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Extensions 1→N→G→Q→1 with N=C10 and Q=C4○D12

Direct product G=N×Q with N=C10 and Q=C4○D12
dρLabelID
C10×C4○D12240C10xC4oD12480,1153

Semidirect products G=N:Q with N=C10 and Q=C4○D12
extensionφ:Q→Aut NdρLabelID
C10⋊1(C4○D12) = C2×C12.28D10φ: C4○D12/Dic6 → C2 ⊆ Aut C10240C10:1(C4oD12)480,1085
C10⋊2(C4○D12) = C2×D6.D10φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10:2(C4oD12)480,1083
C10⋊3(C4○D12) = C2×D12⋊5D5φ: C4○D12/D12 → C2 ⊆ Aut C10240C10:3(C4oD12)480,1084
C10⋊4(C4○D12) = C2×Dic3.D10φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10:4(C4oD12)480,1116
C10⋊5(C4○D12) = C2×D60⋊11C2φ: C4○D12/C2×C12 → C2 ⊆ Aut C10240C10:5(C4oD12)480,1168

Non-split extensions G=N.Q with N=C10 and Q=C4○D12
extensionφ:Q→Aut NdρLabelID
C10.1(C4○D12) = Dic5×Dic6φ: C4○D12/Dic6 → C2 ⊆ Aut C10480C10.1(C4oD12)480,408
C10.2(C4○D12) = C4⋊Dic3⋊D5φ: C4○D12/Dic6 → C2 ⊆ Aut C10240C10.2(C4oD12)480,413
C10.3(C4○D12) = Dic3.Dic10φ: C4○D12/Dic6 → C2 ⊆ Aut C10480C10.3(C4oD12)480,419
C10.4(C4○D12) = D30.D4φ: C4○D12/Dic6 → C2 ⊆ Aut C10240C10.4(C4oD12)480,432
C10.5(C4○D12) = C60.67D4φ: C4○D12/Dic6 → C2 ⊆ Aut C10240C10.5(C4oD12)480,435
C10.6(C4○D12) = (C2×C60).C22φ: C4○D12/Dic6 → C2 ⊆ Aut C10240C10.6(C4oD12)480,438
C10.7(C4○D12) = C60.70D4φ: C4○D12/Dic6 → C2 ⊆ Aut C10240C10.7(C4oD12)480,451
C10.8(C4○D12) = (C4×Dic5)⋊S3φ: C4○D12/Dic6 → C2 ⊆ Aut C10240C10.8(C4oD12)480,463
C10.9(C4○D12) = C20.Dic6φ: C4○D12/Dic6 → C2 ⊆ Aut C10480C10.9(C4oD12)480,464
C10.10(C4○D12) = D30.C2⋊C4φ: C4○D12/Dic6 → C2 ⊆ Aut C10240C10.10(C4oD12)480,478
C10.11(C4○D12) = D60⋊17C4φ: C4○D12/Dic6 → C2 ⊆ Aut C10240C10.11(C4oD12)480,494
C10.12(C4○D12) = D30⋊3Q8φ: C4○D12/Dic6 → C2 ⊆ Aut C10240C10.12(C4oD12)480,500
C10.13(C4○D12) = D30.6D4φ: C4○D12/Dic6 → C2 ⊆ Aut C10240C10.13(C4oD12)480,509
C10.14(C4○D12) = C15⋊20(C4×D4)φ: C4○D12/Dic6 → C2 ⊆ Aut C10240C10.14(C4oD12)480,520
C10.15(C4○D12) = C12⋊7D20φ: C4○D12/Dic6 → C2 ⊆ Aut C10240C10.15(C4oD12)480,526
C10.16(C4○D12) = (C2×Dic6)⋊D5φ: C4○D12/Dic6 → C2 ⊆ Aut C10240C10.16(C4oD12)480,531
C10.17(C4○D12) = D30⋊2D4φ: C4○D12/Dic6 → C2 ⊆ Aut C10240C10.17(C4oD12)480,535
C10.18(C4○D12) = Dic3⋊C4⋊D5φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.18(C4oD12)480,424
C10.19(C4○D12) = D10⋊Dic6φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.19(C4oD12)480,425
C10.20(C4○D12) = Dic5.8D12φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.20(C4oD12)480,426
C10.21(C4○D12) = D6⋊Dic5⋊C2φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.21(C4oD12)480,427
C10.22(C4○D12) = D6⋊Dic10φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.22(C4oD12)480,428
C10.23(C4○D12) = Dic3.D20φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.23(C4oD12)480,429
C10.24(C4○D12) = D30.34D4φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.24(C4oD12)480,430
C10.25(C4○D12) = D30.35D4φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.25(C4oD12)480,431
C10.26(C4○D12) = (D5×C12)⋊C4φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.26(C4oD12)480,433
C10.27(C4○D12) = (C4×Dic3)⋊D5φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.27(C4oD12)480,439
C10.28(C4○D12) = (C4×Dic15)⋊C2φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.28(C4oD12)480,442
C10.29(C4○D12) = D6⋊Dic5.C2φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.29(C4oD12)480,443
C10.30(C4○D12) = (S3×C20)⋊7C4φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.30(C4oD12)480,447
C10.31(C4○D12) = D30⋊8Q8φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.31(C4oD12)480,453
C10.32(C4○D12) = Dic5.7Dic6φ: C4○D12/C4×S3 → C2 ⊆ Aut C10480C10.32(C4oD12)480,454
C10.33(C4○D12) = Dic3.3Dic10φ: C4○D12/C4×S3 → C2 ⊆ Aut C10480C10.33(C4oD12)480,455
C10.34(C4○D12) = C10.D4⋊S3φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.34(C4oD12)480,456
C10.35(C4○D12) = Dic15.4Q8φ: C4○D12/C4×S3 → C2 ⊆ Aut C10480C10.35(C4oD12)480,458
C10.36(C4○D12) = (C4×D15)⋊10C4φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.36(C4oD12)480,462
C10.37(C4○D12) = C4×C15⋊D4φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.37(C4oD12)480,515
C10.38(C4○D12) = C4×C3⋊D20φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.38(C4oD12)480,519
C10.39(C4○D12) = C4×C5⋊D12φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.39(C4oD12)480,521
C10.40(C4○D12) = D6⋊C4⋊D5φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.40(C4oD12)480,523
C10.41(C4○D12) = D10⋊D12φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.41(C4oD12)480,524
C10.42(C4○D12) = D10⋊C4⋊S3φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.42(C4oD12)480,528
C10.43(C4○D12) = D6⋊D20φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.43(C4oD12)480,530
C10.44(C4○D12) = D30⋊12D4φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.44(C4oD12)480,537
C10.45(C4○D12) = Dic15.31D4φ: C4○D12/C4×S3 → C2 ⊆ Aut C10240C10.45(C4oD12)480,540
C10.46(C4○D12) = C4×C15⋊Q8φ: C4○D12/C4×S3 → C2 ⊆ Aut C10480C10.46(C4oD12)480,543
C10.47(C4○D12) = Dic30⋊17C4φ: C4○D12/D12 → C2 ⊆ Aut C10480C10.47(C4oD12)480,409
C10.48(C4○D12) = Dic15.Q8φ: C4○D12/D12 → C2 ⊆ Aut C10480C10.48(C4oD12)480,412
C10.49(C4○D12) = C60⋊5C4⋊C2φ: C4○D12/D12 → C2 ⊆ Aut C10240C10.49(C4oD12)480,418
C10.50(C4○D12) = (C4×D5)⋊Dic3φ: C4○D12/D12 → C2 ⊆ Aut C10240C10.50(C4oD12)480,434
C10.51(C4○D12) = C60.68D4φ: C4○D12/D12 → C2 ⊆ Aut C10240C10.51(C4oD12)480,436
C10.52(C4○D12) = (C2×C12).D10φ: C4○D12/D12 → C2 ⊆ Aut C10240C10.52(C4oD12)480,437
C10.53(C4○D12) = C5⋊(C42⋊3S3)φ: C4○D12/D12 → C2 ⊆ Aut C10240C10.53(C4oD12)480,448
C10.54(C4○D12) = C60.69D4φ: C4○D12/D12 → C2 ⊆ Aut C10240C10.54(C4oD12)480,449
C10.55(C4○D12) = D6.(C4×D5)φ: C4○D12/D12 → C2 ⊆ Aut C10240C10.55(C4oD12)480,474
C10.56(C4○D12) = Dic5×D12φ: C4○D12/D12 → C2 ⊆ Aut C10240C10.56(C4oD12)480,491
C10.57(C4○D12) = (C2×D12).D5φ: C4○D12/D12 → C2 ⊆ Aut C10240C10.57(C4oD12)480,499
C10.58(C4○D12) = D6⋊3Dic10φ: C4○D12/D12 → C2 ⊆ Aut C10240C10.58(C4oD12)480,508
C10.59(C4○D12) = D6⋊(C4×D5)φ: C4○D12/D12 → C2 ⊆ Aut C10240C10.59(C4oD12)480,516
C10.60(C4○D12) = C60⋊D4φ: C4○D12/D12 → C2 ⊆ Aut C10240C10.60(C4oD12)480,525
C10.61(C4○D12) = Dic15⋊2D4φ: C4○D12/D12 → C2 ⊆ Aut C10240C10.61(C4oD12)480,529
C10.62(C4○D12) = D6.9D20φ: C4○D12/D12 → C2 ⊆ Aut C10240C10.62(C4oD12)480,533
C10.63(C4○D12) = Dic15.10D4φ: C4○D12/D12 → C2 ⊆ Aut C10240C10.63(C4oD12)480,538
C10.64(C4○D12) = Dic5⋊5Dic6φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10480C10.64(C4oD12)480,399
C10.65(C4○D12) = Dic15.2Q8φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10480C10.65(C4oD12)480,415
C10.66(C4○D12) = D6⋊C4.D5φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.66(C4oD12)480,417
C10.67(C4○D12) = C4⋊Dic5⋊S3φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.67(C4oD12)480,421
C10.68(C4○D12) = Dic3.2Dic10φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10480C10.68(C4oD12)480,422
C10.69(C4○D12) = Dic5⋊4D12φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.69(C4oD12)480,481
C10.70(C4○D12) = D6.D20φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.70(C4oD12)480,503
C10.71(C4○D12) = D30⋊4Q8φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.71(C4oD12)480,505
C10.72(C4○D12) = D6⋊4Dic10φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.72(C4oD12)480,512
C10.73(C4○D12) = D30.7D4φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.73(C4oD12)480,514
C10.74(C4○D12) = C23.D5⋊S3φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.74(C4oD12)480,601
C10.75(C4○D12) = Dic15.19D4φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.75(C4oD12)480,602
C10.76(C4○D12) = (C6×Dic5)⋊7C4φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.76(C4oD12)480,604
C10.77(C4○D12) = C23.13(S3×D5)φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.77(C4oD12)480,606
C10.78(C4○D12) = C23.14(S3×D5)φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.78(C4oD12)480,607
C10.79(C4○D12) = C30.(C2×D4)φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.79(C4oD12)480,615
C10.80(C4○D12) = C6.D4⋊D5φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.80(C4oD12)480,622
C10.81(C4○D12) = Dic5×C3⋊D4φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.81(C4oD12)480,627
C10.82(C4○D12) = C15⋊26(C4×D4)φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.82(C4oD12)480,628
C10.83(C4○D12) = (S3×C10).D4φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.83(C4oD12)480,631
C10.84(C4○D12) = D30⋊7D4φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.84(C4oD12)480,633
C10.85(C4○D12) = Dic15⋊4D4φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.85(C4oD12)480,634
C10.86(C4○D12) = D30.16D4φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.86(C4oD12)480,638
C10.87(C4○D12) = (C2×C10)⋊4D12φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.87(C4oD12)480,642
C10.88(C4○D12) = (C2×C30)⋊Q8φ: C4○D12/C3⋊D4 → C2 ⊆ Aut C10240C10.88(C4oD12)480,650
C10.89(C4○D12) = C4×Dic30φ: C4○D12/C2×C12 → C2 ⊆ Aut C10480C10.89(C4oD12)480,833
C10.90(C4○D12) = C60.24Q8φ: C4○D12/C2×C12 → C2 ⊆ Aut C10480C10.90(C4oD12)480,835
C10.91(C4○D12) = C42⋊2D15φ: C4○D12/C2×C12 → C2 ⊆ Aut C10240C10.91(C4oD12)480,837
C10.92(C4○D12) = C4×D60φ: C4○D12/C2×C12 → C2 ⊆ Aut C10240C10.92(C4oD12)480,838
C10.93(C4○D12) = C42⋊7D15φ: C4○D12/C2×C12 → C2 ⊆ Aut C10240C10.93(C4oD12)480,840
C10.94(C4○D12) = C42⋊3D15φ: C4○D12/C2×C12 → C2 ⊆ Aut C10240C10.94(C4oD12)480,841
C10.95(C4○D12) = C23.8D30φ: C4○D12/C2×C12 → C2 ⊆ Aut C10240C10.95(C4oD12)480,844
C10.96(C4○D12) = D30.28D4φ: C4○D12/C2×C12 → C2 ⊆ Aut C10240C10.96(C4oD12)480,848
C10.97(C4○D12) = D30⋊9D4φ: C4○D12/C2×C12 → C2 ⊆ Aut C10240C10.97(C4oD12)480,849
C10.98(C4○D12) = C23.11D30φ: C4○D12/C2×C12 → C2 ⊆ Aut C10240C10.98(C4oD12)480,850
C10.99(C4○D12) = Dic15.3Q8φ: C4○D12/C2×C12 → C2 ⊆ Aut C10480C10.99(C4oD12)480,854
C10.100(C4○D12) = D30.29D4φ: C4○D12/C2×C12 → C2 ⊆ Aut C10240C10.100(C4oD12)480,859
C10.101(C4○D12) = D30⋊5Q8φ: C4○D12/C2×C12 → C2 ⊆ Aut C10240C10.101(C4oD12)480,861
C10.102(C4○D12) = C4⋊C4⋊D15φ: C4○D12/C2×C12 → C2 ⊆ Aut C10240C10.102(C4oD12)480,863
C10.103(C4○D12) = C60.205D4φ: C4○D12/C2×C12 → C2 ⊆ Aut C10240C10.103(C4oD12)480,889
C10.104(C4○D12) = C23.26D30φ: C4○D12/C2×C12 → C2 ⊆ Aut C10240C10.104(C4oD12)480,891
C10.105(C4○D12) = C4×C15⋊7D4φ: C4○D12/C2×C12 → C2 ⊆ Aut C10240C10.105(C4oD12)480,893
C10.106(C4○D12) = C23.28D30φ: C4○D12/C2×C12 → C2 ⊆ Aut C10240C10.106(C4oD12)480,894
C10.107(C4○D12) = C60⋊29D4φ: C4○D12/C2×C12 → C2 ⊆ Aut C10240C10.107(C4oD12)480,895
C10.108(C4○D12) = C20×Dic6central extension (φ=1)480C10.108(C4oD12)480,747
C10.109(C4○D12) = C5×C12.6Q8central extension (φ=1)480C10.109(C4oD12)480,749
C10.110(C4○D12) = C5×C42⋊2S3central extension (φ=1)240C10.110(C4oD12)480,751
C10.111(C4○D12) = C20×D12central extension (φ=1)240C10.111(C4oD12)480,752
C10.112(C4○D12) = C5×C42⋊7S3central extension (φ=1)240C10.112(C4oD12)480,754
C10.113(C4○D12) = C5×C42⋊3S3central extension (φ=1)240C10.113(C4oD12)480,755
C10.114(C4○D12) = C5×C23.8D6central extension (φ=1)240C10.114(C4oD12)480,758
C10.115(C4○D12) = C5×C23.9D6central extension (φ=1)240C10.115(C4oD12)480,762
C10.116(C4○D12) = C5×Dic3⋊D4central extension (φ=1)240C10.116(C4oD12)480,763
C10.117(C4○D12) = C5×C23.11D6central extension (φ=1)240C10.117(C4oD12)480,764
C10.118(C4○D12) = C5×Dic3.Q8central extension (φ=1)480C10.118(C4oD12)480,768
C10.119(C4○D12) = C5×D6.D4central extension (φ=1)240C10.119(C4oD12)480,773
C10.120(C4○D12) = C5×D6⋊Q8central extension (φ=1)240C10.120(C4oD12)480,775
C10.121(C4○D12) = C5×C4⋊C4⋊S3central extension (φ=1)240C10.121(C4oD12)480,777
C10.122(C4○D12) = C5×C12.48D4central extension (φ=1)240C10.122(C4oD12)480,803
C10.123(C4○D12) = C5×C23.26D6central extension (φ=1)240C10.123(C4oD12)480,805
C10.124(C4○D12) = C20×C3⋊D4central extension (φ=1)240C10.124(C4oD12)480,807
C10.125(C4○D12) = C5×C23.28D6central extension (φ=1)240C10.125(C4oD12)480,808
C10.126(C4○D12) = C5×C12⋊7D4central extension (φ=1)240C10.126(C4oD12)480,809

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