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Extensions 1→N→G→Q→1 with N=C10 and Q=C2×D12

Direct product G=N×Q with N=C10 and Q=C2×D12
dρLabelID
C2×C10×D12240C2xC10xD12480,1152

Semidirect products G=N:Q with N=C10 and Q=C2×D12
extensionφ:Q→Aut NdρLabelID
C10⋊1(C2×D12) = C2×D5×D12φ: C2×D12/D12 → C2 ⊆ Aut C10120C10:1(C2xD12)480,1087
C10⋊2(C2×D12) = C22×D60φ: C2×D12/C2×C12 → C2 ⊆ Aut C10240C10:2(C2xD12)480,1167
C10⋊3(C2×D12) = C22×C5⋊D12φ: C2×D12/C22×S3 → C2 ⊆ Aut C10240C10:3(C2xD12)480,1120

Non-split extensions G=N.Q with N=C10 and Q=C2×D12
extensionφ:Q→Aut NdρLabelID
C10.1(C2×D12) = D5×C24⋊C2φ: C2×D12/D12 → C2 ⊆ Aut C101204C10.1(C2xD12)480,323
C10.2(C2×D12) = D5×D24φ: C2×D12/D12 → C2 ⊆ Aut C101204+C10.2(C2xD12)480,324
C10.3(C2×D12) = C24⋊D10φ: C2×D12/D12 → C2 ⊆ Aut C101204+C10.3(C2xD12)480,325
C10.4(C2×D12) = D24⋊D5φ: C2×D12/D12 → C2 ⊆ Aut C101204C10.4(C2xD12)480,326
C10.5(C2×D12) = D5×Dic12φ: C2×D12/D12 → C2 ⊆ Aut C102404-C10.5(C2xD12)480,335
C10.6(C2×D12) = Dic60⋊C2φ: C2×D12/D12 → C2 ⊆ Aut C102404-C10.6(C2xD12)480,336
C10.7(C2×D12) = C24.2D10φ: C2×D12/D12 → C2 ⊆ Aut C102404C10.7(C2xD12)480,337
C10.8(C2×D12) = C40.31D6φ: C2×D12/D12 → C2 ⊆ Aut C102404C10.8(C2xD12)480,345
C10.9(C2×D12) = D24⋊7D5φ: C2×D12/D12 → C2 ⊆ Aut C102404-C10.9(C2xD12)480,346
C10.10(C2×D12) = D120⋊C2φ: C2×D12/D12 → C2 ⊆ Aut C102404+C10.10(C2xD12)480,347
C10.11(C2×D12) = Dic5.8D12φ: C2×D12/D12 → C2 ⊆ Aut C10240C10.11(C2xD12)480,426
C10.12(C2×D12) = Dic5⋊4D12φ: C2×D12/D12 → C2 ⊆ Aut C10240C10.12(C2xD12)480,481
C10.13(C2×D12) = D5×C4⋊Dic3φ: C2×D12/D12 → C2 ⊆ Aut C10240C10.13(C2xD12)480,488
C10.14(C2×D12) = D10.16D12φ: C2×D12/D12 → C2 ⊆ Aut C10240C10.14(C2xD12)480,489
C10.15(C2×D12) = D10.17D12φ: C2×D12/D12 → C2 ⊆ Aut C10240C10.15(C2xD12)480,490
C10.16(C2×D12) = Dic5×D12φ: C2×D12/D12 → C2 ⊆ Aut C10240C10.16(C2xD12)480,491
C10.17(C2×D12) = Dic5⋊D12φ: C2×D12/D12 → C2 ⊆ Aut C10240C10.17(C2xD12)480,492
C10.18(C2×D12) = D6⋊2Dic10φ: C2×D12/D12 → C2 ⊆ Aut C10240C10.18(C2xD12)480,493
C10.19(C2×D12) = D60⋊17C4φ: C2×D12/D12 → C2 ⊆ Aut C10240C10.19(C2xD12)480,494
C10.20(C2×D12) = D30⋊2Q8φ: C2×D12/D12 → C2 ⊆ Aut C10240C10.20(C2xD12)480,495
C10.21(C2×D12) = D30⋊D4φ: C2×D12/D12 → C2 ⊆ Aut C10240C10.21(C2xD12)480,496
C10.22(C2×D12) = D10⋊D12φ: C2×D12/D12 → C2 ⊆ Aut C10240C10.22(C2xD12)480,524
C10.23(C2×D12) = C60⋊D4φ: C2×D12/D12 → C2 ⊆ Aut C10240C10.23(C2xD12)480,525
C10.24(C2×D12) = C12⋊7D20φ: C2×D12/D12 → C2 ⊆ Aut C10240C10.24(C2xD12)480,526
C10.25(C2×D12) = C20⋊D12φ: C2×D12/D12 → C2 ⊆ Aut C10240C10.25(C2xD12)480,527
C10.26(C2×D12) = C60⋊Q8φ: C2×D12/D12 → C2 ⊆ Aut C10480C10.26(C2xD12)480,544
C10.27(C2×D12) = D5×D6⋊C4φ: C2×D12/D12 → C2 ⊆ Aut C10120C10.27(C2xD12)480,547
C10.28(C2×D12) = D30⋊4D4φ: C2×D12/D12 → C2 ⊆ Aut C10120C10.28(C2xD12)480,551
C10.29(C2×D12) = D30⋊5D4φ: C2×D12/D12 → C2 ⊆ Aut C10120C10.29(C2xD12)480,552
C10.30(C2×D12) = C60⋊8Q8φ: C2×D12/C2×C12 → C2 ⊆ Aut C10480C10.30(C2xD12)480,834
C10.31(C2×D12) = C4×D60φ: C2×D12/C2×C12 → C2 ⊆ Aut C10240C10.31(C2xD12)480,838
C10.32(C2×D12) = C42⋊6D15φ: C2×D12/C2×C12 → C2 ⊆ Aut C10240C10.32(C2xD12)480,839
C10.33(C2×D12) = C42⋊7D15φ: C2×D12/C2×C12 → C2 ⊆ Aut C10240C10.33(C2xD12)480,840
C10.34(C2×D12) = D30⋊16D4φ: C2×D12/C2×C12 → C2 ⊆ Aut C10120C10.34(C2xD12)480,847
C10.35(C2×D12) = C22.D60φ: C2×D12/C2×C12 → C2 ⊆ Aut C10240C10.35(C2xD12)480,851
C10.36(C2×D12) = C4⋊D60φ: C2×D12/C2×C12 → C2 ⊆ Aut C10240C10.36(C2xD12)480,860
C10.37(C2×D12) = D30⋊6Q8φ: C2×D12/C2×C12 → C2 ⊆ Aut C10240C10.37(C2xD12)480,862
C10.38(C2×D12) = C2×C24⋊D5φ: C2×D12/C2×C12 → C2 ⊆ Aut C10240C10.38(C2xD12)480,867
C10.39(C2×D12) = C2×D120φ: C2×D12/C2×C12 → C2 ⊆ Aut C10240C10.39(C2xD12)480,868
C10.40(C2×D12) = C40.69D6φ: C2×D12/C2×C12 → C2 ⊆ Aut C102402C10.40(C2xD12)480,869
C10.41(C2×D12) = C2×Dic60φ: C2×D12/C2×C12 → C2 ⊆ Aut C10480C10.41(C2xD12)480,870
C10.42(C2×D12) = C8⋊D30φ: C2×D12/C2×C12 → C2 ⊆ Aut C101204+C10.42(C2xD12)480,873
C10.43(C2×D12) = C8.D30φ: C2×D12/C2×C12 → C2 ⊆ Aut C102404-C10.43(C2xD12)480,874
C10.44(C2×D12) = C2×C60⋊5C4φ: C2×D12/C2×C12 → C2 ⊆ Aut C10480C10.44(C2xD12)480,890
C10.45(C2×D12) = C2×D30⋊3C4φ: C2×D12/C2×C12 → C2 ⊆ Aut C10240C10.45(C2xD12)480,892
C10.46(C2×D12) = C60⋊29D4φ: C2×D12/C2×C12 → C2 ⊆ Aut C10240C10.46(C2xD12)480,895
C10.47(C2×D12) = C2×C5⋊D24φ: C2×D12/C22×S3 → C2 ⊆ Aut C10240C10.47(C2xD12)480,378
C10.48(C2×D12) = C20.60D12φ: C2×D12/C22×S3 → C2 ⊆ Aut C102404C10.48(C2xD12)480,379
C10.49(C2×D12) = D60⋊36C22φ: C2×D12/C22×S3 → C2 ⊆ Aut C101204C10.49(C2xD12)480,380
C10.50(C2×D12) = C60.38D4φ: C2×D12/C22×S3 → C2 ⊆ Aut C101204+C10.50(C2xD12)480,381
C10.51(C2×D12) = C2×D12.D5φ: C2×D12/C22×S3 → C2 ⊆ Aut C10240C10.51(C2xD12)480,392
C10.52(C2×D12) = C2×Dic6⋊D5φ: C2×D12/C22×S3 → C2 ⊆ Aut C10240C10.52(C2xD12)480,393
C10.53(C2×D12) = C2×C5⋊Dic12φ: C2×D12/C22×S3 → C2 ⊆ Aut C10480C10.53(C2xD12)480,396
C10.54(C2×D12) = C20.D12φ: C2×D12/C22×S3 → C2 ⊆ Aut C102404C10.54(C2xD12)480,397
C10.55(C2×D12) = D12.33D10φ: C2×D12/C22×S3 → C2 ⊆ Aut C102404-C10.55(C2xD12)480,398
C10.56(C2×D12) = C60.45D4φ: C2×D12/C22×S3 → C2 ⊆ Aut C10240C10.56(C2xD12)480,441
C10.57(C2×D12) = C60.69D4φ: C2×D12/C22×S3 → C2 ⊆ Aut C10240C10.57(C2xD12)480,449
C10.58(C2×D12) = C60.70D4φ: C2×D12/C22×S3 → C2 ⊆ Aut C10240C10.58(C2xD12)480,451
C10.59(C2×D12) = Dic5⋊Dic6φ: C2×D12/C22×S3 → C2 ⊆ Aut C10480C10.59(C2xD12)480,452
C10.60(C2×D12) = D30⋊9Q8φ: C2×D12/C22×S3 → C2 ⊆ Aut C10240C10.60(C2xD12)480,459
C10.61(C2×D12) = C4×C5⋊D12φ: C2×D12/C22×S3 → C2 ⊆ Aut C10240C10.61(C2xD12)480,521
C10.62(C2×D12) = C60⋊6D4φ: C2×D12/C22×S3 → C2 ⊆ Aut C10240C10.62(C2xD12)480,536
C10.63(C2×D12) = C20⋊2D12φ: C2×D12/C22×S3 → C2 ⊆ Aut C10240C10.63(C2xD12)480,542
C10.64(C2×D12) = C2×D6⋊Dic5φ: C2×D12/C22×S3 → C2 ⊆ Aut C10240C10.64(C2xD12)480,614
C10.65(C2×D12) = C2×D30⋊4C4φ: C2×D12/C22×S3 → C2 ⊆ Aut C10240C10.65(C2xD12)480,616
C10.66(C2×D12) = C2×C30.Q8φ: C2×D12/C22×S3 → C2 ⊆ Aut C10480C10.66(C2xD12)480,617
C10.67(C2×D12) = C10.(C2×D12)φ: C2×D12/C22×S3 → C2 ⊆ Aut C10240C10.67(C2xD12)480,618
C10.68(C2×D12) = (C2×C10).D12φ: C2×D12/C22×S3 → C2 ⊆ Aut C10240C10.68(C2xD12)480,619
C10.69(C2×D12) = (C2×C10)⋊4D12φ: C2×D12/C22×S3 → C2 ⊆ Aut C10240C10.69(C2xD12)480,642
C10.70(C2×D12) = (C2×C10)⋊11D12φ: C2×D12/C22×S3 → C2 ⊆ Aut C10120C10.70(C2xD12)480,646
C10.71(C2×D12) = D30⋊19D4φ: C2×D12/C22×S3 → C2 ⊆ Aut C10120C10.71(C2xD12)480,649
C10.72(C2×D12) = C5×C12⋊2Q8central extension (φ=1)480C10.72(C2xD12)480,748
C10.73(C2×D12) = C20×D12central extension (φ=1)240C10.73(C2xD12)480,752
C10.74(C2×D12) = C5×C4⋊D12central extension (φ=1)240C10.74(C2xD12)480,753
C10.75(C2×D12) = C5×C42⋊7S3central extension (φ=1)240C10.75(C2xD12)480,754
C10.76(C2×D12) = C5×D6⋊D4central extension (φ=1)120C10.76(C2xD12)480,761
C10.77(C2×D12) = C5×C23.21D6central extension (φ=1)240C10.77(C2xD12)480,765
C10.78(C2×D12) = C5×C12⋊D4central extension (φ=1)240C10.78(C2xD12)480,774
C10.79(C2×D12) = C5×C4.D12central extension (φ=1)240C10.79(C2xD12)480,776
C10.80(C2×D12) = C10×C24⋊C2central extension (φ=1)240C10.80(C2xD12)480,781
C10.81(C2×D12) = C10×D24central extension (φ=1)240C10.81(C2xD12)480,782
C10.82(C2×D12) = C5×C4○D24central extension (φ=1)2402C10.82(C2xD12)480,783
C10.83(C2×D12) = C10×Dic12central extension (φ=1)480C10.83(C2xD12)480,784
C10.84(C2×D12) = C5×C8⋊D6central extension (φ=1)1204C10.84(C2xD12)480,787
C10.85(C2×D12) = C5×C8.D6central extension (φ=1)2404C10.85(C2xD12)480,788
C10.86(C2×D12) = C10×C4⋊Dic3central extension (φ=1)480C10.86(C2xD12)480,804
C10.87(C2×D12) = C10×D6⋊C4central extension (φ=1)240C10.87(C2xD12)480,806
C10.88(C2×D12) = C5×C12⋊7D4central extension (φ=1)240C10.88(C2xD12)480,809

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