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Extensions 1→N→G→Q→1 with N=C10 and Q=D4⋊2S3

Direct product G=N×Q with N=C10 and Q=D4⋊2S3
dρLabelID
C10×D4⋊2S3240C10xD4:2S3480,1155

Semidirect products G=N:Q with N=C10 and Q=D4⋊2S3
extensionφ:Q→Aut NdρLabelID
C10⋊1(D4⋊2S3) = C2×D20⋊S3φ: D4⋊2S3/Dic6 → C2 ⊆ Aut C10240C10:1(D4:2S3)480,1075
C10⋊2(D4⋊2S3) = C2×D20⋊5S3φ: D4⋊2S3/C4×S3 → C2 ⊆ Aut C10240C10:2(D4:2S3)480,1074
C10⋊3(D4⋊2S3) = C2×Dic5.D6φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10:3(D4:2S3)480,1113
C10⋊4(D4⋊2S3) = C2×C30.C23φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10:4(D4:2S3)480,1114
C10⋊5(D4⋊2S3) = C2×D4⋊2D15φ: D4⋊2S3/C3×D4 → C2 ⊆ Aut C10240C10:5(D4:2S3)480,1170

Non-split extensions G=N.Q with N=C10 and Q=D4⋊2S3
extensionφ:Q→Aut NdρLabelID
C10.1(D4⋊2S3) = Dic15⋊7Q8φ: D4⋊2S3/Dic6 → C2 ⊆ Aut C10480C10.1(D4:2S3)480,420
C10.2(D4⋊2S3) = C4⋊Dic5⋊S3φ: D4⋊2S3/Dic6 → C2 ⊆ Aut C10240C10.2(D4:2S3)480,421
C10.3(D4⋊2S3) = Dic3.2Dic10φ: D4⋊2S3/Dic6 → C2 ⊆ Aut C10480C10.3(D4:2S3)480,422
C10.4(D4⋊2S3) = (C4×D15)⋊8C4φ: D4⋊2S3/Dic6 → C2 ⊆ Aut C10240C10.4(D4:2S3)480,423
C10.5(D4⋊2S3) = D30.34D4φ: D4⋊2S3/Dic6 → C2 ⊆ Aut C10240C10.5(D4:2S3)480,430
C10.6(D4⋊2S3) = (C2×C12).D10φ: D4⋊2S3/Dic6 → C2 ⊆ Aut C10240C10.6(D4:2S3)480,437
C10.7(D4⋊2S3) = C60.88D4φ: D4⋊2S3/Dic6 → C2 ⊆ Aut C10240C10.7(D4:2S3)480,444
C10.8(D4⋊2S3) = D30⋊9Q8φ: D4⋊2S3/Dic6 → C2 ⊆ Aut C10240C10.8(D4:2S3)480,459
C10.9(D4⋊2S3) = C12.Dic10φ: D4⋊2S3/Dic6 → C2 ⊆ Aut C10480C10.9(D4:2S3)480,460
C10.10(D4⋊2S3) = D10.19(C4×S3)φ: D4⋊2S3/Dic6 → C2 ⊆ Aut C10240C10.10(D4:2S3)480,470
C10.11(D4⋊2S3) = Dic15⋊13D4φ: D4⋊2S3/Dic6 → C2 ⊆ Aut C10240C10.11(D4:2S3)480,472
C10.12(D4⋊2S3) = Dic3⋊D20φ: D4⋊2S3/Dic6 → C2 ⊆ Aut C10240C10.12(D4:2S3)480,485
C10.13(D4⋊2S3) = D10⋊1Dic6φ: D4⋊2S3/Dic6 → C2 ⊆ Aut C10240C10.13(D4:2S3)480,497
C10.14(D4⋊2S3) = D20⋊8Dic3φ: D4⋊2S3/Dic6 → C2 ⊆ Aut C10240C10.14(D4:2S3)480,510
C10.15(D4⋊2S3) = (C2×Dic6)⋊D5φ: D4⋊2S3/Dic6 → C2 ⊆ Aut C10240C10.15(D4:2S3)480,531
C10.16(D4⋊2S3) = C12⋊2D20φ: D4⋊2S3/Dic6 → C2 ⊆ Aut C10240C10.16(D4:2S3)480,541
C10.17(D4⋊2S3) = (S3×C20)⋊5C4φ: D4⋊2S3/C4×S3 → C2 ⊆ Aut C10240C10.17(D4:2S3)480,414
C10.18(D4⋊2S3) = Dic15.2Q8φ: D4⋊2S3/C4×S3 → C2 ⊆ Aut C10480C10.18(D4:2S3)480,415
C10.19(D4⋊2S3) = Dic30⋊14C4φ: D4⋊2S3/C4×S3 → C2 ⊆ Aut C10480C10.19(D4:2S3)480,416
C10.20(D4⋊2S3) = D6⋊C4.D5φ: D4⋊2S3/C4×S3 → C2 ⊆ Aut C10240C10.20(D4:2S3)480,417
C10.21(D4⋊2S3) = (C4×Dic3)⋊D5φ: D4⋊2S3/C4×S3 → C2 ⊆ Aut C10240C10.21(D4:2S3)480,439
C10.22(D4⋊2S3) = C60.44D4φ: D4⋊2S3/C4×S3 → C2 ⊆ Aut C10240C10.22(D4:2S3)480,440
C10.23(D4⋊2S3) = C60.45D4φ: D4⋊2S3/C4×S3 → C2 ⊆ Aut C10240C10.23(D4:2S3)480,441
C10.24(D4⋊2S3) = C60.6Q8φ: D4⋊2S3/C4×S3 → C2 ⊆ Aut C10480C10.24(D4:2S3)480,457
C10.25(D4⋊2S3) = (D5×Dic3)⋊C4φ: D4⋊2S3/C4×S3 → C2 ⊆ Aut C10240C10.25(D4:2S3)480,469
C10.26(D4⋊2S3) = (C6×D5).D4φ: D4⋊2S3/C4×S3 → C2 ⊆ Aut C10240C10.26(D4:2S3)480,483
C10.27(D4⋊2S3) = Dic15⋊D4φ: D4⋊2S3/C4×S3 → C2 ⊆ Aut C10240C10.27(D4:2S3)480,484
C10.28(D4⋊2S3) = D10.17D12φ: D4⋊2S3/C4×S3 → C2 ⊆ Aut C10240C10.28(D4:2S3)480,490
C10.29(D4⋊2S3) = Dic3×D20φ: D4⋊2S3/C4×S3 → C2 ⊆ Aut C10240C10.29(D4:2S3)480,501
C10.30(D4⋊2S3) = D10⋊4Dic6φ: D4⋊2S3/C4×S3 → C2 ⊆ Aut C10240C10.30(D4:2S3)480,507
C10.31(D4⋊2S3) = C15⋊17(C4×D4)φ: D4⋊2S3/C4×S3 → C2 ⊆ Aut C10240C10.31(D4:2S3)480,517
C10.32(D4⋊2S3) = D10⋊C4⋊S3φ: D4⋊2S3/C4×S3 → C2 ⊆ Aut C10240C10.32(D4:2S3)480,528
C10.33(D4⋊2S3) = C60⋊4D4φ: D4⋊2S3/C4×S3 → C2 ⊆ Aut C10240C10.33(D4:2S3)480,532
C10.34(D4⋊2S3) = Dic15.10D4φ: D4⋊2S3/C4×S3 → C2 ⊆ Aut C10240C10.34(D4:2S3)480,538
C10.35(D4⋊2S3) = Dic3⋊5Dic10φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10480C10.35(D4:2S3)480,400
C10.36(D4⋊2S3) = Dic5.2Dic6φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10480C10.36(D4:2S3)480,411
C10.37(D4⋊2S3) = Dic15.Q8φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10480C10.37(D4:2S3)480,412
C10.38(D4⋊2S3) = C4⋊Dic3⋊D5φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.38(D4:2S3)480,413
C10.39(D4⋊2S3) = Dic3.D20φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.39(D4:2S3)480,429
C10.40(D4⋊2S3) = D30.D4φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.40(D4:2S3)480,432
C10.41(D4⋊2S3) = Dic3.3Dic10φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10480C10.41(D4:2S3)480,455
C10.42(D4⋊2S3) = C10.D4⋊S3φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.42(D4:2S3)480,456
C10.43(D4⋊2S3) = Dic3⋊4D20φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.43(D4:2S3)480,471
C10.44(D4⋊2S3) = D30.23(C2×C4)φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.44(D4:2S3)480,479
C10.45(D4⋊2S3) = D10.16D12φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.45(D4:2S3)480,489
C10.46(D4⋊2S3) = D30⋊2Q8φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.46(D4:2S3)480,495
C10.47(D4⋊2S3) = Dic15.D4φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.47(D4:2S3)480,506
C10.48(D4⋊2S3) = Dic15.19D4φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.48(D4:2S3)480,602
C10.49(D4⋊2S3) = C23.26(S3×D5)φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.49(D4:2S3)480,605
C10.50(D4⋊2S3) = D30⋊6D4φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.50(D4:2S3)480,609
C10.51(D4⋊2S3) = C6.(D4×D5)φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.51(D4:2S3)480,610
C10.52(D4⋊2S3) = (C2×C30).D4φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.52(D4:2S3)480,612
C10.53(D4⋊2S3) = C10.(C2×D12)φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.53(D4:2S3)480,618
C10.54(D4⋊2S3) = C23.17(S3×D5)φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.54(D4:2S3)480,624
C10.55(D4⋊2S3) = Dic15⋊3D4φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.55(D4:2S3)480,626
C10.56(D4⋊2S3) = Dic3×C5⋊D4φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.56(D4:2S3)480,629
C10.57(D4⋊2S3) = C15⋊28(C4×D4)φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.57(D4:2S3)480,632
C10.58(D4⋊2S3) = D30.16D4φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.58(D4:2S3)480,638
C10.59(D4⋊2S3) = (C2×C6)⋊D20φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.59(D4:2S3)480,645
C10.60(D4⋊2S3) = (C2×C10)⋊8Dic6φ: D4⋊2S3/C2×Dic3 → C2 ⊆ Aut C10240C10.60(D4:2S3)480,651
C10.61(D4⋊2S3) = Dic15⋊5Q8φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10480C10.61(D4:2S3)480,401
C10.62(D4⋊2S3) = Dic5.1Dic6φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10480C10.62(D4:2S3)480,410
C10.63(D4⋊2S3) = C60⋊5C4⋊C2φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.63(D4:2S3)480,418
C10.64(D4⋊2S3) = Dic3.Dic10φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10480C10.64(D4:2S3)480,419
C10.65(D4⋊2S3) = (C2×C60).C22φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.65(D4:2S3)480,438
C10.66(D4⋊2S3) = (C4×Dic15)⋊C2φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.66(D4:2S3)480,442
C10.67(D4⋊2S3) = D6⋊Dic5.C2φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.67(D4:2S3)480,443
C10.68(D4⋊2S3) = Dic15.4Q8φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10480C10.68(D4:2S3)480,458
C10.69(D4⋊2S3) = (S3×Dic5)⋊C4φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.69(D4:2S3)480,476
C10.70(D4⋊2S3) = D6⋊2Dic10φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.70(D4:2S3)480,493
C10.71(D4⋊2S3) = D10⋊2Dic6φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.71(D4:2S3)480,498
C10.72(D4⋊2S3) = Dic15⋊9D4φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.72(D4:2S3)480,518
C10.73(D4⋊2S3) = D6.9D20φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.73(D4:2S3)480,533
C10.74(D4⋊2S3) = Dic15.31D4φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.74(D4:2S3)480,540
C10.75(D4⋊2S3) = C23.D5⋊S3φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.75(D4:2S3)480,601
C10.76(D4⋊2S3) = C23.13(S3×D5)φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.76(D4:2S3)480,606
C10.77(D4⋊2S3) = C23.14(S3×D5)φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.77(D4:2S3)480,607
C10.78(D4⋊2S3) = C23.48(S3×D5)φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.78(D4:2S3)480,608
C10.79(D4⋊2S3) = C6.(C2×D20)φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.79(D4:2S3)480,613
C10.80(D4⋊2S3) = (C2×C10).D12φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.80(D4:2S3)480,619
C10.81(D4⋊2S3) = (C6×D5)⋊D4φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.81(D4:2S3)480,625
C10.82(D4⋊2S3) = (S3×C10).D4φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.82(D4:2S3)480,631
C10.83(D4⋊2S3) = Dic15⋊16D4φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.83(D4:2S3)480,635
C10.84(D4⋊2S3) = Dic15⋊17D4φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.84(D4:2S3)480,636
C10.85(D4⋊2S3) = (S3×C10)⋊D4φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.85(D4:2S3)480,641
C10.86(D4⋊2S3) = Dic15⋊18D4φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.86(D4:2S3)480,647
C10.87(D4⋊2S3) = Dic15.48D4φ: D4⋊2S3/C3⋊D4 → C2 ⊆ Aut C10240C10.87(D4:2S3)480,652
C10.88(D4⋊2S3) = C23.15D30φ: D4⋊2S3/C3×D4 → C2 ⊆ Aut C10240C10.88(D4:2S3)480,842
C10.89(D4⋊2S3) = C22⋊2Dic30φ: D4⋊2S3/C3×D4 → C2 ⊆ Aut C10240C10.89(D4:2S3)480,843
C10.90(D4⋊2S3) = C23.8D30φ: D4⋊2S3/C3×D4 → C2 ⊆ Aut C10240C10.90(D4:2S3)480,844
C10.91(D4⋊2S3) = Dic15⋊19D4φ: D4⋊2S3/C3×D4 → C2 ⊆ Aut C10240C10.91(D4:2S3)480,846
C10.92(D4⋊2S3) = D30.28D4φ: D4⋊2S3/C3×D4 → C2 ⊆ Aut C10240C10.92(D4:2S3)480,848
C10.93(D4⋊2S3) = C23.11D30φ: D4⋊2S3/C3×D4 → C2 ⊆ Aut C10240C10.93(D4:2S3)480,850
C10.94(D4⋊2S3) = C22.D60φ: D4⋊2S3/C3×D4 → C2 ⊆ Aut C10240C10.94(D4:2S3)480,851
C10.95(D4⋊2S3) = Dic15⋊10Q8φ: D4⋊2S3/C3×D4 → C2 ⊆ Aut C10480C10.95(D4:2S3)480,852
C10.96(D4⋊2S3) = Dic15.3Q8φ: D4⋊2S3/C3×D4 → C2 ⊆ Aut C10480C10.96(D4:2S3)480,854
C10.97(D4⋊2S3) = C4.Dic30φ: D4⋊2S3/C3×D4 → C2 ⊆ Aut C10480C10.97(D4:2S3)480,855
C10.98(D4⋊2S3) = C4⋊C4⋊7D15φ: D4⋊2S3/C3×D4 → C2 ⊆ Aut C10240C10.98(D4:2S3)480,857
C10.99(D4⋊2S3) = D30⋊6Q8φ: D4⋊2S3/C3×D4 → C2 ⊆ Aut C10240C10.99(D4:2S3)480,862
C10.100(D4⋊2S3) = C4⋊C4⋊D15φ: D4⋊2S3/C3×D4 → C2 ⊆ Aut C10240C10.100(D4:2S3)480,863
C10.101(D4⋊2S3) = D4×Dic15φ: D4⋊2S3/C3×D4 → C2 ⊆ Aut C10240C10.101(D4:2S3)480,899
C10.102(D4⋊2S3) = C23.22D30φ: D4⋊2S3/C3×D4 → C2 ⊆ Aut C10240C10.102(D4:2S3)480,900
C10.103(D4⋊2S3) = C60.17D4φ: D4⋊2S3/C3×D4 → C2 ⊆ Aut C10240C10.103(D4:2S3)480,901
C10.104(D4⋊2S3) = C60⋊2D4φ: D4⋊2S3/C3×D4 → C2 ⊆ Aut C10240C10.104(D4:2S3)480,903
C10.105(D4⋊2S3) = Dic15⋊12D4φ: D4⋊2S3/C3×D4 → C2 ⊆ Aut C10240C10.105(D4:2S3)480,904
C10.106(D4⋊2S3) = C5×C23.16D6central extension (φ=1)240C10.106(D4:2S3)480,756
C10.107(D4⋊2S3) = C5×Dic3.D4central extension (φ=1)240C10.107(D4:2S3)480,757
C10.108(D4⋊2S3) = C5×C23.8D6central extension (φ=1)240C10.108(D4:2S3)480,758
C10.109(D4⋊2S3) = C5×Dic3⋊4D4central extension (φ=1)240C10.109(D4:2S3)480,760
C10.110(D4⋊2S3) = C5×C23.9D6central extension (φ=1)240C10.110(D4:2S3)480,762
C10.111(D4⋊2S3) = C5×C23.11D6central extension (φ=1)240C10.111(D4:2S3)480,764
C10.112(D4⋊2S3) = C5×C23.21D6central extension (φ=1)240C10.112(D4:2S3)480,765
C10.113(D4⋊2S3) = C5×Dic6⋊C4central extension (φ=1)480C10.113(D4:2S3)480,766
C10.114(D4⋊2S3) = C5×Dic3.Q8central extension (φ=1)480C10.114(D4:2S3)480,768
C10.115(D4⋊2S3) = C5×C4.Dic6central extension (φ=1)480C10.115(D4:2S3)480,769
C10.116(D4⋊2S3) = C5×C4⋊C4⋊7S3central extension (φ=1)240C10.116(D4:2S3)480,771
C10.117(D4⋊2S3) = C5×C4.D12central extension (φ=1)240C10.117(D4:2S3)480,776
C10.118(D4⋊2S3) = C5×C4⋊C4⋊S3central extension (φ=1)240C10.118(D4:2S3)480,777
C10.119(D4⋊2S3) = C5×D4×Dic3central extension (φ=1)240C10.119(D4:2S3)480,813
C10.120(D4⋊2S3) = C5×C23.23D6central extension (φ=1)240C10.120(D4:2S3)480,814
C10.121(D4⋊2S3) = C5×C23.12D6central extension (φ=1)240C10.121(D4:2S3)480,815
C10.122(D4⋊2S3) = C5×D6⋊3D4central extension (φ=1)240C10.122(D4:2S3)480,817
C10.123(D4⋊2S3) = C5×C23.14D6central extension (φ=1)240C10.123(D4:2S3)480,818

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