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Extensions 1→N→G→Q→1 with N=C23 and Q=C5⋊D4

Direct product G=N×Q with N=C23 and Q=C5⋊D4
dρLabelID
C23×C5⋊D4160C2^3xC5:D4320,1627

Semidirect products G=N:Q with N=C23 and Q=C5⋊D4
extensionφ:Q→Aut NdρLabelID
C23⋊1(C5⋊D4) = C24⋊2D10φ: C5⋊D4/C5 → D4 ⊆ Aut C23404C2^3:1(C5:D4)320,659
C23⋊2(C5⋊D4) = 2+ 1+4⋊2D5φ: C5⋊D4/C5 → D4 ⊆ Aut C23408+C2^3:2(C5:D4)320,871
C23⋊3(C5⋊D4) = C24.21D10φ: C5⋊D4/C10 → C22 ⊆ Aut C23160C2^3:3(C5:D4)320,850
C23⋊4(C5⋊D4) = C24⋊8D10φ: C5⋊D4/C10 → C22 ⊆ Aut C2380C2^3:4(C5:D4)320,1476
C23⋊5(C5⋊D4) = C2×Dic5⋊D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C23160C2^3:5(C5:D4)320,1474
C23⋊6(C5⋊D4) = C2×C23⋊D10φ: C5⋊D4/D10 → C2 ⊆ Aut C2380C2^3:6(C5:D4)320,1471
C23⋊7(C5⋊D4) = C2×C24⋊2D5φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2380C2^3:7(C5:D4)320,1512

Non-split extensions G=N.Q with N=C23 and Q=C5⋊D4
extensionφ:Q→Aut NdρLabelID
C23.1(C5⋊D4) = C5⋊3C2≀C4φ: C5⋊D4/C5 → D4 ⊆ Aut C23408+C2^3.1(C5:D4)320,29
C23.2(C5⋊D4) = (C2×C20).D4φ: C5⋊D4/C5 → D4 ⊆ Aut C23808-C2^3.2(C5:D4)320,30
C23.3(C5⋊D4) = C23.D20φ: C5⋊D4/C5 → D4 ⊆ Aut C23808-C2^3.3(C5:D4)320,31
C23.4(C5⋊D4) = C23.2D20φ: C5⋊D4/C5 → D4 ⊆ Aut C23408+C2^3.4(C5:D4)320,32
C23.5(C5⋊D4) = C24⋊2Dic5φ: C5⋊D4/C5 → D4 ⊆ Aut C23404C2^3.5(C5:D4)320,94
C23.6(C5⋊D4) = (C22×C20)⋊C4φ: C5⋊D4/C5 → D4 ⊆ Aut C23804C2^3.6(C5:D4)320,97
C23.7(C5⋊D4) = C42⋊Dic5φ: C5⋊D4/C5 → D4 ⊆ Aut C23804C2^3.7(C5:D4)320,99
C23.8(C5⋊D4) = C42⋊3Dic5φ: C5⋊D4/C5 → D4 ⊆ Aut C23404C2^3.8(C5:D4)320,103
C23.9(C5⋊D4) = C22⋊C4⋊D10φ: C5⋊D4/C5 → D4 ⊆ Aut C23804C2^3.9(C5:D4)320,680
C23.10(C5⋊D4) = C42⋊5D10φ: C5⋊D4/C5 → D4 ⊆ Aut C23804C2^3.10(C5:D4)320,688
C23.11(C5⋊D4) = D20⋊5D4φ: C5⋊D4/C5 → D4 ⊆ Aut C23404C2^3.11(C5:D4)320,704
C23.12(C5⋊D4) = 2+ 1+4⋊D5φ: C5⋊D4/C5 → D4 ⊆ Aut C23408+C2^3.12(C5:D4)320,868
C23.13(C5⋊D4) = 2+ 1+4.D5φ: C5⋊D4/C5 → D4 ⊆ Aut C23808-C2^3.13(C5:D4)320,869
C23.14(C5⋊D4) = 2+ 1+4.2D5φ: C5⋊D4/C5 → D4 ⊆ Aut C23808-C2^3.14(C5:D4)320,870
C23.15(C5⋊D4) = C24.2D10φ: C5⋊D4/C10 → C22 ⊆ Aut C2380C2^3.15(C5:D4)320,85
C23.16(C5⋊D4) = C42⋊1Dic5φ: C5⋊D4/C10 → C22 ⊆ Aut C23804C2^3.16(C5:D4)320,89
C23.17(C5⋊D4) = C24.9D10φ: C5⋊D4/C10 → C22 ⊆ Aut C23160C2^3.17(C5:D4)320,579
C23.18(C5⋊D4) = C24.14D10φ: C5⋊D4/C10 → C22 ⊆ Aut C23160C2^3.18(C5:D4)320,586
C23.19(C5⋊D4) = C4⋊C4.233D10φ: C5⋊D4/C10 → C22 ⊆ Aut C23160C2^3.19(C5:D4)320,623
C23.20(C5⋊D4) = C4⋊C4.236D10φ: C5⋊D4/C10 → C22 ⊆ Aut C23160C2^3.20(C5:D4)320,630
C23.21(C5⋊D4) = C42⋊4D10φ: C5⋊D4/C10 → C22 ⊆ Aut C23804C2^3.21(C5:D4)320,632
C23.22(C5⋊D4) = (C2×D4).D10φ: C5⋊D4/C10 → C22 ⊆ Aut C23160C2^3.22(C5:D4)320,662
C23.23(C5⋊D4) = D20⋊17D4φ: C5⋊D4/C10 → C22 ⊆ Aut C23160C2^3.23(C5:D4)320,664
C23.24(C5⋊D4) = C4⋊D4⋊D5φ: C5⋊D4/C10 → C22 ⊆ Aut C23160C2^3.24(C5:D4)320,666
C23.25(C5⋊D4) = C4.(D4×D5)φ: C5⋊D4/C10 → C22 ⊆ Aut C23160C2^3.25(C5:D4)320,669
C23.26(C5⋊D4) = C10.(C4○D8)φ: C5⋊D4/C10 → C22 ⊆ Aut C23160C2^3.26(C5:D4)320,672
C23.27(C5⋊D4) = D20.37D4φ: C5⋊D4/C10 → C22 ⊆ Aut C23160C2^3.27(C5:D4)320,674
C23.28(C5⋊D4) = C22⋊Q8⋊D5φ: C5⋊D4/C10 → C22 ⊆ Aut C23160C2^3.28(C5:D4)320,676
C23.29(C5⋊D4) = C5⋊(C8.D4)φ: C5⋊D4/C10 → C22 ⊆ Aut C23160C2^3.29(C5:D4)320,679
C23.30(C5⋊D4) = C24.20D10φ: C5⋊D4/C10 → C22 ⊆ Aut C23160C2^3.30(C5:D4)320,849
C23.31(C5⋊D4) = (D4×C10)⋊21C4φ: C5⋊D4/C10 → C22 ⊆ Aut C23804C2^3.31(C5:D4)320,863
C23.32(C5⋊D4) = (C5×D4)⋊14D4φ: C5⋊D4/C10 → C22 ⊆ Aut C23160C2^3.32(C5:D4)320,865
C23.33(C5⋊D4) = (C5×D4).32D4φ: C5⋊D4/C10 → C22 ⊆ Aut C23160C2^3.33(C5:D4)320,866
C23.34(C5⋊D4) = C20.C24φ: C5⋊D4/C10 → C22 ⊆ Aut C23804C2^3.34(C5:D4)320,1494
C23.35(C5⋊D4) = C24.44D10φ: C5⋊D4/Dic5 → C2 ⊆ Aut C23160C2^3.35(C5:D4)320,569
C23.36(C5⋊D4) = C23.45D20φ: C5⋊D4/Dic5 → C2 ⊆ Aut C23160C2^3.36(C5:D4)320,585
C23.37(C5⋊D4) = C20.76(C4⋊C4)φ: C5⋊D4/Dic5 → C2 ⊆ Aut C23160C2^3.37(C5:D4)320,625
C23.38(C5⋊D4) = C4○D20⋊10C4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C23160C2^3.38(C5:D4)320,629
C23.39(C5⋊D4) = (C2×C10)⋊D8φ: C5⋊D4/Dic5 → C2 ⊆ Aut C23160C2^3.39(C5:D4)320,665
C23.40(C5⋊D4) = C5⋊2C8⋊23D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C23160C2^3.40(C5:D4)320,668
C23.41(C5⋊D4) = C5⋊2C8⋊24D4φ: C5⋊D4/Dic5 → C2 ⊆ Aut C23160C2^3.41(C5:D4)320,675
C23.42(C5⋊D4) = (C2×C10)⋊Q16φ: C5⋊D4/Dic5 → C2 ⊆ Aut C23160C2^3.42(C5:D4)320,678
C23.43(C5⋊D4) = C24.18D10φ: C5⋊D4/Dic5 → C2 ⊆ Aut C23160C2^3.43(C5:D4)320,847
C23.44(C5⋊D4) = C20.(C2×D4)φ: C5⋊D4/Dic5 → C2 ⊆ Aut C23160C2^3.44(C5:D4)320,860
C23.45(C5⋊D4) = C2×D4.8D10φ: C5⋊D4/Dic5 → C2 ⊆ Aut C23160C2^3.45(C5:D4)320,1493
C23.46(C5⋊D4) = C24.D10φ: C5⋊D4/D10 → C2 ⊆ Aut C2380C2^3.46(C5:D4)320,84
C23.47(C5⋊D4) = C20.32C42φ: C5⋊D4/D10 → C2 ⊆ Aut C2380C2^3.47(C5:D4)320,90
C23.48(C5⋊D4) = C4⋊C4⋊Dic5φ: C5⋊D4/D10 → C2 ⊆ Aut C2380C2^3.48(C5:D4)320,95
C23.49(C5⋊D4) = C10.29C4≀C2φ: C5⋊D4/D10 → C2 ⊆ Aut C2380C2^3.49(C5:D4)320,96
C23.50(C5⋊D4) = C23.42D20φ: C5⋊D4/D10 → C2 ⊆ Aut C23160C2^3.50(C5:D4)320,570
C23.51(C5⋊D4) = C24.46D10φ: C5⋊D4/D10 → C2 ⊆ Aut C23160C2^3.51(C5:D4)320,573
C23.52(C5⋊D4) = C24.48D10φ: C5⋊D4/D10 → C2 ⊆ Aut C2380C2^3.52(C5:D4)320,582
C23.53(C5⋊D4) = C20.64(C4⋊C4)φ: C5⋊D4/D10 → C2 ⊆ Aut C23160C2^3.53(C5:D4)320,622
C23.54(C5⋊D4) = C4⋊C4⋊36D10φ: C5⋊D4/D10 → C2 ⊆ Aut C2380C2^3.54(C5:D4)320,628
C23.55(C5⋊D4) = C4.(C2×D20)φ: C5⋊D4/D10 → C2 ⊆ Aut C23160C2^3.55(C5:D4)320,631
C23.56(C5⋊D4) = (C2×C10).D8φ: C5⋊D4/D10 → C2 ⊆ Aut C23160C2^3.56(C5:D4)320,660
C23.57(C5⋊D4) = C4⋊D4.D5φ: C5⋊D4/D10 → C2 ⊆ Aut C23160C2^3.57(C5:D4)320,661
C23.58(C5⋊D4) = D20⋊16D4φ: C5⋊D4/D10 → C2 ⊆ Aut C2380C2^3.58(C5:D4)320,663
C23.59(C5⋊D4) = Dic10⋊17D4φ: C5⋊D4/D10 → C2 ⊆ Aut C23160C2^3.59(C5:D4)320,667
C23.60(C5⋊D4) = C22⋊Q8.D5φ: C5⋊D4/D10 → C2 ⊆ Aut C23160C2^3.60(C5:D4)320,670
C23.61(C5⋊D4) = (C2×C10).Q16φ: C5⋊D4/D10 → C2 ⊆ Aut C23160C2^3.61(C5:D4)320,671
C23.62(C5⋊D4) = D20.36D4φ: C5⋊D4/D10 → C2 ⊆ Aut C2380C2^3.62(C5:D4)320,673
C23.63(C5⋊D4) = Dic10.37D4φ: C5⋊D4/D10 → C2 ⊆ Aut C23160C2^3.63(C5:D4)320,677
C23.64(C5⋊D4) = C2×C23⋊Dic5φ: C5⋊D4/D10 → C2 ⊆ Aut C2380C2^3.64(C5:D4)320,846
C23.65(C5⋊D4) = C4○D4⋊Dic5φ: C5⋊D4/D10 → C2 ⊆ Aut C23160C2^3.65(C5:D4)320,859
C23.66(C5⋊D4) = C2×D4⋊2Dic5φ: C5⋊D4/D10 → C2 ⊆ Aut C2380C2^3.66(C5:D4)320,862
C23.67(C5⋊D4) = C2×C23.18D10φ: C5⋊D4/D10 → C2 ⊆ Aut C23160C2^3.67(C5:D4)320,1468
C23.68(C5⋊D4) = C2×D4⋊D10φ: C5⋊D4/D10 → C2 ⊆ Aut C2380C2^3.68(C5:D4)320,1492
C23.69(C5⋊D4) = C2×D4.9D10φ: C5⋊D4/D10 → C2 ⊆ Aut C23160C2^3.69(C5:D4)320,1495
C23.70(C5⋊D4) = (C2×D20)⋊C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2380C2^3.70(C5:D4)320,9
C23.71(C5⋊D4) = C4⋊Dic5⋊C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2380C2^3.71(C5:D4)320,10
C23.72(C5⋊D4) = C42⋊6Dic5φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2380C2^3.72(C5:D4)320,81
C23.73(C5⋊D4) = C2×D20⋊4C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2380C2^3.73(C5:D4)320,554
C23.74(C5⋊D4) = C2×C23.1D10φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2380C2^3.74(C5:D4)320,581
C23.75(C5⋊D4) = C20.47(C4⋊C4)φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C23160C2^3.75(C5:D4)320,591
C23.76(C5⋊D4) = C4○D20⋊9C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C23160C2^3.76(C5:D4)320,593
C23.77(C5⋊D4) = (C2×C10).40D8φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C23160C2^3.77(C5:D4)320,594
C23.78(C5⋊D4) = C4⋊C4.228D10φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C23160C2^3.78(C5:D4)320,595
C23.79(C5⋊D4) = C4⋊C4.230D10φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C23160C2^3.79(C5:D4)320,597
C23.80(C5⋊D4) = C4⋊C4.231D10φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C23160C2^3.80(C5:D4)320,598
C23.81(C5⋊D4) = C24.62D10φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C23160C2^3.81(C5:D4)320,837
C23.82(C5⋊D4) = C24.63D10φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C23160C2^3.82(C5:D4)320,838
C23.83(C5⋊D4) = C24.65D10φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C23160C2^3.83(C5:D4)320,840
C23.84(C5⋊D4) = (D4×C10)⋊18C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2380C2^3.84(C5:D4)320,842
C23.85(C5⋊D4) = (C2×C10)⋊8D8φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2380C2^3.85(C5:D4)320,844
C23.86(C5⋊D4) = (C5×D4).31D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2380C2^3.86(C5:D4)320,845
C23.87(C5⋊D4) = (Q8×C10)⋊16C4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C23160C2^3.87(C5:D4)320,852
C23.88(C5⋊D4) = (C5×Q8)⋊13D4φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C23160C2^3.88(C5:D4)320,854
C23.89(C5⋊D4) = (C2×C10)⋊8Q16φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C23160C2^3.89(C5:D4)320,855
C23.90(C5⋊D4) = C25.2D5φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2380C2^3.90(C5:D4)320,874
C23.91(C5⋊D4) = C2×C23.23D10φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C23160C2^3.91(C5:D4)320,1461
C23.92(C5⋊D4) = C2×D4.D10φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C2380C2^3.92(C5:D4)320,1465
C23.93(C5⋊D4) = C2×C20.C23φ: C5⋊D4/C2×C10 → C2 ⊆ Aut C23160C2^3.93(C5:D4)320,1480
C23.94(C5⋊D4) = C20.31C42central extension (φ=1)320C2^3.94(C5:D4)320,87
C23.95(C5⋊D4) = C2×C10.D8central extension (φ=1)320C2^3.95(C5:D4)320,589
C23.96(C5⋊D4) = C2×C20.Q8central extension (φ=1)320C2^3.96(C5:D4)320,590
C23.97(C5⋊D4) = C2×D20⋊6C4central extension (φ=1)160C2^3.97(C5:D4)320,592
C23.98(C5⋊D4) = C2×C10.Q16central extension (φ=1)320C2^3.98(C5:D4)320,596
C23.99(C5⋊D4) = C2×C10.10C42central extension (φ=1)320C2^3.99(C5:D4)320,835
C23.100(C5⋊D4) = C2×D4⋊Dic5central extension (φ=1)160C2^3.100(C5:D4)320,841
C23.101(C5⋊D4) = C2×Q8⋊Dic5central extension (φ=1)320C2^3.101(C5:D4)320,851
C23.102(C5⋊D4) = C22×C10.D4central extension (φ=1)320C2^3.102(C5:D4)320,1455
C23.103(C5⋊D4) = C22×D10⋊C4central extension (φ=1)160C2^3.103(C5:D4)320,1459
C23.104(C5⋊D4) = C22×D4⋊D5central extension (φ=1)160C2^3.104(C5:D4)320,1464
C23.105(C5⋊D4) = C22×D4.D5central extension (φ=1)160C2^3.105(C5:D4)320,1466
C23.106(C5⋊D4) = C22×Q8⋊D5central extension (φ=1)160C2^3.106(C5:D4)320,1479
C23.107(C5⋊D4) = C22×C5⋊Q16central extension (φ=1)320C2^3.107(C5:D4)320,1481
C23.108(C5⋊D4) = C22×C23.D5central extension (φ=1)160C2^3.108(C5:D4)320,1511

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