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Extensions 1→N→G→Q→1 with N=D20 and Q=C2×C4

Direct product G=N×Q with N=D20 and Q=C2×C4
dρLabelID
C2×C4×D20160C2xC4xD20320,1145

Semidirect products G=N:Q with N=D20 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
D20⋊1(C2×C4) = D8×F5φ: C2×C4/C1 → C2×C4 ⊆ Out D20408+D20:1(C2xC4)320,1068
D20⋊2(C2×C4) = D40⋊C4φ: C2×C4/C1 → C2×C4 ⊆ Out D20408+D20:2(C2xC4)320,1069
D20⋊3(C2×C4) = C2×D20⋊C4φ: C2×C4/C2 → C4 ⊆ Out D2080D20:3(C2xC4)320,1104
D20⋊4(C2×C4) = C2×Q8⋊2F5φ: C2×C4/C2 → C4 ⊆ Out D2080D20:4(C2xC4)320,1121
D20⋊5(C2×C4) = D5⋊C4≀C2φ: C2×C4/C2 → C4 ⊆ Out D20408D20:5(C2xC4)320,1130
D20⋊6(C2×C4) = C4○D4⋊F5φ: C2×C4/C2 → C4 ⊆ Out D20408D20:6(C2xC4)320,1131
D20⋊7(C2×C4) = C2×D4×F5φ: C2×C4/C2 → C4 ⊆ Out D2040D20:7(C2xC4)320,1595
D20⋊8(C2×C4) = D10.C24φ: C2×C4/C2 → C4 ⊆ Out D20408+D20:8(C2xC4)320,1596
D20⋊9(C2×C4) = C4○D4×F5φ: C2×C4/C2 → C4 ⊆ Out D20408D20:9(C2xC4)320,1603
D20⋊10(C2×C4) = D5.2+ 1+4φ: C2×C4/C2 → C4 ⊆ Out D20408D20:10(C2xC4)320,1604
D20⋊11(C2×C4) = Dic5⋊4D8φ: C2×C4/C2 → C22 ⊆ Out D20160D20:11(C2xC4)320,383
D20⋊12(C2×C4) = D5×D4⋊C4φ: C2×C4/C2 → C22 ⊆ Out D2080D20:12(C2xC4)320,396
D20⋊13(C2×C4) = D4⋊D5⋊6C4φ: C2×C4/C2 → C22 ⊆ Out D20160D20:13(C2xC4)320,412
D20⋊14(C2×C4) = Q8⋊(C4×D5)φ: C2×C4/C2 → C22 ⊆ Out D20160D20:14(C2xC4)320,430
D20⋊15(C2×C4) = D5×C4≀C2φ: C2×C4/C2 → C22 ⊆ Out D20404D20:15(C2xC4)320,447
D20⋊16(C2×C4) = D40⋊15C4φ: C2×C4/C2 → C22 ⊆ Out D20160D20:16(C2xC4)320,496
D20⋊17(C2×C4) = D40⋊12C4φ: C2×C4/C2 → C22 ⊆ Out D20160D20:17(C2xC4)320,499
D20⋊18(C2×C4) = C4×D40φ: C2×C4/C4 → C2 ⊆ Out D20160D20:18(C2xC4)320,319
D20⋊19(C2×C4) = D40⋊9C4φ: C2×C4/C4 → C2 ⊆ Out D20160D20:19(C2xC4)320,338
D20⋊20(C2×C4) = C4×D4⋊D5φ: C2×C4/C4 → C2 ⊆ Out D20160D20:20(C2xC4)320,640
D20⋊21(C2×C4) = C42.48D10φ: C2×C4/C4 → C2 ⊆ Out D20160D20:21(C2xC4)320,641
D20⋊22(C2×C4) = C4×D4×D5φ: C2×C4/C4 → C2 ⊆ Out D2080D20:22(C2xC4)320,1216
D20⋊23(C2×C4) = C42⋊11D10φ: C2×C4/C4 → C2 ⊆ Out D2080D20:23(C2xC4)320,1217
D20⋊24(C2×C4) = C4×Q8⋊2D5φ: C2×C4/C4 → C2 ⊆ Out D20160D20:24(C2xC4)320,1245
D20⋊25(C2×C4) = C42.126D10φ: C2×C4/C4 → C2 ⊆ Out D20160D20:25(C2xC4)320,1246
D20⋊26(C2×C4) = C2×D20⋊4C4φ: C2×C4/C22 → C2 ⊆ Out D2080D20:26(C2xC4)320,554
D20⋊27(C2×C4) = C2×D20⋊5C4φ: C2×C4/C22 → C2 ⊆ Out D20160D20:27(C2xC4)320,739
D20⋊28(C2×C4) = C23.49D20φ: C2×C4/C22 → C2 ⊆ Out D20160D20:28(C2xC4)320,760
D20⋊29(C2×C4) = C2×D20⋊6C4φ: C2×C4/C22 → C2 ⊆ Out D20160D20:29(C2xC4)320,592
D20⋊30(C2×C4) = C4○D20⋊9C4φ: C2×C4/C22 → C2 ⊆ Out D20160D20:30(C2xC4)320,593
D20⋊31(C2×C4) = C2×D20⋊7C4φ: C2×C4/C22 → C2 ⊆ Out D2080D20:31(C2xC4)320,765
D20⋊32(C2×C4) = C2×D20⋊8C4φ: C2×C4/C22 → C2 ⊆ Out D20160D20:32(C2xC4)320,1175
D20⋊33(C2×C4) = C10.82+ 1+4φ: C2×C4/C22 → C2 ⊆ Out D20160D20:33(C2xC4)320,1176
D20⋊34(C2×C4) = C42.188D10φ: C2×C4/C22 → C2 ⊆ Out D20160D20:34(C2xC4)320,1194
D20⋊35(C2×C4) = C4×C4○D20φ: trivial image160D20:35(C2xC4)320,1146
D20⋊36(C2×C4) = C42⋊7D10φ: trivial image80D20:36(C2xC4)320,1193
D20⋊37(C2×C4) = C42.91D10φ: trivial image160D20:37(C2xC4)320,1195

Non-split extensions G=N.Q with N=D20 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
D20.1(C2×C4) = SD16×F5φ: C2×C4/C1 → C2×C4 ⊆ Out D20408D20.1(C2xC4)320,1072
D20.2(C2×C4) = SD16⋊F5φ: C2×C4/C1 → C2×C4 ⊆ Out D20408D20.2(C2xC4)320,1073
D20.3(C2×C4) = SD16⋊3F5φ: C2×C4/C1 → C2×C4 ⊆ Out D20808D20.3(C2xC4)320,1074
D20.4(C2×C4) = SD16⋊2F5φ: C2×C4/C1 → C2×C4 ⊆ Out D20808D20.4(C2xC4)320,1075
D20.5(C2×C4) = Q16⋊5F5φ: C2×C4/C1 → C2×C4 ⊆ Out D20808+D20.5(C2xC4)320,1078
D20.6(C2×C4) = Q16⋊F5φ: C2×C4/C1 → C2×C4 ⊆ Out D20808+D20.6(C2xC4)320,1079
D20.7(C2×C4) = (D4×C10)⋊C4φ: C2×C4/C2 → C4 ⊆ Out D20408+D20.7(C2xC4)320,1105
D20.8(C2×C4) = (C2×Q8)⋊6F5φ: C2×C4/C2 → C4 ⊆ Out D20808+D20.8(C2xC4)320,1122
D20.9(C2×C4) = C4○D20⋊C4φ: C2×C4/C2 → C4 ⊆ Out D20808D20.9(C2xC4)320,1132
D20.10(C2×C4) = D4⋊F5⋊C2φ: C2×C4/C2 → C4 ⊆ Out D20808D20.10(C2xC4)320,1133
D20.11(C2×C4) = C2×Q8.F5φ: C2×C4/C2 → C4 ⊆ Out D20160D20.11(C2xC4)320,1597
D20.12(C2×C4) = Dic5.20C24φ: C2×C4/C2 → C4 ⊆ Out D20808+D20.12(C2xC4)320,1598
D20.13(C2×C4) = Dic5.21C24φ: C2×C4/C2 → C4 ⊆ Out D20808D20.13(C2xC4)320,1601
D20.14(C2×C4) = Dic5.22C24φ: C2×C4/C2 → C4 ⊆ Out D20808D20.14(C2xC4)320,1602
D20.15(C2×C4) = (D4×D5)⋊C4φ: C2×C4/C2 → C22 ⊆ Out D2080D20.15(C2xC4)320,397
D20.16(C2×C4) = Dic5⋊7SD16φ: C2×C4/C2 → C22 ⊆ Out D20160D20.16(C2xC4)320,415
D20.17(C2×C4) = Q8⋊2D5⋊C4φ: C2×C4/C2 → C22 ⊆ Out D20160D20.17(C2xC4)320,431
D20.18(C2×C4) = Q8⋊D5⋊6C4φ: C2×C4/C2 → C22 ⊆ Out D20160D20.18(C2xC4)320,444
D20.19(C2×C4) = C42⋊D10φ: C2×C4/C2 → C22 ⊆ Out D20804D20.19(C2xC4)320,448
D20.20(C2×C4) = M4(2).22D10φ: C2×C4/C2 → C22 ⊆ Out D20804D20.20(C2xC4)320,450
D20.21(C2×C4) = C42.196D10φ: C2×C4/C2 → C22 ⊆ Out D20804D20.21(C2xC4)320,451
D20.22(C2×C4) = Dic5⋊8SD16φ: C2×C4/C2 → C22 ⊆ Out D20160D20.22(C2xC4)320,479
D20.23(C2×C4) = C40⋊21(C2×C4)φ: C2×C4/C2 → C22 ⊆ Out D20160D20.23(C2xC4)320,516
D20.24(C2×C4) = D40⋊16C4φ: C2×C4/C2 → C22 ⊆ Out D20804D20.24(C2xC4)320,521
D20.25(C2×C4) = D40⋊13C4φ: C2×C4/C2 → C22 ⊆ Out D20804D20.25(C2xC4)320,522
D20.26(C2×C4) = C4×C40⋊C2φ: C2×C4/C4 → C2 ⊆ Out D20160D20.26(C2xC4)320,318
D20.27(C2×C4) = D40⋊17C4φ: C2×C4/C4 → C2 ⊆ Out D20802D20.27(C2xC4)320,327
D20.28(C2×C4) = C42.16D10φ: C2×C4/C4 → C2 ⊆ Out D20160D20.28(C2xC4)320,337
D20.29(C2×C4) = D40⋊10C4φ: C2×C4/C4 → C2 ⊆ Out D20804D20.29(C2xC4)320,344
D20.30(C2×C4) = C4×Q8⋊D5φ: C2×C4/C4 → C2 ⊆ Out D20160D20.30(C2xC4)320,652
D20.31(C2×C4) = C42.56D10φ: C2×C4/C4 → C2 ⊆ Out D20160D20.31(C2xC4)320,653
D20.32(C2×C4) = C40.93D4φ: C2×C4/C4 → C2 ⊆ Out D20804D20.32(C2xC4)320,771
D20.33(C2×C4) = C40.50D4φ: C2×C4/C4 → C2 ⊆ Out D20804D20.33(C2xC4)320,772
D20.34(C2×C4) = D5×C8○D4φ: C2×C4/C4 → C2 ⊆ Out D20804D20.34(C2xC4)320,1421
D20.35(C2×C4) = C20.72C24φ: C2×C4/C4 → C2 ⊆ Out D20804D20.35(C2xC4)320,1422
D20.36(C2×C4) = C42⋊4D10φ: C2×C4/C22 → C2 ⊆ Out D20804D20.36(C2xC4)320,632
D20.37(C2×C4) = C23.23D20φ: C2×C4/C22 → C2 ⊆ Out D20160D20.37(C2xC4)320,740
D20.38(C2×C4) = C23.48D20φ: C2×C4/C22 → C2 ⊆ Out D2080D20.38(C2xC4)320,758
D20.39(C2×C4) = C4⋊C4⋊36D10φ: C2×C4/C22 → C2 ⊆ Out D2080D20.39(C2xC4)320,628
D20.40(C2×C4) = C4○D20⋊10C4φ: C2×C4/C22 → C2 ⊆ Out D20160D20.40(C2xC4)320,629
D20.41(C2×C4) = C23.20D20φ: C2×C4/C22 → C2 ⊆ Out D20804D20.41(C2xC4)320,766
D20.42(C2×C4) = C2×D20.2C4φ: C2×C4/C22 → C2 ⊆ Out D20160D20.42(C2xC4)320,1416
D20.43(C2×C4) = C40.47C23φ: C2×C4/C22 → C2 ⊆ Out D20804D20.43(C2xC4)320,1417
D20.44(C2×C4) = C2×D20.3C4φ: trivial image160D20.44(C2xC4)320,1410

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