# Extensions 1→N→G→Q→1 with N=C10 and Q=C2×M4(2)

Direct product G=N×Q with N=C10 and Q=C2×M4(2)
dρLabelID
M4(2)×C2×C10160M4(2)xC2xC10320,1568

Semidirect products G=N:Q with N=C10 and Q=C2×M4(2)
extensionφ:Q→Aut NdρLabelID
C101(C2×M4(2)) = C22×C4.F5φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10160C10:1(C2xM4(2))320,1588
C102(C2×M4(2)) = C2×D5⋊M4(2)φ: C2×M4(2)/C2×C4C4 ⊆ Aut C1080C10:2(C2xM4(2))320,1589
C103(C2×M4(2)) = C22×C22.F5φ: C2×M4(2)/C23C4 ⊆ Aut C10160C10:3(C2xM4(2))320,1606
C104(C2×M4(2)) = C22×C8⋊D5φ: C2×M4(2)/C2×C8C2 ⊆ Aut C10160C10:4(C2xM4(2))320,1409
C105(C2×M4(2)) = C2×D5×M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C1080C10:5(C2xM4(2))320,1415
C106(C2×M4(2)) = C22×C4.Dic5φ: C2×M4(2)/C22×C4C2 ⊆ Aut C10160C10:6(C2xM4(2))320,1453

Non-split extensions G=N.Q with N=C10 and Q=C2×M4(2)
extensionφ:Q→Aut NdρLabelID
C10.1(C2×M4(2)) = C42.5F5φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10160C10.1(C2xM4(2))320,1014
C10.2(C2×M4(2)) = C4×C4.F5φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10160C10.2(C2xM4(2))320,1015
C10.3(C2×M4(2)) = C42.6F5φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10160C10.3(C2xM4(2))320,1016
C10.4(C2×M4(2)) = C42.11F5φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10160C10.4(C2xM4(2))320,1017
C10.5(C2×M4(2)) = C42.12F5φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10160C10.5(C2xM4(2))320,1018
C10.6(C2×M4(2)) = C203M4(2)φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10160C10.6(C2xM4(2))320,1019
C10.7(C2×M4(2)) = C42.14F5φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10160C10.7(C2xM4(2))320,1020
C10.8(C2×M4(2)) = C42.15F5φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10160C10.8(C2xM4(2))320,1021
C10.9(C2×M4(2)) = C42.7F5φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10160C10.9(C2xM4(2))320,1022
C10.10(C2×M4(2)) = C5⋊C8⋊D4φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10160C10.10(C2xM4(2))320,1031
C10.11(C2×M4(2)) = D10⋊M4(2)φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10160C10.11(C2xM4(2))320,1032
C10.12(C2×M4(2)) = Dic5⋊M4(2)φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10160C10.12(C2xM4(2))320,1033
C10.13(C2×M4(2)) = D102M4(2)φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10160C10.13(C2xM4(2))320,1042
C10.14(C2×M4(2)) = C20⋊M4(2)φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10160C10.14(C2xM4(2))320,1043
C10.15(C2×M4(2)) = Dic5.M4(2)φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10320C10.15(C2xM4(2))320,1045
C10.16(C2×M4(2)) = C20.M4(2)φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10320C10.16(C2xM4(2))320,1047
C10.17(C2×M4(2)) = C2×C20⋊C8φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10320C10.17(C2xM4(2))320,1085
C10.18(C2×M4(2)) = Dic5.12M4(2)φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10160C10.18(C2xM4(2))320,1086
C10.19(C2×M4(2)) = C2×D10⋊C8φ: C2×M4(2)/C2×C4C4 ⊆ Aut C10160C10.19(C2xM4(2))320,1089
C10.20(C2×M4(2)) = D10.11M4(2)φ: C2×M4(2)/C2×C4C4 ⊆ Aut C1080C10.20(C2xM4(2))320,1091
C10.21(C2×M4(2)) = D109M4(2)φ: C2×M4(2)/C2×C4C4 ⊆ Aut C1080C10.21(C2xM4(2))320,1093
C10.22(C2×M4(2)) = D1010M4(2)φ: C2×M4(2)/C2×C4C4 ⊆ Aut C1080C10.22(C2xM4(2))320,1094
C10.23(C2×M4(2)) = C2×C10.C42φ: C2×M4(2)/C23C4 ⊆ Aut C10320C10.23(C2xM4(2))320,1087
C10.24(C2×M4(2)) = C4×C22.F5φ: C2×M4(2)/C23C4 ⊆ Aut C10160C10.24(C2xM4(2))320,1088
C10.25(C2×M4(2)) = C2×Dic5⋊C8φ: C2×M4(2)/C23C4 ⊆ Aut C10320C10.25(C2xM4(2))320,1090
C10.26(C2×M4(2)) = C20.34M4(2)φ: C2×M4(2)/C23C4 ⊆ Aut C10160C10.26(C2xM4(2))320,1092
C10.27(C2×M4(2)) = Dic5.13M4(2)φ: C2×M4(2)/C23C4 ⊆ Aut C10160C10.27(C2xM4(2))320,1095
C10.28(C2×M4(2)) = C208M4(2)φ: C2×M4(2)/C23C4 ⊆ Aut C10160C10.28(C2xM4(2))320,1096
C10.29(C2×M4(2)) = C20.30M4(2)φ: C2×M4(2)/C23C4 ⊆ Aut C10160C10.29(C2xM4(2))320,1097
C10.30(C2×M4(2)) = C5⋊C87D4φ: C2×M4(2)/C23C4 ⊆ Aut C10160C10.30(C2xM4(2))320,1111
C10.31(C2×M4(2)) = C202M4(2)φ: C2×M4(2)/C23C4 ⊆ Aut C10160C10.31(C2xM4(2))320,1112
C10.32(C2×M4(2)) = C20.6M4(2)φ: C2×M4(2)/C23C4 ⊆ Aut C10320C10.32(C2xM4(2))320,1126
C10.33(C2×M4(2)) = C2×C23.2F5φ: C2×M4(2)/C23C4 ⊆ Aut C10160C10.33(C2xM4(2))320,1135
C10.34(C2×M4(2)) = C24.4F5φ: C2×M4(2)/C23C4 ⊆ Aut C1080C10.34(C2xM4(2))320,1136
C10.35(C2×M4(2)) = C4011Q8φ: C2×M4(2)/C2×C8C2 ⊆ Aut C10320C10.35(C2xM4(2))320,306
C10.36(C2×M4(2)) = C42.282D10φ: C2×M4(2)/C2×C8C2 ⊆ Aut C10160C10.36(C2xM4(2))320,312
C10.37(C2×M4(2)) = C4×C8⋊D5φ: C2×M4(2)/C2×C8C2 ⊆ Aut C10160C10.37(C2xM4(2))320,314
C10.38(C2×M4(2)) = C86D20φ: C2×M4(2)/C2×C8C2 ⊆ Aut C10160C10.38(C2xM4(2))320,315
C10.39(C2×M4(2)) = D107M4(2)φ: C2×M4(2)/C2×C8C2 ⊆ Aut C1080C10.39(C2xM4(2))320,353
C10.40(C2×M4(2)) = C52C826D4φ: C2×M4(2)/C2×C8C2 ⊆ Aut C10160C10.40(C2xM4(2))320,357
C10.41(C2×M4(2)) = C42.198D10φ: C2×M4(2)/C2×C8C2 ⊆ Aut C10320C10.41(C2xM4(2))320,458
C10.42(C2×M4(2)) = C205M4(2)φ: C2×M4(2)/C2×C8C2 ⊆ Aut C10160C10.42(C2xM4(2))320,464
C10.43(C2×M4(2)) = C206M4(2)φ: C2×M4(2)/C2×C8C2 ⊆ Aut C10160C10.43(C2xM4(2))320,465
C10.44(C2×M4(2)) = C2×C20.8Q8φ: C2×M4(2)/C2×C8C2 ⊆ Aut C10320C10.44(C2xM4(2))320,726
C10.45(C2×M4(2)) = C2×C408C4φ: C2×M4(2)/C2×C8C2 ⊆ Aut C10320C10.45(C2xM4(2))320,727
C10.46(C2×M4(2)) = C2×D101C8φ: C2×M4(2)/C2×C8C2 ⊆ Aut C10160C10.46(C2xM4(2))320,735
C10.47(C2×M4(2)) = C4032D4φ: C2×M4(2)/C2×C8C2 ⊆ Aut C10160C10.47(C2xM4(2))320,738
C10.48(C2×M4(2)) = C40⋊Q8φ: C2×M4(2)/M4(2)C2 ⊆ Aut C10320C10.48(C2xM4(2))320,328
C10.49(C2×M4(2)) = D5×C8⋊C4φ: C2×M4(2)/M4(2)C2 ⊆ Aut C10160C10.49(C2xM4(2))320,331
C10.50(C2×M4(2)) = C42.182D10φ: C2×M4(2)/M4(2)C2 ⊆ Aut C10160C10.50(C2xM4(2))320,332
C10.51(C2×M4(2)) = C89D20φ: C2×M4(2)/M4(2)C2 ⊆ Aut C10160C10.51(C2xM4(2))320,333
C10.52(C2×M4(2)) = D10.6C42φ: C2×M4(2)/M4(2)C2 ⊆ Aut C10160C10.52(C2xM4(2))320,334
C10.53(C2×M4(2)) = Dic5.14M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C10160C10.53(C2xM4(2))320,345
C10.54(C2×M4(2)) = Dic5.9M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C10160C10.54(C2xM4(2))320,346
C10.55(C2×M4(2)) = D5×C22⋊C8φ: C2×M4(2)/M4(2)C2 ⊆ Aut C1080C10.55(C2xM4(2))320,351
C10.56(C2×M4(2)) = D104M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C10160C10.56(C2xM4(2))320,355
C10.57(C2×M4(2)) = Dic52M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C10160C10.57(C2xM4(2))320,356
C10.58(C2×M4(2)) = Dic5.5M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C10320C10.58(C2xM4(2))320,455
C10.59(C2×M4(2)) = D5×C4⋊C8φ: C2×M4(2)/M4(2)C2 ⊆ Aut C10160C10.59(C2xM4(2))320,459
C10.60(C2×M4(2)) = C42.200D10φ: C2×M4(2)/M4(2)C2 ⊆ Aut C10160C10.60(C2xM4(2))320,460
C10.61(C2×M4(2)) = C42.202D10φ: C2×M4(2)/M4(2)C2 ⊆ Aut C10160C10.61(C2xM4(2))320,462
C10.62(C2×M4(2)) = D105M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C10160C10.62(C2xM4(2))320,463
C10.63(C2×M4(2)) = M4(2)×Dic5φ: C2×M4(2)/M4(2)C2 ⊆ Aut C10160C10.63(C2xM4(2))320,744
C10.64(C2×M4(2)) = Dic55M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C10160C10.64(C2xM4(2))320,745
C10.65(C2×M4(2)) = D108M4(2)φ: C2×M4(2)/M4(2)C2 ⊆ Aut C1080C10.65(C2xM4(2))320,753
C10.66(C2×M4(2)) = C40⋊D4φ: C2×M4(2)/M4(2)C2 ⊆ Aut C10160C10.66(C2xM4(2))320,754
C10.67(C2×M4(2)) = C4018D4φ: C2×M4(2)/M4(2)C2 ⊆ Aut C10160C10.67(C2xM4(2))320,755
C10.68(C2×M4(2)) = C2×C42.D5φ: C2×M4(2)/C22×C4C2 ⊆ Aut C10320C10.68(C2xM4(2))320,548
C10.69(C2×M4(2)) = C4×C4.Dic5φ: C2×M4(2)/C22×C4C2 ⊆ Aut C10160C10.69(C2xM4(2))320,549
C10.70(C2×M4(2)) = C2×C203C8φ: C2×M4(2)/C22×C4C2 ⊆ Aut C10320C10.70(C2xM4(2))320,550
C10.71(C2×M4(2)) = C2013M4(2)φ: C2×M4(2)/C22×C4C2 ⊆ Aut C10160C10.71(C2xM4(2))320,551
C10.72(C2×M4(2)) = C42.6Dic5φ: C2×M4(2)/C22×C4C2 ⊆ Aut C10160C10.72(C2xM4(2))320,552
C10.73(C2×M4(2)) = C42.7Dic5φ: C2×M4(2)/C22×C4C2 ⊆ Aut C10160C10.73(C2xM4(2))320,553
C10.74(C2×M4(2)) = C42.47D10φ: C2×M4(2)/C22×C4C2 ⊆ Aut C10160C10.74(C2xM4(2))320,638
C10.75(C2×M4(2)) = C207M4(2)φ: C2×M4(2)/C22×C4C2 ⊆ Aut C10160C10.75(C2xM4(2))320,639
C10.76(C2×M4(2)) = C42.210D10φ: C2×M4(2)/C22×C4C2 ⊆ Aut C10320C10.76(C2xM4(2))320,651
C10.77(C2×M4(2)) = C2×C20.55D4φ: C2×M4(2)/C22×C4C2 ⊆ Aut C10160C10.77(C2xM4(2))320,833
C10.78(C2×M4(2)) = C24.4Dic5φ: C2×M4(2)/C22×C4C2 ⊆ Aut C1080C10.78(C2xM4(2))320,834
C10.79(C2×M4(2)) = C10×C8⋊C4central extension (φ=1)320C10.79(C2xM4(2))320,904
C10.80(C2×M4(2)) = M4(2)×C20central extension (φ=1)160C10.80(C2xM4(2))320,905
C10.81(C2×M4(2)) = C10×C22⋊C8central extension (φ=1)160C10.81(C2xM4(2))320,907
C10.82(C2×M4(2)) = C5×C24.4C4central extension (φ=1)80C10.82(C2xM4(2))320,908
C10.83(C2×M4(2)) = C10×C4⋊C8central extension (φ=1)320C10.83(C2xM4(2))320,923
C10.84(C2×M4(2)) = C5×C4⋊M4(2)central extension (φ=1)160C10.84(C2xM4(2))320,924
C10.85(C2×M4(2)) = C5×C42.12C4central extension (φ=1)160C10.85(C2xM4(2))320,932
C10.86(C2×M4(2)) = C5×C42.6C4central extension (φ=1)160C10.86(C2xM4(2))320,933
C10.87(C2×M4(2)) = C5×C89D4central extension (φ=1)160C10.87(C2xM4(2))320,936
C10.88(C2×M4(2)) = C5×C86D4central extension (φ=1)160C10.88(C2xM4(2))320,937
C10.89(C2×M4(2)) = C5×C84Q8central extension (φ=1)320C10.89(C2xM4(2))320,947

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