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

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

Semidirect products G=N:Q with N=C4 and Q=D4×C10
extensionφ:Q→Aut NdρLabelID
C41(D4×C10) = C10×C41D4φ: D4×C10/C2×C20C2 ⊆ Aut C4160C4:1(D4xC10)320,1532
C42(D4×C10) = C5×D42φ: D4×C10/C5×D4C2 ⊆ Aut C480C4:2(D4xC10)320,1547
C43(D4×C10) = C10×C4⋊D4φ: D4×C10/C22×C10C2 ⊆ Aut C4160C4:3(D4xC10)320,1524

Non-split extensions G=N.Q with N=C4 and Q=D4×C10
extensionφ:Q→Aut NdρLabelID
C4.1(D4×C10) = C5×C85D4φ: D4×C10/C2×C20C2 ⊆ Aut C4160C4.1(D4xC10)320,993
C4.2(D4×C10) = C5×C84D4φ: D4×C10/C2×C20C2 ⊆ Aut C4160C4.2(D4xC10)320,994
C4.3(D4×C10) = C5×C4⋊Q16φ: D4×C10/C2×C20C2 ⊆ Aut C4320C4.3(D4xC10)320,995
C4.4(D4×C10) = C5×C8.12D4φ: D4×C10/C2×C20C2 ⊆ Aut C4160C4.4(D4xC10)320,996
C4.5(D4×C10) = C5×C83D4φ: D4×C10/C2×C20C2 ⊆ Aut C4160C4.5(D4xC10)320,997
C4.6(D4×C10) = C5×C8.2D4φ: D4×C10/C2×C20C2 ⊆ Aut C4160C4.6(D4xC10)320,998
C4.7(D4×C10) = C10×D16φ: D4×C10/C2×C20C2 ⊆ Aut C4160C4.7(D4xC10)320,1006
C4.8(D4×C10) = C10×SD32φ: D4×C10/C2×C20C2 ⊆ Aut C4160C4.8(D4xC10)320,1007
C4.9(D4×C10) = C10×Q32φ: D4×C10/C2×C20C2 ⊆ Aut C4320C4.9(D4xC10)320,1008
C4.10(D4×C10) = C5×C4○D16φ: D4×C10/C2×C20C2 ⊆ Aut C41602C4.10(D4xC10)320,1009
C4.11(D4×C10) = C5×C16⋊C22φ: D4×C10/C2×C20C2 ⊆ Aut C4804C4.11(D4xC10)320,1010
C4.12(D4×C10) = C5×Q32⋊C2φ: D4×C10/C2×C20C2 ⊆ Aut C41604C4.12(D4xC10)320,1011
C4.13(D4×C10) = C10×C4.4D4φ: D4×C10/C2×C20C2 ⊆ Aut C4160C4.13(D4xC10)320,1528
C4.14(D4×C10) = C10×C4⋊Q8φ: D4×C10/C2×C20C2 ⊆ Aut C4320C4.14(D4xC10)320,1533
C4.15(D4×C10) = C5×C22.26C24φ: D4×C10/C2×C20C2 ⊆ Aut C4160C4.15(D4xC10)320,1534
C4.16(D4×C10) = C5×C22.29C24φ: D4×C10/C2×C20C2 ⊆ Aut C480C4.16(D4xC10)320,1537
C4.17(D4×C10) = C5×C23.38C23φ: D4×C10/C2×C20C2 ⊆ Aut C4160C4.17(D4xC10)320,1538
C4.18(D4×C10) = D8×C2×C10φ: D4×C10/C2×C20C2 ⊆ Aut C4160C4.18(D4xC10)320,1571
C4.19(D4×C10) = SD16×C2×C10φ: D4×C10/C2×C20C2 ⊆ Aut C4160C4.19(D4xC10)320,1572
C4.20(D4×C10) = Q16×C2×C10φ: D4×C10/C2×C20C2 ⊆ Aut C4320C4.20(D4xC10)320,1573
C4.21(D4×C10) = C5×C22⋊D8φ: D4×C10/C5×D4C2 ⊆ Aut C480C4.21(D4xC10)320,948
C4.22(D4×C10) = C5×Q8⋊D4φ: D4×C10/C5×D4C2 ⊆ Aut C4160C4.22(D4xC10)320,949
C4.23(D4×C10) = C5×D4⋊D4φ: D4×C10/C5×D4C2 ⊆ Aut C4160C4.23(D4xC10)320,950
C4.24(D4×C10) = C5×C22⋊SD16φ: D4×C10/C5×D4C2 ⊆ Aut C480C4.24(D4xC10)320,951
C4.25(D4×C10) = C5×C22⋊Q16φ: D4×C10/C5×D4C2 ⊆ Aut C4160C4.25(D4xC10)320,952
C4.26(D4×C10) = C5×D4.7D4φ: D4×C10/C5×D4C2 ⊆ Aut C4160C4.26(D4xC10)320,953
C4.27(D4×C10) = C5×D44D4φ: D4×C10/C5×D4C2 ⊆ Aut C4404C4.27(D4xC10)320,954
C4.28(D4×C10) = C5×D4.8D4φ: D4×C10/C5×D4C2 ⊆ Aut C4804C4.28(D4xC10)320,955
C4.29(D4×C10) = C5×D4.9D4φ: D4×C10/C5×D4C2 ⊆ Aut C4804C4.29(D4xC10)320,956
C4.30(D4×C10) = C5×D4.10D4φ: D4×C10/C5×D4C2 ⊆ Aut C4804C4.30(D4xC10)320,957
C4.31(D4×C10) = C5×C4⋊D8φ: D4×C10/C5×D4C2 ⊆ Aut C4160C4.31(D4xC10)320,960
C4.32(D4×C10) = C5×C4⋊SD16φ: D4×C10/C5×D4C2 ⊆ Aut C4160C4.32(D4xC10)320,961
C4.33(D4×C10) = C5×D4.D4φ: D4×C10/C5×D4C2 ⊆ Aut C4160C4.33(D4xC10)320,962
C4.34(D4×C10) = C5×C42Q16φ: D4×C10/C5×D4C2 ⊆ Aut C4320C4.34(D4xC10)320,963
C4.35(D4×C10) = C5×D4.2D4φ: D4×C10/C5×D4C2 ⊆ Aut C4160C4.35(D4xC10)320,964
C4.36(D4×C10) = C5×Q8.D4φ: D4×C10/C5×D4C2 ⊆ Aut C4160C4.36(D4xC10)320,965
C4.37(D4×C10) = C5×D4.3D4φ: D4×C10/C5×D4C2 ⊆ Aut C4804C4.37(D4xC10)320,972
C4.38(D4×C10) = C5×D4.4D4φ: D4×C10/C5×D4C2 ⊆ Aut C4804C4.38(D4xC10)320,973
C4.39(D4×C10) = C5×D4.5D4φ: D4×C10/C5×D4C2 ⊆ Aut C41604C4.39(D4xC10)320,974
C4.40(D4×C10) = C5×D45D4φ: D4×C10/C5×D4C2 ⊆ Aut C480C4.40(D4xC10)320,1548
C4.41(D4×C10) = C5×D46D4φ: D4×C10/C5×D4C2 ⊆ Aut C4160C4.41(D4xC10)320,1549
C4.42(D4×C10) = C5×Q85D4φ: D4×C10/C5×D4C2 ⊆ Aut C4160C4.42(D4xC10)320,1550
C4.43(D4×C10) = C5×D4×Q8φ: D4×C10/C5×D4C2 ⊆ Aut C4160C4.43(D4xC10)320,1551
C4.44(D4×C10) = C5×Q86D4φ: D4×C10/C5×D4C2 ⊆ Aut C4160C4.44(D4xC10)320,1552
C4.45(D4×C10) = C5×D4○D8φ: D4×C10/C5×D4C2 ⊆ Aut C4804C4.45(D4xC10)320,1578
C4.46(D4×C10) = C5×D4○SD16φ: D4×C10/C5×D4C2 ⊆ Aut C4804C4.46(D4xC10)320,1579
C4.47(D4×C10) = C5×Q8○D8φ: D4×C10/C5×D4C2 ⊆ Aut C41604C4.47(D4xC10)320,1580
C4.48(D4×C10) = C10×C4.D4φ: D4×C10/C22×C10C2 ⊆ Aut C480C4.48(D4xC10)320,912
C4.49(D4×C10) = C10×C4.10D4φ: D4×C10/C22×C10C2 ⊆ Aut C4160C4.49(D4xC10)320,913
C4.50(D4×C10) = C5×M4(2).8C22φ: D4×C10/C22×C10C2 ⊆ Aut C4804C4.50(D4xC10)320,914
C4.51(D4×C10) = C10×D4⋊C4φ: D4×C10/C22×C10C2 ⊆ Aut C4160C4.51(D4xC10)320,915
C4.52(D4×C10) = C10×Q8⋊C4φ: D4×C10/C22×C10C2 ⊆ Aut C4320C4.52(D4xC10)320,916
C4.53(D4×C10) = C5×C23.24D4φ: D4×C10/C22×C10C2 ⊆ Aut C4160C4.53(D4xC10)320,917
C4.54(D4×C10) = C5×C23.36D4φ: D4×C10/C22×C10C2 ⊆ Aut C4160C4.54(D4xC10)320,918
C4.55(D4×C10) = C5×C23.37D4φ: D4×C10/C22×C10C2 ⊆ Aut C480C4.55(D4xC10)320,919
C4.56(D4×C10) = C5×C23.38D4φ: D4×C10/C22×C10C2 ⊆ Aut C4160C4.56(D4xC10)320,920
C4.57(D4×C10) = C5×C88D4φ: D4×C10/C22×C10C2 ⊆ Aut C4160C4.57(D4xC10)320,966
C4.58(D4×C10) = C5×C87D4φ: D4×C10/C22×C10C2 ⊆ Aut C4160C4.58(D4xC10)320,967
C4.59(D4×C10) = C5×C8.18D4φ: D4×C10/C22×C10C2 ⊆ Aut C4160C4.59(D4xC10)320,968
C4.60(D4×C10) = C5×C8⋊D4φ: D4×C10/C22×C10C2 ⊆ Aut C4160C4.60(D4xC10)320,969
C4.61(D4×C10) = C5×C82D4φ: D4×C10/C22×C10C2 ⊆ Aut C4160C4.61(D4xC10)320,970
C4.62(D4×C10) = C5×C8.D4φ: D4×C10/C22×C10C2 ⊆ Aut C4160C4.62(D4xC10)320,971
C4.63(D4×C10) = C10×C22⋊Q8φ: D4×C10/C22×C10C2 ⊆ Aut C4160C4.63(D4xC10)320,1525
C4.64(D4×C10) = C5×C22.19C24φ: D4×C10/C22×C10C2 ⊆ Aut C480C4.64(D4xC10)320,1527
C4.65(D4×C10) = C5×C22.31C24φ: D4×C10/C22×C10C2 ⊆ Aut C4160C4.65(D4xC10)320,1539
C4.66(D4×C10) = C10×C8⋊C22φ: D4×C10/C22×C10C2 ⊆ Aut C480C4.66(D4xC10)320,1575
C4.67(D4×C10) = C10×C8.C22φ: D4×C10/C22×C10C2 ⊆ Aut C4160C4.67(D4xC10)320,1576
C4.68(D4×C10) = C5×D8⋊C22φ: D4×C10/C22×C10C2 ⊆ Aut C4804C4.68(D4xC10)320,1577
C4.69(D4×C10) = C10×C22⋊C8central extension (φ=1)160C4.69(D4xC10)320,907
C4.70(D4×C10) = C5×C24.4C4central extension (φ=1)80C4.70(D4xC10)320,908
C4.71(D4×C10) = C5×(C22×C8)⋊C2central extension (φ=1)160C4.71(D4xC10)320,909
C4.72(D4×C10) = C10×C4≀C2central extension (φ=1)80C4.72(D4xC10)320,921
C4.73(D4×C10) = C5×C42⋊C22central extension (φ=1)804C4.73(D4xC10)320,922
C4.74(D4×C10) = C10×C4⋊C8central extension (φ=1)320C4.74(D4xC10)320,923
C4.75(D4×C10) = C5×C4⋊M4(2)central extension (φ=1)160C4.75(D4xC10)320,924
C4.76(D4×C10) = C5×C42.6C22central extension (φ=1)160C4.76(D4xC10)320,925
C4.77(D4×C10) = C10×C8.C4central extension (φ=1)160C4.77(D4xC10)320,930
C4.78(D4×C10) = C5×M4(2).C4central extension (φ=1)804C4.78(D4xC10)320,931
C4.79(D4×C10) = D4×C40central extension (φ=1)160C4.79(D4xC10)320,935
C4.80(D4×C10) = C5×C89D4central extension (φ=1)160C4.80(D4xC10)320,936
C4.81(D4×C10) = C5×C86D4central extension (φ=1)160C4.81(D4xC10)320,937
C4.82(D4×C10) = C5×C8○D8central extension (φ=1)802C4.82(D4xC10)320,944
C4.83(D4×C10) = C5×C8.26D4central extension (φ=1)804C4.83(D4xC10)320,945
C4.84(D4×C10) = C10×C4○D8central extension (φ=1)160C4.84(D4xC10)320,1574

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