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Extensions 1→N→G→Q→1 with N=C5⋊2C8 and Q=C2×C4

Direct product G=N×Q with N=C5⋊2C8 and Q=C2×C4
dρLabelID
C2×C4×C5⋊2C8320C2xC4xC5:2C8320,547

Semidirect products G=N:Q with N=C5⋊2C8 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
C5⋊2C8⋊1(C2×C4) = D4.D5⋊5C4φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8160C5:2C8:1(C2xC4)320,384
C5⋊2C8⋊2(C2×C4) = D4⋊D5⋊6C4φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8160C5:2C8:2(C2xC4)320,412
C5⋊2C8⋊3(C2×C4) = Q8⋊D5⋊6C4φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8160C5:2C8:3(C2xC4)320,444
C5⋊2C8⋊4(C2×C4) = C8⋊(C4×D5)φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8160C5:2C8:4(C2xC4)320,488
C5⋊2C8⋊5(C2×C4) = C40⋊20(C2×C4)φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8160C5:2C8:5(C2xC4)320,508
C5⋊2C8⋊6(C2×C4) = C20.47(C4⋊C4)φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8160C5:2C8:6(C2xC4)320,591
C5⋊2C8⋊7(C2×C4) = C20.64(C4⋊C4)φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8160C5:2C8:7(C2xC4)320,622
C5⋊2C8⋊8(C2×C4) = C42.48D10φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8160C5:2C8:8(C2xC4)320,641
C5⋊2C8⋊9(C2×C4) = C42.51D10φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8160C5:2C8:9(C2xC4)320,645
C5⋊2C8⋊10(C2×C4) = C42.56D10φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8160C5:2C8:10(C2xC4)320,653
C5⋊2C8⋊11(C2×C4) = D8×F5φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8408+C5:2C8:11(C2xC4)320,1068
C5⋊2C8⋊12(C2×C4) = D40⋊C4φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8408+C5:2C8:12(C2xC4)320,1069
C5⋊2C8⋊13(C2×C4) = SD16×F5φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8408C5:2C8:13(C2xC4)320,1072
C5⋊2C8⋊14(C2×C4) = SD16⋊F5φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8408C5:2C8:14(C2xC4)320,1073
C5⋊2C8⋊15(C2×C4) = M4(2)⋊1F5φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8408C5:2C8:15(C2xC4)320,1065
C5⋊2C8⋊16(C2×C4) = M4(2)×F5φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8408C5:2C8:16(C2xC4)320,1064
C5⋊2C8⋊17(C2×C4) = Dic5⋊4D8φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8160C5:2C8:17(C2xC4)320,383
C5⋊2C8⋊18(C2×C4) = Dic5⋊6SD16φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8160C5:2C8:18(C2xC4)320,385
C5⋊2C8⋊19(C2×C4) = Dic5⋊7SD16φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8160C5:2C8:19(C2xC4)320,415
C5⋊2C8⋊20(C2×C4) = C4×D4⋊D5φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8160C5:2C8:20(C2xC4)320,640
C5⋊2C8⋊21(C2×C4) = C4×D4.D5φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8160C5:2C8:21(C2xC4)320,644
C5⋊2C8⋊22(C2×C4) = C4×Q8⋊D5φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8160C5:2C8:22(C2xC4)320,652
C5⋊2C8⋊23(C2×C4) = C4×C8⋊D5φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8160C5:2C8:23(C2xC4)320,314
C5⋊2C8⋊24(C2×C4) = D10.6C42φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8160C5:2C8:24(C2xC4)320,334
C5⋊2C8⋊25(C2×C4) = C4×C4.Dic5φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8160C5:2C8:25(C2xC4)320,549
C5⋊2C8⋊26(C2×C4) = M4(2)×Dic5φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8160C5:2C8:26(C2xC4)320,744
C5⋊2C8⋊27(C2×C4) = D5×C4.Q8φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8160C5:2C8:27(C2xC4)320,486
C5⋊2C8⋊28(C2×C4) = D5×C2.D8φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8160C5:2C8:28(C2xC4)320,506
C5⋊2C8⋊29(C2×C4) = C2×C10.D8φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8320C5:2C8:29(C2xC4)320,589
C5⋊2C8⋊30(C2×C4) = C2×C20.Q8φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8320C5:2C8:30(C2xC4)320,590
C5⋊2C8⋊31(C2×C4) = D5×C8⋊C4φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8160C5:2C8:31(C2xC4)320,331
C5⋊2C8⋊32(C2×C4) = C2×C42.D5φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8320C5:2C8:32(C2xC4)320,548
C5⋊2C8⋊33(C2×C4) = C2×C40⋊8C4φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8320C5:2C8:33(C2xC4)320,727
C5⋊2C8⋊34(C2×C4) = C2×C40⋊C4φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C880C5:2C8:34(C2xC4)320,1057
C5⋊2C8⋊35(C2×C4) = C2×D5.D8φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C880C5:2C8:35(C2xC4)320,1058
C5⋊2C8⋊36(C2×C4) = C2×C8×F5φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C880C5:2C8:36(C2xC4)320,1054
C5⋊2C8⋊37(C2×C4) = C2×C8⋊F5φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C880C5:2C8:37(C2xC4)320,1055
C5⋊2C8⋊38(C2×C4) = D5×C4×C8φ: trivial image160C5:2C8:38(C2xC4)320,311
C5⋊2C8⋊39(C2×C4) = C2×C8×Dic5φ: trivial image320C5:2C8:39(C2xC4)320,725

Non-split extensions G=N.Q with N=C5⋊2C8 and Q=C2×C4
extensionφ:Q→Out NdρLabelID
C5⋊2C8.1(C2×C4) = C5⋊Q16⋊5C4φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8320C5:2C8.1(C2xC4)320,416
C5⋊2C8.2(C2×C4) = M4(2).22D10φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8804C5:2C8.2(C2xC4)320,450
C5⋊2C8.3(C2×C4) = M4(2).25D10φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8804C5:2C8.3(C2xC4)320,520
C5⋊2C8.4(C2×C4) = C42.59D10φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8320C5:2C8.4(C2xC4)320,657
C5⋊2C8.5(C2×C4) = C23.Dic10φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8804C5:2C8.5(C2xC4)320,751
C5⋊2C8.6(C2×C4) = C40.50D4φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8804C5:2C8.6(C2xC4)320,772
C5⋊2C8.7(C2×C4) = D8⋊5F5φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8808-C5:2C8.7(C2xC4)320,1070
C5⋊2C8.8(C2×C4) = D8⋊F5φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8808-C5:2C8.8(C2xC4)320,1071
C5⋊2C8.9(C2×C4) = SD16⋊3F5φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8808C5:2C8.9(C2xC4)320,1074
C5⋊2C8.10(C2×C4) = SD16⋊2F5φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8808C5:2C8.10(C2xC4)320,1075
C5⋊2C8.11(C2×C4) = Q16×F5φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8808-C5:2C8.11(C2xC4)320,1076
C5⋊2C8.12(C2×C4) = Dic20⋊C4φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8808-C5:2C8.12(C2xC4)320,1077
C5⋊2C8.13(C2×C4) = Q16⋊5F5φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8808+C5:2C8.13(C2xC4)320,1078
C5⋊2C8.14(C2×C4) = Q16⋊F5φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8808+C5:2C8.14(C2xC4)320,1079
C5⋊2C8.15(C2×C4) = M4(2).1F5φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8808C5:2C8.15(C2xC4)320,1067
C5⋊2C8.16(C2×C4) = C16⋊F5φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8804C5:2C8.16(C2xC4)320,183
C5⋊2C8.17(C2×C4) = C16⋊4F5φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8804C5:2C8.17(C2xC4)320,184
C5⋊2C8.18(C2×C4) = C42.3F5φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8804C5:2C8.18(C2xC4)320,198
C5⋊2C8.19(C2×C4) = C20.23C42φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8804C5:2C8.19(C2xC4)320,228
C5⋊2C8.20(C2×C4) = Dic10.C8φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C81608C5:2C8.20(C2xC4)320,1063
C5⋊2C8.21(C2×C4) = M4(2)⋊5F5φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C8808C5:2C8.21(C2xC4)320,1066
C5⋊2C8.22(C2×C4) = C5⋊C16.C22φ: C2×C4/C2 → C22 ⊆ Out C5⋊2C81608C5:2C8.22(C2xC4)320,1129
C5⋊2C8.23(C2×C4) = Dic5⋊4Q16φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8320C5:2C8.23(C2xC4)320,417
C5⋊2C8.24(C2×C4) = C42.196D10φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8804C5:2C8.24(C2xC4)320,451
C5⋊2C8.25(C2×C4) = C4×C5⋊Q16φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8320C5:2C8.25(C2xC4)320,656
C5⋊2C8.26(C2×C4) = C40.93D4φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8804C5:2C8.26(C2xC4)320,771
C5⋊2C8.27(C2×C4) = D10.5C42φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8160C5:2C8.27(C2xC4)320,316
C5⋊2C8.28(C2×C4) = D10.7C42φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8160C5:2C8.28(C2xC4)320,335
C5⋊2C8.29(C2×C4) = D20.6C8φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C81602C5:2C8.29(C2xC4)320,528
C5⋊2C8.30(C2×C4) = D20.5C8φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C81604C5:2C8.30(C2xC4)320,534
C5⋊2C8.31(C2×C4) = C20.42C42φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8160C5:2C8.31(C2xC4)320,728
C5⋊2C8.32(C2×C4) = C16×F5φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8804C5:2C8.32(C2xC4)320,181
C5⋊2C8.33(C2×C4) = C16⋊7F5φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8804C5:2C8.33(C2xC4)320,182
C5⋊2C8.34(C2×C4) = C4×C5⋊C16φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8320C5:2C8.34(C2xC4)320,195
C5⋊2C8.35(C2×C4) = C42.4F5φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8320C5:2C8.35(C2xC4)320,197
C5⋊2C8.36(C2×C4) = Dic5⋊C16φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8320C5:2C8.36(C2xC4)320,223
C5⋊2C8.37(C2×C4) = C40.C8φ: C2×C4/C4 → C2 ⊆ Out C5⋊2C8320C5:2C8.37(C2xC4)320,224
C5⋊2C8.38(C2×C4) = (C8×D5)⋊C4φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8160C5:2C8.38(C2xC4)320,487
C5⋊2C8.39(C2×C4) = C8.27(C4×D5)φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8160C5:2C8.39(C2xC4)320,507
C5⋊2C8.40(C2×C4) = D5×C8.C4φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8804C5:2C8.40(C2xC4)320,519
C5⋊2C8.41(C2×C4) = C20.76(C4⋊C4)φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8160C5:2C8.41(C2xC4)320,625
C5⋊2C8.42(C2×C4) = C2×C20.53D4φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8160C5:2C8.42(C2xC4)320,750
C5⋊2C8.43(C2×C4) = C2×C80⋊C2φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8160C5:2C8.43(C2xC4)320,527
C5⋊2C8.44(C2×C4) = D5×M5(2)φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8804C5:2C8.44(C2xC4)320,533
C5⋊2C8.45(C2×C4) = C20.35C42φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8160C5:2C8.45(C2xC4)320,624
C5⋊2C8.46(C2×C4) = C20.37C42φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8160C5:2C8.46(C2xC4)320,749
C5⋊2C8.47(C2×C4) = (C2×C8)⋊6F5φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8804C5:2C8.47(C2xC4)320,1059
C5⋊2C8.48(C2×C4) = C2×C40.C4φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8160C5:2C8.48(C2xC4)320,1060
C5⋊2C8.49(C2×C4) = C2×D10.Q8φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8160C5:2C8.49(C2xC4)320,1061
C5⋊2C8.50(C2×C4) = (C8×D5).C4φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8804C5:2C8.50(C2xC4)320,1062
C5⋊2C8.51(C2×C4) = C2×D5⋊C16φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8160C5:2C8.51(C2xC4)320,1051
C5⋊2C8.52(C2×C4) = C2×C8.F5φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8160C5:2C8.52(C2xC4)320,1052
C5⋊2C8.53(C2×C4) = D5⋊M5(2)φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8804C5:2C8.53(C2xC4)320,1053
C5⋊2C8.54(C2×C4) = C20.12C42φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8804C5:2C8.54(C2xC4)320,1056
C5⋊2C8.55(C2×C4) = C22×C5⋊C16φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8320C5:2C8.55(C2xC4)320,1080
C5⋊2C8.56(C2×C4) = C2×C20.C8φ: C2×C4/C22 → C2 ⊆ Out C5⋊2C8160C5:2C8.56(C2xC4)320,1081
C5⋊2C8.57(C2×C4) = D5×C2×C16φ: trivial image160C5:2C8.57(C2xC4)320,526

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