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Extensions 1→N→G→Q→1 with N=C6 and Q=C4○D20

Direct product G=N×Q with N=C6 and Q=C4○D20
dρLabelID
C6×C4○D20240C6xC4oD20480,1138

Semidirect products G=N:Q with N=C6 and Q=C4○D20
extensionφ:Q→Aut NdρLabelID
C6⋊1(C4○D20) = C2×D60⋊C2φ: C4○D20/Dic10 → C2 ⊆ Aut C6240C6:1(C4oD20)480,1081
C6⋊2(C4○D20) = C2×D6.D10φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6:2(C4oD20)480,1083
C6⋊3(C4○D20) = C2×D20⋊5S3φ: C4○D20/D20 → C2 ⊆ Aut C6240C6:3(C4oD20)480,1074
C6⋊4(C4○D20) = C2×Dic5.D6φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6:4(C4oD20)480,1113
C6⋊5(C4○D20) = C2×D60⋊11C2φ: C4○D20/C2×C20 → C2 ⊆ Aut C6240C6:5(C4oD20)480,1168

Non-split extensions G=N.Q with N=C6 and Q=C4○D20
extensionφ:Q→Aut NdρLabelID
C6.1(C4○D20) = (C2×C20).D6φ: C4○D20/Dic10 → C2 ⊆ Aut C6240C6.1(C4oD20)480,402
C6.2(C4○D20) = Dic3×Dic10φ: C4○D20/Dic10 → C2 ⊆ Aut C6480C6.2(C4oD20)480,406
C6.3(C4○D20) = Dic5.1Dic6φ: C4○D20/Dic10 → C2 ⊆ Aut C6480C6.3(C4oD20)480,410
C6.4(C4○D20) = C60⋊5C4⋊C2φ: C4○D20/Dic10 → C2 ⊆ Aut C6240C6.4(C4oD20)480,418
C6.5(C4○D20) = C4⋊Dic5⋊S3φ: C4○D20/Dic10 → C2 ⊆ Aut C6240C6.5(C4oD20)480,421
C6.6(C4○D20) = C60.46D4φ: C4○D20/Dic10 → C2 ⊆ Aut C6240C6.6(C4oD20)480,445
C6.7(C4○D20) = C60.47D4φ: C4○D20/Dic10 → C2 ⊆ Aut C6240C6.7(C4oD20)480,450
C6.8(C4○D20) = D30⋊Q8φ: C4○D20/Dic10 → C2 ⊆ Aut C6240C6.8(C4oD20)480,487
C6.9(C4○D20) = D30⋊D4φ: C4○D20/Dic10 → C2 ⊆ Aut C6240C6.9(C4oD20)480,496
C6.10(C4○D20) = D60⋊14C4φ: C4○D20/Dic10 → C2 ⊆ Aut C6240C6.10(C4oD20)480,504
C6.11(C4○D20) = D30.6D4φ: C4○D20/Dic10 → C2 ⊆ Aut C6240C6.11(C4oD20)480,509
C6.12(C4○D20) = D30.7D4φ: C4○D20/Dic10 → C2 ⊆ Aut C6240C6.12(C4oD20)480,514
C6.13(C4○D20) = C15⋊22(C4×D4)φ: C4○D20/Dic10 → C2 ⊆ Aut C6240C6.13(C4oD20)480,522
C6.14(C4○D20) = C60⋊6D4φ: C4○D20/Dic10 → C2 ⊆ Aut C6240C6.14(C4oD20)480,536
C6.15(C4○D20) = Dic3⋊C4⋊D5φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.15(C4oD20)480,424
C6.16(C4○D20) = D10⋊Dic6φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.16(C4oD20)480,425
C6.17(C4○D20) = Dic5.8D12φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.17(C4oD20)480,426
C6.18(C4○D20) = D6⋊Dic5⋊C2φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.18(C4oD20)480,427
C6.19(C4○D20) = D6⋊Dic10φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.19(C4oD20)480,428
C6.20(C4○D20) = Dic3.D20φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.20(C4oD20)480,429
C6.21(C4○D20) = D30.34D4φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.21(C4oD20)480,430
C6.22(C4○D20) = D30.35D4φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.22(C4oD20)480,431
C6.23(C4○D20) = (D5×C12)⋊C4φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.23(C4oD20)480,433
C6.24(C4○D20) = (C4×Dic15)⋊C2φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.24(C4oD20)480,442
C6.25(C4○D20) = D6⋊Dic5.C2φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.25(C4oD20)480,443
C6.26(C4○D20) = (S3×C20)⋊7C4φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.26(C4oD20)480,447
C6.27(C4○D20) = C5⋊(C42⋊3S3)φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.27(C4oD20)480,448
C6.28(C4○D20) = D30⋊8Q8φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.28(C4oD20)480,453
C6.29(C4○D20) = Dic5.7Dic6φ: C4○D20/C4×D5 → C2 ⊆ Aut C6480C6.29(C4oD20)480,454
C6.30(C4○D20) = Dic3.3Dic10φ: C4○D20/C4×D5 → C2 ⊆ Aut C6480C6.30(C4oD20)480,455
C6.31(C4○D20) = Dic15.4Q8φ: C4○D20/C4×D5 → C2 ⊆ Aut C6480C6.31(C4oD20)480,458
C6.32(C4○D20) = (C4×D15)⋊10C4φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.32(C4oD20)480,462
C6.33(C4○D20) = (C4×Dic5)⋊S3φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.33(C4oD20)480,463
C6.34(C4○D20) = C4×C15⋊D4φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.34(C4oD20)480,515
C6.35(C4○D20) = C4×C3⋊D20φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.35(C4oD20)480,519
C6.36(C4○D20) = C4×C5⋊D12φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.36(C4oD20)480,521
C6.37(C4○D20) = D6⋊C4⋊D5φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.37(C4oD20)480,523
C6.38(C4○D20) = D10⋊D12φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.38(C4oD20)480,524
C6.39(C4○D20) = D10⋊C4⋊S3φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.39(C4oD20)480,528
C6.40(C4○D20) = D6⋊D20φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.40(C4oD20)480,530
C6.41(C4○D20) = D30⋊12D4φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.41(C4oD20)480,537
C6.42(C4○D20) = Dic15.31D4φ: C4○D20/C4×D5 → C2 ⊆ Aut C6240C6.42(C4oD20)480,540
C6.43(C4○D20) = C4×C15⋊Q8φ: C4○D20/C4×D5 → C2 ⊆ Aut C6480C6.43(C4oD20)480,543
C6.44(C4○D20) = (S3×C20)⋊5C4φ: C4○D20/D20 → C2 ⊆ Aut C6240C6.44(C4oD20)480,414
C6.45(C4○D20) = Dic15.2Q8φ: C4○D20/D20 → C2 ⊆ Aut C6480C6.45(C4oD20)480,415
C6.46(C4○D20) = Dic30⋊14C4φ: C4○D20/D20 → C2 ⊆ Aut C6480C6.46(C4oD20)480,416
C6.47(C4○D20) = D6⋊C4.D5φ: C4○D20/D20 → C2 ⊆ Aut C6240C6.47(C4oD20)480,417
C6.48(C4○D20) = (C2×C60).C22φ: C4○D20/D20 → C2 ⊆ Aut C6240C6.48(C4oD20)480,438
C6.49(C4○D20) = C60.44D4φ: C4○D20/D20 → C2 ⊆ Aut C6240C6.49(C4oD20)480,440
C6.50(C4○D20) = C60.45D4φ: C4○D20/D20 → C2 ⊆ Aut C6240C6.50(C4oD20)480,441
C6.51(C4○D20) = C60.6Q8φ: C4○D20/D20 → C2 ⊆ Aut C6480C6.51(C4oD20)480,457
C6.52(C4○D20) = (C6×D5).D4φ: C4○D20/D20 → C2 ⊆ Aut C6240C6.52(C4oD20)480,483
C6.53(C4○D20) = Dic15⋊D4φ: C4○D20/D20 → C2 ⊆ Aut C6240C6.53(C4oD20)480,484
C6.54(C4○D20) = D10.17D12φ: C4○D20/D20 → C2 ⊆ Aut C6240C6.54(C4oD20)480,490
C6.55(C4○D20) = Dic3×D20φ: C4○D20/D20 → C2 ⊆ Aut C6240C6.55(C4oD20)480,501
C6.56(C4○D20) = D10⋊4Dic6φ: C4○D20/D20 → C2 ⊆ Aut C6240C6.56(C4oD20)480,507
C6.57(C4○D20) = C15⋊17(C4×D4)φ: C4○D20/D20 → C2 ⊆ Aut C6240C6.57(C4oD20)480,517
C6.58(C4○D20) = C60⋊4D4φ: C4○D20/D20 → C2 ⊆ Aut C6240C6.58(C4oD20)480,532
C6.59(C4○D20) = Dic15.10D4φ: C4○D20/D20 → C2 ⊆ Aut C6240C6.59(C4oD20)480,538
C6.60(C4○D20) = Dic3⋊5Dic10φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6480C6.60(C4oD20)480,400
C6.61(C4○D20) = Dic5.2Dic6φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6480C6.61(C4oD20)480,411
C6.62(C4○D20) = Dic15.Q8φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6480C6.62(C4oD20)480,412
C6.63(C4○D20) = C4⋊Dic3⋊D5φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.63(C4oD20)480,413
C6.64(C4○D20) = D30.D4φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.64(C4oD20)480,432
C6.65(C4○D20) = (C2×C12).D10φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.65(C4oD20)480,437
C6.66(C4○D20) = (C4×Dic3)⋊D5φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.66(C4oD20)480,439
C6.67(C4○D20) = C10.D4⋊S3φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.67(C4oD20)480,456
C6.68(C4○D20) = (D5×Dic3)⋊C4φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.68(C4oD20)480,469
C6.69(C4○D20) = Dic3⋊4D20φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.69(C4oD20)480,471
C6.70(C4○D20) = D30.23(C2×C4)φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.70(C4oD20)480,479
C6.71(C4○D20) = D10.16D12φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.71(C4oD20)480,489
C6.72(C4○D20) = D30⋊2Q8φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.72(C4oD20)480,495
C6.73(C4○D20) = Dic15.D4φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.73(C4oD20)480,506
C6.74(C4○D20) = Dic15.19D4φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.74(C4oD20)480,602
C6.75(C4○D20) = C23.26(S3×D5)φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.75(C4oD20)480,605
C6.76(C4○D20) = C23.13(S3×D5)φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.76(C4oD20)480,606
C6.77(C4○D20) = C23.14(S3×D5)φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.77(C4oD20)480,607
C6.78(C4○D20) = D30⋊6D4φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.78(C4oD20)480,609
C6.79(C4○D20) = C6.(D4×D5)φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.79(C4oD20)480,610
C6.80(C4○D20) = (C2×C30).D4φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.80(C4oD20)480,612
C6.81(C4○D20) = C10.(C2×D12)φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.81(C4oD20)480,618
C6.82(C4○D20) = C23.17(S3×D5)φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.82(C4oD20)480,624
C6.83(C4○D20) = Dic15⋊3D4φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.83(C4oD20)480,626
C6.84(C4○D20) = Dic3×C5⋊D4φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.84(C4oD20)480,629
C6.85(C4○D20) = C15⋊28(C4×D4)φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.85(C4oD20)480,632
C6.86(C4○D20) = D30.16D4φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.86(C4oD20)480,638
C6.87(C4○D20) = (C2×C6)⋊D20φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.87(C4oD20)480,645
C6.88(C4○D20) = (C2×C10)⋊8Dic6φ: C4○D20/C5⋊D4 → C2 ⊆ Aut C6240C6.88(C4oD20)480,651
C6.89(C4○D20) = C4×Dic30φ: C4○D20/C2×C20 → C2 ⊆ Aut C6480C6.89(C4oD20)480,833
C6.90(C4○D20) = C60.24Q8φ: C4○D20/C2×C20 → C2 ⊆ Aut C6480C6.90(C4oD20)480,835
C6.91(C4○D20) = C42⋊2D15φ: C4○D20/C2×C20 → C2 ⊆ Aut C6240C6.91(C4oD20)480,837
C6.92(C4○D20) = C4×D60φ: C4○D20/C2×C20 → C2 ⊆ Aut C6240C6.92(C4oD20)480,838
C6.93(C4○D20) = C42⋊7D15φ: C4○D20/C2×C20 → C2 ⊆ Aut C6240C6.93(C4oD20)480,840
C6.94(C4○D20) = C42⋊3D15φ: C4○D20/C2×C20 → C2 ⊆ Aut C6240C6.94(C4oD20)480,841
C6.95(C4○D20) = C23.8D30φ: C4○D20/C2×C20 → C2 ⊆ Aut C6240C6.95(C4oD20)480,844
C6.96(C4○D20) = D30.28D4φ: C4○D20/C2×C20 → C2 ⊆ Aut C6240C6.96(C4oD20)480,848
C6.97(C4○D20) = D30⋊9D4φ: C4○D20/C2×C20 → C2 ⊆ Aut C6240C6.97(C4oD20)480,849
C6.98(C4○D20) = C23.11D30φ: C4○D20/C2×C20 → C2 ⊆ Aut C6240C6.98(C4oD20)480,850
C6.99(C4○D20) = Dic15.3Q8φ: C4○D20/C2×C20 → C2 ⊆ Aut C6480C6.99(C4oD20)480,854
C6.100(C4○D20) = D30.29D4φ: C4○D20/C2×C20 → C2 ⊆ Aut C6240C6.100(C4oD20)480,859
C6.101(C4○D20) = D30⋊5Q8φ: C4○D20/C2×C20 → C2 ⊆ Aut C6240C6.101(C4oD20)480,861
C6.102(C4○D20) = C4⋊C4⋊D15φ: C4○D20/C2×C20 → C2 ⊆ Aut C6240C6.102(C4oD20)480,863
C6.103(C4○D20) = C60.205D4φ: C4○D20/C2×C20 → C2 ⊆ Aut C6240C6.103(C4oD20)480,889
C6.104(C4○D20) = C23.26D30φ: C4○D20/C2×C20 → C2 ⊆ Aut C6240C6.104(C4oD20)480,891
C6.105(C4○D20) = C4×C15⋊7D4φ: C4○D20/C2×C20 → C2 ⊆ Aut C6240C6.105(C4oD20)480,893
C6.106(C4○D20) = C23.28D30φ: C4○D20/C2×C20 → C2 ⊆ Aut C6240C6.106(C4oD20)480,894
C6.107(C4○D20) = C60⋊29D4φ: C4○D20/C2×C20 → C2 ⊆ Aut C6240C6.107(C4oD20)480,895
C6.108(C4○D20) = C12×Dic10central extension (φ=1)480C6.108(C4oD20)480,661
C6.109(C4○D20) = C3×C20.6Q8central extension (φ=1)480C6.109(C4oD20)480,663
C6.110(C4○D20) = C3×C42⋊D5central extension (φ=1)240C6.110(C4oD20)480,665
C6.111(C4○D20) = C12×D20central extension (φ=1)240C6.111(C4oD20)480,666
C6.112(C4○D20) = C3×C4.D20central extension (φ=1)240C6.112(C4oD20)480,668
C6.113(C4○D20) = C3×C42⋊2D5central extension (φ=1)240C6.113(C4oD20)480,669
C6.114(C4○D20) = C3×C23.D10central extension (φ=1)240C6.114(C4oD20)480,672
C6.115(C4○D20) = C3×D10.12D4central extension (φ=1)240C6.115(C4oD20)480,676
C6.116(C4○D20) = C3×D10⋊D4central extension (φ=1)240C6.116(C4oD20)480,677
C6.117(C4○D20) = C3×Dic5.5D4central extension (φ=1)240C6.117(C4oD20)480,678
C6.118(C4○D20) = C3×Dic5.Q8central extension (φ=1)480C6.118(C4oD20)480,682
C6.119(C4○D20) = C3×D10.13D4central extension (φ=1)240C6.119(C4oD20)480,687
C6.120(C4○D20) = C3×D10⋊Q8central extension (φ=1)240C6.120(C4oD20)480,689
C6.121(C4○D20) = C3×C4⋊C4⋊D5central extension (φ=1)240C6.121(C4oD20)480,691
C6.122(C4○D20) = C3×C20.48D4central extension (φ=1)240C6.122(C4oD20)480,717
C6.123(C4○D20) = C3×C23.21D10central extension (φ=1)240C6.123(C4oD20)480,719
C6.124(C4○D20) = C12×C5⋊D4central extension (φ=1)240C6.124(C4oD20)480,721
C6.125(C4○D20) = C3×C23.23D10central extension (φ=1)240C6.125(C4oD20)480,722
C6.126(C4○D20) = C3×C20⋊7D4central extension (φ=1)240C6.126(C4oD20)480,723

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