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

Direct product G=N×Q with N=C30 and Q=C4⋊C4
dρLabelID
C4⋊C4×C30480C4:C4xC30480,921

Semidirect products G=N:Q with N=C30 and Q=C4⋊C4
extensionφ:Q→Aut NdρLabelID
C30⋊(C4⋊C4) = C2×Dic3⋊F5φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C30120C30:(C4:C4)480,1001
C30⋊2(C4⋊C4) = C2×C60⋊C4φ: C4⋊C4/C4 → C4 ⊆ Aut C30120C30:2(C4:C4)480,1064
C30⋊3(C4⋊C4) = C6×C4⋊F5φ: C4⋊C4/C4 → C4 ⊆ Aut C30120C30:3(C4:C4)480,1051
C30⋊4(C4⋊C4) = C2×C30.Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C30480C30:4(C4:C4)480,617
C30⋊5(C4⋊C4) = C2×Dic15⋊5C4φ: C4⋊C4/C22 → C22 ⊆ Aut C30480C30:5(C4:C4)480,620
C30⋊6(C4⋊C4) = C2×C6.Dic10φ: C4⋊C4/C22 → C22 ⊆ Aut C30480C30:6(C4:C4)480,621
C30⋊7(C4⋊C4) = C2×C30.4Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30:7(C4:C4)480,888
C30⋊8(C4⋊C4) = C2×C60⋊5C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30:8(C4:C4)480,890
C30⋊9(C4⋊C4) = C6×C10.D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30:9(C4:C4)480,716
C30⋊10(C4⋊C4) = C6×C4⋊Dic5φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30:10(C4:C4)480,718
C30⋊11(C4⋊C4) = C10×Dic3⋊C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30:11(C4:C4)480,802
C30⋊12(C4⋊C4) = C10×C4⋊Dic3φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30:12(C4:C4)480,804

Non-split extensions G=N.Q with N=C30 and Q=C4⋊C4
extensionφ:Q→Aut NdρLabelID
C30.1(C4⋊C4) = Dic5.Dic6φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C301208C30.1(C4:C4)480,235
C30.2(C4⋊C4) = Dic5.4Dic6φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C301208C30.2(C4:C4)480,236
C30.3(C4⋊C4) = D10.Dic6φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C302408C30.3(C4:C4)480,237
C30.4(C4⋊C4) = D10.2Dic6φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C302408C30.4(C4:C4)480,238
C30.5(C4⋊C4) = D10.20D12φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C30120C30.5(C4:C4)480,243
C30.6(C4⋊C4) = C30.4M4(2)φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C30480C30.6(C4:C4)480,252
C30.7(C4⋊C4) = Dic15⋊C8φ: C4⋊C4/C2 → C2×C4 ⊆ Aut C30480C30.7(C4:C4)480,253
C30.8(C4⋊C4) = C120⋊C4φ: C4⋊C4/C4 → C4 ⊆ Aut C301204C30.8(C4:C4)480,298
C30.9(C4⋊C4) = D5.D24φ: C4⋊C4/C4 → C4 ⊆ Aut C301204C30.9(C4:C4)480,299
C30.10(C4⋊C4) = C40.Dic3φ: C4⋊C4/C4 → C4 ⊆ Aut C302404C30.10(C4:C4)480,300
C30.11(C4⋊C4) = C24.1F5φ: C4⋊C4/C4 → C4 ⊆ Aut C302404C30.11(C4:C4)480,301
C30.12(C4⋊C4) = C60⋊C8φ: C4⋊C4/C4 → C4 ⊆ Aut C30480C30.12(C4:C4)480,306
C30.13(C4⋊C4) = Dic5.13D12φ: C4⋊C4/C4 → C4 ⊆ Aut C30480C30.13(C4:C4)480,309
C30.14(C4⋊C4) = D10.10D12φ: C4⋊C4/C4 → C4 ⊆ Aut C30120C30.14(C4:C4)480,311
C30.15(C4⋊C4) = C3×C40⋊C4φ: C4⋊C4/C4 → C4 ⊆ Aut C301204C30.15(C4:C4)480,273
C30.16(C4⋊C4) = C3×D5.D8φ: C4⋊C4/C4 → C4 ⊆ Aut C301204C30.16(C4:C4)480,274
C30.17(C4⋊C4) = C3×C40.C4φ: C4⋊C4/C4 → C4 ⊆ Aut C302404C30.17(C4:C4)480,275
C30.18(C4⋊C4) = C3×D10.Q8φ: C4⋊C4/C4 → C4 ⊆ Aut C302404C30.18(C4:C4)480,276
C30.19(C4⋊C4) = C3×C20⋊C8φ: C4⋊C4/C4 → C4 ⊆ Aut C30480C30.19(C4:C4)480,281
C30.20(C4⋊C4) = C3×Dic5⋊C8φ: C4⋊C4/C4 → C4 ⊆ Aut C30480C30.20(C4:C4)480,284
C30.21(C4⋊C4) = C3×D10.3Q8φ: C4⋊C4/C4 → C4 ⊆ Aut C30120C30.21(C4:C4)480,286
C30.22(C4⋊C4) = C60.13Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C30480C30.22(C4:C4)480,58
C30.23(C4⋊C4) = C60.14Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C30480C30.23(C4:C4)480,59
C30.24(C4⋊C4) = C60.15Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C30480C30.24(C4:C4)480,60
C30.25(C4⋊C4) = C60.7Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C30480C30.25(C4:C4)480,61
C30.26(C4⋊C4) = C30.SD16φ: C4⋊C4/C22 → C22 ⊆ Aut C30480C30.26(C4:C4)480,62
C30.27(C4⋊C4) = C60.Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C30480C30.27(C4:C4)480,63
C30.28(C4⋊C4) = C60.8Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C30480C30.28(C4:C4)480,64
C30.29(C4⋊C4) = C30.20D8φ: C4⋊C4/C22 → C22 ⊆ Aut C30480C30.29(C4:C4)480,65
C30.30(C4⋊C4) = C60.5Q8φ: C4⋊C4/C22 → C22 ⊆ Aut C30480C30.30(C4:C4)480,66
C30.31(C4⋊C4) = C60.105D4φ: C4⋊C4/C22 → C22 ⊆ Aut C302404C30.31(C4:C4)480,67
C30.32(C4⋊C4) = C60.D4φ: C4⋊C4/C22 → C22 ⊆ Aut C302404C30.32(C4:C4)480,68
C30.33(C4⋊C4) = C12.59D20φ: C4⋊C4/C22 → C22 ⊆ Aut C302404C30.33(C4:C4)480,69
C30.34(C4⋊C4) = C30.24C42φ: C4⋊C4/C22 → C22 ⊆ Aut C30480C30.34(C4:C4)480,70
C30.35(C4⋊C4) = C60⋊5C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.35(C4:C4)480,164
C30.36(C4⋊C4) = C60.1Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.36(C4:C4)480,167
C30.37(C4⋊C4) = C60.2Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.37(C4:C4)480,168
C30.38(C4⋊C4) = C60.26Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.38(C4:C4)480,174
C30.39(C4⋊C4) = C120⋊10C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.39(C4:C4)480,177
C30.40(C4⋊C4) = C120⋊9C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.40(C4:C4)480,178
C30.41(C4⋊C4) = C4.18D60φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C302402C30.41(C4:C4)480,179
C30.42(C4⋊C4) = C60.210D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C302404C30.42(C4:C4)480,182
C30.43(C4⋊C4) = C30.29C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.43(C4:C4)480,191
C30.44(C4⋊C4) = C3×C20⋊3C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.44(C4:C4)480,82
C30.45(C4⋊C4) = C3×C10.D8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.45(C4:C4)480,85
C30.46(C4⋊C4) = C3×C20.Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.46(C4:C4)480,86
C30.47(C4⋊C4) = C3×C20.8Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.47(C4:C4)480,92
C30.48(C4⋊C4) = C3×C40⋊6C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.48(C4:C4)480,95
C30.49(C4⋊C4) = C3×C40⋊5C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.49(C4:C4)480,96
C30.50(C4⋊C4) = C3×C40.6C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C302402C30.50(C4:C4)480,97
C30.51(C4⋊C4) = C3×C20.53D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C302404C30.51(C4:C4)480,100
C30.52(C4⋊C4) = C3×C10.10C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.52(C4:C4)480,109
C30.53(C4⋊C4) = C5×C12⋊C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.53(C4:C4)480,123
C30.54(C4⋊C4) = C5×C6.Q16φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.54(C4:C4)480,126
C30.55(C4⋊C4) = C5×C12.Q8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.55(C4:C4)480,127
C30.56(C4⋊C4) = C5×Dic3⋊C8φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.56(C4:C4)480,133
C30.57(C4⋊C4) = C5×C8⋊Dic3φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.57(C4:C4)480,136
C30.58(C4⋊C4) = C5×C24⋊1C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.58(C4:C4)480,137
C30.59(C4⋊C4) = C5×C24.C4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C302402C30.59(C4:C4)480,138
C30.60(C4⋊C4) = C5×C12.53D4φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C302404C30.60(C4:C4)480,141
C30.61(C4⋊C4) = C5×C6.C42φ: C4⋊C4/C2×C4 → C2 ⊆ Aut C30480C30.61(C4:C4)480,150
C30.62(C4⋊C4) = C15×C2.C42central extension (φ=1)480C30.62(C4:C4)480,198
C30.63(C4⋊C4) = C15×C4⋊C8central extension (φ=1)480C30.63(C4:C4)480,208
C30.64(C4⋊C4) = C15×C4.Q8central extension (φ=1)480C30.64(C4:C4)480,209
C30.65(C4⋊C4) = C15×C2.D8central extension (φ=1)480C30.65(C4:C4)480,210
C30.66(C4⋊C4) = C15×C8.C4central extension (φ=1)2402C30.66(C4:C4)480,211

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