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

Direct product G=N×Q with N=C30 and Q=C22⋊C4
dρLabelID
C22⋊C4×C30240C2^2:C4xC30480,920

Semidirect products G=N:Q with N=C30 and Q=C22⋊C4
extensionφ:Q→Aut NdρLabelID
C30⋊(C22⋊C4) = C2×D6⋊F5φ: C22⋊C4/C2 → C2×C4 ⊆ Aut C30120C30:(C2^2:C4)480,1000
C30⋊2(C22⋊C4) = C2×D10.D6φ: C22⋊C4/C22 → C4 ⊆ Aut C30120C30:2(C2^2:C4)480,1072
C30⋊3(C22⋊C4) = C6×C22⋊F5φ: C22⋊C4/C22 → C4 ⊆ Aut C30120C30:3(C2^2:C4)480,1059
C30⋊4(C22⋊C4) = C2×D10⋊Dic3φ: C22⋊C4/C22 → C22 ⊆ Aut C30240C30:4(C2^2:C4)480,611
C30⋊5(C22⋊C4) = C2×D6⋊Dic5φ: C22⋊C4/C22 → C22 ⊆ Aut C30240C30:5(C2^2:C4)480,614
C30⋊6(C22⋊C4) = C2×D30⋊4C4φ: C22⋊C4/C22 → C22 ⊆ Aut C30240C30:6(C2^2:C4)480,616
C30⋊7(C22⋊C4) = C2×D30⋊3C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C30240C30:7(C2^2:C4)480,892
C30⋊8(C22⋊C4) = C6×D10⋊C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C30240C30:8(C2^2:C4)480,720
C30⋊9(C22⋊C4) = C10×D6⋊C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C30240C30:9(C2^2:C4)480,806
C30⋊10(C22⋊C4) = C2×C30.38D4φ: C22⋊C4/C23 → C2 ⊆ Aut C30240C30:10(C2^2:C4)480,917
C30⋊11(C22⋊C4) = C6×C23.D5φ: C22⋊C4/C23 → C2 ⊆ Aut C30240C30:11(C2^2:C4)480,745
C30⋊12(C22⋊C4) = C10×C6.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 → C2×C4 ⊆ Aut C301208+C30.1(C2^2:C4)480,227
C30.2(C22⋊C4) = D12⋊F5φ: C22⋊C4/C2 → C2×C4 ⊆ Aut C301208+C30.2(C2^2:C4)480,228
C30.3(C22⋊C4) = Dic6⋊F5φ: C22⋊C4/C2 → C2×C4 ⊆ Aut C301208-C30.3(C2^2:C4)480,229
C30.4(C22⋊C4) = Dic30⋊C4φ: C22⋊C4/C2 → C2×C4 ⊆ Aut C301208-C30.4(C2^2:C4)480,230
C30.5(C22⋊C4) = D12⋊4F5φ: C22⋊C4/C2 → C2×C4 ⊆ Aut C301208-C30.5(C2^2:C4)480,231
C30.6(C22⋊C4) = D12⋊2F5φ: C22⋊C4/C2 → C2×C4 ⊆ Aut C301208-C30.6(C2^2:C4)480,232
C30.7(C22⋊C4) = D60⋊2C4φ: C22⋊C4/C2 → C2×C4 ⊆ Aut C301208+C30.7(C2^2:C4)480,233
C30.8(C22⋊C4) = D60⋊5C4φ: C22⋊C4/C2 → C2×C4 ⊆ Aut C301208+C30.8(C2^2:C4)480,234
C30.9(C22⋊C4) = D10.20D12φ: C22⋊C4/C2 → C2×C4 ⊆ Aut C30120C30.9(C2^2:C4)480,243
C30.10(C22⋊C4) = Dic5.22D12φ: C22⋊C4/C2 → C2×C4 ⊆ Aut C30240C30.10(C2^2:C4)480,246
C30.11(C22⋊C4) = D30⋊C8φ: C22⋊C4/C2 → C2×C4 ⊆ Aut C30240C30.11(C2^2:C4)480,247
C30.12(C22⋊C4) = D10.D12φ: C22⋊C4/C2 → C2×C4 ⊆ Aut C301208-C30.12(C2^2:C4)480,248
C30.13(C22⋊C4) = D10.4D12φ: C22⋊C4/C2 → C2×C4 ⊆ Aut C301208+C30.13(C2^2:C4)480,249
C30.14(C22⋊C4) = Dic5.D12φ: C22⋊C4/C2 → C2×C4 ⊆ Aut C301208+C30.14(C2^2:C4)480,250
C30.15(C22⋊C4) = Dic5.4D12φ: C22⋊C4/C2 → C2×C4 ⊆ Aut C302408-C30.15(C2^2:C4)480,251
C30.16(C22⋊C4) = (C2×C60)⋊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) = (C2×C60).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) = C3×D10.D4φ: C22⋊C4/C22 → C4 ⊆ Aut C301204C30.27(C2^2:C4)480,279
C30.28(C22⋊C4) = C3×D10⋊C8φ: C22⋊C4/C22 → C4 ⊆ Aut C30240C30.28(C2^2:C4)480,283
C30.29(C22⋊C4) = C3×Dic5.D4φ: C22⋊C4/C22 → C4 ⊆ Aut C302404C30.29(C2^2:C4)480,285
C30.30(C22⋊C4) = C3×D10.3Q8φ: C22⋊C4/C22 → C4 ⊆ Aut C30120C30.30(C2^2:C4)480,286
C30.31(C22⋊C4) = C3×D20⋊C4φ: C22⋊C4/C22 → C4 ⊆ Aut C301208C30.31(C2^2:C4)480,287
C30.32(C22⋊C4) = C3×D4⋊F5φ: C22⋊C4/C22 → C4 ⊆ Aut C301208C30.32(C2^2:C4)480,288
C30.33(C22⋊C4) = C3×Q8⋊F5φ: C22⋊C4/C22 → C4 ⊆ Aut C301208C30.33(C2^2:C4)480,289
C30.34(C22⋊C4) = C3×Q8⋊2F5φ: C22⋊C4/C22 → C4 ⊆ Aut C301208C30.34(C2^2:C4)480,290
C30.35(C22⋊C4) = C3×C23⋊F5φ: C22⋊C4/C22 → C4 ⊆ Aut C301204C30.35(C2^2:C4)480,291
C30.36(C22⋊C4) = C3×C23.2F5φ: C22⋊C4/C22 → C4 ⊆ Aut C30240C30.36(C2^2:C4)480,292
C30.37(C22⋊C4) = C3×C23.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) = (C2×C6).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/C2×C4 → C2 ⊆ Aut C301202C30.69(C2^2:C4)480,165
C30.70(C22⋊C4) = C23.6D30φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C301204C30.70(C2^2:C4)480,166
C30.71(C22⋊C4) = D60⋊9C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C30240C30.71(C2^2:C4)480,169
C30.72(C22⋊C4) = Dic30⋊9C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.72(C2^2:C4)480,170
C30.73(C22⋊C4) = Dic30⋊8C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.73(C2^2:C4)480,176
C30.74(C22⋊C4) = D30⋊3C8φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C30240C30.74(C2^2:C4)480,180
C30.75(C22⋊C4) = D60⋊8C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C30240C30.75(C2^2:C4)480,181
C30.76(C22⋊C4) = M4(2)⋊D15φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C301204+C30.76(C2^2:C4)480,183
C30.77(C22⋊C4) = C4.D60φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C302404-C30.77(C2^2:C4)480,184
C30.78(C22⋊C4) = D60⋊10C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C301204C30.78(C2^2:C4)480,185
C30.79(C22⋊C4) = C30.29C42φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.79(C2^2:C4)480,191
C30.80(C22⋊C4) = C3×D20⋊4C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C301202C30.80(C2^2:C4)480,83
C30.81(C22⋊C4) = C3×C23.1D10φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C301204C30.81(C2^2:C4)480,84
C30.82(C22⋊C4) = C3×D20⋊6C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C30240C30.82(C2^2:C4)480,87
C30.83(C22⋊C4) = C3×C10.Q16φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.83(C2^2:C4)480,88
C30.84(C22⋊C4) = C3×C20.44D4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.84(C2^2:C4)480,94
C30.85(C22⋊C4) = C3×D10⋊1C8φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C30240C30.85(C2^2:C4)480,98
C30.86(C22⋊C4) = C3×D20⋊5C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C30240C30.86(C2^2:C4)480,99
C30.87(C22⋊C4) = C3×C20.46D4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C301204C30.87(C2^2:C4)480,101
C30.88(C22⋊C4) = C3×C4.12D20φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C302404C30.88(C2^2:C4)480,102
C30.89(C22⋊C4) = C3×D20⋊7C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C301204C30.89(C2^2:C4)480,103
C30.90(C22⋊C4) = C5×C42⋊4S3φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C301202C30.90(C2^2:C4)480,124
C30.91(C22⋊C4) = C5×C23.6D6φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C301204C30.91(C2^2:C4)480,125
C30.92(C22⋊C4) = C5×C6.D8φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C30240C30.92(C2^2:C4)480,128
C30.93(C22⋊C4) = C5×C6.SD16φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.93(C2^2:C4)480,129
C30.94(C22⋊C4) = C5×C2.Dic12φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.94(C2^2:C4)480,135
C30.95(C22⋊C4) = C5×D6⋊C8φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C30240C30.95(C2^2:C4)480,139
C30.96(C22⋊C4) = C5×C2.D24φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C30240C30.96(C2^2:C4)480,140
C30.97(C22⋊C4) = C5×C12.46D4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C301204C30.97(C2^2:C4)480,142
C30.98(C22⋊C4) = C5×C12.47D4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C302404C30.98(C2^2:C4)480,143
C30.99(C22⋊C4) = C5×D12⋊C4φ: C22⋊C4/C2×C4 → C2 ⊆ Aut C301204C30.99(C2^2:C4)480,144
C30.100(C22⋊C4) = C5×C6.C42φ: C22⋊C4/C2×C4 → 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) = C3×C20.55D4φ: C22⋊C4/C23 → C2 ⊆ Aut C30240C30.108(C2^2:C4)480,108
C30.109(C22⋊C4) = C3×C10.10C42φ: C22⋊C4/C23 → C2 ⊆ Aut C30480C30.109(C2^2:C4)480,109
C30.110(C22⋊C4) = C3×D4⋊Dic5φ: C22⋊C4/C23 → C2 ⊆ Aut C30240C30.110(C2^2:C4)480,110
C30.111(C22⋊C4) = C3×C20.D4φ: C22⋊C4/C23 → C2 ⊆ Aut C301204C30.111(C2^2:C4)480,111
C30.112(C22⋊C4) = C3×C23⋊Dic5φ: C22⋊C4/C23 → C2 ⊆ Aut C301204C30.112(C2^2:C4)480,112
C30.113(C22⋊C4) = C3×Q8⋊Dic5φ: C22⋊C4/C23 → C2 ⊆ Aut C30480C30.113(C2^2:C4)480,113
C30.114(C22⋊C4) = C3×C20.10D4φ: C22⋊C4/C23 → C2 ⊆ Aut C302404C30.114(C2^2:C4)480,114
C30.115(C22⋊C4) = C3×D4⋊2Dic5φ: C22⋊C4/C23 → C2 ⊆ Aut C301204C30.115(C2^2:C4)480,115
C30.116(C22⋊C4) = C5×C12.55D4φ: C22⋊C4/C23 → C2 ⊆ Aut C30240C30.116(C2^2:C4)480,149
C30.117(C22⋊C4) = C5×D4⋊Dic3φ: C22⋊C4/C23 → C2 ⊆ Aut C30240C30.117(C2^2:C4)480,151
C30.118(C22⋊C4) = C5×C12.D4φ: C22⋊C4/C23 → C2 ⊆ Aut C301204C30.118(C2^2:C4)480,152
C30.119(C22⋊C4) = C5×C23.7D6φ: C22⋊C4/C23 → C2 ⊆ Aut C301204C30.119(C2^2:C4)480,153
C30.120(C22⋊C4) = C5×Q8⋊2Dic3φ: C22⋊C4/C23 → C2 ⊆ Aut C30480C30.120(C2^2:C4)480,154
C30.121(C22⋊C4) = C5×C12.10D4φ: C22⋊C4/C23 → C2 ⊆ Aut C302404C30.121(C2^2:C4)480,155
C30.122(C22⋊C4) = C5×Q8⋊3Dic3φ: C22⋊C4/C23 → C2 ⊆ Aut C301204C30.122(C2^2:C4)480,156
C30.123(C22⋊C4) = C15×C2.C42central extension (φ=1)480C30.123(C2^2:C4)480,198
C30.124(C22⋊C4) = C15×C22⋊C8central extension (φ=1)240C30.124(C2^2:C4)480,201
C30.125(C22⋊C4) = C15×C23⋊C4central extension (φ=1)1204C30.125(C2^2:C4)480,202
C30.126(C22⋊C4) = C15×C4.D4central extension (φ=1)1204C30.126(C2^2:C4)480,203
C30.127(C22⋊C4) = C15×C4.10D4central extension (φ=1)2404C30.127(C2^2:C4)480,204
C30.128(C22⋊C4) = C15×D4⋊C4central extension (φ=1)240C30.128(C2^2:C4)480,205
C30.129(C22⋊C4) = C15×Q8⋊C4central extension (φ=1)480C30.129(C2^2:C4)480,206
C30.130(C22⋊C4) = C15×C4≀C2central extension (φ=1)1202C30.130(C2^2:C4)480,207

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