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Extensions 1→N→G→Q→1 with N=C6 and Q=C2×C4×D5

Direct product G=N×Q with N=C6 and Q=C2×C4×D5
dρLabelID
D5×C22×C12240D5xC2^2xC12480,1136

Semidirect products G=N:Q with N=C6 and Q=C2×C4×D5
extensionφ:Q→Aut NdρLabelID
C6⋊1(C2×C4×D5) = S3×C2×C4×D5φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6120C6:1(C2xC4xD5)480,1086
C6⋊2(C2×C4×D5) = C22×D30.C2φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C6240C6:2(C2xC4xD5)480,1117
C6⋊3(C2×C4×D5) = C22×C4×D15φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C6240C6:3(C2xC4xD5)480,1166
C6⋊4(C2×C4×D5) = C22×D5×Dic3φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C6240C6:4(C2xC4xD5)480,1112

Non-split extensions G=N.Q with N=C6 and Q=C2×C4×D5
extensionφ:Q→Aut NdρLabelID
C6.1(C2×C4×D5) = S3×C8×D5φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C61204C6.1(C2xC4xD5)480,319
C6.2(C2×C4×D5) = D5×C8⋊S3φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C61204C6.2(C2xC4xD5)480,320
C6.3(C2×C4×D5) = S3×C8⋊D5φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C61204C6.3(C2xC4xD5)480,321
C6.4(C2×C4×D5) = C40⋊D6φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C61204C6.4(C2xC4xD5)480,322
C6.5(C2×C4×D5) = C40.54D6φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C62404C6.5(C2xC4xD5)480,341
C6.6(C2×C4×D5) = C40.34D6φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C62404C6.6(C2xC4xD5)480,342
C6.7(C2×C4×D5) = C40.55D6φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C62404C6.7(C2xC4xD5)480,343
C6.8(C2×C4×D5) = C40.35D6φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C62404C6.8(C2xC4xD5)480,344
C6.9(C2×C4×D5) = Dic5⋊5Dic6φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6480C6.9(C2xC4xD5)480,399
C6.10(C2×C4×D5) = Dic3⋊5Dic10φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6480C6.10(C2xC4xD5)480,400
C6.11(C2×C4×D5) = Dic15⋊5Q8φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6480C6.11(C2xC4xD5)480,401
C6.12(C2×C4×D5) = D5×Dic3⋊C4φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.12(C2xC4xD5)480,468
C6.13(C2×C4×D5) = (D5×Dic3)⋊C4φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.13(C2xC4xD5)480,469
C6.14(C2×C4×D5) = D10.19(C4×S3)φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.14(C2xC4xD5)480,470
C6.15(C2×C4×D5) = Dic3⋊4D20φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.15(C2xC4xD5)480,471
C6.16(C2×C4×D5) = Dic15⋊13D4φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.16(C2xC4xD5)480,472
C6.17(C2×C4×D5) = C4×S3×Dic5φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.17(C2xC4xD5)480,473
C6.18(C2×C4×D5) = D6.(C4×D5)φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.18(C2xC4xD5)480,474
C6.19(C2×C4×D5) = S3×C10.D4φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.19(C2xC4xD5)480,475
C6.20(C2×C4×D5) = (S3×Dic5)⋊C4φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.20(C2xC4xD5)480,476
C6.21(C2×C4×D5) = D30.C2⋊C4φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.21(C2xC4xD5)480,478
C6.22(C2×C4×D5) = D30.23(C2×C4)φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.22(C2xC4xD5)480,479
C6.23(C2×C4×D5) = D30.Q8φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.23(C2xC4xD5)480,480
C6.24(C2×C4×D5) = Dic5⋊4D12φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.24(C2xC4xD5)480,481
C6.25(C2×C4×D5) = Dic15⋊14D4φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.25(C2xC4xD5)480,482
C6.26(C2×C4×D5) = C4×C15⋊D4φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.26(C2xC4xD5)480,515
C6.27(C2×C4×D5) = D6⋊(C4×D5)φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.27(C2xC4xD5)480,516
C6.28(C2×C4×D5) = C15⋊17(C4×D4)φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.28(C2xC4xD5)480,517
C6.29(C2×C4×D5) = Dic15⋊9D4φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.29(C2xC4xD5)480,518
C6.30(C2×C4×D5) = C4×C3⋊D20φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.30(C2xC4xD5)480,519
C6.31(C2×C4×D5) = C15⋊20(C4×D4)φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.31(C2xC4xD5)480,520
C6.32(C2×C4×D5) = C4×C5⋊D12φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.32(C2xC4xD5)480,521
C6.33(C2×C4×D5) = C15⋊22(C4×D4)φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6240C6.33(C2xC4xD5)480,522
C6.34(C2×C4×D5) = C4×C15⋊Q8φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6480C6.34(C2xC4xD5)480,543
C6.35(C2×C4×D5) = D5×D6⋊C4φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6120C6.35(C2xC4xD5)480,547
C6.36(C2×C4×D5) = S3×D10⋊C4φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6120C6.36(C2xC4xD5)480,548
C6.37(C2×C4×D5) = D30.27D4φ: C2×C4×D5/C4×D5 → C2 ⊆ Aut C6120C6.37(C2xC4xD5)480,549
C6.38(C2×C4×D5) = C2×D15⋊2C8φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C6240C6.38(C2xC4xD5)480,365
C6.39(C2×C4×D5) = D60.5C4φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C62404C6.39(C2xC4xD5)480,366
C6.40(C2×C4×D5) = D60.4C4φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C62404C6.40(C2xC4xD5)480,367
C6.41(C2×C4×D5) = D15⋊4M4(2)φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C61204C6.41(C2xC4xD5)480,368
C6.42(C2×C4×D5) = C2×D30.5C4φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C6240C6.42(C2xC4xD5)480,371
C6.43(C2×C4×D5) = Dic30⋊17C4φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C6480C6.43(C2xC4xD5)480,409
C6.44(C2×C4×D5) = Dic30⋊14C4φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C6480C6.44(C2xC4xD5)480,416
C6.45(C2×C4×D5) = (C4×D15)⋊8C4φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C6240C6.45(C2xC4xD5)480,423
C6.46(C2×C4×D5) = (C4×D15)⋊10C4φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C6240C6.46(C2xC4xD5)480,462
C6.47(C2×C4×D5) = C4×D30.C2φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C6240C6.47(C2xC4xD5)480,477
C6.48(C2×C4×D5) = D60⋊17C4φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C6240C6.48(C2xC4xD5)480,494
C6.49(C2×C4×D5) = D60⋊14C4φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C6240C6.49(C2xC4xD5)480,504
C6.50(C2×C4×D5) = D30.2Q8φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C6240C6.50(C2xC4xD5)480,513
C6.51(C2×C4×D5) = C23.48(S3×D5)φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C6240C6.51(C2xC4xD5)480,608
C6.52(C2×C4×D5) = C2×D30⋊4C4φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C6240C6.52(C2xC4xD5)480,616
C6.53(C2×C4×D5) = C2×Dic15⋊5C4φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C6480C6.53(C2xC4xD5)480,620
C6.54(C2×C4×D5) = C15⋊26(C4×D4)φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C6240C6.54(C2xC4xD5)480,628
C6.55(C2×C4×D5) = C15⋊28(C4×D4)φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C6240C6.55(C2xC4xD5)480,632
C6.56(C2×C4×D5) = D30.45D4φ: C2×C4×D5/C2×Dic5 → C2 ⊆ Aut C6120C6.56(C2xC4xD5)480,637
C6.57(C2×C4×D5) = C4×Dic30φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C6480C6.57(C2xC4xD5)480,833
C6.58(C2×C4×D5) = C42×D15φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C6240C6.58(C2xC4xD5)480,836
C6.59(C2×C4×D5) = C42⋊2D15φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C6240C6.59(C2xC4xD5)480,837
C6.60(C2×C4×D5) = C4×D60φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C6240C6.60(C2xC4xD5)480,838
C6.61(C2×C4×D5) = C23.15D30φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C6240C6.61(C2xC4xD5)480,842
C6.62(C2×C4×D5) = C22⋊C4×D15φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C6120C6.62(C2xC4xD5)480,845
C6.63(C2×C4×D5) = Dic15⋊19D4φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C6240C6.63(C2xC4xD5)480,846
C6.64(C2×C4×D5) = Dic15⋊10Q8φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C6480C6.64(C2xC4xD5)480,852
C6.65(C2×C4×D5) = C4⋊C4×D15φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C6240C6.65(C2xC4xD5)480,856
C6.66(C2×C4×D5) = C4⋊C4⋊7D15φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C6240C6.66(C2xC4xD5)480,857
C6.67(C2×C4×D5) = D60⋊11C4φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C6240C6.67(C2xC4xD5)480,858
C6.68(C2×C4×D5) = C2×C8×D15φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C6240C6.68(C2xC4xD5)480,864
C6.69(C2×C4×D5) = C2×C40⋊S3φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C6240C6.69(C2xC4xD5)480,865
C6.70(C2×C4×D5) = D60.6C4φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C62402C6.70(C2xC4xD5)480,866
C6.71(C2×C4×D5) = M4(2)×D15φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C61204C6.71(C2xC4xD5)480,871
C6.72(C2×C4×D5) = D60.3C4φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C62404C6.72(C2xC4xD5)480,872
C6.73(C2×C4×D5) = C2×C4×Dic15φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C6480C6.73(C2xC4xD5)480,887
C6.74(C2×C4×D5) = C2×C30.4Q8φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C6480C6.74(C2xC4xD5)480,888
C6.75(C2×C4×D5) = C2×D30⋊3C4φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C6240C6.75(C2xC4xD5)480,892
C6.76(C2×C4×D5) = C4×C15⋊7D4φ: C2×C4×D5/C2×C20 → C2 ⊆ Aut C6240C6.76(C2xC4xD5)480,893
C6.77(C2×C4×D5) = C2×D5×C3⋊C8φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C6240C6.77(C2xC4xD5)480,357
C6.78(C2×C4×D5) = D5×C4.Dic3φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C61204C6.78(C2xC4xD5)480,358
C6.79(C2×C4×D5) = D20.3Dic3φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C62404C6.79(C2xC4xD5)480,359
C6.80(C2×C4×D5) = D20.2Dic3φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C62404C6.80(C2xC4xD5)480,360
C6.81(C2×C4×D5) = C2×C20.32D6φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C6240C6.81(C2xC4xD5)480,369
C6.82(C2×C4×D5) = Dic3×Dic10φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C6480C6.82(C2xC4xD5)480,406
C6.83(C2×C4×D5) = Dic15⋊6Q8φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C6480C6.83(C2xC4xD5)480,407
C6.84(C2×C4×D5) = (D5×C12)⋊C4φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C6240C6.84(C2xC4xD5)480,433
C6.85(C2×C4×D5) = (C4×D5)⋊Dic3φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C6240C6.85(C2xC4xD5)480,434
C6.86(C2×C4×D5) = C4×D5×Dic3φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C6240C6.86(C2xC4xD5)480,467
C6.87(C2×C4×D5) = D5×C4⋊Dic3φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C6240C6.87(C2xC4xD5)480,488
C6.88(C2×C4×D5) = Dic3×D20φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C6240C6.88(C2xC4xD5)480,501
C6.89(C2×C4×D5) = D20⋊8Dic3φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C6240C6.89(C2xC4xD5)480,510
C6.90(C2×C4×D5) = C2×Dic3×Dic5φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C6480C6.90(C2xC4xD5)480,603
C6.91(C2×C4×D5) = (C6×Dic5)⋊7C4φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C6240C6.91(C2xC4xD5)480,604
C6.92(C2×C4×D5) = C2×D10⋊Dic3φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C6240C6.92(C2xC4xD5)480,611
C6.93(C2×C4×D5) = C2×C30.Q8φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C6480C6.93(C2xC4xD5)480,617
C6.94(C2×C4×D5) = D5×C6.D4φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C6120C6.94(C2xC4xD5)480,623
C6.95(C2×C4×D5) = Dic3×C5⋊D4φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C6240C6.95(C2xC4xD5)480,629
C6.96(C2×C4×D5) = Dic15⋊16D4φ: C2×C4×D5/C22×D5 → C2 ⊆ Aut C6240C6.96(C2xC4xD5)480,635
C6.97(C2×C4×D5) = C12×Dic10central extension (φ=1)480C6.97(C2xC4xD5)480,661
C6.98(C2×C4×D5) = D5×C4×C12central extension (φ=1)240C6.98(C2xC4xD5)480,664
C6.99(C2×C4×D5) = C3×C42⋊D5central extension (φ=1)240C6.99(C2xC4xD5)480,665
C6.100(C2×C4×D5) = C12×D20central extension (φ=1)240C6.100(C2xC4xD5)480,666
C6.101(C2×C4×D5) = C3×C23.11D10central extension (φ=1)240C6.101(C2xC4xD5)480,670
C6.102(C2×C4×D5) = C3×D5×C22⋊C4central extension (φ=1)120C6.102(C2xC4xD5)480,673
C6.103(C2×C4×D5) = C3×Dic5⋊4D4central extension (φ=1)240C6.103(C2xC4xD5)480,674
C6.104(C2×C4×D5) = C3×Dic5⋊3Q8central extension (φ=1)480C6.104(C2xC4xD5)480,680
C6.105(C2×C4×D5) = C3×D5×C4⋊C4central extension (φ=1)240C6.105(C2xC4xD5)480,684
C6.106(C2×C4×D5) = C3×C4⋊C4⋊7D5central extension (φ=1)240C6.106(C2xC4xD5)480,685
C6.107(C2×C4×D5) = C3×D20⋊8C4central extension (φ=1)240C6.107(C2xC4xD5)480,686
C6.108(C2×C4×D5) = D5×C2×C24central extension (φ=1)240C6.108(C2xC4xD5)480,692
C6.109(C2×C4×D5) = C6×C8⋊D5central extension (φ=1)240C6.109(C2xC4xD5)480,693
C6.110(C2×C4×D5) = C3×D20.3C4central extension (φ=1)2402C6.110(C2xC4xD5)480,694
C6.111(C2×C4×D5) = C3×D5×M4(2)central extension (φ=1)1204C6.111(C2xC4xD5)480,699
C6.112(C2×C4×D5) = C3×D20.2C4central extension (φ=1)2404C6.112(C2xC4xD5)480,700
C6.113(C2×C4×D5) = Dic5×C2×C12central extension (φ=1)480C6.113(C2xC4xD5)480,715
C6.114(C2×C4×D5) = C6×C10.D4central extension (φ=1)480C6.114(C2xC4xD5)480,716
C6.115(C2×C4×D5) = C6×D10⋊C4central extension (φ=1)240C6.115(C2xC4xD5)480,720
C6.116(C2×C4×D5) = C12×C5⋊D4central extension (φ=1)240C6.116(C2xC4xD5)480,721

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