Extensions 1→N→G→Q→1 with N=C4 and Q=C2×C4×D5

Direct product G=N×Q with N=C4 and Q=C2×C4×D5
dρLabelID
D5×C2×C42160D5xC2xC4^2320,1143

Semidirect products G=N:Q with N=C4 and Q=C2×C4×D5
extensionφ:Q→Aut NdρLabelID
C41(C2×C4×D5) = C4×D4×D5φ: C2×C4×D5/C4×D5C2 ⊆ Aut C480C4:1(C2xC4xD5)320,1216
C42(C2×C4×D5) = C2×D208C4φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C4160C4:2(C2xC4xD5)320,1175
C43(C2×C4×D5) = C2×C4×D20φ: C2×C4×D5/C2×C20C2 ⊆ Aut C4160C4:3(C2xC4xD5)320,1145
C44(C2×C4×D5) = C2×D5×C4⋊C4φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4160C4:4(C2xC4xD5)320,1173

Non-split extensions G=N.Q with N=C4 and Q=C2×C4×D5
extensionφ:Q→Aut NdρLabelID
C4.1(C2×C4×D5) = Dic54D8φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.1(C2xC4xD5)320,383
C4.2(C2×C4×D5) = D4.D55C4φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.2(C2xC4xD5)320,384
C4.3(C2×C4×D5) = Dic56SD16φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.3(C2xC4xD5)320,385
C4.4(C2×C4×D5) = D5×D4⋊C4φ: C2×C4×D5/C4×D5C2 ⊆ Aut C480C4.4(C2xC4xD5)320,396
C4.5(C2×C4×D5) = (D4×D5)⋊C4φ: C2×C4×D5/C4×D5C2 ⊆ Aut C480C4.5(C2xC4xD5)320,397
C4.6(C2×C4×D5) = D4⋊(C4×D5)φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.6(C2xC4xD5)320,398
C4.7(C2×C4×D5) = D42D5⋊C4φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.7(C2xC4xD5)320,399
C4.8(C2×C4×D5) = D4⋊D56C4φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.8(C2xC4xD5)320,412
C4.9(C2×C4×D5) = Dic57SD16φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.9(C2xC4xD5)320,415
C4.10(C2×C4×D5) = C5⋊Q165C4φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4320C4.10(C2xC4xD5)320,416
C4.11(C2×C4×D5) = Dic54Q16φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4320C4.11(C2xC4xD5)320,417
C4.12(C2×C4×D5) = D5×Q8⋊C4φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.12(C2xC4xD5)320,428
C4.13(C2×C4×D5) = (Q8×D5)⋊C4φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.13(C2xC4xD5)320,429
C4.14(C2×C4×D5) = Q8⋊(C4×D5)φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.14(C2xC4xD5)320,430
C4.15(C2×C4×D5) = Q82D5⋊C4φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.15(C2xC4xD5)320,431
C4.16(C2×C4×D5) = Q8⋊D56C4φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.16(C2xC4xD5)320,444
C4.17(C2×C4×D5) = D5×C4≀C2φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4404C4.17(C2xC4xD5)320,447
C4.18(C2×C4×D5) = C42⋊D10φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4804C4.18(C2xC4xD5)320,448
C4.19(C2×C4×D5) = M4(2).22D10φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4804C4.19(C2xC4xD5)320,450
C4.20(C2×C4×D5) = C42.196D10φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4804C4.20(C2xC4xD5)320,451
C4.21(C2×C4×D5) = C4×D4⋊D5φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.21(C2xC4xD5)320,640
C4.22(C2×C4×D5) = C42.48D10φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.22(C2xC4xD5)320,641
C4.23(C2×C4×D5) = C4×D4.D5φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.23(C2xC4xD5)320,644
C4.24(C2×C4×D5) = C42.51D10φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.24(C2xC4xD5)320,645
C4.25(C2×C4×D5) = C4×Q8⋊D5φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.25(C2xC4xD5)320,652
C4.26(C2×C4×D5) = C42.56D10φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.26(C2xC4xD5)320,653
C4.27(C2×C4×D5) = C4×C5⋊Q16φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4320C4.27(C2xC4xD5)320,656
C4.28(C2×C4×D5) = C42.59D10φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4320C4.28(C2xC4xD5)320,657
C4.29(C2×C4×D5) = C40.93D4φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4804C4.29(C2xC4xD5)320,771
C4.30(C2×C4×D5) = C40.50D4φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4804C4.30(C2xC4xD5)320,772
C4.31(C2×C4×D5) = C4×D42D5φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.31(C2xC4xD5)320,1208
C4.32(C2×C4×D5) = C4211D10φ: C2×C4×D5/C4×D5C2 ⊆ Aut C480C4.32(C2xC4xD5)320,1217
C4.33(C2×C4×D5) = C42.108D10φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.33(C2xC4xD5)320,1218
C4.34(C2×C4×D5) = C4×Q8×D5φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.34(C2xC4xD5)320,1243
C4.35(C2×C4×D5) = C42.125D10φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.35(C2xC4xD5)320,1244
C4.36(C2×C4×D5) = C4×Q82D5φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.36(C2xC4xD5)320,1245
C4.37(C2×C4×D5) = C42.126D10φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4160C4.37(C2xC4xD5)320,1246
C4.38(C2×C4×D5) = D5×C8○D4φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4804C4.38(C2xC4xD5)320,1421
C4.39(C2×C4×D5) = C20.72C24φ: C2×C4×D5/C4×D5C2 ⊆ Aut C4804C4.39(C2xC4xD5)320,1422
C4.40(C2×C4×D5) = Dic58SD16φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C4160C4.40(C2xC4xD5)320,479
C4.41(C2×C4×D5) = Dic2015C4φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C4320C4.41(C2xC4xD5)320,480
C4.42(C2×C4×D5) = D4015C4φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C4160C4.42(C2xC4xD5)320,496
C4.43(C2×C4×D5) = D4012C4φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C4160C4.43(C2xC4xD5)320,499
C4.44(C2×C4×D5) = Dic55Q16φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C4320C4.44(C2xC4xD5)320,500
C4.45(C2×C4×D5) = C4021(C2×C4)φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C4160C4.45(C2xC4xD5)320,516
C4.46(C2×C4×D5) = D4016C4φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C4804C4.46(C2xC4xD5)320,521
C4.47(C2×C4×D5) = D4013C4φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C4804C4.47(C2xC4xD5)320,522
C4.48(C2×C4×D5) = C2×D206C4φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C4160C4.48(C2xC4xD5)320,592
C4.49(C2×C4×D5) = C4○D209C4φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C4160C4.49(C2xC4xD5)320,593
C4.50(C2×C4×D5) = C2×C10.Q16φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C4320C4.50(C2xC4xD5)320,596
C4.51(C2×C4×D5) = C4⋊C436D10φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C480C4.51(C2xC4xD5)320,628
C4.52(C2×C4×D5) = C4○D2010C4φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C4160C4.52(C2xC4xD5)320,629
C4.53(C2×C4×D5) = C4.(C2×D20)φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C4160C4.53(C2xC4xD5)320,631
C4.54(C2×C4×D5) = C2×D207C4φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C480C4.54(C2xC4xD5)320,765
C4.55(C2×C4×D5) = C23.20D20φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C4804C4.55(C2xC4xD5)320,766
C4.56(C2×C4×D5) = C2×Dic53Q8φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C4320C4.56(C2xC4xD5)320,1168
C4.57(C2×C4×D5) = C42.87D10φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C4160C4.57(C2xC4xD5)320,1188
C4.58(C2×C4×D5) = C427D10φ: C2×C4×D5/C2×Dic5C2 ⊆ Aut C480C4.58(C2xC4xD5)320,1193
C4.59(C2×C4×D5) = C4×C40⋊C2φ: C2×C4×D5/C2×C20C2 ⊆ Aut C4160C4.59(C2xC4xD5)320,318
C4.60(C2×C4×D5) = C4×D40φ: C2×C4×D5/C2×C20C2 ⊆ Aut C4160C4.60(C2xC4xD5)320,319
C4.61(C2×C4×D5) = C4×Dic20φ: C2×C4×D5/C2×C20C2 ⊆ Aut C4320C4.61(C2xC4xD5)320,325
C4.62(C2×C4×D5) = D4017C4φ: C2×C4×D5/C2×C20C2 ⊆ Aut C4802C4.62(C2xC4xD5)320,327
C4.63(C2×C4×D5) = C42.16D10φ: C2×C4×D5/C2×C20C2 ⊆ Aut C4160C4.63(C2xC4xD5)320,337
C4.64(C2×C4×D5) = D409C4φ: C2×C4×D5/C2×C20C2 ⊆ Aut C4160C4.64(C2xC4xD5)320,338
C4.65(C2×C4×D5) = Dic209C4φ: C2×C4×D5/C2×C20C2 ⊆ Aut C4320C4.65(C2xC4xD5)320,343
C4.66(C2×C4×D5) = D4010C4φ: C2×C4×D5/C2×C20C2 ⊆ Aut C4804C4.66(C2xC4xD5)320,344
C4.67(C2×C4×D5) = C2×D204C4φ: C2×C4×D5/C2×C20C2 ⊆ Aut C480C4.67(C2xC4xD5)320,554
C4.68(C2×C4×D5) = C424D10φ: C2×C4×D5/C2×C20C2 ⊆ Aut C4804C4.68(C2xC4xD5)320,632
C4.69(C2×C4×D5) = C2×C20.44D4φ: C2×C4×D5/C2×C20C2 ⊆ Aut C4320C4.69(C2xC4xD5)320,730
C4.70(C2×C4×D5) = C2×D205C4φ: C2×C4×D5/C2×C20C2 ⊆ Aut C4160C4.70(C2xC4xD5)320,739
C4.71(C2×C4×D5) = C23.23D20φ: C2×C4×D5/C2×C20C2 ⊆ Aut C4160C4.71(C2xC4xD5)320,740
C4.72(C2×C4×D5) = C23.46D20φ: C2×C4×D5/C2×C20C2 ⊆ Aut C4160C4.72(C2xC4xD5)320,747
C4.73(C2×C4×D5) = C23.48D20φ: C2×C4×D5/C2×C20C2 ⊆ Aut C480C4.73(C2xC4xD5)320,758
C4.74(C2×C4×D5) = C23.49D20φ: C2×C4×D5/C2×C20C2 ⊆ Aut C4160C4.74(C2xC4xD5)320,760
C4.75(C2×C4×D5) = C2×C4×Dic10φ: C2×C4×D5/C2×C20C2 ⊆ Aut C4320C4.75(C2xC4xD5)320,1139
C4.76(C2×C4×D5) = D5×C4.Q8φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4160C4.76(C2xC4xD5)320,486
C4.77(C2×C4×D5) = (C8×D5)⋊C4φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4160C4.77(C2xC4xD5)320,487
C4.78(C2×C4×D5) = C8⋊(C4×D5)φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4160C4.78(C2xC4xD5)320,488
C4.79(C2×C4×D5) = D5×C2.D8φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4160C4.79(C2xC4xD5)320,506
C4.80(C2×C4×D5) = C8.27(C4×D5)φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4160C4.80(C2xC4xD5)320,507
C4.81(C2×C4×D5) = C4020(C2×C4)φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4160C4.81(C2xC4xD5)320,508
C4.82(C2×C4×D5) = D5×C8.C4φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4804C4.82(C2xC4xD5)320,519
C4.83(C2×C4×D5) = M4(2).25D10φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4804C4.83(C2xC4xD5)320,520
C4.84(C2×C4×D5) = C2×C10.D8φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4320C4.84(C2xC4xD5)320,589
C4.85(C2×C4×D5) = C2×C20.Q8φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4320C4.85(C2xC4xD5)320,590
C4.86(C2×C4×D5) = C20.47(C4⋊C4)φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4160C4.86(C2xC4xD5)320,591
C4.87(C2×C4×D5) = C20.64(C4⋊C4)φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4160C4.87(C2xC4xD5)320,622
C4.88(C2×C4×D5) = C20.76(C4⋊C4)φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4160C4.88(C2xC4xD5)320,625
C4.89(C2×C4×D5) = C2×C20.53D4φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4160C4.89(C2xC4xD5)320,750
C4.90(C2×C4×D5) = C23.Dic10φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4804C4.90(C2xC4xD5)320,751
C4.91(C2×C4×D5) = C2×C4⋊C47D5φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4160C4.91(C2xC4xD5)320,1174
C4.92(C2×C4×D5) = C10.82+ 1+4φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4160C4.92(C2xC4xD5)320,1176
C4.93(C2×C4×D5) = D5×C42⋊C2φ: C2×C4×D5/C22×D5C2 ⊆ Aut C480C4.93(C2xC4xD5)320,1192
C4.94(C2×C4×D5) = C42.91D10φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4160C4.94(C2xC4xD5)320,1195
C4.95(C2×C4×D5) = C40.47C23φ: C2×C4×D5/C22×D5C2 ⊆ Aut C4804C4.95(C2xC4xD5)320,1417
C4.96(C2×C4×D5) = D5×C4×C8central extension (φ=1)160C4.96(C2xC4xD5)320,311
C4.97(C2×C4×D5) = C4×C8⋊D5central extension (φ=1)160C4.97(C2xC4xD5)320,314
C4.98(C2×C4×D5) = D10.5C42central extension (φ=1)160C4.98(C2xC4xD5)320,316
C4.99(C2×C4×D5) = D5×C8⋊C4central extension (φ=1)160C4.99(C2xC4xD5)320,331
C4.100(C2×C4×D5) = D10.6C42central extension (φ=1)160C4.100(C2xC4xD5)320,334
C4.101(C2×C4×D5) = D10.7C42central extension (φ=1)160C4.101(C2xC4xD5)320,335
C4.102(C2×C4×D5) = D5×C2×C16central extension (φ=1)160C4.102(C2xC4xD5)320,526
C4.103(C2×C4×D5) = C2×C80⋊C2central extension (φ=1)160C4.103(C2xC4xD5)320,527
C4.104(C2×C4×D5) = D20.6C8central extension (φ=1)1602C4.104(C2xC4xD5)320,528
C4.105(C2×C4×D5) = D5×M5(2)central extension (φ=1)804C4.105(C2xC4xD5)320,533
C4.106(C2×C4×D5) = D20.5C8central extension (φ=1)1604C4.106(C2xC4xD5)320,534
C4.107(C2×C4×D5) = C2×C4×C52C8central extension (φ=1)320C4.107(C2xC4xD5)320,547
C4.108(C2×C4×D5) = C2×C42.D5central extension (φ=1)320C4.108(C2xC4xD5)320,548
C4.109(C2×C4×D5) = C4×C4.Dic5central extension (φ=1)160C4.109(C2xC4xD5)320,549
C4.110(C2×C4×D5) = C20.35C42central extension (φ=1)160C4.110(C2xC4xD5)320,624
C4.111(C2×C4×D5) = C2×C8×Dic5central extension (φ=1)320C4.111(C2xC4xD5)320,725
C4.112(C2×C4×D5) = C2×C408C4central extension (φ=1)320C4.112(C2xC4xD5)320,727
C4.113(C2×C4×D5) = C20.42C42central extension (φ=1)160C4.113(C2xC4xD5)320,728
C4.114(C2×C4×D5) = M4(2)×Dic5central extension (φ=1)160C4.114(C2xC4xD5)320,744
C4.115(C2×C4×D5) = C20.37C42central extension (φ=1)160C4.115(C2xC4xD5)320,749
C4.116(C2×C4×D5) = C2×C42⋊D5central extension (φ=1)160C4.116(C2xC4xD5)320,1144
C4.117(C2×C4×D5) = C4×C4○D20central extension (φ=1)160C4.117(C2xC4xD5)320,1146
C4.118(C2×C4×D5) = C42.188D10central extension (φ=1)160C4.118(C2xC4xD5)320,1194
C4.119(C2×C4×D5) = D5×C22×C8central extension (φ=1)160C4.119(C2xC4xD5)320,1408
C4.120(C2×C4×D5) = C22×C8⋊D5central extension (φ=1)160C4.120(C2xC4xD5)320,1409
C4.121(C2×C4×D5) = C2×D20.3C4central extension (φ=1)160C4.121(C2xC4xD5)320,1410
C4.122(C2×C4×D5) = C2×D5×M4(2)central extension (φ=1)80C4.122(C2xC4xD5)320,1415
C4.123(C2×C4×D5) = C2×D20.2C4central extension (φ=1)160C4.123(C2xC4xD5)320,1416

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