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Extensions 1→N→G→Q→1 with N=C4⋊C4 and Q=C2×C10

Direct product G=N×Q with N=C4⋊C4 and Q=C2×C10
dρLabelID
C4⋊C4×C2×C10320C4:C4xC2xC10320,1515

Semidirect products G=N:Q with N=C4⋊C4 and Q=C2×C10
extensionφ:Q→Out NdρLabelID
C4⋊C4⋊1(C2×C10) = C5×C22⋊D8φ: C2×C10/C5 → C22 ⊆ Out C4⋊C480C4:C4:1(C2xC10)320,948
C4⋊C4⋊2(C2×C10) = C5×C22⋊SD16φ: C2×C10/C5 → C22 ⊆ Out C4⋊C480C4:C4:2(C2xC10)320,951
C4⋊C4⋊3(C2×C10) = C5×C23⋊3D4φ: C2×C10/C5 → C22 ⊆ Out C4⋊C480C4:C4:3(C2xC10)320,1536
C4⋊C4⋊4(C2×C10) = C5×C23⋊2Q8φ: C2×C10/C5 → C22 ⊆ Out C4⋊C480C4:C4:4(C2xC10)320,1545
C4⋊C4⋊5(C2×C10) = C5×D4⋊5D4φ: C2×C10/C5 → C22 ⊆ Out C4⋊C480C4:C4:5(C2xC10)320,1548
C4⋊C4⋊6(C2×C10) = C5×C22.54C24φ: C2×C10/C5 → C22 ⊆ Out C4⋊C480C4:C4:6(C2xC10)320,1562
C4⋊C4⋊7(C2×C10) = C10×D4⋊C4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4:7(C2xC10)320,915
C4⋊C4⋊8(C2×C10) = C5×C23.37D4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C480C4:C4:8(C2xC10)320,919
C4⋊C4⋊9(C2×C10) = C10×C4⋊D4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4:9(C2xC10)320,1524
C4⋊C4⋊10(C2×C10) = C10×C22⋊Q8φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4:10(C2xC10)320,1525
C4⋊C4⋊11(C2×C10) = C10×C22.D4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4:11(C2xC10)320,1526
C4⋊C4⋊12(C2×C10) = C5×C22.19C24φ: C2×C10/C10 → C2 ⊆ Out C4⋊C480C4:C4:12(C2xC10)320,1527
C4⋊C4⋊13(C2×C10) = C10×C42⋊2C2φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4:13(C2xC10)320,1530
C4⋊C4⋊14(C2×C10) = C5×C22.29C24φ: C2×C10/C10 → C2 ⊆ Out C4⋊C480C4:C4:14(C2xC10)320,1537
C4⋊C4⋊15(C2×C10) = C5×C22.32C24φ: C2×C10/C10 → C2 ⊆ Out C4⋊C480C4:C4:15(C2xC10)320,1540
C4⋊C4⋊16(C2×C10) = C5×D42φ: C2×C10/C10 → C2 ⊆ Out C4⋊C480C4:C4:16(C2xC10)320,1547
C4⋊C4⋊17(C2×C10) = C5×C22.45C24φ: C2×C10/C10 → C2 ⊆ Out C4⋊C480C4:C4:17(C2xC10)320,1553
C4⋊C4⋊18(C2×C10) = C10×C42⋊C2φ: trivial image160C4:C4:18(C2xC10)320,1516
C4⋊C4⋊19(C2×C10) = D4×C2×C20φ: trivial image160C4:C4:19(C2xC10)320,1517
C4⋊C4⋊20(C2×C10) = C5×C22.11C24φ: trivial image80C4:C4:20(C2xC10)320,1520

Non-split extensions G=N.Q with N=C4⋊C4 and Q=C2×C10
extensionφ:Q→Out NdρLabelID
C4⋊C4.1(C2×C10) = C5×Q8⋊D4φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.1(C2xC10)320,949
C4⋊C4.2(C2×C10) = C5×D4⋊D4φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.2(C2xC10)320,950
C4⋊C4.3(C2×C10) = C5×C22⋊Q16φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.3(C2xC10)320,952
C4⋊C4.4(C2×C10) = C5×D4.7D4φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.4(C2xC10)320,953
C4⋊C4.5(C2×C10) = C5×C8⋊8D4φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.5(C2xC10)320,966
C4⋊C4.6(C2×C10) = C5×C8⋊7D4φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.6(C2xC10)320,967
C4⋊C4.7(C2×C10) = C5×C8.18D4φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.7(C2xC10)320,968
C4⋊C4.8(C2×C10) = C5×C8⋊D4φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.8(C2xC10)320,969
C4⋊C4.9(C2×C10) = C5×C8⋊2D4φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.9(C2xC10)320,970
C4⋊C4.10(C2×C10) = C5×C8.D4φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.10(C2xC10)320,971
C4⋊C4.11(C2×C10) = C5×D4⋊Q8φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.11(C2xC10)320,975
C4⋊C4.12(C2×C10) = C5×Q8⋊Q8φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4320C4:C4.12(C2xC10)320,976
C4⋊C4.13(C2×C10) = C5×D4⋊2Q8φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.13(C2xC10)320,977
C4⋊C4.14(C2×C10) = C5×C4.Q16φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4320C4:C4.14(C2xC10)320,978
C4⋊C4.15(C2×C10) = C5×D4.Q8φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.15(C2xC10)320,979
C4⋊C4.16(C2×C10) = C5×Q8.Q8φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4320C4:C4.16(C2xC10)320,980
C4⋊C4.17(C2×C10) = C5×C4.4D8φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.17(C2xC10)320,987
C4⋊C4.18(C2×C10) = C5×C4.SD16φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4320C4:C4.18(C2xC10)320,988
C4⋊C4.19(C2×C10) = C5×C42.78C22φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.19(C2xC10)320,989
C4⋊C4.20(C2×C10) = C5×C42.28C22φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.20(C2xC10)320,990
C4⋊C4.21(C2×C10) = C5×C42.29C22φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.21(C2xC10)320,991
C4⋊C4.22(C2×C10) = C5×C42.30C22φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4320C4:C4.22(C2xC10)320,992
C4⋊C4.23(C2×C10) = C5×C8⋊3Q8φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4320C4:C4.23(C2xC10)320,999
C4⋊C4.24(C2×C10) = C5×C8.5Q8φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4320C4:C4.24(C2xC10)320,1000
C4⋊C4.25(C2×C10) = C5×C8⋊2Q8φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4320C4:C4.25(C2xC10)320,1001
C4⋊C4.26(C2×C10) = C5×C8⋊Q8φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4320C4:C4.26(C2xC10)320,1002
C4⋊C4.27(C2×C10) = C5×C23.38C23φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.27(C2xC10)320,1538
C4⋊C4.28(C2×C10) = C5×C22.31C24φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.28(C2xC10)320,1539
C4⋊C4.29(C2×C10) = C5×C22.34C24φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.29(C2xC10)320,1542
C4⋊C4.30(C2×C10) = C5×C23.41C23φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.30(C2xC10)320,1546
C4⋊C4.31(C2×C10) = C5×D4⋊6D4φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.31(C2xC10)320,1549
C4⋊C4.32(C2×C10) = C5×D4×Q8φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.32(C2xC10)320,1551
C4⋊C4.33(C2×C10) = C5×C22.46C24φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.33(C2xC10)320,1554
C4⋊C4.34(C2×C10) = C5×C22.56C24φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.34(C2xC10)320,1564
C4⋊C4.35(C2×C10) = C5×C22.57C24φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4160C4:C4.35(C2xC10)320,1565
C4⋊C4.36(C2×C10) = C5×C22.58C24φ: C2×C10/C5 → C22 ⊆ Out C4⋊C4320C4:C4.36(C2xC10)320,1566
C4⋊C4.37(C2×C10) = C10×Q8⋊C4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4320C4:C4.37(C2xC10)320,916
C4⋊C4.38(C2×C10) = C5×C23.24D4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.38(C2xC10)320,917
C4⋊C4.39(C2×C10) = C5×C23.36D4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.39(C2xC10)320,918
C4⋊C4.40(C2×C10) = C5×C23.38D4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.40(C2xC10)320,920
C4⋊C4.41(C2×C10) = C10×C4.Q8φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4320C4:C4.41(C2xC10)320,926
C4⋊C4.42(C2×C10) = C10×C2.D8φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4320C4:C4.42(C2xC10)320,927
C4⋊C4.43(C2×C10) = C5×C23.25D4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.43(C2xC10)320,928
C4⋊C4.44(C2×C10) = C5×M4(2)⋊C4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.44(C2xC10)320,929
C4⋊C4.45(C2×C10) = D8×C20φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.45(C2xC10)320,938
C4⋊C4.46(C2×C10) = SD16×C20φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.46(C2xC10)320,939
C4⋊C4.47(C2×C10) = Q16×C20φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4320C4:C4.47(C2xC10)320,940
C4⋊C4.48(C2×C10) = C5×SD16⋊C4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.48(C2xC10)320,941
C4⋊C4.49(C2×C10) = C5×Q16⋊C4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4320C4:C4.49(C2xC10)320,942
C4⋊C4.50(C2×C10) = C5×D8⋊C4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.50(C2xC10)320,943
C4⋊C4.51(C2×C10) = C5×C4⋊D8φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.51(C2xC10)320,960
C4⋊C4.52(C2×C10) = C5×C4⋊SD16φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.52(C2xC10)320,961
C4⋊C4.53(C2×C10) = C5×D4.D4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.53(C2xC10)320,962
C4⋊C4.54(C2×C10) = C5×C4⋊2Q16φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4320C4:C4.54(C2xC10)320,963
C4⋊C4.55(C2×C10) = C5×D4.2D4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.55(C2xC10)320,964
C4⋊C4.56(C2×C10) = C5×Q8.D4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.56(C2xC10)320,965
C4⋊C4.57(C2×C10) = C5×C22.D8φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.57(C2xC10)320,981
C4⋊C4.58(C2×C10) = C5×C23.46D4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.58(C2xC10)320,982
C4⋊C4.59(C2×C10) = C5×C23.19D4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.59(C2xC10)320,983
C4⋊C4.60(C2×C10) = C5×C23.47D4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.60(C2xC10)320,984
C4⋊C4.61(C2×C10) = C5×C23.48D4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.61(C2xC10)320,985
C4⋊C4.62(C2×C10) = C5×C23.20D4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.62(C2xC10)320,986
C4⋊C4.63(C2×C10) = C10×C42.C2φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4320C4:C4.63(C2xC10)320,1529
C4⋊C4.64(C2×C10) = C5×C23.36C23φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.64(C2xC10)320,1531
C4⋊C4.65(C2×C10) = C10×C4⋊Q8φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4320C4:C4.65(C2xC10)320,1533
C4⋊C4.66(C2×C10) = C5×C22.26C24φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.66(C2xC10)320,1534
C4⋊C4.67(C2×C10) = C5×C23.37C23φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.67(C2xC10)320,1535
C4⋊C4.68(C2×C10) = C5×C22.33C24φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.68(C2xC10)320,1541
C4⋊C4.69(C2×C10) = C5×C22.35C24φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.69(C2xC10)320,1543
C4⋊C4.70(C2×C10) = C5×C22.36C24φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.70(C2xC10)320,1544
C4⋊C4.71(C2×C10) = C5×Q8⋊5D4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.71(C2xC10)320,1550
C4⋊C4.72(C2×C10) = C5×Q8⋊6D4φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.72(C2xC10)320,1552
C4⋊C4.73(C2×C10) = C5×C22.47C24φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.73(C2xC10)320,1555
C4⋊C4.74(C2×C10) = C5×D4⋊3Q8φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.74(C2xC10)320,1556
C4⋊C4.75(C2×C10) = C5×C22.49C24φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.75(C2xC10)320,1557
C4⋊C4.76(C2×C10) = C5×C22.50C24φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.76(C2xC10)320,1558
C4⋊C4.77(C2×C10) = C5×Q8⋊3Q8φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4320C4:C4.77(C2xC10)320,1559
C4⋊C4.78(C2×C10) = C5×Q82φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4320C4:C4.78(C2xC10)320,1560
C4⋊C4.79(C2×C10) = C5×C22.53C24φ: C2×C10/C10 → C2 ⊆ Out C4⋊C4160C4:C4.79(C2xC10)320,1561
C4⋊C4.80(C2×C10) = Q8×C2×C20φ: trivial image320C4:C4.80(C2xC10)320,1518
C4⋊C4.81(C2×C10) = C4○D4×C20φ: trivial image160C4:C4.81(C2xC10)320,1519
C4⋊C4.82(C2×C10) = C5×C23.32C23φ: trivial image160C4:C4.82(C2xC10)320,1521
C4⋊C4.83(C2×C10) = C5×C23.33C23φ: trivial image160C4:C4.83(C2xC10)320,1522

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