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Extensions 1→N→G→Q→1 with N=D10 and Q=C2×D4

Direct product G=N×Q with N=D10 and Q=C2×D4
dρLabelID
C22×D4×D580C2^2xD4xD5320,1612

Semidirect products G=N:Q with N=D10 and Q=C2×D4
extensionφ:Q→Out NdρLabelID
D10⋊1(C2×D4) = C2×D10⋊D4φ: C2×D4/C2×C4 → C2 ⊆ Out D10160D10:1(C2xD4)320,1161
D10⋊2(C2×D4) = C2×C4⋊D20φ: C2×D4/C2×C4 → C2 ⊆ Out D10160D10:2(C2xD4)320,1178
D10⋊3(C2×D4) = D5×C4⋊D4φ: C2×D4/C2×C4 → C2 ⊆ Out D1080D10:3(C2xD4)320,1276
D10⋊4(C2×D4) = C2×C20⋊2D4φ: C2×D4/C2×C4 → C2 ⊆ Out D10160D10:4(C2xD4)320,1472
D10⋊5(C2×D4) = D4×D20φ: C2×D4/D4 → C2 ⊆ Out D1080D10:5(C2xD4)320,1221
D10⋊6(C2×D4) = C24⋊4D10φ: C2×D4/D4 → C2 ⊆ Out D1080D10:6(C2xD4)320,1262
D10⋊7(C2×D4) = D20⋊19D4φ: C2×D4/D4 → C2 ⊆ Out D1080D10:7(C2xD4)320,1281
D10⋊8(C2×D4) = D20⋊11D4φ: C2×D4/D4 → C2 ⊆ Out D1080D10:8(C2xD4)320,1389
D10⋊9(C2×D4) = D4×C5⋊D4φ: C2×D4/D4 → C2 ⊆ Out D1080D10:9(C2xD4)320,1473
D10⋊10(C2×D4) = C2×C22⋊D20φ: C2×D4/C23 → C2 ⊆ Out D1080D10:10(C2xD4)320,1159
D10⋊11(C2×D4) = D5×C22≀C2φ: C2×D4/C23 → C2 ⊆ Out D1040D10:11(C2xD4)320,1260
D10⋊12(C2×D4) = C2×C23⋊D10φ: C2×D4/C23 → C2 ⊆ Out D1080D10:12(C2xD4)320,1471

Non-split extensions G=N.Q with N=D10 and Q=C2×D4
extensionφ:Q→Out NdρLabelID
D10.1(C2×D4) = C2×D10.D4φ: C2×D4/C22 → C22 ⊆ Out D1080D10.1(C2xD4)320,1082
D10.2(C2×D4) = C23⋊F5⋊5C2φ: C2×D4/C22 → C22 ⊆ Out D10804D10.2(C2xD4)320,1083
D10.3(C2×D4) = C2×D4⋊F5φ: C2×D4/C22 → C22 ⊆ Out D1080D10.3(C2xD4)320,1106
D10.4(C2×D4) = (C2×D4)⋊6F5φ: C2×D4/C22 → C22 ⊆ Out D10808-D10.4(C2xD4)320,1107
D10.5(C2×D4) = (C2×D4)⋊7F5φ: C2×D4/C22 → C22 ⊆ Out D10408+D10.5(C2xD4)320,1108
D10.6(C2×D4) = (C2×D4)⋊8F5φ: C2×D4/C22 → C22 ⊆ Out D10808-D10.6(C2xD4)320,1109
D10.7(C2×D4) = C2×Q8⋊2F5φ: C2×D4/C22 → C22 ⊆ Out D1080D10.7(C2xD4)320,1121
D10.8(C2×D4) = (C2×Q8)⋊6F5φ: C2×D4/C22 → C22 ⊆ Out D10808+D10.8(C2xD4)320,1122
D10.9(C2×D4) = (C2×Q8)⋊7F5φ: C2×D4/C22 → C22 ⊆ Out D10808+D10.9(C2xD4)320,1123
D10.10(C2×D4) = D5⋊C4≀C2φ: C2×D4/C22 → C22 ⊆ Out D10408D10.10(C2xD4)320,1130
D10.11(C2×D4) = D4⋊F5⋊C2φ: C2×D4/C22 → C22 ⊆ Out D10808D10.11(C2xD4)320,1133
D10.12(C2×D4) = C2×C23⋊F5φ: C2×D4/C22 → C22 ⊆ Out D1080D10.12(C2xD4)320,1134
D10.13(C2×D4) = C42.228D10φ: C2×D4/C2×C4 → C2 ⊆ Out D10160D10.13(C2xD4)320,1220
D10.14(C2×D4) = C24⋊3D10φ: C2×D4/C2×C4 → C2 ⊆ Out D1080D10.14(C2xD4)320,1261
D10.15(C2×D4) = C10.392+ 1+4φ: C2×D4/C2×C4 → C2 ⊆ Out D10160D10.15(C2xD4)320,1280
D10.16(C2×D4) = C10.172- 1+4φ: C2×D4/C2×C4 → C2 ⊆ Out D10160D10.16(C2xD4)320,1301
D10.17(C2×D4) = C10.1202+ 1+4φ: C2×D4/C2×C4 → C2 ⊆ Out D1080D10.17(C2xD4)320,1325
D10.18(C2×D4) = C42.233D10φ: C2×D4/C2×C4 → C2 ⊆ Out D10160D10.18(C2xD4)320,1340
D10.19(C2×D4) = C42.238D10φ: C2×D4/C2×C4 → C2 ⊆ Out D10160D10.19(C2xD4)320,1388
D10.20(C2×D4) = C42.240D10φ: C2×D4/C2×C4 → C2 ⊆ Out D10160D10.20(C2xD4)320,1397
D10.21(C2×D4) = C2×D8⋊3D5φ: C2×D4/C2×C4 → C2 ⊆ Out D10160D10.21(C2xD4)320,1428
D10.22(C2×D4) = C2×SD16⋊3D5φ: C2×D4/C2×C4 → C2 ⊆ Out D10160D10.22(C2xD4)320,1433
D10.23(C2×D4) = C2×Q8.D10φ: C2×D4/C2×C4 → C2 ⊆ Out D10160D10.23(C2xD4)320,1437
D10.24(C2×D4) = C4×C4⋊F5φ: C2×D4/C2×C4 → C2 ⊆ Out D1080D10.24(C2xD4)320,1025
D10.25(C2×D4) = C42⋊8F5φ: C2×D4/C2×C4 → C2 ⊆ Out D1080D10.25(C2xD4)320,1026
D10.26(C2×D4) = C42⋊9F5φ: C2×D4/C2×C4 → C2 ⊆ Out D1080D10.26(C2xD4)320,1027
D10.27(C2×D4) = D10⋊(C4⋊C4)φ: C2×D4/C2×C4 → C2 ⊆ Out D1040D10.27(C2xD4)320,1037
D10.28(C2×D4) = C20⋊(C4⋊C4)φ: C2×D4/C2×C4 → C2 ⊆ Out D1080D10.28(C2xD4)320,1050
D10.29(C2×D4) = C2×C40⋊C4φ: C2×D4/C2×C4 → C2 ⊆ Out D1080D10.29(C2xD4)320,1057
D10.30(C2×D4) = C2×D5.D8φ: C2×D4/C2×C4 → C2 ⊆ Out D1080D10.30(C2xD4)320,1058
D10.31(C2×D4) = (C2×C8)⋊6F5φ: C2×D4/C2×C4 → C2 ⊆ Out D10804D10.31(C2xD4)320,1059
D10.32(C2×D4) = M4(2)⋊1F5φ: C2×D4/C2×C4 → C2 ⊆ Out D10408D10.32(C2xD4)320,1065
D10.33(C2×D4) = D10⋊6(C4⋊C4)φ: C2×D4/C2×C4 → C2 ⊆ Out D1080D10.33(C2xD4)320,1103
D10.34(C2×D4) = C22×C4⋊F5φ: C2×D4/C2×C4 → C2 ⊆ Out D1080D10.34(C2xD4)320,1591
D10.35(C2×D4) = C24.27D10φ: C2×D4/D4 → C2 ⊆ Out D1080D10.35(C2xD4)320,1162
D10.36(C2×D4) = C10.2- 1+4φ: C2×D4/D4 → C2 ⊆ Out D10160D10.36(C2xD4)320,1179
D10.37(C2×D4) = D20⋊23D4φ: C2×D4/D4 → C2 ⊆ Out D1080D10.37(C2xD4)320,1222
D10.38(C2×D4) = D20⋊24D4φ: C2×D4/D4 → C2 ⊆ Out D10160D10.38(C2xD4)320,1223
D10.39(C2×D4) = C24.33D10φ: C2×D4/D4 → C2 ⊆ Out D1080D10.39(C2xD4)320,1263
D10.40(C2×D4) = C10.402+ 1+4φ: C2×D4/D4 → C2 ⊆ Out D1080D10.40(C2xD4)320,1282
D10.41(C2×D4) = C10.732- 1+4φ: C2×D4/D4 → C2 ⊆ Out D10160D10.41(C2xD4)320,1283
D10.42(C2×D4) = D20⋊20D4φ: C2×D4/D4 → C2 ⊆ Out D1080D10.42(C2xD4)320,1284
D10.43(C2×D4) = D20⋊21D4φ: C2×D4/D4 → C2 ⊆ Out D1080D10.43(C2xD4)320,1302
D10.44(C2×D4) = D20⋊22D4φ: C2×D4/D4 → C2 ⊆ Out D10160D10.44(C2xD4)320,1303
D10.45(C2×D4) = C10.1212+ 1+4φ: C2×D4/D4 → C2 ⊆ Out D1080D10.45(C2xD4)320,1326
D10.46(C2×D4) = C10.822- 1+4φ: C2×D4/D4 → C2 ⊆ Out D10160D10.46(C2xD4)320,1327
D10.47(C2×D4) = D20⋊10D4φ: C2×D4/D4 → C2 ⊆ Out D1080D10.47(C2xD4)320,1348
D10.48(C2×D4) = D20⋊12D4φ: C2×D4/D4 → C2 ⊆ Out D10160D10.48(C2xD4)320,1398
D10.49(C2×D4) = D8⋊13D10φ: C2×D4/D4 → C2 ⊆ Out D10804D10.49(C2xD4)320,1429
D10.50(C2×D4) = D20.29D4φ: C2×D4/D4 → C2 ⊆ Out D10804D10.50(C2xD4)320,1434
D10.51(C2×D4) = D20.30D4φ: C2×D4/D4 → C2 ⊆ Out D101604D10.51(C2xD4)320,1438
D10.52(C2×D4) = D8⋊15D10φ: C2×D4/D4 → C2 ⊆ Out D10804+D10.52(C2xD4)320,1441
D10.53(C2×D4) = D8⋊11D10φ: C2×D4/D4 → C2 ⊆ Out D10804D10.53(C2xD4)320,1442
D10.54(C2×D4) = D20.47D4φ: C2×D4/D4 → C2 ⊆ Out D101604-D10.54(C2xD4)320,1443
D10.55(C2×D4) = D8⋊5D10φ: C2×D4/D4 → C2 ⊆ Out D10808+D10.55(C2xD4)320,1446
D10.56(C2×D4) = D8⋊6D10φ: C2×D4/D4 → C2 ⊆ Out D10808-D10.56(C2xD4)320,1447
D10.57(C2×D4) = C40.C23φ: C2×D4/D4 → C2 ⊆ Out D10808+D10.57(C2xD4)320,1450
D10.58(C2×D4) = D20.44D4φ: C2×D4/D4 → C2 ⊆ Out D101608-D10.58(C2xD4)320,1451
D10.59(C2×D4) = C22⋊C4×F5φ: C2×D4/D4 → C2 ⊆ Out D1040D10.59(C2xD4)320,1036
D10.60(C2×D4) = C10.(C4×D4)φ: C2×D4/D4 → C2 ⊆ Out D1080D10.60(C2xD4)320,1038
D10.61(C2×D4) = C4⋊C4×F5φ: C2×D4/D4 → C2 ⊆ Out D1080D10.61(C2xD4)320,1048
D10.62(C2×D4) = C4⋊C4⋊5F5φ: C2×D4/D4 → C2 ⊆ Out D1080D10.62(C2xD4)320,1049
D10.63(C2×D4) = D8×F5φ: C2×D4/D4 → C2 ⊆ Out D10408+D10.63(C2xD4)320,1068
D10.64(C2×D4) = D40⋊C4φ: C2×D4/D4 → C2 ⊆ Out D10408+D10.64(C2xD4)320,1069
D10.65(C2×D4) = SD16×F5φ: C2×D4/D4 → C2 ⊆ Out D10408D10.65(C2xD4)320,1072
D10.66(C2×D4) = SD16⋊F5φ: C2×D4/D4 → C2 ⊆ Out D10408D10.66(C2xD4)320,1073
D10.67(C2×D4) = Q16×F5φ: C2×D4/D4 → C2 ⊆ Out D10808-D10.67(C2xD4)320,1076
D10.68(C2×D4) = Dic20⋊C4φ: C2×D4/D4 → C2 ⊆ Out D10808-D10.68(C2xD4)320,1077
D10.69(C2×D4) = C2×D4×F5φ: C2×D4/D4 → C2 ⊆ Out D1040D10.69(C2xD4)320,1595
D10.70(C2×D4) = C2×D10.12D4φ: C2×D4/C23 → C2 ⊆ Out D10160D10.70(C2xD4)320,1160
D10.71(C2×D4) = C2×D10.13D4φ: C2×D4/C23 → C2 ⊆ Out D10160D10.71(C2xD4)320,1177
D10.72(C2×D4) = C42⋊12D10φ: C2×D4/C23 → C2 ⊆ Out D1080D10.72(C2xD4)320,1219
D10.73(C2×D4) = C10.372+ 1+4φ: C2×D4/C23 → C2 ⊆ Out D1080D10.73(C2xD4)320,1277
D10.74(C2×D4) = C4⋊C4⋊21D10φ: C2×D4/C23 → C2 ⊆ Out D1080D10.74(C2xD4)320,1278
D10.75(C2×D4) = C10.382+ 1+4φ: C2×D4/C23 → C2 ⊆ Out D1080D10.75(C2xD4)320,1279
D10.76(C2×D4) = C4⋊C4⋊26D10φ: C2×D4/C23 → C2 ⊆ Out D1080D10.76(C2xD4)320,1299
D10.77(C2×D4) = C10.162- 1+4φ: C2×D4/C23 → C2 ⊆ Out D10160D10.77(C2xD4)320,1300
D10.78(C2×D4) = D5×C22.D4φ: C2×D4/C23 → C2 ⊆ Out D1080D10.78(C2xD4)320,1324
D10.79(C2×D4) = C42⋊18D10φ: C2×D4/C23 → C2 ⊆ Out D1080D10.79(C2xD4)320,1346
D10.80(C2×D4) = C42.141D10φ: C2×D4/C23 → C2 ⊆ Out D10160D10.80(C2xD4)320,1347
D10.81(C2×D4) = C42⋊26D10φ: C2×D4/C23 → C2 ⊆ Out D1080D10.81(C2xD4)320,1387
D10.82(C2×D4) = C42.171D10φ: C2×D4/C23 → C2 ⊆ Out D10160D10.82(C2xD4)320,1396
D10.83(C2×D4) = C2×D8⋊D5φ: C2×D4/C23 → C2 ⊆ Out D1080D10.83(C2xD4)320,1427
D10.84(C2×D4) = C2×D40⋊C2φ: C2×D4/C23 → C2 ⊆ Out D1080D10.84(C2xD4)320,1431
D10.85(C2×D4) = C2×SD16⋊D5φ: C2×D4/C23 → C2 ⊆ Out D10160D10.85(C2xD4)320,1432
D10.86(C2×D4) = C2×Q16⋊D5φ: C2×D4/C23 → C2 ⊆ Out D10160D10.86(C2xD4)320,1436
D10.87(C2×D4) = Q16⋊D10φ: C2×D4/C23 → C2 ⊆ Out D10804D10.87(C2xD4)320,1440
D10.88(C2×D4) = SD16⋊D10φ: C2×D4/C23 → C2 ⊆ Out D10808-D10.88(C2xD4)320,1445
D10.89(C2×D4) = D40⋊C22φ: C2×D4/C23 → C2 ⊆ Out D10808+D10.89(C2xD4)320,1449
D10.90(C2×D4) = C2×D10.3Q8φ: C2×D4/C23 → C2 ⊆ Out D1080D10.90(C2xD4)320,1100
D10.91(C2×D4) = C4×C22⋊F5φ: C2×D4/C23 → C2 ⊆ Out D1080D10.91(C2xD4)320,1101
D10.92(C2×D4) = (C22×C4)⋊7F5φ: C2×D4/C23 → C2 ⊆ Out D1080D10.92(C2xD4)320,1102
D10.93(C2×D4) = C2×D20⋊C4φ: C2×D4/C23 → C2 ⊆ Out D1080D10.93(C2xD4)320,1104
D10.94(C2×D4) = (D4×C10)⋊C4φ: C2×D4/C23 → C2 ⊆ Out D10408+D10.94(C2xD4)320,1105
D10.95(C2×D4) = (C2×F5)⋊D4φ: C2×D4/C23 → C2 ⊆ Out D1040D10.95(C2xD4)320,1117
D10.96(C2×D4) = C2.(D4×F5)φ: C2×D4/C23 → C2 ⊆ Out D1080D10.96(C2xD4)320,1118
D10.97(C2×D4) = C2×Q8⋊F5φ: C2×D4/C23 → C2 ⊆ Out D1080D10.97(C2xD4)320,1119
D10.98(C2×D4) = (C2×Q8)⋊4F5φ: C2×D4/C23 → C2 ⊆ Out D10808-D10.98(C2xD4)320,1120
D10.99(C2×D4) = (C2×F5)⋊Q8φ: C2×D4/C23 → C2 ⊆ Out D1080D10.99(C2xD4)320,1128
D10.100(C2×D4) = C4○D4⋊F5φ: C2×D4/C23 → C2 ⊆ Out D10408D10.100(C2xD4)320,1131
D10.101(C2×D4) = C4○D20⋊C4φ: C2×D4/C23 → C2 ⊆ Out D10808D10.101(C2xD4)320,1132
D10.102(C2×D4) = C24⋊4F5φ: C2×D4/C23 → C2 ⊆ Out D1040D10.102(C2xD4)320,1138
D10.103(C2×D4) = C22×C22⋊F5φ: C2×D4/C23 → C2 ⊆ Out D1080D10.103(C2xD4)320,1607
D10.104(C2×D4) = C2×D5×C22⋊C4φ: trivial image80D10.104(C2xD4)320,1156
D10.105(C2×D4) = C2×D5×C4⋊C4φ: trivial image160D10.105(C2xD4)320,1173
D10.106(C2×D4) = C4×D4×D5φ: trivial image80D10.106(C2xD4)320,1216
D10.107(C2×D4) = D5×C22⋊Q8φ: trivial image80D10.107(C2xD4)320,1298
D10.108(C2×D4) = D5×C4.4D4φ: trivial image80D10.108(C2xD4)320,1345
D10.109(C2×D4) = D5×C4⋊1D4φ: trivial image80D10.109(C2xD4)320,1386
D10.110(C2×D4) = D5×C4⋊Q8φ: trivial image160D10.110(C2xD4)320,1395
D10.111(C2×D4) = C2×D5×D8φ: trivial image80D10.111(C2xD4)320,1426
D10.112(C2×D4) = C2×D5×SD16φ: trivial image80D10.112(C2xD4)320,1430
D10.113(C2×D4) = C2×D5×Q16φ: trivial image160D10.113(C2xD4)320,1435
D10.114(C2×D4) = D5×C4○D8φ: trivial image804D10.114(C2xD4)320,1439
D10.115(C2×D4) = D5×C8⋊C22φ: trivial image408+D10.115(C2xD4)320,1444
D10.116(C2×D4) = D5×C8.C22φ: trivial image808-D10.116(C2xD4)320,1448

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