# Extensions 1→N→G→Q→1 with N=C42 and Q=C2×C10

Direct product G=N×Q with N=C42 and Q=C2×C10
dρLabelID
C22×C4×C20320C2^2xC4xC20320,1513

Semidirect products G=N:Q with N=C42 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
C421(C2×C10) = C5×C42⋊C22φ: C2×C10/C5C22 ⊆ Aut C42804C4^2:1(C2xC10)320,922
C422(C2×C10) = C5×D44D4φ: C2×C10/C5C22 ⊆ Aut C42404C4^2:2(C2xC10)320,954
C423(C2×C10) = C5×D4.9D4φ: C2×C10/C5C22 ⊆ Aut C42804C4^2:3(C2xC10)320,956
C424(C2×C10) = C5×C22.11C24φ: C2×C10/C5C22 ⊆ Aut C4280C4^2:4(C2xC10)320,1520
C425(C2×C10) = C5×C22.19C24φ: C2×C10/C5C22 ⊆ Aut C4280C4^2:5(C2xC10)320,1527
C426(C2×C10) = C5×C22.29C24φ: C2×C10/C5C22 ⊆ Aut C4280C4^2:6(C2xC10)320,1537
C427(C2×C10) = C5×C22.32C24φ: C2×C10/C5C22 ⊆ Aut C4280C4^2:7(C2xC10)320,1540
C428(C2×C10) = C5×D42φ: C2×C10/C5C22 ⊆ Aut C4280C4^2:8(C2xC10)320,1547
C429(C2×C10) = C5×D45D4φ: C2×C10/C5C22 ⊆ Aut C4280C4^2:9(C2xC10)320,1548
C4210(C2×C10) = C5×C22.45C24φ: C2×C10/C5C22 ⊆ Aut C4280C4^2:10(C2xC10)320,1553
C4211(C2×C10) = C5×C22.54C24φ: C2×C10/C5C22 ⊆ Aut C4280C4^2:11(C2xC10)320,1562
C4212(C2×C10) = C5×C24⋊C22φ: C2×C10/C5C22 ⊆ Aut C4280C4^2:12(C2xC10)320,1563
C4213(C2×C10) = C10×C42⋊C2φ: C2×C10/C10C2 ⊆ Aut C42160C4^2:13(C2xC10)320,1516
C4214(C2×C10) = C10×C422C2φ: C2×C10/C10C2 ⊆ Aut C42160C4^2:14(C2xC10)320,1530
C4215(C2×C10) = C10×C4≀C2φ: C2×C10/C10C2 ⊆ Aut C4280C4^2:15(C2xC10)320,921
C4216(C2×C10) = D4×C2×C20φ: C2×C10/C10C2 ⊆ Aut C42160C4^2:16(C2xC10)320,1517
C4217(C2×C10) = C10×C4.4D4φ: C2×C10/C10C2 ⊆ Aut C42160C4^2:17(C2xC10)320,1528
C4218(C2×C10) = C10×C41D4φ: C2×C10/C10C2 ⊆ Aut C42160C4^2:18(C2xC10)320,1532

Non-split extensions G=N.Q with N=C42 and Q=C2×C10
extensionφ:Q→Aut NdρLabelID
C42.1(C2×C10) = C5×C42.C22φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.1(C2xC10)320,134
C42.2(C2×C10) = C5×C42.2C22φ: C2×C10/C5C22 ⊆ Aut C42320C4^2.2(C2xC10)320,135
C42.3(C2×C10) = C5×C4.D8φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.3(C2xC10)320,136
C42.4(C2×C10) = C5×C4.10D8φ: C2×C10/C5C22 ⊆ Aut C42320C4^2.4(C2xC10)320,137
C42.5(C2×C10) = C5×C4.6Q16φ: C2×C10/C5C22 ⊆ Aut C42320C4^2.5(C2xC10)320,138
C42.6(C2×C10) = C5×C42.6C22φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.6(C2xC10)320,925
C42.7(C2×C10) = C5×C89D4φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.7(C2xC10)320,936
C42.8(C2×C10) = C5×SD16⋊C4φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.8(C2xC10)320,941
C42.9(C2×C10) = C5×Q16⋊C4φ: C2×C10/C5C22 ⊆ Aut C42320C4^2.9(C2xC10)320,942
C42.10(C2×C10) = C5×D8⋊C4φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.10(C2xC10)320,943
C42.11(C2×C10) = C5×C8.26D4φ: C2×C10/C5C22 ⊆ Aut C42804C4^2.11(C2xC10)320,945
C42.12(C2×C10) = C5×D4.8D4φ: C2×C10/C5C22 ⊆ Aut C42804C4^2.12(C2xC10)320,955
C42.13(C2×C10) = C5×D4.10D4φ: C2×C10/C5C22 ⊆ Aut C42804C4^2.13(C2xC10)320,957
C42.14(C2×C10) = C5×C4⋊D8φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.14(C2xC10)320,960
C42.15(C2×C10) = C5×C4⋊SD16φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.15(C2xC10)320,961
C42.16(C2×C10) = C5×D4.D4φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.16(C2xC10)320,962
C42.17(C2×C10) = C5×C42Q16φ: C2×C10/C5C22 ⊆ Aut C42320C4^2.17(C2xC10)320,963
C42.18(C2×C10) = C5×D4.2D4φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.18(C2xC10)320,964
C42.19(C2×C10) = C5×Q8.D4φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.19(C2xC10)320,965
C42.20(C2×C10) = C5×D4⋊Q8φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.20(C2xC10)320,975
C42.21(C2×C10) = C5×Q8⋊Q8φ: C2×C10/C5C22 ⊆ Aut C42320C4^2.21(C2xC10)320,976
C42.22(C2×C10) = C5×D42Q8φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.22(C2xC10)320,977
C42.23(C2×C10) = C5×C4.Q16φ: C2×C10/C5C22 ⊆ Aut C42320C4^2.23(C2xC10)320,978
C42.24(C2×C10) = C5×D4.Q8φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.24(C2xC10)320,979
C42.25(C2×C10) = C5×Q8.Q8φ: C2×C10/C5C22 ⊆ Aut C42320C4^2.25(C2xC10)320,980
C42.26(C2×C10) = C5×C42.28C22φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.26(C2xC10)320,990
C42.27(C2×C10) = C5×C42.29C22φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.27(C2xC10)320,991
C42.28(C2×C10) = C5×C42.30C22φ: C2×C10/C5C22 ⊆ Aut C42320C4^2.28(C2xC10)320,992
C42.29(C2×C10) = C5×C83D4φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.29(C2xC10)320,997
C42.30(C2×C10) = C5×C8.2D4φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.30(C2xC10)320,998
C42.31(C2×C10) = C5×C8⋊Q8φ: C2×C10/C5C22 ⊆ Aut C42320C4^2.31(C2xC10)320,1002
C42.32(C2×C10) = C5×C23.32C23φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.32(C2xC10)320,1521
C42.33(C2×C10) = C5×C23.33C23φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.33(C2xC10)320,1522
C42.34(C2×C10) = C5×C23.36C23φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.34(C2xC10)320,1531
C42.35(C2×C10) = C5×C23.37C23φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.35(C2xC10)320,1535
C42.36(C2×C10) = C5×C23.38C23φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.36(C2xC10)320,1538
C42.37(C2×C10) = C5×C22.33C24φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.37(C2xC10)320,1541
C42.38(C2×C10) = C5×C22.34C24φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.38(C2xC10)320,1542
C42.39(C2×C10) = C5×C22.35C24φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.39(C2xC10)320,1543
C42.40(C2×C10) = C5×C22.36C24φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.40(C2xC10)320,1544
C42.41(C2×C10) = C5×C23.41C23φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.41(C2xC10)320,1546
C42.42(C2×C10) = C5×D46D4φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.42(C2xC10)320,1549
C42.43(C2×C10) = C5×Q85D4φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.43(C2xC10)320,1550
C42.44(C2×C10) = C5×D4×Q8φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.44(C2xC10)320,1551
C42.45(C2×C10) = C5×Q86D4φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.45(C2xC10)320,1552
C42.46(C2×C10) = C5×C22.46C24φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.46(C2xC10)320,1554
C42.47(C2×C10) = C5×C22.47C24φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.47(C2xC10)320,1555
C42.48(C2×C10) = C5×D43Q8φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.48(C2xC10)320,1556
C42.49(C2×C10) = C5×C22.49C24φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.49(C2xC10)320,1557
C42.50(C2×C10) = C5×C22.50C24φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.50(C2xC10)320,1558
C42.51(C2×C10) = C5×Q83Q8φ: C2×C10/C5C22 ⊆ Aut C42320C4^2.51(C2xC10)320,1559
C42.52(C2×C10) = C5×Q82φ: C2×C10/C5C22 ⊆ Aut C42320C4^2.52(C2xC10)320,1560
C42.53(C2×C10) = C5×C22.53C24φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.53(C2xC10)320,1561
C42.54(C2×C10) = C5×C22.56C24φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.54(C2xC10)320,1564
C42.55(C2×C10) = C5×C22.57C24φ: C2×C10/C5C22 ⊆ Aut C42160C4^2.55(C2xC10)320,1565
C42.56(C2×C10) = C5×C22.58C24φ: C2×C10/C5C22 ⊆ Aut C42320C4^2.56(C2xC10)320,1566
C42.57(C2×C10) = C10×C8⋊C4φ: C2×C10/C10C2 ⊆ Aut C42320C4^2.57(C2xC10)320,904
C42.58(C2×C10) = M4(2)×C20φ: C2×C10/C10C2 ⊆ Aut C42160C4^2.58(C2xC10)320,905
C42.59(C2×C10) = C5×C82M4(2)φ: C2×C10/C10C2 ⊆ Aut C42160C4^2.59(C2xC10)320,906
C42.60(C2×C10) = C5×C42.6C4φ: C2×C10/C10C2 ⊆ Aut C42160C4^2.60(C2xC10)320,933
C42.61(C2×C10) = C5×C42.7C22φ: C2×C10/C10C2 ⊆ Aut C42160C4^2.61(C2xC10)320,934
C42.62(C2×C10) = C5×D4⋊C8φ: C2×C10/C10C2 ⊆ Aut C42160C4^2.62(C2xC10)320,130
C42.63(C2×C10) = C5×Q8⋊C8φ: C2×C10/C10C2 ⊆ Aut C42320C4^2.63(C2xC10)320,131
C42.64(C2×C10) = C5×C82C8φ: C2×C10/C10C2 ⊆ Aut C42320C4^2.64(C2xC10)320,139
C42.65(C2×C10) = C5×C81C8φ: C2×C10/C10C2 ⊆ Aut C42320C4^2.65(C2xC10)320,140
C42.66(C2×C10) = C10×C4⋊C8φ: C2×C10/C10C2 ⊆ Aut C42320C4^2.66(C2xC10)320,923
C42.67(C2×C10) = C5×C4⋊M4(2)φ: C2×C10/C10C2 ⊆ Aut C42160C4^2.67(C2xC10)320,924
C42.68(C2×C10) = D4×C40φ: C2×C10/C10C2 ⊆ Aut C42160C4^2.68(C2xC10)320,935
C42.69(C2×C10) = C5×C86D4φ: C2×C10/C10C2 ⊆ Aut C42160C4^2.69(C2xC10)320,937
C42.70(C2×C10) = D8×C20φ: C2×C10/C10C2 ⊆ Aut C42160C4^2.70(C2xC10)320,938
C42.71(C2×C10) = SD16×C20φ: C2×C10/C10C2 ⊆ Aut C42160C4^2.71(C2xC10)320,939
C42.72(C2×C10) = Q16×C20φ: C2×C10/C10C2 ⊆ Aut C42320C4^2.72(C2xC10)320,940
C42.73(C2×C10) = C5×C8○D8φ: C2×C10/C10C2 ⊆ Aut C42802C4^2.73(C2xC10)320,944
C42.74(C2×C10) = Q8×C40φ: C2×C10/C10C2 ⊆ Aut C42320C4^2.74(C2xC10)320,946
C42.75(C2×C10) = C5×C84Q8φ: C2×C10/C10C2 ⊆ Aut C42320C4^2.75(C2xC10)320,947
C42.76(C2×C10) = C5×C4.4D8φ: C2×C10/C10C2 ⊆ Aut C42160C4^2.76(C2xC10)320,987
C42.77(C2×C10) = C5×C4.SD16φ: C2×C10/C10C2 ⊆ Aut C42320C4^2.77(C2xC10)320,988
C42.78(C2×C10) = C5×C42.78C22φ: C2×C10/C10C2 ⊆ Aut C42160C4^2.78(C2xC10)320,989
C42.79(C2×C10) = C5×C85D4φ: C2×C10/C10C2 ⊆ Aut C42160C4^2.79(C2xC10)320,993
C42.80(C2×C10) = C5×C84D4φ: C2×C10/C10C2 ⊆ Aut C42160C4^2.80(C2xC10)320,994
C42.81(C2×C10) = C5×C4⋊Q16φ: C2×C10/C10C2 ⊆ Aut C42320C4^2.81(C2xC10)320,995
C42.82(C2×C10) = C5×C8.12D4φ: C2×C10/C10C2 ⊆ Aut C42160C4^2.82(C2xC10)320,996
C42.83(C2×C10) = C5×C83Q8φ: C2×C10/C10C2 ⊆ Aut C42320C4^2.83(C2xC10)320,999
C42.84(C2×C10) = C5×C8.5Q8φ: C2×C10/C10C2 ⊆ Aut C42320C4^2.84(C2xC10)320,1000
C42.85(C2×C10) = C5×C82Q8φ: C2×C10/C10C2 ⊆ Aut C42320C4^2.85(C2xC10)320,1001
C42.86(C2×C10) = Q8×C2×C20φ: C2×C10/C10C2 ⊆ Aut C42320C4^2.86(C2xC10)320,1518
C42.87(C2×C10) = C4○D4×C20φ: C2×C10/C10C2 ⊆ Aut C42160C4^2.87(C2xC10)320,1519
C42.88(C2×C10) = C10×C42.C2φ: C2×C10/C10C2 ⊆ Aut C42320C4^2.88(C2xC10)320,1529
C42.89(C2×C10) = C10×C4⋊Q8φ: C2×C10/C10C2 ⊆ Aut C42320C4^2.89(C2xC10)320,1533
C42.90(C2×C10) = C5×C22.26C24φ: C2×C10/C10C2 ⊆ Aut C42160C4^2.90(C2xC10)320,1534
C42.91(C2×C10) = C5×C8⋊C8central extension (φ=1)320C4^2.91(C2xC10)320,127
C42.92(C2×C10) = C5×C42.12C4central extension (φ=1)160C4^2.92(C2xC10)320,932

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