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Extensions 1→N→G→Q→1 with N=C30 and Q=C2×C8

Direct product G=N×Q with N=C30 and Q=C2×C8
dρLabelID
C22×C120480C2^2xC120480,934

Semidirect products G=N:Q with N=C30 and Q=C2×C8
extensionφ:Q→Aut NdρLabelID
C30⋊1(C2×C8) = C2×S3×C5⋊C8φ: C2×C8/C2 → C2×C4 ⊆ Aut C30240C30:1(C2xC8)480,1002
C30⋊2(C2×C8) = C2×D15⋊C8φ: C2×C8/C2 → C2×C4 ⊆ Aut C30240C30:2(C2xC8)480,1006
C30⋊3(C2×C8) = C2×C60.C4φ: C2×C8/C4 → C4 ⊆ Aut C30240C30:3(C2xC8)480,1060
C30⋊4(C2×C8) = C6×D5⋊C8φ: C2×C8/C4 → C4 ⊆ Aut C30240C30:4(C2xC8)480,1047
C30⋊5(C2×C8) = C2×D5×C3⋊C8φ: C2×C8/C4 → C22 ⊆ Aut C30240C30:5(C2xC8)480,357
C30⋊6(C2×C8) = C2×S3×C5⋊2C8φ: C2×C8/C4 → C22 ⊆ Aut C30240C30:6(C2xC8)480,361
C30⋊7(C2×C8) = C2×D15⋊2C8φ: C2×C8/C4 → C22 ⊆ Aut C30240C30:7(C2xC8)480,365
C30⋊8(C2×C8) = C22×C15⋊C8φ: C2×C8/C22 → C4 ⊆ Aut C30480C30:8(C2xC8)480,1070
C30⋊9(C2×C8) = C2×C6×C5⋊C8φ: C2×C8/C22 → C4 ⊆ Aut C30480C30:9(C2xC8)480,1057
C30⋊10(C2×C8) = C2×C8×D15φ: C2×C8/C8 → C2 ⊆ Aut C30240C30:10(C2xC8)480,864
C30⋊11(C2×C8) = D5×C2×C24φ: C2×C8/C8 → C2 ⊆ Aut C30240C30:11(C2xC8)480,692
C30⋊12(C2×C8) = S3×C2×C40φ: C2×C8/C8 → C2 ⊆ Aut C30240C30:12(C2xC8)480,778
C30⋊13(C2×C8) = C22×C15⋊3C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C30480C30:13(C2xC8)480,885
C30⋊14(C2×C8) = C2×C6×C5⋊2C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C30480C30:14(C2xC8)480,713
C30⋊15(C2×C8) = C2×C10×C3⋊C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C30480C30:15(C2xC8)480,799

Non-split extensions G=N.Q with N=C30 and Q=C2×C8
extensionφ:Q→Aut NdρLabelID
C30.1(C2×C8) = S3×C5⋊C16φ: C2×C8/C2 → C2×C4 ⊆ Aut C302408C30.1(C2xC8)480,239
C30.2(C2×C8) = D15⋊C16φ: C2×C8/C2 → C2×C4 ⊆ Aut C302408C30.2(C2xC8)480,240
C30.3(C2×C8) = C15⋊M5(2)φ: C2×C8/C2 → C2×C4 ⊆ Aut C302408C30.3(C2xC8)480,241
C30.4(C2×C8) = D30.C8φ: C2×C8/C2 → C2×C4 ⊆ Aut C302408C30.4(C2xC8)480,242
C30.5(C2×C8) = Dic3×C5⋊C8φ: C2×C8/C2 → C2×C4 ⊆ Aut C30480C30.5(C2xC8)480,244
C30.6(C2×C8) = Dic5.22D12φ: C2×C8/C2 → C2×C4 ⊆ Aut C30240C30.6(C2xC8)480,246
C30.7(C2×C8) = D30⋊C8φ: C2×C8/C2 → C2×C4 ⊆ Aut C30240C30.7(C2xC8)480,247
C30.8(C2×C8) = C30.4M4(2)φ: C2×C8/C2 → C2×C4 ⊆ Aut C30480C30.8(C2xC8)480,252
C30.9(C2×C8) = Dic15⋊C8φ: C2×C8/C2 → C2×C4 ⊆ Aut C30480C30.9(C2xC8)480,253
C30.10(C2×C8) = C24.F5φ: C2×C8/C4 → C4 ⊆ Aut C302404C30.10(C2xC8)480,294
C30.11(C2×C8) = C120.C4φ: C2×C8/C4 → C4 ⊆ Aut C302404C30.11(C2xC8)480,295
C30.12(C2×C8) = C30.7M4(2)φ: C2×C8/C4 → C4 ⊆ Aut C30240C30.12(C2xC8)480,308
C30.13(C2×C8) = Dic5.13D12φ: C2×C8/C4 → C4 ⊆ Aut C30480C30.13(C2xC8)480,309
C30.14(C2×C8) = C3×D5⋊C16φ: C2×C8/C4 → C4 ⊆ Aut C302404C30.14(C2xC8)480,269
C30.15(C2×C8) = C3×C8.F5φ: C2×C8/C4 → C4 ⊆ Aut C302404C30.15(C2xC8)480,270
C30.16(C2×C8) = C12×C5⋊C8φ: C2×C8/C4 → C4 ⊆ Aut C30480C30.16(C2xC8)480,280
C30.17(C2×C8) = C3×D10⋊C8φ: C2×C8/C4 → C4 ⊆ Aut C30240C30.17(C2xC8)480,283
C30.18(C2×C8) = C3×Dic5⋊C8φ: C2×C8/C4 → C4 ⊆ Aut C30480C30.18(C2xC8)480,284
C30.19(C2×C8) = D5×C3⋊C16φ: C2×C8/C4 → C22 ⊆ Aut C302404C30.19(C2xC8)480,7
C30.20(C2×C8) = S3×C5⋊2C16φ: C2×C8/C4 → C22 ⊆ Aut C302404C30.20(C2xC8)480,8
C30.21(C2×C8) = D15⋊2C16φ: C2×C8/C4 → C22 ⊆ Aut C302404C30.21(C2xC8)480,9
C30.22(C2×C8) = C40.51D6φ: C2×C8/C4 → C22 ⊆ Aut C302404C30.22(C2xC8)480,10
C30.23(C2×C8) = C40.52D6φ: C2×C8/C4 → C22 ⊆ Aut C302404C30.23(C2xC8)480,11
C30.24(C2×C8) = D30.5C8φ: C2×C8/C4 → C22 ⊆ Aut C302404C30.24(C2xC8)480,12
C30.25(C2×C8) = Dic5×C3⋊C8φ: C2×C8/C4 → C22 ⊆ Aut C30480C30.25(C2xC8)480,25
C30.26(C2×C8) = Dic3×C5⋊2C8φ: C2×C8/C4 → C22 ⊆ Aut C30480C30.26(C2xC8)480,26
C30.27(C2×C8) = Dic15⋊4C8φ: C2×C8/C4 → C22 ⊆ Aut C30480C30.27(C2xC8)480,27
C30.28(C2×C8) = C60.93D4φ: C2×C8/C4 → C22 ⊆ Aut C30240C30.28(C2xC8)480,31
C30.29(C2×C8) = C60.94D4φ: C2×C8/C4 → C22 ⊆ Aut C30240C30.29(C2xC8)480,32
C30.30(C2×C8) = D30⋊4C8φ: C2×C8/C4 → C22 ⊆ Aut C30240C30.30(C2xC8)480,33
C30.31(C2×C8) = C60.13Q8φ: C2×C8/C4 → C22 ⊆ Aut C30480C30.31(C2xC8)480,58
C30.32(C2×C8) = C60.14Q8φ: C2×C8/C4 → C22 ⊆ Aut C30480C30.32(C2xC8)480,59
C30.33(C2×C8) = C60.15Q8φ: C2×C8/C4 → C22 ⊆ Aut C30480C30.33(C2xC8)480,60
C30.34(C2×C8) = C2×C15⋊C16φ: C2×C8/C22 → C4 ⊆ Aut C30480C30.34(C2xC8)480,302
C30.35(C2×C8) = C60.C8φ: C2×C8/C22 → C4 ⊆ Aut C302404C30.35(C2xC8)480,303
C30.36(C2×C8) = C4×C15⋊C8φ: C2×C8/C22 → C4 ⊆ Aut C30480C30.36(C2xC8)480,305
C30.37(C2×C8) = C60⋊C8φ: C2×C8/C22 → C4 ⊆ Aut C30480C30.37(C2xC8)480,306
C30.38(C2×C8) = C30.22M4(2)φ: C2×C8/C22 → C4 ⊆ Aut C30240C30.38(C2xC8)480,317
C30.39(C2×C8) = C6×C5⋊C16φ: C2×C8/C22 → C4 ⊆ Aut C30480C30.39(C2xC8)480,277
C30.40(C2×C8) = C3×C20.C8φ: C2×C8/C22 → C4 ⊆ Aut C302404C30.40(C2xC8)480,278
C30.41(C2×C8) = C3×C20⋊C8φ: C2×C8/C22 → C4 ⊆ Aut C30480C30.41(C2xC8)480,281
C30.42(C2×C8) = C3×C23.2F5φ: C2×C8/C22 → C4 ⊆ Aut C30240C30.42(C2xC8)480,292
C30.43(C2×C8) = C16×D15φ: C2×C8/C8 → C2 ⊆ Aut C302402C30.43(C2xC8)480,157
C30.44(C2×C8) = C80⋊S3φ: C2×C8/C8 → C2 ⊆ Aut C302402C30.44(C2xC8)480,158
C30.45(C2×C8) = C8×Dic15φ: C2×C8/C8 → C2 ⊆ Aut C30480C30.45(C2xC8)480,173
C30.46(C2×C8) = C60.26Q8φ: C2×C8/C8 → C2 ⊆ Aut C30480C30.46(C2xC8)480,174
C30.47(C2×C8) = D30⋊3C8φ: C2×C8/C8 → C2 ⊆ Aut C30240C30.47(C2xC8)480,180
C30.48(C2×C8) = D5×C48φ: C2×C8/C8 → C2 ⊆ Aut C302402C30.48(C2xC8)480,75
C30.49(C2×C8) = C3×C80⋊C2φ: C2×C8/C8 → C2 ⊆ Aut C302402C30.49(C2xC8)480,76
C30.50(C2×C8) = Dic5×C24φ: C2×C8/C8 → C2 ⊆ Aut C30480C30.50(C2xC8)480,91
C30.51(C2×C8) = C3×C20.8Q8φ: C2×C8/C8 → C2 ⊆ Aut C30480C30.51(C2xC8)480,92
C30.52(C2×C8) = C3×D10⋊1C8φ: C2×C8/C8 → C2 ⊆ Aut C30240C30.52(C2xC8)480,98
C30.53(C2×C8) = S3×C80φ: C2×C8/C8 → C2 ⊆ Aut C302402C30.53(C2xC8)480,116
C30.54(C2×C8) = C5×D6.C8φ: C2×C8/C8 → C2 ⊆ Aut C302402C30.54(C2xC8)480,117
C30.55(C2×C8) = Dic3×C40φ: C2×C8/C8 → C2 ⊆ Aut C30480C30.55(C2xC8)480,132
C30.56(C2×C8) = C5×Dic3⋊C8φ: C2×C8/C8 → C2 ⊆ Aut C30480C30.56(C2xC8)480,133
C30.57(C2×C8) = C5×D6⋊C8φ: C2×C8/C8 → C2 ⊆ Aut C30240C30.57(C2xC8)480,139
C30.58(C2×C8) = C4×C15⋊3C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C30480C30.58(C2xC8)480,162
C30.59(C2×C8) = C60⋊5C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C30480C30.59(C2xC8)480,164
C30.60(C2×C8) = C2×C15⋊3C16φ: C2×C8/C2×C4 → C2 ⊆ Aut C30480C30.60(C2xC8)480,171
C30.61(C2×C8) = C60.7C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C302402C30.61(C2xC8)480,172
C30.62(C2×C8) = C60.212D4φ: C2×C8/C2×C4 → C2 ⊆ Aut C30240C30.62(C2xC8)480,190
C30.63(C2×C8) = C12×C5⋊2C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C30480C30.63(C2xC8)480,80
C30.64(C2×C8) = C3×C20⋊3C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C30480C30.64(C2xC8)480,82
C30.65(C2×C8) = C6×C5⋊2C16φ: C2×C8/C2×C4 → C2 ⊆ Aut C30480C30.65(C2xC8)480,89
C30.66(C2×C8) = C3×C20.4C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C302402C30.66(C2xC8)480,90
C30.67(C2×C8) = C3×C20.55D4φ: C2×C8/C2×C4 → C2 ⊆ Aut C30240C30.67(C2xC8)480,108
C30.68(C2×C8) = C20×C3⋊C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C30480C30.68(C2xC8)480,121
C30.69(C2×C8) = C5×C12⋊C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C30480C30.69(C2xC8)480,123
C30.70(C2×C8) = C10×C3⋊C16φ: C2×C8/C2×C4 → C2 ⊆ Aut C30480C30.70(C2xC8)480,130
C30.71(C2×C8) = C5×C12.C8φ: C2×C8/C2×C4 → C2 ⊆ Aut C302402C30.71(C2xC8)480,131
C30.72(C2×C8) = C5×C12.55D4φ: C2×C8/C2×C4 → C2 ⊆ Aut C30240C30.72(C2xC8)480,149
C30.73(C2×C8) = C15×C22⋊C8central extension (φ=1)240C30.73(C2xC8)480,201
C30.74(C2×C8) = C15×C4⋊C8central extension (φ=1)480C30.74(C2xC8)480,208
C30.75(C2×C8) = C15×M5(2)central extension (φ=1)2402C30.75(C2xC8)480,213

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