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Extensions 1→N→G→Q→1 with N=C6 and Q=C2×D20

Direct product G=N×Q with N=C6 and Q=C2×D20
dρLabelID
C2×C6×D20240C2xC6xD20480,1137

Semidirect products G=N:Q with N=C6 and Q=C2×D20
extensionφ:Q→Aut NdρLabelID
C6⋊1(C2×D20) = C2×S3×D20φ: C2×D20/D20 → C2 ⊆ Aut C6120C6:1(C2xD20)480,1088
C6⋊2(C2×D20) = C22×D60φ: C2×D20/C2×C20 → C2 ⊆ Aut C6240C6:2(C2xD20)480,1167
C6⋊3(C2×D20) = C22×C3⋊D20φ: C2×D20/C22×D5 → C2 ⊆ Aut C6240C6:3(C2xD20)480,1119

Non-split extensions G=N.Q with N=C6 and Q=C2×D20
extensionφ:Q→Aut NdρLabelID
C6.1(C2×D20) = S3×C40⋊C2φ: C2×D20/D20 → C2 ⊆ Aut C61204C6.1(C2xD20)480,327
C6.2(C2×D20) = S3×D40φ: C2×D20/D20 → C2 ⊆ Aut C61204+C6.2(C2xD20)480,328
C6.3(C2×D20) = C40⋊1D6φ: C2×D20/D20 → C2 ⊆ Aut C61204+C6.3(C2xD20)480,329
C6.4(C2×D20) = D40⋊S3φ: C2×D20/D20 → C2 ⊆ Aut C61204C6.4(C2xD20)480,330
C6.5(C2×D20) = S3×Dic20φ: C2×D20/D20 → C2 ⊆ Aut C62404-C6.5(C2xD20)480,338
C6.6(C2×D20) = Dic20⋊S3φ: C2×D20/D20 → C2 ⊆ Aut C62404C6.6(C2xD20)480,339
C6.7(C2×D20) = D6.1D20φ: C2×D20/D20 → C2 ⊆ Aut C62404C6.7(C2xD20)480,348
C6.8(C2×D20) = D40⋊7S3φ: C2×D20/D20 → C2 ⊆ Aut C62404-C6.8(C2xD20)480,349
C6.9(C2×D20) = C40.2D6φ: C2×D20/D20 → C2 ⊆ Aut C62404-C6.9(C2xD20)480,350
C6.10(C2×D20) = D120⋊5C2φ: C2×D20/D20 → C2 ⊆ Aut C62404+C6.10(C2xD20)480,351
C6.11(C2×D20) = Dic3.D20φ: C2×D20/D20 → C2 ⊆ Aut C6240C6.11(C2xD20)480,429
C6.12(C2×D20) = Dic3⋊4D20φ: C2×D20/D20 → C2 ⊆ Aut C6240C6.12(C2xD20)480,471
C6.13(C2×D20) = Dic3⋊D20φ: C2×D20/D20 → C2 ⊆ Aut C6240C6.13(C2xD20)480,485
C6.14(C2×D20) = D10⋊2Dic6φ: C2×D20/D20 → C2 ⊆ Aut C6240C6.14(C2xD20)480,498
C6.15(C2×D20) = Dic3×D20φ: C2×D20/D20 → C2 ⊆ Aut C6240C6.15(C2xD20)480,501
C6.16(C2×D20) = S3×C4⋊Dic5φ: C2×D20/D20 → C2 ⊆ Aut C6240C6.16(C2xD20)480,502
C6.17(C2×D20) = D6.D20φ: C2×D20/D20 → C2 ⊆ Aut C6240C6.17(C2xD20)480,503
C6.18(C2×D20) = D60⋊14C4φ: C2×D20/D20 → C2 ⊆ Aut C6240C6.18(C2xD20)480,504
C6.19(C2×D20) = D30⋊4Q8φ: C2×D20/D20 → C2 ⊆ Aut C6240C6.19(C2xD20)480,505
C6.20(C2×D20) = D6⋊D20φ: C2×D20/D20 → C2 ⊆ Aut C6240C6.20(C2xD20)480,530
C6.21(C2×D20) = C60⋊4D4φ: C2×D20/D20 → C2 ⊆ Aut C6240C6.21(C2xD20)480,532
C6.22(C2×D20) = D6.9D20φ: C2×D20/D20 → C2 ⊆ Aut C6240C6.22(C2xD20)480,533
C6.23(C2×D20) = D30⋊2D4φ: C2×D20/D20 → C2 ⊆ Aut C6240C6.23(C2xD20)480,535
C6.24(C2×D20) = C60⋊6D4φ: C2×D20/D20 → C2 ⊆ Aut C6240C6.24(C2xD20)480,536
C6.25(C2×D20) = C20⋊4Dic6φ: C2×D20/D20 → C2 ⊆ Aut C6480C6.25(C2xD20)480,545
C6.26(C2×D20) = S3×D10⋊C4φ: C2×D20/D20 → C2 ⊆ Aut C6120C6.26(C2xD20)480,548
C6.27(C2×D20) = D6⋊4D20φ: C2×D20/D20 → C2 ⊆ Aut C6120C6.27(C2xD20)480,550
C6.28(C2×D20) = D30⋊5D4φ: C2×D20/D20 → C2 ⊆ Aut C6120C6.28(C2xD20)480,552
C6.29(C2×D20) = C60⋊8Q8φ: C2×D20/C2×C20 → C2 ⊆ Aut C6480C6.29(C2xD20)480,834
C6.30(C2×D20) = C4×D60φ: C2×D20/C2×C20 → C2 ⊆ Aut C6240C6.30(C2xD20)480,838
C6.31(C2×D20) = C42⋊6D15φ: C2×D20/C2×C20 → C2 ⊆ Aut C6240C6.31(C2xD20)480,839
C6.32(C2×D20) = C42⋊7D15φ: C2×D20/C2×C20 → C2 ⊆ Aut C6240C6.32(C2xD20)480,840
C6.33(C2×D20) = D30⋊16D4φ: C2×D20/C2×C20 → C2 ⊆ Aut C6120C6.33(C2xD20)480,847
C6.34(C2×D20) = C22.D60φ: C2×D20/C2×C20 → C2 ⊆ Aut C6240C6.34(C2xD20)480,851
C6.35(C2×D20) = C4⋊D60φ: C2×D20/C2×C20 → C2 ⊆ Aut C6240C6.35(C2xD20)480,860
C6.36(C2×D20) = D30⋊6Q8φ: C2×D20/C2×C20 → C2 ⊆ Aut C6240C6.36(C2xD20)480,862
C6.37(C2×D20) = C2×C24⋊D5φ: C2×D20/C2×C20 → C2 ⊆ Aut C6240C6.37(C2xD20)480,867
C6.38(C2×D20) = C2×D120φ: C2×D20/C2×C20 → C2 ⊆ Aut C6240C6.38(C2xD20)480,868
C6.39(C2×D20) = C40.69D6φ: C2×D20/C2×C20 → C2 ⊆ Aut C62402C6.39(C2xD20)480,869
C6.40(C2×D20) = C2×Dic60φ: C2×D20/C2×C20 → C2 ⊆ Aut C6480C6.40(C2xD20)480,870
C6.41(C2×D20) = C8⋊D30φ: C2×D20/C2×C20 → C2 ⊆ Aut C61204+C6.41(C2xD20)480,873
C6.42(C2×D20) = C8.D30φ: C2×D20/C2×C20 → C2 ⊆ Aut C62404-C6.42(C2xD20)480,874
C6.43(C2×D20) = C2×C60⋊5C4φ: C2×D20/C2×C20 → C2 ⊆ Aut C6480C6.43(C2xD20)480,890
C6.44(C2×D20) = C2×D30⋊3C4φ: C2×D20/C2×C20 → C2 ⊆ Aut C6240C6.44(C2xD20)480,892
C6.45(C2×D20) = C60⋊29D4φ: C2×D20/C2×C20 → C2 ⊆ Aut C6240C6.45(C2xD20)480,895
C6.46(C2×D20) = C2×C3⋊D40φ: C2×D20/C22×D5 → C2 ⊆ Aut C6240C6.46(C2xD20)480,376
C6.47(C2×D20) = D20⋊19D6φ: C2×D20/C22×D5 → C2 ⊆ Aut C61204+C6.47(C2xD20)480,377
C6.48(C2×D20) = C2×C6.D20φ: C2×D20/C22×D5 → C2 ⊆ Aut C6240C6.48(C2xD20)480,386
C6.49(C2×D20) = D20.31D6φ: C2×D20/C22×D5 → C2 ⊆ Aut C62404C6.49(C2xD20)480,387
C6.50(C2×D20) = D60⋊30C22φ: C2×D20/C22×D5 → C2 ⊆ Aut C61204C6.50(C2xD20)480,388
C6.51(C2×D20) = C60.63D4φ: C2×D20/C22×D5 → C2 ⊆ Aut C62404-C6.51(C2xD20)480,389
C6.52(C2×D20) = C2×C15⋊SD16φ: C2×D20/C22×D5 → C2 ⊆ Aut C6240C6.52(C2xD20)480,390
C6.53(C2×D20) = C12.D20φ: C2×D20/C22×D5 → C2 ⊆ Aut C62404C6.53(C2xD20)480,391
C6.54(C2×D20) = C2×C3⋊Dic20φ: C2×D20/C22×D5 → C2 ⊆ Aut C6480C6.54(C2xD20)480,395
C6.55(C2×D20) = C60.68D4φ: C2×D20/C22×D5 → C2 ⊆ Aut C6240C6.55(C2xD20)480,436
C6.56(C2×D20) = C60.44D4φ: C2×D20/C22×D5 → C2 ⊆ Aut C6240C6.56(C2xD20)480,440
C6.57(C2×D20) = C60.47D4φ: C2×D20/C22×D5 → C2 ⊆ Aut C6240C6.57(C2xD20)480,450
C6.58(C2×D20) = C60.48D4φ: C2×D20/C22×D5 → C2 ⊆ Aut C6480C6.58(C2xD20)480,465
C6.59(C2×D20) = D30⋊10Q8φ: C2×D20/C22×D5 → C2 ⊆ Aut C6240C6.59(C2xD20)480,466
C6.60(C2×D20) = C4×C3⋊D20φ: C2×D20/C22×D5 → C2 ⊆ Aut C6240C6.60(C2xD20)480,519
C6.61(C2×D20) = C12⋊7D20φ: C2×D20/C22×D5 → C2 ⊆ Aut C6240C6.61(C2xD20)480,526
C6.62(C2×D20) = C12⋊D20φ: C2×D20/C22×D5 → C2 ⊆ Aut C6240C6.62(C2xD20)480,534
C6.63(C2×D20) = C12⋊2D20φ: C2×D20/C22×D5 → C2 ⊆ Aut C6240C6.63(C2xD20)480,541
C6.64(C2×D20) = C2×D10⋊Dic3φ: C2×D20/C22×D5 → C2 ⊆ Aut C6240C6.64(C2xD20)480,611
C6.65(C2×D20) = C6.(C2×D20)φ: C2×D20/C22×D5 → C2 ⊆ Aut C6240C6.65(C2xD20)480,613
C6.66(C2×D20) = C2×D30⋊4C4φ: C2×D20/C22×D5 → C2 ⊆ Aut C6240C6.66(C2xD20)480,616
C6.67(C2×D20) = C2×C6.Dic10φ: C2×D20/C22×D5 → C2 ⊆ Aut C6480C6.67(C2xD20)480,621
C6.68(C2×D20) = C6.D4⋊D5φ: C2×D20/C22×D5 → C2 ⊆ Aut C6240C6.68(C2xD20)480,622
C6.69(C2×D20) = (C2×C6)⋊8D20φ: C2×D20/C22×D5 → C2 ⊆ Aut C6120C6.69(C2xD20)480,640
C6.70(C2×D20) = (C2×C6)⋊D20φ: C2×D20/C22×D5 → C2 ⊆ Aut C6240C6.70(C2xD20)480,645
C6.71(C2×D20) = D30⋊18D4φ: C2×D20/C22×D5 → C2 ⊆ Aut C6120C6.71(C2xD20)480,648
C6.72(C2×D20) = C3×C20⋊2Q8central extension (φ=1)480C6.72(C2xD20)480,662
C6.73(C2×D20) = C12×D20central extension (φ=1)240C6.73(C2xD20)480,666
C6.74(C2×D20) = C3×C20⋊4D4central extension (φ=1)240C6.74(C2xD20)480,667
C6.75(C2×D20) = C3×C4.D20central extension (φ=1)240C6.75(C2xD20)480,668
C6.76(C2×D20) = C3×C22⋊D20central extension (φ=1)120C6.76(C2xD20)480,675
C6.77(C2×D20) = C3×C22.D20central extension (φ=1)240C6.77(C2xD20)480,679
C6.78(C2×D20) = C3×C4⋊D20central extension (φ=1)240C6.78(C2xD20)480,688
C6.79(C2×D20) = C3×D10⋊2Q8central extension (φ=1)240C6.79(C2xD20)480,690
C6.80(C2×D20) = C6×C40⋊C2central extension (φ=1)240C6.80(C2xD20)480,695
C6.81(C2×D20) = C6×D40central extension (φ=1)240C6.81(C2xD20)480,696
C6.82(C2×D20) = C3×D40⋊7C2central extension (φ=1)2402C6.82(C2xD20)480,697
C6.83(C2×D20) = C6×Dic20central extension (φ=1)480C6.83(C2xD20)480,698
C6.84(C2×D20) = C3×C8⋊D10central extension (φ=1)1204C6.84(C2xD20)480,701
C6.85(C2×D20) = C3×C8.D10central extension (φ=1)2404C6.85(C2xD20)480,702
C6.86(C2×D20) = C6×C4⋊Dic5central extension (φ=1)480C6.86(C2xD20)480,718
C6.87(C2×D20) = C6×D10⋊C4central extension (φ=1)240C6.87(C2xD20)480,720
C6.88(C2×D20) = C3×C20⋊7D4central extension (φ=1)240C6.88(C2xD20)480,723

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