dic30:12C4φ: C22:C4/C22 → C22 ⊆ Aut C30480C30.57(C2^2:C4)480,50
C30.58(C22:C4) = Dic30:15C4φ: C22:C4/C22 → C22 ⊆ Aut C30480C30.58(C2^2:C4)480,51
C30.59(C22:C4) = C60.96D4φ: C22:C4/C22 → C22 ⊆ Aut C301204C30.59(C2^2:C4)480,52
C30.60(C22:C4) = C60.97D4φ: C22:C4/C22 → C22 ⊆ Aut C301204C30.60(C2^2:C4)480,53
C30.61(C22:C4) = C60.98D4φ: C22:C4/C22 → C22 ⊆ Aut C301204C30.61(C2^2:C4)480,54
C30.62(C22:C4) = C60.99D4φ: C22:C4/C22 → C22 ⊆ Aut C301204C30.62(C2^2:C4)480,55
C30.63(C22:C4) = D60:13C4φ: C22:C4/C22 → C22 ⊆ Aut C301204C30.63(C2^2:C4)480,56
C30.64(C22:C4) = D60:16C4φ: C22:C4/C22 → C22 ⊆ Aut C301204C30.64(C2^2:C4)480,57
C30.65(C22:C4) = C30.24C42φ: C22:C4/C22 → C22 ⊆ Aut C30480C30.65(C2^2:C4)480,70
C30.66(C22:C4) = (C2xC6).D20φ: C22:C4/C22 → C22 ⊆ Aut C301204C30.66(C2^2:C4)480,71
C30.67(C22:C4) = C15:8(C23:C4)φ: C22:C4/C22 → C22 ⊆ Aut C301204C30.67(C2^2:C4)480,72
C30.68(C22:C4) = C15:9(C23:C4)φ: C22:C4/C22 → C22 ⊆ Aut C301204C30.68(C2^2:C4)480,73
C30.69(C22:C4) = D60:7C4φ: C22:C4/C2xC4 → C2 ⊆ Aut C301202C30.69(C2^2:C4)480,165
C30.70(C22:C4) = C23.6D30φ: C22:C4/C2xC4 → C2 ⊆ Aut C301204C30.70(C2^2:C4)480,166
C30.71(C22:C4) = D60:9C4φ: C22:C4/C2xC4 → C2 ⊆ Aut C30240C30.71(C2^2:C4)480,169
C30.72(C22:C4) = Dic30:9C4φ: C22:C4/C2xC4 → C2 ⊆ Aut C30480C30.72(C2^2:C4)480,170
C30.73(C22:C4) = Dic30:8C4φ: C22:C4/C2xC4 → C2 ⊆ Aut C30480C30.73(C2^2:C4)480,176
C30.74(C22:C4) = D30:3C8φ: C22:C4/C2xC4 → C2 ⊆ Aut C30240C30.74(C2^2:C4)480,180
C30.75(C22:C4) = D60:8C4φ: C22:C4/C2xC4 → C2 ⊆ Aut C30240C30.75(C2^2:C4)480,181
C30.76(C22:C4) = M4(2):D15φ: C22:C4/C2xC4 → C2 ⊆ Aut C301204+C30.76(C2^2:C4)480,183
C30.77(C22:C4) = C4.D60φ: C22:C4/C2xC4 → C2 ⊆ Aut C302404-C30.77(C2^2:C4)480,184
C30.78(C22:C4) = D60:10C4φ: C22:C4/C2xC4 → C2 ⊆ Aut C301204C30.78(C2^2:C4)480,185
C30.79(C22:C4) = C30.29C42φ: C22:C4/C2xC4 → C2 ⊆ Aut C30480C30.79(C2^2:C4)480,191
C30.80(C22:C4) = C3xD20:4C4φ: C22:C4/C2xC4 → C2 ⊆ Aut C301202C30.80(C2^2:C4)480,83
C30.81(C22:C4) = C3xC23.1D10φ: C22:C4/C2xC4 → C2 ⊆ Aut C301204C30.81(C2^2:C4)480,84
C30.82(C22:C4) = C3xD20:6C4φ: C22:C4/C2xC4 → C2 ⊆ Aut C30240C30.82(C2^2:C4)480,87
C30.83(C22:C4) = C3xC10.Q16φ: C22:C4/C2xC4 → C2 ⊆ Aut C30480C30.83(C2^2:C4)480,88
C30.84(C22:C4) = C3xC20.44D4φ: C22:C4/C2xC4 → C2 ⊆ Aut C30480C30.84(C2^2:C4)480,94
C30.85(C22:C4) = C3xD10:1C8φ: C22:C4/C2xC4 → C2 ⊆ Aut C30240C30.85(C2^2:C4)480,98
C30.86(C22:C4) = C3xD20:5C4φ: C22:C4/C2xC4 → C2 ⊆ Aut C30240C30.86(C2^2:C4)480,99
C30.87(C22:C4) = C3xC20.46D4φ: C22:C4/C2xC4 → C2 ⊆ Aut C301204C30.87(C2^2:C4)480,101
C30.88(C22:C4) = C3xC4.12D20φ: C22:C4/C2xC4 → C2 ⊆ Aut C302404C30.88(C2^2:C4)480,102
C30.89(C22:C4) = C3xD20:7C4φ: C22:C4/C2xC4 → C2 ⊆ Aut C301204C30.89(C2^2:C4)480,103
C30.90(C22:C4) = C5xC42:4S3φ: C22:C4/C2xC4 → C2 ⊆ Aut C301202C30.90(C2^2:C4)480,124
C30.91(C22:C4) = C5xC23.6D6φ: C22:C4/C2xC4 → C2 ⊆ Aut C301204C30.91(C2^2:C4)480,125
C30.92(C22:C4) = C5xC6.D8φ: C22:C4/C2xC4 → C2 ⊆ Aut C30240C30.92(C2^2:C4)480,128
C30.93(C22:C4) = C5xC6.SD16φ: C22:C4/C2xC4 → C2 ⊆ Aut C30480C30.93(C2^2:C4)480,129
C30.94(C22:C4) = C5xC2.Dic12φ: C22:C4/C2xC4 → C2 ⊆ Aut C30480C30.94(C2^2:C4)480,135
C30.95(C22:C4) = C5xD6:C8φ: C22:C4/C2xC4 → C2 ⊆ Aut C30240C30.95(C2^2:C4)480,139
C30.96(C22:C4) = C5xC2.D24φ: C22:C4/C2xC4 → C2 ⊆ Aut C30240C30.96(C2^2:C4)480,140
C30.97(C22:C4) = C5xC12.46D4φ: C22:C4/C2xC4 → C2 ⊆ Aut C301204C30.97(C2^2:C4)480,142
C30.98(C22:C4) = C5xC12.47D4φ: C22:C4/C2xC4 → C2 ⊆ Aut C302404C30.98(C2^2:C4)480,143
C30.99(C22:C4) = C5xD12:C4φ: C22:C4/C2xC4 → C2 ⊆ Aut C301204C30.99(C2^2:C4)480,144
C30.100(C22:C4) = C5xC6.C42φ: C22:C4/C2xC4 → C2 ⊆ Aut C30480C30.100(C2^2:C4)480,150
C30.101(C22:C4) = C60.212D4φ: C22:C4/C23 → C2 ⊆ Aut C30240C30.101(C2^2:C4)480,190
C30.102(C22:C4) = D4:Dic15φ: C22:C4/C23 → C2 ⊆ Aut C30240C30.102(C2^2:C4)480,192
C30.103(C22:C4) = C60.8D4φ: C22:C4/C23 → C2 ⊆ Aut C301204C30.103(C2^2:C4)480,193
C30.104(C22:C4) = C23.7D30φ: C22:C4/C23 → C2 ⊆ Aut C301204C30.104(C2^2:C4)480,194
C30.105(C22:C4) = Q8:2Dic15φ: C22:C4/C23 → C2 ⊆ Aut C30480C30.105(C2^2:C4)480,195
C30.106(C22:C4) = C60.10D4φ: C22:C4/C23 → C2 ⊆ Aut C302404C30.106(C2^2:C4)480,196
C30.107(C22:C4) = Q8:3Dic15φ: C22:C4/C23 → C2 ⊆ Aut C301204C30.107(C2^2:C4)480,197
C30.108(C22:C4) = C3xC20.55D4φ: C22:C4/C23 → C2 ⊆ Aut C30240C30.108(C2^2:C4)480,108
C30.109(C22:C4) = C3xC10.10C42φ: C22:C4/C23 → C2 ⊆ Aut C30480C30.109(C2^2:C4)480,109
C30.110(C22:C4) = C3xD4:Dic5φ: C22:C4/C23 → C2 ⊆ Aut C30240C30.110(C2^2:C4)480,110
C30.111(C22:C4) = C3xC20.D4φ: C22:C4/C23 → C2 ⊆ Aut C301204C30.111(C2^2:C4)480,111
C30.112(C22:C4) = C3xC23:Dic5φ: C22:C4/C23 → C2 ⊆ Aut C301204C30.112(C2^2:C4)480,112
C30.113(C22:C4) = C3xQ8:Dic5φ: C22:C4/C23 → C2 ⊆ Aut C30480C30.113(C2^2:C4)480,113
C30.114(C22:C4) = C3xC20.10D4φ: C22:C4/C23 → C2 ⊆ Aut C302404C30.114(C2^2:C4)480,114
C30.115(C22:C4) = C3xD4:2Dic5φ: C22:C4/C23 → C2 ⊆ Aut C301204C30.115(C2^2:C4)480,115
C30.116(C22:C4) = C5xC12.55D4φ: C22:C4/C23 → C2 ⊆ Aut C30240C30.116(C2^2:C4)480,149
C30.117(C22:C4) = C5xD4:Dic3φ: C22:C4/C23 → C2 ⊆ Aut C30240C30.117(C2^2:C4)480,151
C30.118(C22:C4) = C5xC12.D4φ: C22:C4/C23 → C2 ⊆ Aut C301204C30.118(C2^2:C4)480,152
C30.119(C22:C4) = C5xC23.7D6φ: C22:C4/C23 → C2 ⊆ Aut C301204C30.119(C2^2:C4)480,153
C30.120(C22:C4) = C5xQ8:2Dic3φ: C22:C4/C23 → C2 ⊆ Aut C30480C30.120(C2^2:C4)480,154
C30.121(C22:C4) = C5xC12.10D4φ: C22:C4/C23 → C2 ⊆ Aut C302404C30.121(C2^2:C4)480,155
C30.122(C22:C4) = C5xQ8:3Dic3φ: C22:C4/C23 → C2 ⊆ Aut C301204C30.122(C2^2:C4)480,156
C30.123(C22:C4) = C15xC2.C42central extension (φ=1)480C30.123(C2^2:C4)480,198
C30.124(C22:C4) = C15xC22:C8central extension (φ=1)240C30.124(C2^2:C4)480,201
C30.125(C22:C4) = C15xC23:C4central extension (φ=1)1204C30.125(C2^2:C4)480,202
C30.126(C22:C4) = C15xC4.D4central extension (φ=1)1204C30.126(C2^2:C4)480,203
C30.127(C22:C4) = C15xC4.10D4central extension (φ=1)2404C30.127(C2^2:C4)480,204
C30.128(C22:C4) = C15xD4:C4central extension (φ=1)240C30.128(C2^2:C4)480,205
C30.129(C22:C4) = C15xQ8:C4central extension (φ=1)480C30.129(C2^2:C4)480,206
C30.130(C22:C4) = C15xC4wrC2central extension (φ=1)1202C30.130(C2^2:C4)480,207

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