# Extensions 1→N→G→Q→1 with N=C6 and Q=D4×C10

Direct product G=N×Q with N=C6 and Q=D4×C10
dρLabelID
D4×C2×C30240D4xC2xC30480,1181

Semidirect products G=N:Q with N=C6 and Q=D4×C10
extensionφ:Q→Aut NdρLabelID
C61(D4×C10) = C2×C10×D12φ: D4×C10/C2×C20C2 ⊆ Aut C6240C6:1(D4xC10)480,1152
C62(D4×C10) = S3×D4×C10φ: D4×C10/C5×D4C2 ⊆ Aut C6120C6:2(D4xC10)480,1154
C63(D4×C10) = C2×C10×C3⋊D4φ: D4×C10/C22×C10C2 ⊆ Aut C6240C6:3(D4xC10)480,1164

Non-split extensions G=N.Q with N=C6 and Q=D4×C10
extensionφ:Q→Aut NdρLabelID
C6.1(D4×C10) = C5×C122Q8φ: D4×C10/C2×C20C2 ⊆ Aut C6480C6.1(D4xC10)480,748
C6.2(D4×C10) = C20×D12φ: D4×C10/C2×C20C2 ⊆ Aut C6240C6.2(D4xC10)480,752
C6.3(D4×C10) = C5×C4⋊D12φ: D4×C10/C2×C20C2 ⊆ Aut C6240C6.3(D4xC10)480,753
C6.4(D4×C10) = C5×C427S3φ: D4×C10/C2×C20C2 ⊆ Aut C6240C6.4(D4xC10)480,754
C6.5(D4×C10) = C5×D6⋊D4φ: D4×C10/C2×C20C2 ⊆ Aut C6120C6.5(D4xC10)480,761
C6.6(D4×C10) = C5×C23.21D6φ: D4×C10/C2×C20C2 ⊆ Aut C6240C6.6(D4xC10)480,765
C6.7(D4×C10) = C5×C12⋊D4φ: D4×C10/C2×C20C2 ⊆ Aut C6240C6.7(D4xC10)480,774
C6.8(D4×C10) = C5×C4.D12φ: D4×C10/C2×C20C2 ⊆ Aut C6240C6.8(D4xC10)480,776
C6.9(D4×C10) = C10×C24⋊C2φ: D4×C10/C2×C20C2 ⊆ Aut C6240C6.9(D4xC10)480,781
C6.10(D4×C10) = C10×D24φ: D4×C10/C2×C20C2 ⊆ Aut C6240C6.10(D4xC10)480,782
C6.11(D4×C10) = C5×C4○D24φ: D4×C10/C2×C20C2 ⊆ Aut C62402C6.11(D4xC10)480,783
C6.12(D4×C10) = C10×Dic12φ: D4×C10/C2×C20C2 ⊆ Aut C6480C6.12(D4xC10)480,784
C6.13(D4×C10) = C5×C8⋊D6φ: D4×C10/C2×C20C2 ⊆ Aut C61204C6.13(D4xC10)480,787
C6.14(D4×C10) = C5×C8.D6φ: D4×C10/C2×C20C2 ⊆ Aut C62404C6.14(D4xC10)480,788
C6.15(D4×C10) = C10×C4⋊Dic3φ: D4×C10/C2×C20C2 ⊆ Aut C6480C6.15(D4xC10)480,804
C6.16(D4×C10) = C5×Dic3.D4φ: D4×C10/C5×D4C2 ⊆ Aut C6240C6.16(D4xC10)480,757
C6.17(D4×C10) = C5×S3×C22⋊C4φ: D4×C10/C5×D4C2 ⊆ Aut C6120C6.17(D4xC10)480,759
C6.18(D4×C10) = C5×Dic34D4φ: D4×C10/C5×D4C2 ⊆ Aut C6240C6.18(D4xC10)480,760
C6.19(D4×C10) = C5×C23.9D6φ: D4×C10/C5×D4C2 ⊆ Aut C6240C6.19(D4xC10)480,762
C6.20(D4×C10) = C5×Dic3⋊D4φ: D4×C10/C5×D4C2 ⊆ Aut C6240C6.20(D4xC10)480,763
C6.21(D4×C10) = C5×C23.11D6φ: D4×C10/C5×D4C2 ⊆ Aut C6240C6.21(D4xC10)480,764
C6.22(D4×C10) = C5×C12⋊Q8φ: D4×C10/C5×D4C2 ⊆ Aut C6480C6.22(D4xC10)480,767
C6.23(D4×C10) = C5×S3×C4⋊C4φ: D4×C10/C5×D4C2 ⊆ Aut C6240C6.23(D4xC10)480,770
C6.24(D4×C10) = C5×Dic35D4φ: D4×C10/C5×D4C2 ⊆ Aut C6240C6.24(D4xC10)480,772
C6.25(D4×C10) = C5×D6.D4φ: D4×C10/C5×D4C2 ⊆ Aut C6240C6.25(D4xC10)480,773
C6.26(D4×C10) = C5×D6⋊Q8φ: D4×C10/C5×D4C2 ⊆ Aut C6240C6.26(D4xC10)480,775
C6.27(D4×C10) = C5×S3×D8φ: D4×C10/C5×D4C2 ⊆ Aut C61204C6.27(D4xC10)480,789
C6.28(D4×C10) = C5×D8⋊S3φ: D4×C10/C5×D4C2 ⊆ Aut C61204C6.28(D4xC10)480,790
C6.29(D4×C10) = C5×D83S3φ: D4×C10/C5×D4C2 ⊆ Aut C62404C6.29(D4xC10)480,791
C6.30(D4×C10) = C5×S3×SD16φ: D4×C10/C5×D4C2 ⊆ Aut C61204C6.30(D4xC10)480,792
C6.31(D4×C10) = C5×Q83D6φ: D4×C10/C5×D4C2 ⊆ Aut C61204C6.31(D4xC10)480,793
C6.32(D4×C10) = C5×D4.D6φ: D4×C10/C5×D4C2 ⊆ Aut C62404C6.32(D4xC10)480,794
C6.33(D4×C10) = C5×Q8.7D6φ: D4×C10/C5×D4C2 ⊆ Aut C62404C6.33(D4xC10)480,795
C6.34(D4×C10) = C5×S3×Q16φ: D4×C10/C5×D4C2 ⊆ Aut C62404C6.34(D4xC10)480,796
C6.35(D4×C10) = C5×Q16⋊S3φ: D4×C10/C5×D4C2 ⊆ Aut C62404C6.35(D4xC10)480,797
C6.36(D4×C10) = C5×D24⋊C2φ: D4×C10/C5×D4C2 ⊆ Aut C62404C6.36(D4xC10)480,798
C6.37(D4×C10) = C5×D4×Dic3φ: D4×C10/C5×D4C2 ⊆ Aut C6240C6.37(D4xC10)480,813
C6.38(D4×C10) = C10×Dic3⋊C4φ: D4×C10/C22×C10C2 ⊆ Aut C6480C6.38(D4xC10)480,802
C6.39(D4×C10) = C5×C12.48D4φ: D4×C10/C22×C10C2 ⊆ Aut C6240C6.39(D4xC10)480,803
C6.40(D4×C10) = C10×D6⋊C4φ: D4×C10/C22×C10C2 ⊆ Aut C6240C6.40(D4xC10)480,806
C6.41(D4×C10) = C20×C3⋊D4φ: D4×C10/C22×C10C2 ⊆ Aut C6240C6.41(D4xC10)480,807
C6.42(D4×C10) = C5×C23.28D6φ: D4×C10/C22×C10C2 ⊆ Aut C6240C6.42(D4xC10)480,808
C6.43(D4×C10) = C5×C127D4φ: D4×C10/C22×C10C2 ⊆ Aut C6240C6.43(D4xC10)480,809
C6.44(D4×C10) = C10×D4⋊S3φ: D4×C10/C22×C10C2 ⊆ Aut C6240C6.44(D4xC10)480,810
C6.45(D4×C10) = C5×D126C22φ: D4×C10/C22×C10C2 ⊆ Aut C61204C6.45(D4xC10)480,811
C6.46(D4×C10) = C10×D4.S3φ: D4×C10/C22×C10C2 ⊆ Aut C6240C6.46(D4xC10)480,812
C6.47(D4×C10) = C5×C23.23D6φ: D4×C10/C22×C10C2 ⊆ Aut C6240C6.47(D4xC10)480,814
C6.48(D4×C10) = C5×C23.12D6φ: D4×C10/C22×C10C2 ⊆ Aut C6240C6.48(D4xC10)480,815
C6.49(D4×C10) = C5×C232D6φ: D4×C10/C22×C10C2 ⊆ Aut C6120C6.49(D4xC10)480,816
C6.50(D4×C10) = C5×D63D4φ: D4×C10/C22×C10C2 ⊆ Aut C6240C6.50(D4xC10)480,817
C6.51(D4×C10) = C5×C23.14D6φ: D4×C10/C22×C10C2 ⊆ Aut C6240C6.51(D4xC10)480,818
C6.52(D4×C10) = C5×C123D4φ: D4×C10/C22×C10C2 ⊆ Aut C6240C6.52(D4xC10)480,819
C6.53(D4×C10) = C10×Q82S3φ: D4×C10/C22×C10C2 ⊆ Aut C6240C6.53(D4xC10)480,820
C6.54(D4×C10) = C5×Q8.11D6φ: D4×C10/C22×C10C2 ⊆ Aut C62404C6.54(D4xC10)480,821
C6.55(D4×C10) = C10×C3⋊Q16φ: D4×C10/C22×C10C2 ⊆ Aut C6480C6.55(D4xC10)480,822
C6.56(D4×C10) = C5×Dic3⋊Q8φ: D4×C10/C22×C10C2 ⊆ Aut C6480C6.56(D4xC10)480,823
C6.57(D4×C10) = C5×D63Q8φ: D4×C10/C22×C10C2 ⊆ Aut C6240C6.57(D4xC10)480,825
C6.58(D4×C10) = C5×C12.23D4φ: D4×C10/C22×C10C2 ⊆ Aut C6240C6.58(D4xC10)480,826
C6.59(D4×C10) = C5×D4⋊D6φ: D4×C10/C22×C10C2 ⊆ Aut C61204C6.59(D4xC10)480,828
C6.60(D4×C10) = C5×Q8.13D6φ: D4×C10/C22×C10C2 ⊆ Aut C62404C6.60(D4xC10)480,829
C6.61(D4×C10) = C5×Q8.14D6φ: D4×C10/C22×C10C2 ⊆ Aut C62404C6.61(D4xC10)480,830
C6.62(D4×C10) = C10×C6.D4φ: D4×C10/C22×C10C2 ⊆ Aut C6240C6.62(D4xC10)480,831
C6.63(D4×C10) = C5×C244S3φ: D4×C10/C22×C10C2 ⊆ Aut C6120C6.63(D4xC10)480,832
C6.64(D4×C10) = C22⋊C4×C30central extension (φ=1)240C6.64(D4xC10)480,920
C6.65(D4×C10) = C4⋊C4×C30central extension (φ=1)480C6.65(D4xC10)480,921
C6.66(D4×C10) = D4×C60central extension (φ=1)240C6.66(D4xC10)480,923
C6.67(D4×C10) = C15×C22≀C2central extension (φ=1)120C6.67(D4xC10)480,925
C6.68(D4×C10) = C15×C4⋊D4central extension (φ=1)240C6.68(D4xC10)480,926
C6.69(D4×C10) = C15×C22⋊Q8central extension (φ=1)240C6.69(D4xC10)480,927
C6.70(D4×C10) = C15×C22.D4central extension (φ=1)240C6.70(D4xC10)480,928
C6.71(D4×C10) = C15×C4.4D4central extension (φ=1)240C6.71(D4xC10)480,929
C6.72(D4×C10) = C15×C41D4central extension (φ=1)240C6.72(D4xC10)480,932
C6.73(D4×C10) = C15×C4⋊Q8central extension (φ=1)480C6.73(D4xC10)480,933
C6.74(D4×C10) = D8×C30central extension (φ=1)240C6.74(D4xC10)480,937
C6.75(D4×C10) = SD16×C30central extension (φ=1)240C6.75(D4xC10)480,938
C6.76(D4×C10) = Q16×C30central extension (φ=1)480C6.76(D4xC10)480,939
C6.77(D4×C10) = C15×C4○D8central extension (φ=1)2402C6.77(D4xC10)480,940
C6.78(D4×C10) = C15×C8⋊C22central extension (φ=1)1204C6.78(D4xC10)480,941
C6.79(D4×C10) = C15×C8.C22central extension (φ=1)2404C6.79(D4xC10)480,942

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