Extensions 1→N→G→Q→1 with N=C10 and Q=C4×D4

Direct product G=N×Q with N=C10 and Q=C4×D4
dρLabelID
D4×C2×C20160D4xC2xC20320,1517

Semidirect products G=N:Q with N=C10 and Q=C4×D4
extensionφ:Q→Aut NdρLabelID
C10⋊(C4×D4) = C2×D4×F5φ: C4×D4/D4C4 ⊆ Aut C1040C10:(C4xD4)320,1595
C102(C4×D4) = C2×C4×D20φ: C4×D4/C42C2 ⊆ Aut C10160C10:2(C4xD4)320,1145
C103(C4×D4) = C2×Dic54D4φ: C4×D4/C22⋊C4C2 ⊆ Aut C10160C10:3(C4xD4)320,1157
C104(C4×D4) = C2×D208C4φ: C4×D4/C4⋊C4C2 ⊆ Aut C10160C10:4(C4xD4)320,1175
C105(C4×D4) = C2×C4×C5⋊D4φ: C4×D4/C22×C4C2 ⊆ Aut C10160C10:5(C4xD4)320,1460
C106(C4×D4) = C2×D4×Dic5φ: C4×D4/C2×D4C2 ⊆ Aut C10160C10:6(C4xD4)320,1467

Non-split extensions G=N.Q with N=C10 and Q=C4×D4
extensionφ:Q→Aut NdρLabelID
C10.1(C4×D4) = C5⋊C88D4φ: C4×D4/D4C4 ⊆ Aut C10160C10.1(C4xD4)320,1030
C10.2(C4×D4) = C5⋊C8⋊D4φ: C4×D4/D4C4 ⊆ Aut C10160C10.2(C4xD4)320,1031
C10.3(C4×D4) = D10⋊M4(2)φ: C4×D4/D4C4 ⊆ Aut C10160C10.3(C4xD4)320,1032
C10.4(C4×D4) = Dic5⋊M4(2)φ: C4×D4/D4C4 ⊆ Aut C10160C10.4(C4xD4)320,1033
C10.5(C4×D4) = C22⋊C4×F5φ: C4×D4/D4C4 ⊆ Aut C1040C10.5(C4xD4)320,1036
C10.6(C4×D4) = D10⋊(C4⋊C4)φ: C4×D4/D4C4 ⊆ Aut C1040C10.6(C4xD4)320,1037
C10.7(C4×D4) = C10.(C4×D4)φ: C4×D4/D4C4 ⊆ Aut C1080C10.7(C4xD4)320,1038
C10.8(C4×D4) = D202C8φ: C4×D4/D4C4 ⊆ Aut C10160C10.8(C4xD4)320,1040
C10.9(C4×D4) = D102M4(2)φ: C4×D4/D4C4 ⊆ Aut C10160C10.9(C4xD4)320,1042
C10.10(C4×D4) = C20⋊M4(2)φ: C4×D4/D4C4 ⊆ Aut C10160C10.10(C4xD4)320,1043
C10.11(C4×D4) = C4⋊C4×F5φ: C4×D4/D4C4 ⊆ Aut C1080C10.11(C4xD4)320,1048
C10.12(C4×D4) = C4⋊C45F5φ: C4×D4/D4C4 ⊆ Aut C1080C10.12(C4xD4)320,1049
C10.13(C4×D4) = C20⋊(C4⋊C4)φ: C4×D4/D4C4 ⊆ Aut C1080C10.13(C4xD4)320,1050
C10.14(C4×D4) = D8×F5φ: C4×D4/D4C4 ⊆ Aut C10408+C10.14(C4xD4)320,1068
C10.15(C4×D4) = D40⋊C4φ: C4×D4/D4C4 ⊆ Aut C10408+C10.15(C4xD4)320,1069
C10.16(C4×D4) = D85F5φ: C4×D4/D4C4 ⊆ Aut C10808-C10.16(C4xD4)320,1070
C10.17(C4×D4) = D8⋊F5φ: C4×D4/D4C4 ⊆ Aut C10808-C10.17(C4xD4)320,1071
C10.18(C4×D4) = SD16×F5φ: C4×D4/D4C4 ⊆ Aut C10408C10.18(C4xD4)320,1072
C10.19(C4×D4) = SD16⋊F5φ: C4×D4/D4C4 ⊆ Aut C10408C10.19(C4xD4)320,1073
C10.20(C4×D4) = SD163F5φ: C4×D4/D4C4 ⊆ Aut C10808C10.20(C4xD4)320,1074
C10.21(C4×D4) = SD162F5φ: C4×D4/D4C4 ⊆ Aut C10808C10.21(C4xD4)320,1075
C10.22(C4×D4) = Q16×F5φ: C4×D4/D4C4 ⊆ Aut C10808-C10.22(C4xD4)320,1076
C10.23(C4×D4) = Dic20⋊C4φ: C4×D4/D4C4 ⊆ Aut C10808-C10.23(C4xD4)320,1077
C10.24(C4×D4) = Q165F5φ: C4×D4/D4C4 ⊆ Aut C10808+C10.24(C4xD4)320,1078
C10.25(C4×D4) = Q16⋊F5φ: C4×D4/D4C4 ⊆ Aut C10808+C10.25(C4xD4)320,1079
C10.26(C4×D4) = D4×C5⋊C8φ: C4×D4/D4C4 ⊆ Aut C10160C10.26(C4xD4)320,1110
C10.27(C4×D4) = C5⋊C87D4φ: C4×D4/D4C4 ⊆ Aut C10160C10.27(C4xD4)320,1111
C10.28(C4×D4) = C202M4(2)φ: C4×D4/D4C4 ⊆ Aut C10160C10.28(C4xD4)320,1112
C10.29(C4×D4) = (C2×F5)⋊D4φ: C4×D4/D4C4 ⊆ Aut C1040C10.29(C4xD4)320,1117
C10.30(C4×D4) = C2.(D4×F5)φ: C4×D4/D4C4 ⊆ Aut C1080C10.30(C4xD4)320,1118
C10.31(C4×D4) = C2.(C4×D20)φ: C4×D4/C42C2 ⊆ Aut C10320C10.31(C4xD4)320,280
C10.32(C4×D4) = (C2×C4)⋊9D20φ: C4×D4/C42C2 ⊆ Aut C10160C10.32(C4xD4)320,292
C10.33(C4×D4) = D103(C4⋊C4)φ: C4×D4/C42C2 ⊆ Aut C10160C10.33(C4xD4)320,295
C10.34(C4×D4) = C8×D20φ: C4×D4/C42C2 ⊆ Aut C10160C10.34(C4xD4)320,313
C10.35(C4×D4) = C86D20φ: C4×D4/C42C2 ⊆ Aut C10160C10.35(C4xD4)320,315
C10.36(C4×D4) = C4×C40⋊C2φ: C4×D4/C42C2 ⊆ Aut C10160C10.36(C4xD4)320,318
C10.37(C4×D4) = C4×D40φ: C4×D4/C42C2 ⊆ Aut C10160C10.37(C4xD4)320,319
C10.38(C4×D4) = C4×Dic20φ: C4×D4/C42C2 ⊆ Aut C10320C10.38(C4xD4)320,325
C10.39(C4×D4) = D4017C4φ: C4×D4/C42C2 ⊆ Aut C10802C10.39(C4xD4)320,327
C10.40(C4×D4) = C89D20φ: C4×D4/C42C2 ⊆ Aut C10160C10.40(C4xD4)320,333
C10.41(C4×D4) = C42.16D10φ: C4×D4/C42C2 ⊆ Aut C10160C10.41(C4xD4)320,337
C10.42(C4×D4) = D409C4φ: C4×D4/C42C2 ⊆ Aut C10160C10.42(C4xD4)320,338
C10.43(C4×D4) = Dic209C4φ: C4×D4/C42C2 ⊆ Aut C10320C10.43(C4xD4)320,343
C10.44(C4×D4) = D4010C4φ: C4×D4/C42C2 ⊆ Aut C10804C10.44(C4xD4)320,344
C10.45(C4×D4) = C207(C4⋊C4)φ: C4×D4/C42C2 ⊆ Aut C10320C10.45(C4xD4)320,555
C10.46(C4×D4) = C4×C4⋊Dic5φ: C4×D4/C42C2 ⊆ Aut C10320C10.46(C4xD4)320,561
C10.47(C4×D4) = C4×D10⋊C4φ: C4×D4/C42C2 ⊆ Aut C10160C10.47(C4xD4)320,565
C10.48(C4×D4) = (C2×C4)⋊6D20φ: C4×D4/C42C2 ⊆ Aut C10160C10.48(C4xD4)320,566
C10.49(C4×D4) = C10.49(C4×D4)φ: C4×D4/C22⋊C4C2 ⊆ Aut C10320C10.49(C4xD4)320,274
C10.50(C4×D4) = Dic52C42φ: C4×D4/C22⋊C4C2 ⊆ Aut C10320C10.50(C4xD4)320,276
C10.51(C4×D4) = C10.51(C4×D4)φ: C4×D4/C22⋊C4C2 ⊆ Aut C10320C10.51(C4xD4)320,279
C10.52(C4×D4) = C10.52(C4×D4)φ: C4×D4/C22⋊C4C2 ⊆ Aut C10320C10.52(C4xD4)320,282
C10.53(C4×D4) = D102C42φ: C4×D4/C22⋊C4C2 ⊆ Aut C10160C10.53(C4xD4)320,293
C10.54(C4×D4) = C10.54(C4×D4)φ: C4×D4/C22⋊C4C2 ⊆ Aut C10160C10.54(C4xD4)320,296
C10.55(C4×D4) = C10.55(C4×D4)φ: C4×D4/C22⋊C4C2 ⊆ Aut C10160C10.55(C4xD4)320,297
C10.56(C4×D4) = C55(C8×D4)φ: C4×D4/C22⋊C4C2 ⊆ Aut C10160C10.56(C4xD4)320,352
C10.57(C4×D4) = D104M4(2)φ: C4×D4/C22⋊C4C2 ⊆ Aut C10160C10.57(C4xD4)320,355
C10.58(C4×D4) = Dic52M4(2)φ: C4×D4/C22⋊C4C2 ⊆ Aut C10160C10.58(C4xD4)320,356
C10.59(C4×D4) = C52C826D4φ: C4×D4/C22⋊C4C2 ⊆ Aut C10160C10.59(C4xD4)320,357
C10.60(C4×D4) = Dic54D8φ: C4×D4/C22⋊C4C2 ⊆ Aut C10160C10.60(C4xD4)320,383
C10.61(C4×D4) = D4.D55C4φ: C4×D4/C22⋊C4C2 ⊆ Aut C10160C10.61(C4xD4)320,384
C10.62(C4×D4) = Dic56SD16φ: C4×D4/C22⋊C4C2 ⊆ Aut C10160C10.62(C4xD4)320,385
C10.63(C4×D4) = D4⋊D56C4φ: C4×D4/C22⋊C4C2 ⊆ Aut C10160C10.63(C4xD4)320,412
C10.64(C4×D4) = Dic57SD16φ: C4×D4/C22⋊C4C2 ⊆ Aut C10160C10.64(C4xD4)320,415
C10.65(C4×D4) = C5⋊Q165C4φ: C4×D4/C22⋊C4C2 ⊆ Aut C10320C10.65(C4xD4)320,416
C10.66(C4×D4) = Dic54Q16φ: C4×D4/C22⋊C4C2 ⊆ Aut C10320C10.66(C4xD4)320,417
C10.67(C4×D4) = Q8⋊D56C4φ: C4×D4/C22⋊C4C2 ⊆ Aut C10160C10.67(C4xD4)320,444
C10.68(C4×D4) = M4(2).22D10φ: C4×D4/C22⋊C4C2 ⊆ Aut C10804C10.68(C4xD4)320,450
C10.69(C4×D4) = C42.196D10φ: C4×D4/C22⋊C4C2 ⊆ Aut C10804C10.69(C4xD4)320,451
C10.70(C4×D4) = C22⋊C4×Dic5φ: C4×D4/C22⋊C4C2 ⊆ Aut C10160C10.70(C4xD4)320,568
C10.71(C4×D4) = C24.3D10φ: C4×D4/C22⋊C4C2 ⊆ Aut C10160C10.71(C4xD4)320,571
C10.72(C4×D4) = C24.4D10φ: C4×D4/C22⋊C4C2 ⊆ Aut C10160C10.72(C4xD4)320,572
C10.73(C4×D4) = C24.46D10φ: C4×D4/C22⋊C4C2 ⊆ Aut C10160C10.73(C4xD4)320,573
C10.74(C4×D4) = C23.45D20φ: C4×D4/C22⋊C4C2 ⊆ Aut C10160C10.74(C4xD4)320,585
C10.75(C4×D4) = C4⋊Dic515C4φ: C4×D4/C4⋊C4C2 ⊆ Aut C10320C10.75(C4xD4)320,281
C10.76(C4×D4) = D205C8φ: C4×D4/C4⋊C4C2 ⊆ Aut C10160C10.76(C4xD4)320,461
C10.77(C4×D4) = D105M4(2)φ: C4×D4/C4⋊C4C2 ⊆ Aut C10160C10.77(C4xD4)320,463
C10.78(C4×D4) = C206M4(2)φ: C4×D4/C4⋊C4C2 ⊆ Aut C10160C10.78(C4xD4)320,465
C10.79(C4×D4) = Dic58SD16φ: C4×D4/C4⋊C4C2 ⊆ Aut C10160C10.79(C4xD4)320,479
C10.80(C4×D4) = Dic2015C4φ: C4×D4/C4⋊C4C2 ⊆ Aut C10320C10.80(C4xD4)320,480
C10.81(C4×D4) = D4015C4φ: C4×D4/C4⋊C4C2 ⊆ Aut C10160C10.81(C4xD4)320,496
C10.82(C4×D4) = D4012C4φ: C4×D4/C4⋊C4C2 ⊆ Aut C10160C10.82(C4xD4)320,499
C10.83(C4×D4) = Dic55Q16φ: C4×D4/C4⋊C4C2 ⊆ Aut C10320C10.83(C4xD4)320,500
C10.84(C4×D4) = C4021(C2×C4)φ: C4×D4/C4⋊C4C2 ⊆ Aut C10160C10.84(C4xD4)320,516
C10.85(C4×D4) = D4016C4φ: C4×D4/C4⋊C4C2 ⊆ Aut C10804C10.85(C4xD4)320,521
C10.86(C4×D4) = D4013C4φ: C4×D4/C4⋊C4C2 ⊆ Aut C10804C10.86(C4xD4)320,522
C10.87(C4×D4) = C204(C4⋊C4)φ: C4×D4/C4⋊C4C2 ⊆ Aut C10320C10.87(C4xD4)320,600
C10.88(C4×D4) = C4⋊C4×Dic5φ: C4×D4/C4⋊C4C2 ⊆ Aut C10320C10.88(C4xD4)320,602
C10.89(C4×D4) = (C2×D20)⋊22C4φ: C4×D4/C4⋊C4C2 ⊆ Aut C10160C10.89(C4xD4)320,615
C10.90(C4×D4) = C10.90(C4×D4)φ: C4×D4/C4⋊C4C2 ⊆ Aut C10160C10.90(C4xD4)320,617
C10.91(C4×D4) = C4×C10.D4φ: C4×D4/C22×C4C2 ⊆ Aut C10320C10.91(C4xD4)320,558
C10.92(C4×D4) = C10.92(C4×D4)φ: C4×D4/C22×C4C2 ⊆ Aut C10320C10.92(C4xD4)320,560
C10.93(C4×D4) = (C2×C42)⋊D5φ: C4×D4/C22×C4C2 ⊆ Aut C10160C10.93(C4xD4)320,567
C10.94(C4×D4) = C24.12D10φ: C4×D4/C22×C4C2 ⊆ Aut C10160C10.94(C4xD4)320,583
C10.95(C4×D4) = C24.13D10φ: C4×D4/C22×C4C2 ⊆ Aut C10160C10.95(C4xD4)320,584
C10.96(C4×D4) = C10.96(C4×D4)φ: C4×D4/C22×C4C2 ⊆ Aut C10320C10.96(C4xD4)320,599
C10.97(C4×D4) = C10.97(C4×D4)φ: C4×D4/C22×C4C2 ⊆ Aut C10320C10.97(C4xD4)320,605
C10.98(C4×D4) = D105(C4⋊C4)φ: C4×D4/C22×C4C2 ⊆ Aut C10160C10.98(C4xD4)320,616
C10.99(C4×D4) = C4×D4⋊D5φ: C4×D4/C22×C4C2 ⊆ Aut C10160C10.99(C4xD4)320,640
C10.100(C4×D4) = C42.48D10φ: C4×D4/C22×C4C2 ⊆ Aut C10160C10.100(C4xD4)320,641
C10.101(C4×D4) = C4×D4.D5φ: C4×D4/C22×C4C2 ⊆ Aut C10160C10.101(C4xD4)320,644
C10.102(C4×D4) = C42.51D10φ: C4×D4/C22×C4C2 ⊆ Aut C10160C10.102(C4xD4)320,645
C10.103(C4×D4) = C4×Q8⋊D5φ: C4×D4/C22×C4C2 ⊆ Aut C10160C10.103(C4xD4)320,652
C10.104(C4×D4) = C42.56D10φ: C4×D4/C22×C4C2 ⊆ Aut C10160C10.104(C4xD4)320,653
C10.105(C4×D4) = C4×C5⋊Q16φ: C4×D4/C22×C4C2 ⊆ Aut C10320C10.105(C4xD4)320,656
C10.106(C4×D4) = C42.59D10φ: C4×D4/C22×C4C2 ⊆ Aut C10320C10.106(C4xD4)320,657
C10.107(C4×D4) = C8×C5⋊D4φ: C4×D4/C22×C4C2 ⊆ Aut C10160C10.107(C4xD4)320,736
C10.108(C4×D4) = C4032D4φ: C4×D4/C22×C4C2 ⊆ Aut C10160C10.108(C4xD4)320,738
C10.109(C4×D4) = C40⋊D4φ: C4×D4/C22×C4C2 ⊆ Aut C10160C10.109(C4xD4)320,754
C10.110(C4×D4) = C4018D4φ: C4×D4/C22×C4C2 ⊆ Aut C10160C10.110(C4xD4)320,755
C10.111(C4×D4) = C40.93D4φ: C4×D4/C22×C4C2 ⊆ Aut C10804C10.111(C4xD4)320,771
C10.112(C4×D4) = C40.50D4φ: C4×D4/C22×C4C2 ⊆ Aut C10804C10.112(C4xD4)320,772
C10.113(C4×D4) = C4×C23.D5φ: C4×D4/C22×C4C2 ⊆ Aut C10160C10.113(C4xD4)320,836
C10.114(C4×D4) = C24.62D10φ: C4×D4/C22×C4C2 ⊆ Aut C10160C10.114(C4xD4)320,837
C10.115(C4×D4) = C24.65D10φ: C4×D4/C22×C4C2 ⊆ Aut C10160C10.115(C4xD4)320,840
C10.116(C4×D4) = C24.47D10φ: C4×D4/C2×D4C2 ⊆ Aut C10160C10.116(C4xD4)320,577
C10.117(C4×D4) = C24.8D10φ: C4×D4/C2×D4C2 ⊆ Aut C10160C10.117(C4xD4)320,578
C10.118(C4×D4) = C4⋊C45Dic5φ: C4×D4/C2×D4C2 ⊆ Aut C10320C10.118(C4xD4)320,608
C10.119(C4×D4) = C206(C4⋊C4)φ: C4×D4/C2×D4C2 ⊆ Aut C10320C10.119(C4xD4)320,612
C10.120(C4×D4) = D4×C52C8φ: C4×D4/C2×D4C2 ⊆ Aut C10160C10.120(C4xD4)320,637
C10.121(C4×D4) = C42.47D10φ: C4×D4/C2×D4C2 ⊆ Aut C10160C10.121(C4xD4)320,638
C10.122(C4×D4) = C207M4(2)φ: C4×D4/C2×D4C2 ⊆ Aut C10160C10.122(C4xD4)320,639
C10.123(C4×D4) = D8×Dic5φ: C4×D4/C2×D4C2 ⊆ Aut C10160C10.123(C4xD4)320,776
C10.124(C4×D4) = D8⋊Dic5φ: C4×D4/C2×D4C2 ⊆ Aut C10160C10.124(C4xD4)320,779
C10.125(C4×D4) = SD16×Dic5φ: C4×D4/C2×D4C2 ⊆ Aut C10160C10.125(C4xD4)320,788
C10.126(C4×D4) = SD16⋊Dic5φ: C4×D4/C2×D4C2 ⊆ Aut C10160C10.126(C4xD4)320,791
C10.127(C4×D4) = Q16×Dic5φ: C4×D4/C2×D4C2 ⊆ Aut C10320C10.127(C4xD4)320,810
C10.128(C4×D4) = Q16⋊Dic5φ: C4×D4/C2×D4C2 ⊆ Aut C10320C10.128(C4xD4)320,811
C10.129(C4×D4) = D85Dic5φ: C4×D4/C2×D4C2 ⊆ Aut C10804C10.129(C4xD4)320,823
C10.130(C4×D4) = D84Dic5φ: C4×D4/C2×D4C2 ⊆ Aut C10804C10.130(C4xD4)320,824
C10.131(C4×D4) = C24.18D10φ: C4×D4/C2×D4C2 ⊆ Aut C10160C10.131(C4xD4)320,847
C10.132(C4×D4) = C24.19D10φ: C4×D4/C2×D4C2 ⊆ Aut C10160C10.132(C4xD4)320,848
C10.133(C4×D4) = C22⋊C4×C20central extension (φ=1)160C10.133(C4xD4)320,878
C10.134(C4×D4) = C4⋊C4×C20central extension (φ=1)320C10.134(C4xD4)320,879
C10.135(C4×D4) = C5×C23.8Q8central extension (φ=1)160C10.135(C4xD4)320,886
C10.136(C4×D4) = C5×C23.23D4central extension (φ=1)160C10.136(C4xD4)320,887
C10.137(C4×D4) = C5×C23.63C23central extension (φ=1)320C10.137(C4xD4)320,888
C10.138(C4×D4) = C5×C24.C22central extension (φ=1)160C10.138(C4xD4)320,889
C10.139(C4×D4) = C5×C23.65C23central extension (φ=1)320C10.139(C4xD4)320,890
C10.140(C4×D4) = C5×C24.3C22central extension (φ=1)160C10.140(C4xD4)320,891
C10.141(C4×D4) = D4×C40central extension (φ=1)160C10.141(C4xD4)320,935
C10.142(C4×D4) = C5×C89D4central extension (φ=1)160C10.142(C4xD4)320,936
C10.143(C4×D4) = C5×C86D4central extension (φ=1)160C10.143(C4xD4)320,937
C10.144(C4×D4) = D8×C20central extension (φ=1)160C10.144(C4xD4)320,938
C10.145(C4×D4) = SD16×C20central extension (φ=1)160C10.145(C4xD4)320,939
C10.146(C4×D4) = Q16×C20central extension (φ=1)320C10.146(C4xD4)320,940
C10.147(C4×D4) = C5×SD16⋊C4central extension (φ=1)160C10.147(C4xD4)320,941
C10.148(C4×D4) = C5×Q16⋊C4central extension (φ=1)320C10.148(C4xD4)320,942
C10.149(C4×D4) = C5×D8⋊C4central extension (φ=1)160C10.149(C4xD4)320,943
C10.150(C4×D4) = C5×C8○D8central extension (φ=1)802C10.150(C4xD4)320,944
C10.151(C4×D4) = C5×C8.26D4central extension (φ=1)804C10.151(C4xD4)320,945

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