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

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

Semidirect products G=N:Q with N=C10 and Q=C6×D4
extensionφ:Q→Aut NdρLabelID
C101(C6×D4) = C2×C6×D20φ: C6×D4/C2×C12C2 ⊆ Aut C10240C10:1(C6xD4)480,1137
C102(C6×D4) = C6×D4×D5φ: C6×D4/C3×D4C2 ⊆ Aut C10120C10:2(C6xD4)480,1139
C103(C6×D4) = C2×C6×C5⋊D4φ: C6×D4/C22×C6C2 ⊆ Aut C10240C10:3(C6xD4)480,1149

Non-split extensions G=N.Q with N=C10 and Q=C6×D4
extensionφ:Q→Aut NdρLabelID
C10.1(C6×D4) = C3×C202Q8φ: C6×D4/C2×C12C2 ⊆ Aut C10480C10.1(C6xD4)480,662
C10.2(C6×D4) = C12×D20φ: C6×D4/C2×C12C2 ⊆ Aut C10240C10.2(C6xD4)480,666
C10.3(C6×D4) = C3×C204D4φ: C6×D4/C2×C12C2 ⊆ Aut C10240C10.3(C6xD4)480,667
C10.4(C6×D4) = C3×C4.D20φ: C6×D4/C2×C12C2 ⊆ Aut C10240C10.4(C6xD4)480,668
C10.5(C6×D4) = C3×C22.D20φ: C6×D4/C2×C12C2 ⊆ Aut C10240C10.5(C6xD4)480,679
C10.6(C6×D4) = C3×D102Q8φ: C6×D4/C2×C12C2 ⊆ Aut C10240C10.6(C6xD4)480,690
C10.7(C6×D4) = C6×C40⋊C2φ: C6×D4/C2×C12C2 ⊆ Aut C10240C10.7(C6xD4)480,695
C10.8(C6×D4) = C6×D40φ: C6×D4/C2×C12C2 ⊆ Aut C10240C10.8(C6xD4)480,696
C10.9(C6×D4) = C3×D407C2φ: C6×D4/C2×C12C2 ⊆ Aut C102402C10.9(C6xD4)480,697
C10.10(C6×D4) = C6×Dic20φ: C6×D4/C2×C12C2 ⊆ Aut C10480C10.10(C6xD4)480,698
C10.11(C6×D4) = C3×C8⋊D10φ: C6×D4/C2×C12C2 ⊆ Aut C101204C10.11(C6xD4)480,701
C10.12(C6×D4) = C3×C8.D10φ: C6×D4/C2×C12C2 ⊆ Aut C102404C10.12(C6xD4)480,702
C10.13(C6×D4) = C6×C4⋊Dic5φ: C6×D4/C2×C12C2 ⊆ Aut C10480C10.13(C6xD4)480,718
C10.14(C6×D4) = C3×Dic5.14D4φ: C6×D4/C3×D4C2 ⊆ Aut C10240C10.14(C6xD4)480,671
C10.15(C6×D4) = C3×D5×C22⋊C4φ: C6×D4/C3×D4C2 ⊆ Aut C10120C10.15(C6xD4)480,673
C10.16(C6×D4) = C3×Dic54D4φ: C6×D4/C3×D4C2 ⊆ Aut C10240C10.16(C6xD4)480,674
C10.17(C6×D4) = C3×C22⋊D20φ: C6×D4/C3×D4C2 ⊆ Aut C10120C10.17(C6xD4)480,675
C10.18(C6×D4) = C3×D10.12D4φ: C6×D4/C3×D4C2 ⊆ Aut C10240C10.18(C6xD4)480,676
C10.19(C6×D4) = C3×D10⋊D4φ: C6×D4/C3×D4C2 ⊆ Aut C10240C10.19(C6xD4)480,677
C10.20(C6×D4) = C3×Dic5.5D4φ: C6×D4/C3×D4C2 ⊆ Aut C10240C10.20(C6xD4)480,678
C10.21(C6×D4) = C3×C20⋊Q8φ: C6×D4/C3×D4C2 ⊆ Aut C10480C10.21(C6xD4)480,681
C10.22(C6×D4) = C3×D5×C4⋊C4φ: C6×D4/C3×D4C2 ⊆ Aut C10240C10.22(C6xD4)480,684
C10.23(C6×D4) = C3×D208C4φ: C6×D4/C3×D4C2 ⊆ Aut C10240C10.23(C6xD4)480,686
C10.24(C6×D4) = C3×D10.13D4φ: C6×D4/C3×D4C2 ⊆ Aut C10240C10.24(C6xD4)480,687
C10.25(C6×D4) = C3×C4⋊D20φ: C6×D4/C3×D4C2 ⊆ Aut C10240C10.25(C6xD4)480,688
C10.26(C6×D4) = C3×D10⋊Q8φ: C6×D4/C3×D4C2 ⊆ Aut C10240C10.26(C6xD4)480,689
C10.27(C6×D4) = C3×D5×D8φ: C6×D4/C3×D4C2 ⊆ Aut C101204C10.27(C6xD4)480,703
C10.28(C6×D4) = C3×D8⋊D5φ: C6×D4/C3×D4C2 ⊆ Aut C101204C10.28(C6xD4)480,704
C10.29(C6×D4) = C3×D83D5φ: C6×D4/C3×D4C2 ⊆ Aut C102404C10.29(C6xD4)480,705
C10.30(C6×D4) = C3×D5×SD16φ: C6×D4/C3×D4C2 ⊆ Aut C101204C10.30(C6xD4)480,706
C10.31(C6×D4) = C3×D40⋊C2φ: C6×D4/C3×D4C2 ⊆ Aut C101204C10.31(C6xD4)480,707
C10.32(C6×D4) = C3×SD16⋊D5φ: C6×D4/C3×D4C2 ⊆ Aut C102404C10.32(C6xD4)480,708
C10.33(C6×D4) = C3×SD163D5φ: C6×D4/C3×D4C2 ⊆ Aut C102404C10.33(C6xD4)480,709
C10.34(C6×D4) = C3×D5×Q16φ: C6×D4/C3×D4C2 ⊆ Aut C102404C10.34(C6xD4)480,710
C10.35(C6×D4) = C3×Q16⋊D5φ: C6×D4/C3×D4C2 ⊆ Aut C102404C10.35(C6xD4)480,711
C10.36(C6×D4) = C3×Q8.D10φ: C6×D4/C3×D4C2 ⊆ Aut C102404C10.36(C6xD4)480,712
C10.37(C6×D4) = C3×D4×Dic5φ: C6×D4/C3×D4C2 ⊆ Aut C10240C10.37(C6xD4)480,727
C10.38(C6×D4) = C3×C23⋊D10φ: C6×D4/C3×D4C2 ⊆ Aut C10120C10.38(C6xD4)480,730
C10.39(C6×D4) = C3×C202D4φ: C6×D4/C3×D4C2 ⊆ Aut C10240C10.39(C6xD4)480,731
C10.40(C6×D4) = C3×Dic5⋊D4φ: C6×D4/C3×D4C2 ⊆ Aut C10240C10.40(C6xD4)480,732
C10.41(C6×D4) = C3×C20⋊D4φ: C6×D4/C3×D4C2 ⊆ Aut C10240C10.41(C6xD4)480,733
C10.42(C6×D4) = C6×C10.D4φ: C6×D4/C22×C6C2 ⊆ Aut C10480C10.42(C6xD4)480,716
C10.43(C6×D4) = C3×C20.48D4φ: C6×D4/C22×C6C2 ⊆ Aut C10240C10.43(C6xD4)480,717
C10.44(C6×D4) = C6×D10⋊C4φ: C6×D4/C22×C6C2 ⊆ Aut C10240C10.44(C6xD4)480,720
C10.45(C6×D4) = C12×C5⋊D4φ: C6×D4/C22×C6C2 ⊆ Aut C10240C10.45(C6xD4)480,721
C10.46(C6×D4) = C3×C23.23D10φ: C6×D4/C22×C6C2 ⊆ Aut C10240C10.46(C6xD4)480,722
C10.47(C6×D4) = C3×C207D4φ: C6×D4/C22×C6C2 ⊆ Aut C10240C10.47(C6xD4)480,723
C10.48(C6×D4) = C6×D4⋊D5φ: C6×D4/C22×C6C2 ⊆ Aut C10240C10.48(C6xD4)480,724
C10.49(C6×D4) = C3×D4.D10φ: C6×D4/C22×C6C2 ⊆ Aut C101204C10.49(C6xD4)480,725
C10.50(C6×D4) = C6×D4.D5φ: C6×D4/C22×C6C2 ⊆ Aut C10240C10.50(C6xD4)480,726
C10.51(C6×D4) = C3×C23.18D10φ: C6×D4/C22×C6C2 ⊆ Aut C10240C10.51(C6xD4)480,728
C10.52(C6×D4) = C3×C20.17D4φ: C6×D4/C22×C6C2 ⊆ Aut C10240C10.52(C6xD4)480,729
C10.53(C6×D4) = C6×Q8⋊D5φ: C6×D4/C22×C6C2 ⊆ Aut C10240C10.53(C6xD4)480,734
C10.54(C6×D4) = C3×C20.C23φ: C6×D4/C22×C6C2 ⊆ Aut C102404C10.54(C6xD4)480,735
C10.55(C6×D4) = C6×C5⋊Q16φ: C6×D4/C22×C6C2 ⊆ Aut C10480C10.55(C6xD4)480,736
C10.56(C6×D4) = C3×Dic5⋊Q8φ: C6×D4/C22×C6C2 ⊆ Aut C10480C10.56(C6xD4)480,737
C10.57(C6×D4) = C3×D103Q8φ: C6×D4/C22×C6C2 ⊆ Aut C10240C10.57(C6xD4)480,739
C10.58(C6×D4) = C3×C20.23D4φ: C6×D4/C22×C6C2 ⊆ Aut C10240C10.58(C6xD4)480,740
C10.59(C6×D4) = C3×D4⋊D10φ: C6×D4/C22×C6C2 ⊆ Aut C101204C10.59(C6xD4)480,742
C10.60(C6×D4) = C3×D4.8D10φ: C6×D4/C22×C6C2 ⊆ Aut C102404C10.60(C6xD4)480,743
C10.61(C6×D4) = C3×D4.9D10φ: C6×D4/C22×C6C2 ⊆ Aut C102404C10.61(C6xD4)480,744
C10.62(C6×D4) = C6×C23.D5φ: C6×D4/C22×C6C2 ⊆ Aut C10240C10.62(C6xD4)480,745
C10.63(C6×D4) = C3×C242D5φ: C6×D4/C22×C6C2 ⊆ Aut C10120C10.63(C6xD4)480,746
C10.64(C6×D4) = C22⋊C4×C30central extension (φ=1)240C10.64(C6xD4)480,920
C10.65(C6×D4) = C4⋊C4×C30central extension (φ=1)480C10.65(C6xD4)480,921
C10.66(C6×D4) = D4×C60central extension (φ=1)240C10.66(C6xD4)480,923
C10.67(C6×D4) = C15×C22≀C2central extension (φ=1)120C10.67(C6xD4)480,925
C10.68(C6×D4) = C15×C4⋊D4central extension (φ=1)240C10.68(C6xD4)480,926
C10.69(C6×D4) = C15×C22⋊Q8central extension (φ=1)240C10.69(C6xD4)480,927
C10.70(C6×D4) = C15×C22.D4central extension (φ=1)240C10.70(C6xD4)480,928
C10.71(C6×D4) = C15×C4.4D4central extension (φ=1)240C10.71(C6xD4)480,929
C10.72(C6×D4) = C15×C41D4central extension (φ=1)240C10.72(C6xD4)480,932
C10.73(C6×D4) = C15×C4⋊Q8central extension (φ=1)480C10.73(C6xD4)480,933
C10.74(C6×D4) = D8×C30central extension (φ=1)240C10.74(C6xD4)480,937
C10.75(C6×D4) = SD16×C30central extension (φ=1)240C10.75(C6xD4)480,938
C10.76(C6×D4) = Q16×C30central extension (φ=1)480C10.76(C6xD4)480,939
C10.77(C6×D4) = C15×C4○D8central extension (φ=1)2402C10.77(C6xD4)480,940
C10.78(C6×D4) = C15×C8⋊C22central extension (φ=1)1204C10.78(C6xD4)480,941
C10.79(C6×D4) = C15×C8.C22central extension (φ=1)2404C10.79(C6xD4)480,942

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