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Extensions 1→N→G→Q→1 with N=C60 and Q=C2×C4

Direct product G=N×Q with N=C60 and Q=C2×C4
dρLabelID
C2×C4×C60480C2xC4xC60480,919

Semidirect products G=N:Q with N=C60 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C60⋊1(C2×C4) = D60⋊3C4φ: C2×C4/C1 → C2×C4 ⊆ Aut C60608+C60:1(C2xC4)480,997
C60⋊2(C2×C4) = F5×D12φ: C2×C4/C1 → C2×C4 ⊆ Aut C60608+C60:2(C2xC4)480,995
C60⋊3(C2×C4) = S3×C4⋊F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C60608C60:3(C2xC4)480,996
C60⋊4(C2×C4) = C4×S3×F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C60608C60:4(C2xC4)480,994
C60⋊5(C2×C4) = D4×C3⋊F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C60608C60:5(C2xC4)480,1067
C60⋊6(C2×C4) = C3×D4×F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C60608C60:6(C2xC4)480,1054
C60⋊7(C2×C4) = C2×C60⋊C4φ: C2×C4/C2 → C4 ⊆ Aut C60120C60:7(C2xC4)480,1064
C60⋊8(C2×C4) = C2×C4×C3⋊F5φ: C2×C4/C2 → C4 ⊆ Aut C60120C60:8(C2xC4)480,1063
C60⋊9(C2×C4) = C6×C4⋊F5φ: C2×C4/C2 → C4 ⊆ Aut C60120C60:9(C2xC4)480,1051
C60⋊10(C2×C4) = F5×C2×C12φ: C2×C4/C2 → C4 ⊆ Aut C60120C60:10(C2xC4)480,1050
C60⋊11(C2×C4) = C4⋊C4×D15φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:11(C2xC4)480,856
C60⋊12(C2×C4) = D60⋊11C4φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:12(C2xC4)480,858
C60⋊13(C2×C4) = D4×Dic15φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:13(C2xC4)480,899
C60⋊14(C2×C4) = Dic3×D20φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:14(C2xC4)480,501
C60⋊15(C2×C4) = S3×C4⋊Dic5φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:15(C2xC4)480,502
C60⋊16(C2×C4) = D60⋊14C4φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:16(C2xC4)480,504
C60⋊17(C2×C4) = D5×C4⋊Dic3φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:17(C2xC4)480,488
C60⋊18(C2×C4) = Dic5×D12φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:18(C2xC4)480,491
C60⋊19(C2×C4) = D60⋊17C4φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:19(C2xC4)480,494
C60⋊20(C2×C4) = D20⋊8Dic3φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:20(C2xC4)480,510
C60⋊21(C2×C4) = Dic15⋊8D4φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:21(C2xC4)480,511
C60⋊22(C2×C4) = D30.2Q8φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:22(C2xC4)480,513
C60⋊23(C2×C4) = C4×D5×Dic3φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:23(C2xC4)480,467
C60⋊24(C2×C4) = C4×S3×Dic5φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:24(C2xC4)480,473
C60⋊25(C2×C4) = C4×D30.C2φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:25(C2xC4)480,477
C60⋊26(C2×C4) = C3×D5×C4⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:26(C2xC4)480,684
C60⋊27(C2×C4) = C3×D20⋊8C4φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:27(C2xC4)480,686
C60⋊28(C2×C4) = C3×D4×Dic5φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:28(C2xC4)480,727
C60⋊29(C2×C4) = C5×S3×C4⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:29(C2xC4)480,770
C60⋊30(C2×C4) = C5×Dic3⋊5D4φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:30(C2xC4)480,772
C60⋊31(C2×C4) = C5×D4×Dic3φ: C2×C4/C2 → C22 ⊆ Aut C60240C60:31(C2xC4)480,813
C60⋊32(C2×C4) = C4×D60φ: C2×C4/C4 → C2 ⊆ Aut C60240C60:32(C2xC4)480,838
C60⋊33(C2×C4) = C42×D15φ: C2×C4/C4 → C2 ⊆ Aut C60240C60:33(C2xC4)480,836
C60⋊34(C2×C4) = C12×D20φ: C2×C4/C4 → C2 ⊆ Aut C60240C60:34(C2xC4)480,666
C60⋊35(C2×C4) = C20×D12φ: C2×C4/C4 → C2 ⊆ Aut C60240C60:35(C2xC4)480,752
C60⋊36(C2×C4) = D5×C4×C12φ: C2×C4/C4 → C2 ⊆ Aut C60240C60:36(C2xC4)480,664
C60⋊37(C2×C4) = S3×C4×C20φ: C2×C4/C4 → C2 ⊆ Aut C60240C60:37(C2xC4)480,750
C60⋊38(C2×C4) = D4×C60φ: C2×C4/C4 → C2 ⊆ Aut C60240C60:38(C2xC4)480,923
C60⋊39(C2×C4) = C2×C60⋊5C4φ: C2×C4/C22 → C2 ⊆ Aut C60480C60:39(C2xC4)480,890
C60⋊40(C2×C4) = C2×C4×Dic15φ: C2×C4/C22 → C2 ⊆ Aut C60480C60:40(C2xC4)480,887
C60⋊41(C2×C4) = C6×C4⋊Dic5φ: C2×C4/C22 → C2 ⊆ Aut C60480C60:41(C2xC4)480,718
C60⋊42(C2×C4) = C10×C4⋊Dic3φ: C2×C4/C22 → C2 ⊆ Aut C60480C60:42(C2xC4)480,804
C60⋊43(C2×C4) = Dic5×C2×C12φ: C2×C4/C22 → C2 ⊆ Aut C60480C60:43(C2xC4)480,715
C60⋊44(C2×C4) = Dic3×C2×C20φ: C2×C4/C22 → C2 ⊆ Aut C60480C60:44(C2xC4)480,801
C60⋊45(C2×C4) = C4⋊C4×C30φ: C2×C4/C22 → C2 ⊆ Aut C60480C60:45(C2xC4)480,921

Non-split extensions G=N.Q with N=C60 and Q=C2×C4
extensionφ:Q→Aut NdρLabelID
C60.1(C2×C4) = D60⋊C4φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208+C60.1(C2xC4)480,227
C60.2(C2×C4) = Dic6⋊F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208-C60.2(C2xC4)480,229
C60.3(C2×C4) = D12⋊4F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208-C60.3(C2xC4)480,231
C60.4(C2×C4) = D60⋊2C4φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208+C60.4(C2xC4)480,233
C60.5(C2×C4) = Dic6⋊5F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208-C60.5(C2xC4)480,984
C60.6(C2×C4) = D12.F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C602408-C60.6(C2xC4)480,989
C60.7(C2×C4) = Dic6.F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C602408+C60.7(C2xC4)480,992
C60.8(C2×C4) = D12⋊F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208+C60.8(C2xC4)480,228
C60.9(C2×C4) = Dic30⋊C4φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208-C60.9(C2xC4)480,230
C60.10(C2×C4) = D12⋊2F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208-C60.10(C2xC4)480,232
C60.11(C2×C4) = D60⋊5C4φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208+C60.11(C2xC4)480,234
C60.12(C2×C4) = F5×Dic6φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208-C60.12(C2xC4)480,982
C60.13(C2×C4) = D12.2F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C602408-C60.13(C2xC4)480,987
C60.14(C2×C4) = D60.C4φ: C2×C4/C1 → C2×C4 ⊆ Aut C602408+C60.14(C2xC4)480,990
C60.15(C2×C4) = Dic5.Dic6φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.15(C2xC4)480,235
C60.16(C2×C4) = Dic5.4Dic6φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.16(C2xC4)480,236
C60.17(C2×C4) = D10.Dic6φ: C2×C4/C1 → C2×C4 ⊆ Aut C602408C60.17(C2xC4)480,237
C60.18(C2×C4) = D10.2Dic6φ: C2×C4/C1 → C2×C4 ⊆ Aut C602408C60.18(C2xC4)480,238
C60.19(C2×C4) = C4⋊F5⋊3S3φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.19(C2xC4)480,983
C60.20(C2×C4) = S3×C4.F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.20(C2xC4)480,988
C60.21(C2×C4) = D15⋊M4(2)φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.21(C2xC4)480,991
C60.22(C2×C4) = F5×C3⋊C8φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.22(C2xC4)480,223
C60.23(C2×C4) = C30.C42φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.23(C2xC4)480,224
C60.24(C2×C4) = C30.3C42φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.24(C2xC4)480,225
C60.25(C2×C4) = C30.4C42φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.25(C2xC4)480,226
C60.26(C2×C4) = S3×C5⋊C16φ: C2×C4/C1 → C2×C4 ⊆ Aut C602408C60.26(C2xC4)480,239
C60.27(C2×C4) = D15⋊C16φ: C2×C4/C1 → C2×C4 ⊆ Aut C602408C60.27(C2xC4)480,240
C60.28(C2×C4) = C15⋊M5(2)φ: C2×C4/C1 → C2×C4 ⊆ Aut C602408C60.28(C2xC4)480,241
C60.29(C2×C4) = D30.C8φ: C2×C4/C1 → C2×C4 ⊆ Aut C602408C60.29(C2xC4)480,242
C60.30(C2×C4) = (C4×S3)⋊F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.30(C2xC4)480,985
C60.31(C2×C4) = S3×D5⋊C8φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.31(C2xC4)480,986
C60.32(C2×C4) = C5⋊C8⋊D6φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.32(C2xC4)480,993
C60.33(C2×C4) = D20⋊Dic3φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.33(C2xC4)480,312
C60.34(C2×C4) = Dic10⋊Dic3φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.34(C2xC4)480,313
C60.35(C2×C4) = Dic10⋊2Dic3φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.35(C2xC4)480,314
C60.36(C2×C4) = D20⋊2Dic3φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.36(C2xC4)480,315
C60.37(C2×C4) = Dic10.Dic3φ: C2×C4/C1 → C2×C4 ⊆ Aut C602408C60.37(C2xC4)480,1066
C60.38(C2×C4) = D20.Dic3φ: C2×C4/C1 → C2×C4 ⊆ Aut C602408C60.38(C2xC4)480,1068
C60.39(C2×C4) = Q8×C3⋊F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.39(C2xC4)480,1069
C60.40(C2×C4) = C3×D20⋊C4φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.40(C2xC4)480,287
C60.41(C2×C4) = C3×D4⋊F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.41(C2xC4)480,288
C60.42(C2×C4) = C3×Q8⋊F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.42(C2xC4)480,289
C60.43(C2×C4) = C3×Q8⋊2F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.43(C2xC4)480,290
C60.44(C2×C4) = C3×D4.F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C602408C60.44(C2xC4)480,1053
C60.45(C2×C4) = C3×Q8.F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C602408C60.45(C2xC4)480,1055
C60.46(C2×C4) = C3×Q8×F5φ: C2×C4/C1 → C2×C4 ⊆ Aut C601208C60.46(C2xC4)480,1056
C60.47(C2×C4) = C120⋊C4φ: C2×C4/C2 → C4 ⊆ Aut C601204C60.47(C2xC4)480,298
C60.48(C2×C4) = D5.D24φ: C2×C4/C2 → C4 ⊆ Aut C601204C60.48(C2xC4)480,299
C60.49(C2×C4) = C40.Dic3φ: C2×C4/C2 → C4 ⊆ Aut C602404C60.49(C2xC4)480,300
C60.50(C2×C4) = C24.1F5φ: C2×C4/C2 → C4 ⊆ Aut C602404C60.50(C2xC4)480,301
C60.51(C2×C4) = C2×C12.F5φ: C2×C4/C2 → C4 ⊆ Aut C60240C60.51(C2xC4)480,1061
C60.52(C2×C4) = C24.F5φ: C2×C4/C2 → C4 ⊆ Aut C602404C60.52(C2xC4)480,294
C60.53(C2×C4) = C120.C4φ: C2×C4/C2 → C4 ⊆ Aut C602404C60.53(C2xC4)480,295
C60.54(C2×C4) = C8×C3⋊F5φ: C2×C4/C2 → C4 ⊆ Aut C601204C60.54(C2xC4)480,296
C60.55(C2×C4) = C24⋊F5φ: C2×C4/C2 → C4 ⊆ Aut C601204C60.55(C2xC4)480,297
C60.56(C2×C4) = C2×C15⋊C16φ: C2×C4/C2 → C4 ⊆ Aut C60480C60.56(C2xC4)480,302
C60.57(C2×C4) = C60.C8φ: C2×C4/C2 → C4 ⊆ Aut C602404C60.57(C2xC4)480,303
C60.58(C2×C4) = C2×C60.C4φ: C2×C4/C2 → C4 ⊆ Aut C60240C60.58(C2xC4)480,1060
C60.59(C2×C4) = C60.59(C2×C4)φ: C2×C4/C2 → C4 ⊆ Aut C601204C60.59(C2xC4)480,1062
C60.60(C2×C4) = (C2×C12)⋊6F5φ: C2×C4/C2 → C4 ⊆ Aut C601204C60.60(C2xC4)480,1065
C60.61(C2×C4) = C3×C40⋊C4φ: C2×C4/C2 → C4 ⊆ Aut C601204C60.61(C2xC4)480,273
C60.62(C2×C4) = C3×D5.D8φ: C2×C4/C2 → C4 ⊆ Aut C601204C60.62(C2xC4)480,274
C60.63(C2×C4) = C3×C40.C4φ: C2×C4/C2 → C4 ⊆ Aut C602404C60.63(C2xC4)480,275
C60.64(C2×C4) = C3×D10.Q8φ: C2×C4/C2 → C4 ⊆ Aut C602404C60.64(C2xC4)480,276
C60.65(C2×C4) = C6×C4.F5φ: C2×C4/C2 → C4 ⊆ Aut C60240C60.65(C2xC4)480,1048
C60.66(C2×C4) = C3×D5⋊C16φ: C2×C4/C2 → C4 ⊆ Aut C602404C60.66(C2xC4)480,269
C60.67(C2×C4) = C3×C8.F5φ: C2×C4/C2 → C4 ⊆ Aut C602404C60.67(C2xC4)480,270
C60.68(C2×C4) = F5×C24φ: C2×C4/C2 → C4 ⊆ Aut C601204C60.68(C2xC4)480,271
C60.69(C2×C4) = C3×C8⋊F5φ: C2×C4/C2 → C4 ⊆ Aut C601204C60.69(C2xC4)480,272
C60.70(C2×C4) = C6×C5⋊C16φ: C2×C4/C2 → C4 ⊆ Aut C60480C60.70(C2xC4)480,277
C60.71(C2×C4) = C3×C20.C8φ: C2×C4/C2 → C4 ⊆ Aut C602404C60.71(C2xC4)480,278
C60.72(C2×C4) = C6×D5⋊C8φ: C2×C4/C2 → C4 ⊆ Aut C60240C60.72(C2xC4)480,1047
C60.73(C2×C4) = C3×D5⋊M4(2)φ: C2×C4/C2 → C4 ⊆ Aut C601204C60.73(C2xC4)480,1049
C60.74(C2×C4) = C3×D10.C23φ: C2×C4/C2 → C4 ⊆ Aut C601204C60.74(C2xC4)480,1052
C60.75(C2×C4) = C60.1Q8φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.75(C2xC4)480,167
C60.76(C2×C4) = C60.2Q8φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.76(C2xC4)480,168
C60.77(C2×C4) = D60⋊9C4φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.77(C2xC4)480,169
C60.78(C2×C4) = Dic30⋊9C4φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.78(C2xC4)480,170
C60.79(C2×C4) = C60.210D4φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.79(C2xC4)480,182
C60.80(C2×C4) = D60⋊10C4φ: C2×C4/C2 → C22 ⊆ Aut C601204C60.80(C2xC4)480,185
C60.81(C2×C4) = D4⋊Dic15φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.81(C2xC4)480,192
C60.82(C2×C4) = Q8⋊2Dic15φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.82(C2xC4)480,195
C60.83(C2×C4) = Q8⋊3Dic15φ: C2×C4/C2 → C22 ⊆ Aut C601204C60.83(C2xC4)480,197
C60.84(C2×C4) = Dic15⋊10Q8φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.84(C2xC4)480,852
C60.85(C2×C4) = C4⋊C4⋊7D15φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.85(C2xC4)480,857
C60.86(C2×C4) = M4(2)×D15φ: C2×C4/C2 → C22 ⊆ Aut C601204C60.86(C2xC4)480,871
C60.87(C2×C4) = D60.3C4φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.87(C2xC4)480,872
C60.88(C2×C4) = Q8×Dic15φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.88(C2xC4)480,910
C60.89(C2×C4) = D4.Dic15φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.89(C2xC4)480,913
C60.90(C2×C4) = C6.D40φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.90(C2xC4)480,41
C60.91(C2×C4) = D60⋊12C4φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.91(C2xC4)480,44
C60.92(C2×C4) = C6.Dic20φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.92(C2xC4)480,47
C60.93(C2×C4) = Dic30⋊12C4φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.93(C2xC4)480,50
C60.94(C2×C4) = C60.97D4φ: C2×C4/C2 → C22 ⊆ Aut C601204C60.94(C2xC4)480,53
C60.95(C2×C4) = D60⋊13C4φ: C2×C4/C2 → C22 ⊆ Aut C601204C60.95(C2xC4)480,56
C60.96(C2×C4) = C60.Q8φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.96(C2xC4)480,63
C60.97(C2×C4) = C60.5Q8φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.97(C2xC4)480,66
C60.98(C2×C4) = C12.59D20φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.98(C2xC4)480,69
C60.99(C2×C4) = D20.3Dic3φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.99(C2xC4)480,359
C60.100(C2×C4) = S3×C4.Dic5φ: C2×C4/C2 → C22 ⊆ Aut C601204C60.100(C2xC4)480,363
C60.101(C2×C4) = D60.4C4φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.101(C2xC4)480,367
C60.102(C2×C4) = Dic3×Dic10φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.102(C2xC4)480,406
C60.103(C2×C4) = (S3×C20)⋊5C4φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.103(C2xC4)480,414
C60.104(C2×C4) = Dic30⋊14C4φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.104(C2xC4)480,416
C60.105(C2×C4) = C10.D24φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.105(C2xC4)480,43
C60.106(C2×C4) = D60⋊15C4φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.106(C2xC4)480,45
C60.107(C2×C4) = C10.Dic12φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.107(C2xC4)480,49
C60.108(C2×C4) = Dic30⋊15C4φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.108(C2xC4)480,51
C60.109(C2×C4) = C60.99D4φ: C2×C4/C2 → C22 ⊆ Aut C601204C60.109(C2xC4)480,55
C60.110(C2×C4) = D60⋊16C4φ: C2×C4/C2 → C22 ⊆ Aut C601204C60.110(C2xC4)480,57
C60.111(C2×C4) = C60.7Q8φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.111(C2xC4)480,61
C60.112(C2×C4) = C60.8Q8φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.112(C2xC4)480,64
C60.113(C2×C4) = C60.105D4φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.113(C2xC4)480,67
C60.114(C2×C4) = D5×C4.Dic3φ: C2×C4/C2 → C22 ⊆ Aut C601204C60.114(C2xC4)480,358
C60.115(C2×C4) = D12.2Dic5φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.115(C2xC4)480,362
C60.116(C2×C4) = D60.5C4φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.116(C2xC4)480,366
C60.117(C2×C4) = Dic5×Dic6φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.117(C2xC4)480,408
C60.118(C2×C4) = Dic30⋊17C4φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.118(C2xC4)480,409
C60.119(C2×C4) = (C4×D5)⋊Dic3φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.119(C2xC4)480,434
C60.120(C2×C4) = C30.D8φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.120(C2xC4)480,40
C60.121(C2×C4) = D12⋊Dic5φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.121(C2xC4)480,42
C60.122(C2×C4) = C30.Q16φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.122(C2xC4)480,46
C60.123(C2×C4) = Dic6⋊Dic5φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.123(C2xC4)480,48
C60.124(C2×C4) = C60.96D4φ: C2×C4/C2 → C22 ⊆ Aut C601204C60.124(C2xC4)480,52
C60.125(C2×C4) = C60.98D4φ: C2×C4/C2 → C22 ⊆ Aut C601204C60.125(C2xC4)480,54
C60.126(C2×C4) = C30.SD16φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.126(C2xC4)480,62
C60.127(C2×C4) = C30.20D8φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.127(C2xC4)480,65
C60.128(C2×C4) = C60.D4φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.128(C2xC4)480,68
C60.129(C2×C4) = D20.2Dic3φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.129(C2xC4)480,360
C60.130(C2×C4) = D12.Dic5φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.130(C2xC4)480,364
C60.131(C2×C4) = D15⋊4M4(2)φ: C2×C4/C2 → C22 ⊆ Aut C601204C60.131(C2xC4)480,368
C60.132(C2×C4) = Dic15⋊6Q8φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.132(C2xC4)480,407
C60.133(C2×C4) = Dic15⋊7Q8φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.133(C2xC4)480,420
C60.134(C2×C4) = (C4×D15)⋊8C4φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.134(C2xC4)480,423
C60.135(C2×C4) = D5×C3⋊C16φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.135(C2xC4)480,7
C60.136(C2×C4) = S3×C5⋊2C16φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.136(C2xC4)480,8
C60.137(C2×C4) = D15⋊2C16φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.137(C2xC4)480,9
C60.138(C2×C4) = C40.51D6φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.138(C2xC4)480,10
C60.139(C2×C4) = C40.52D6φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.139(C2xC4)480,11
C60.140(C2×C4) = D30.5C8φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.140(C2xC4)480,12
C60.141(C2×C4) = Dic5×C3⋊C8φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.141(C2xC4)480,25
C60.142(C2×C4) = Dic3×C5⋊2C8φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.142(C2xC4)480,26
C60.143(C2×C4) = Dic15⋊4C8φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.143(C2xC4)480,27
C60.144(C2×C4) = C30.21C42φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.144(C2xC4)480,28
C60.145(C2×C4) = C30.22C42φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.145(C2xC4)480,29
C60.146(C2×C4) = C30.23C42φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.146(C2xC4)480,30
C60.147(C2×C4) = C2×D5×C3⋊C8φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.147(C2xC4)480,357
C60.148(C2×C4) = C2×S3×C5⋊2C8φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.148(C2xC4)480,361
C60.149(C2×C4) = C2×D15⋊2C8φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.149(C2xC4)480,365
C60.150(C2×C4) = C2×C20.32D6φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.150(C2xC4)480,369
C60.151(C2×C4) = C2×D6.Dic5φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.151(C2xC4)480,370
C60.152(C2×C4) = C2×D30.5C4φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.152(C2xC4)480,371
C60.153(C2×C4) = (D5×C12)⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.153(C2xC4)480,433
C60.154(C2×C4) = (S3×C20)⋊7C4φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.154(C2xC4)480,447
C60.155(C2×C4) = (C4×D15)⋊10C4φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.155(C2xC4)480,462
C60.156(C2×C4) = C3×C10.D8φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.156(C2xC4)480,85
C60.157(C2×C4) = C3×C20.Q8φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.157(C2xC4)480,86
C60.158(C2×C4) = C3×D20⋊6C4φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.158(C2xC4)480,87
C60.159(C2×C4) = C3×C10.Q16φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.159(C2xC4)480,88
C60.160(C2×C4) = C3×C20.53D4φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.160(C2xC4)480,100
C60.161(C2×C4) = C3×D20⋊7C4φ: C2×C4/C2 → C22 ⊆ Aut C601204C60.161(C2xC4)480,103
C60.162(C2×C4) = C3×D4⋊Dic5φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.162(C2xC4)480,110
C60.163(C2×C4) = C3×Q8⋊Dic5φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.163(C2xC4)480,113
C60.164(C2×C4) = C3×D4⋊2Dic5φ: C2×C4/C2 → C22 ⊆ Aut C601204C60.164(C2xC4)480,115
C60.165(C2×C4) = C3×Dic5⋊3Q8φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.165(C2xC4)480,680
C60.166(C2×C4) = C3×C4⋊C4⋊7D5φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.166(C2xC4)480,685
C60.167(C2×C4) = C3×D5×M4(2)φ: C2×C4/C2 → C22 ⊆ Aut C601204C60.167(C2xC4)480,699
C60.168(C2×C4) = C3×D20.2C4φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.168(C2xC4)480,700
C60.169(C2×C4) = C3×Q8×Dic5φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.169(C2xC4)480,738
C60.170(C2×C4) = C3×D4.Dic5φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.170(C2xC4)480,741
C60.171(C2×C4) = C5×C6.Q16φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.171(C2xC4)480,126
C60.172(C2×C4) = C5×C12.Q8φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.172(C2xC4)480,127
C60.173(C2×C4) = C5×C6.D8φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.173(C2xC4)480,128
C60.174(C2×C4) = C5×C6.SD16φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.174(C2xC4)480,129
C60.175(C2×C4) = C5×C12.53D4φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.175(C2xC4)480,141
C60.176(C2×C4) = C5×D12⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C601204C60.176(C2xC4)480,144
C60.177(C2×C4) = C5×D4⋊Dic3φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.177(C2xC4)480,151
C60.178(C2×C4) = C5×Q8⋊2Dic3φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.178(C2xC4)480,154
C60.179(C2×C4) = C5×Q8⋊3Dic3φ: C2×C4/C2 → C22 ⊆ Aut C601204C60.179(C2xC4)480,156
C60.180(C2×C4) = C5×Dic6⋊C4φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.180(C2xC4)480,766
C60.181(C2×C4) = C5×C4⋊C4⋊7S3φ: C2×C4/C2 → C22 ⊆ Aut C60240C60.181(C2xC4)480,771
C60.182(C2×C4) = C5×S3×M4(2)φ: C2×C4/C2 → C22 ⊆ Aut C601204C60.182(C2xC4)480,785
C60.183(C2×C4) = C5×D12.C4φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.183(C2xC4)480,786
C60.184(C2×C4) = C5×Q8×Dic3φ: C2×C4/C2 → C22 ⊆ Aut C60480C60.184(C2xC4)480,824
C60.185(C2×C4) = C5×D4.Dic3φ: C2×C4/C2 → C22 ⊆ Aut C602404C60.185(C2xC4)480,827
C60.186(C2×C4) = D60⋊7C4φ: C2×C4/C4 → C2 ⊆ Aut C601202C60.186(C2xC4)480,165
C60.187(C2×C4) = Dic30⋊8C4φ: C2×C4/C4 → C2 ⊆ Aut C60480C60.187(C2xC4)480,176
C60.188(C2×C4) = D60⋊8C4φ: C2×C4/C4 → C2 ⊆ Aut C60240C60.188(C2xC4)480,181
C60.189(C2×C4) = C4×Dic30φ: C2×C4/C4 → C2 ⊆ Aut C60480C60.189(C2xC4)480,833
C60.190(C2×C4) = D60.6C4φ: C2×C4/C4 → C2 ⊆ Aut C602402C60.190(C2xC4)480,866
C60.191(C2×C4) = C16×D15φ: C2×C4/C4 → C2 ⊆ Aut C602402C60.191(C2xC4)480,157
C60.192(C2×C4) = C80⋊S3φ: C2×C4/C4 → C2 ⊆ Aut C602402C60.192(C2xC4)480,158
C60.193(C2×C4) = C4×C15⋊3C8φ: C2×C4/C4 → C2 ⊆ Aut C60480C60.193(C2xC4)480,162
C60.194(C2×C4) = C42.D15φ: C2×C4/C4 → C2 ⊆ Aut C60480C60.194(C2xC4)480,163
C60.195(C2×C4) = C42⋊2D15φ: C2×C4/C4 → C2 ⊆ Aut C60240C60.195(C2xC4)480,837
C60.196(C2×C4) = C2×C8×D15φ: C2×C4/C4 → C2 ⊆ Aut C60240C60.196(C2xC4)480,864
C60.197(C2×C4) = C2×C40⋊S3φ: C2×C4/C4 → C2 ⊆ Aut C60240C60.197(C2xC4)480,865
C60.198(C2×C4) = C3×D20⋊4C4φ: C2×C4/C4 → C2 ⊆ Aut C601202C60.198(C2xC4)480,83
C60.199(C2×C4) = C3×C20.44D4φ: C2×C4/C4 → C2 ⊆ Aut C60480C60.199(C2xC4)480,94
C60.200(C2×C4) = C3×D20⋊5C4φ: C2×C4/C4 → C2 ⊆ Aut C60240C60.200(C2xC4)480,99
C60.201(C2×C4) = C12×Dic10φ: C2×C4/C4 → C2 ⊆ Aut C60480C60.201(C2xC4)480,661
C60.202(C2×C4) = C3×D20.3C4φ: C2×C4/C4 → C2 ⊆ Aut C602402C60.202(C2xC4)480,694
C60.203(C2×C4) = C5×C42⋊4S3φ: C2×C4/C4 → C2 ⊆ Aut C601202C60.203(C2xC4)480,124
C60.204(C2×C4) = C5×C2.Dic12φ: C2×C4/C4 → C2 ⊆ Aut C60480C60.204(C2xC4)480,135
C60.205(C2×C4) = C5×C2.D24φ: C2×C4/C4 → C2 ⊆ Aut C60240C60.205(C2xC4)480,140
C60.206(C2×C4) = C20×Dic6φ: C2×C4/C4 → C2 ⊆ Aut C60480C60.206(C2xC4)480,747
C60.207(C2×C4) = C5×C8○D12φ: C2×C4/C4 → C2 ⊆ Aut C602402C60.207(C2xC4)480,780
C60.208(C2×C4) = D5×C48φ: C2×C4/C4 → C2 ⊆ Aut C602402C60.208(C2xC4)480,75
C60.209(C2×C4) = C3×C80⋊C2φ: C2×C4/C4 → C2 ⊆ Aut C602402C60.209(C2xC4)480,76
C60.210(C2×C4) = C12×C5⋊2C8φ: C2×C4/C4 → C2 ⊆ Aut C60480C60.210(C2xC4)480,80
C60.211(C2×C4) = C3×C42.D5φ: C2×C4/C4 → C2 ⊆ Aut C60480C60.211(C2xC4)480,81
C60.212(C2×C4) = Dic5×C24φ: C2×C4/C4 → C2 ⊆ Aut C60480C60.212(C2xC4)480,91
C60.213(C2×C4) = C3×C42⋊D5φ: C2×C4/C4 → C2 ⊆ Aut C60240C60.213(C2xC4)480,665
C60.214(C2×C4) = D5×C2×C24φ: C2×C4/C4 → C2 ⊆ Aut C60240C60.214(C2xC4)480,692
C60.215(C2×C4) = C6×C8⋊D5φ: C2×C4/C4 → C2 ⊆ Aut C60240C60.215(C2xC4)480,693
C60.216(C2×C4) = S3×C80φ: C2×C4/C4 → C2 ⊆ Aut C602402C60.216(C2xC4)480,116
C60.217(C2×C4) = C5×D6.C8φ: C2×C4/C4 → C2 ⊆ Aut C602402C60.217(C2xC4)480,117
C60.218(C2×C4) = C20×C3⋊C8φ: C2×C4/C4 → C2 ⊆ Aut C60480C60.218(C2xC4)480,121
C60.219(C2×C4) = C5×C42.S3φ: C2×C4/C4 → C2 ⊆ Aut C60480C60.219(C2xC4)480,122
C60.220(C2×C4) = Dic3×C40φ: C2×C4/C4 → C2 ⊆ Aut C60480C60.220(C2xC4)480,132
C60.221(C2×C4) = C5×C24⋊C4φ: C2×C4/C4 → C2 ⊆ Aut C60480C60.221(C2xC4)480,134
C60.222(C2×C4) = C5×C42⋊2S3φ: C2×C4/C4 → C2 ⊆ Aut C60240C60.222(C2xC4)480,751
C60.223(C2×C4) = S3×C2×C40φ: C2×C4/C4 → C2 ⊆ Aut C60240C60.223(C2xC4)480,778
C60.224(C2×C4) = C10×C8⋊S3φ: C2×C4/C4 → C2 ⊆ Aut C60240C60.224(C2xC4)480,779
C60.225(C2×C4) = C15×D4⋊C4φ: C2×C4/C4 → C2 ⊆ Aut C60240C60.225(C2xC4)480,205
C60.226(C2×C4) = C15×Q8⋊C4φ: C2×C4/C4 → C2 ⊆ Aut C60480C60.226(C2xC4)480,206
C60.227(C2×C4) = C15×C4≀C2φ: C2×C4/C4 → C2 ⊆ Aut C601202C60.227(C2xC4)480,207
C60.228(C2×C4) = Q8×C60φ: C2×C4/C4 → C2 ⊆ Aut C60480C60.228(C2xC4)480,924
C60.229(C2×C4) = C15×C8○D4φ: C2×C4/C4 → C2 ⊆ Aut C602402C60.229(C2xC4)480,936
C60.230(C2×C4) = C120⋊10C4φ: C2×C4/C22 → C2 ⊆ Aut C60480C60.230(C2xC4)480,177
C60.231(C2×C4) = C120⋊9C4φ: C2×C4/C22 → C2 ⊆ Aut C60480C60.231(C2xC4)480,178
C60.232(C2×C4) = C4.18D60φ: C2×C4/C22 → C2 ⊆ Aut C602402C60.232(C2xC4)480,179
C60.233(C2×C4) = C2×C60.7C4φ: C2×C4/C22 → C2 ⊆ Aut C60240C60.233(C2xC4)480,886
C60.234(C2×C4) = C2×C15⋊3C16φ: C2×C4/C22 → C2 ⊆ Aut C60480C60.234(C2xC4)480,171
C60.235(C2×C4) = C60.7C8φ: C2×C4/C22 → C2 ⊆ Aut C602402C60.235(C2xC4)480,172
C60.236(C2×C4) = C8×Dic15φ: C2×C4/C22 → C2 ⊆ Aut C60480C60.236(C2xC4)480,173
C60.237(C2×C4) = C120⋊13C4φ: C2×C4/C22 → C2 ⊆ Aut C60480C60.237(C2xC4)480,175
C60.238(C2×C4) = C22×C15⋊3C8φ: C2×C4/C22 → C2 ⊆ Aut C60480C60.238(C2xC4)480,885
C60.239(C2×C4) = C23.26D30φ: C2×C4/C22 → C2 ⊆ Aut C60240C60.239(C2xC4)480,891
C60.240(C2×C4) = C3×C40⋊6C4φ: C2×C4/C22 → C2 ⊆ Aut C60480C60.240(C2xC4)480,95
C60.241(C2×C4) = C3×C40⋊5C4φ: C2×C4/C22 → C2 ⊆ Aut C60480C60.241(C2xC4)480,96
C60.242(C2×C4) = C3×C40.6C4φ: C2×C4/C22 → C2 ⊆ Aut C602402C60.242(C2xC4)480,97
C60.243(C2×C4) = C6×C4.Dic5φ: C2×C4/C22 → C2 ⊆ Aut C60240C60.243(C2xC4)480,714
C60.244(C2×C4) = C5×C8⋊Dic3φ: C2×C4/C22 → C2 ⊆ Aut C60480C60.244(C2xC4)480,136
C60.245(C2×C4) = C5×C24⋊1C4φ: C2×C4/C22 → C2 ⊆ Aut C60480C60.245(C2xC4)480,137
C60.246(C2×C4) = C5×C24.C4φ: C2×C4/C22 → C2 ⊆ Aut C602402C60.246(C2xC4)480,138
C60.247(C2×C4) = C10×C4.Dic3φ: C2×C4/C22 → C2 ⊆ Aut C60240C60.247(C2xC4)480,800
C60.248(C2×C4) = C6×C5⋊2C16φ: C2×C4/C22 → C2 ⊆ Aut C60480C60.248(C2xC4)480,89
C60.249(C2×C4) = C3×C20.4C8φ: C2×C4/C22 → C2 ⊆ Aut C602402C60.249(C2xC4)480,90
C60.250(C2×C4) = C3×C40⋊8C4φ: C2×C4/C22 → C2 ⊆ Aut C60480C60.250(C2xC4)480,93
C60.251(C2×C4) = C2×C6×C5⋊2C8φ: C2×C4/C22 → C2 ⊆ Aut C60480C60.251(C2xC4)480,713
C60.252(C2×C4) = C3×C23.21D10φ: C2×C4/C22 → C2 ⊆ Aut C60240C60.252(C2xC4)480,719
C60.253(C2×C4) = C10×C3⋊C16φ: C2×C4/C22 → C2 ⊆ Aut C60480C60.253(C2xC4)480,130
C60.254(C2×C4) = C5×C12.C8φ: C2×C4/C22 → C2 ⊆ Aut C602402C60.254(C2xC4)480,131
C60.255(C2×C4) = C2×C10×C3⋊C8φ: C2×C4/C22 → C2 ⊆ Aut C60480C60.255(C2xC4)480,799
C60.256(C2×C4) = C5×C23.26D6φ: C2×C4/C22 → C2 ⊆ Aut C60240C60.256(C2xC4)480,805
C60.257(C2×C4) = C15×C4.Q8φ: C2×C4/C22 → C2 ⊆ Aut C60480C60.257(C2xC4)480,209
C60.258(C2×C4) = C15×C2.D8φ: C2×C4/C22 → C2 ⊆ Aut C60480C60.258(C2xC4)480,210
C60.259(C2×C4) = C15×C8.C4φ: C2×C4/C22 → C2 ⊆ Aut C602402C60.259(C2xC4)480,211
C60.260(C2×C4) = C15×C42⋊C2φ: C2×C4/C22 → C2 ⊆ Aut C60240C60.260(C2xC4)480,922
C60.261(C2×C4) = C15×C8⋊C4central extension (φ=1)480C60.261(C2xC4)480,200
C60.262(C2×C4) = C15×M5(2)central extension (φ=1)2402C60.262(C2xC4)480,213
C60.263(C2×C4) = M4(2)×C30central extension (φ=1)240C60.263(C2xC4)480,935

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