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Extensions 1→N→G→Q→1 with N=C20 and Q=C3×D4

Direct product G=N×Q with N=C20 and Q=C3×D4
dρLabelID
D4×C60240D4xC60480,923

Semidirect products G=N:Q with N=C20 and Q=C3×D4
extensionφ:Q→Aut NdρLabelID
C20⋊1(C3×D4) = C3×C4⋊D20φ: C3×D4/C6 → C22 ⊆ Aut C20240C20:1(C3xD4)480,688
C20⋊2(C3×D4) = C3×C20⋊2D4φ: C3×D4/C6 → C22 ⊆ Aut C20240C20:2(C3xD4)480,731
C20⋊3(C3×D4) = C3×C20⋊D4φ: C3×D4/C6 → C22 ⊆ Aut C20240C20:3(C3xD4)480,733
C20⋊4(C3×D4) = C3×C20⋊4D4φ: C3×D4/C12 → C2 ⊆ Aut C20240C20:4(C3xD4)480,667
C20⋊5(C3×D4) = C12×D20φ: C3×D4/C12 → C2 ⊆ Aut C20240C20:5(C3xD4)480,666
C20⋊6(C3×D4) = C15×C4⋊1D4φ: C3×D4/C12 → C2 ⊆ Aut C20240C20:6(C3xD4)480,932
C20⋊7(C3×D4) = C3×C20⋊7D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C20240C20:7(C3xD4)480,723
C20⋊8(C3×D4) = C12×C5⋊D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C20240C20:8(C3xD4)480,721
C20⋊9(C3×D4) = C15×C4⋊D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C20240C20:9(C3xD4)480,926

Non-split extensions G=N.Q with N=C20 and Q=C3×D4
extensionφ:Q→Aut NdρLabelID
C20.1(C3×D4) = C3×D20⋊6C4φ: C3×D4/C6 → C22 ⊆ Aut C20240C20.1(C3xD4)480,87
C20.2(C3×D4) = C3×C10.Q16φ: C3×D4/C6 → C22 ⊆ Aut C20480C20.2(C3xD4)480,88
C20.3(C3×D4) = C3×C5⋊D16φ: C3×D4/C6 → C22 ⊆ Aut C202404C20.3(C3xD4)480,104
C20.4(C3×D4) = C3×D8.D5φ: C3×D4/C6 → C22 ⊆ Aut C202404C20.4(C3xD4)480,105
C20.5(C3×D4) = C3×C5⋊SD32φ: C3×D4/C6 → C22 ⊆ Aut C202404C20.5(C3xD4)480,106
C20.6(C3×D4) = C3×C5⋊Q32φ: C3×D4/C6 → C22 ⊆ Aut C204804C20.6(C3xD4)480,107
C20.7(C3×D4) = C3×D4⋊Dic5φ: C3×D4/C6 → C22 ⊆ Aut C20240C20.7(C3xD4)480,110
C20.8(C3×D4) = C3×C20.D4φ: C3×D4/C6 → C22 ⊆ Aut C201204C20.8(C3xD4)480,111
C20.9(C3×D4) = C3×Q8⋊Dic5φ: C3×D4/C6 → C22 ⊆ Aut C20480C20.9(C3xD4)480,113
C20.10(C3×D4) = C3×C20.10D4φ: C3×D4/C6 → C22 ⊆ Aut C202404C20.10(C3xD4)480,114
C20.11(C3×D4) = C3×D10⋊2Q8φ: C3×D4/C6 → C22 ⊆ Aut C20240C20.11(C3xD4)480,690
C20.12(C3×D4) = C3×C8⋊D10φ: C3×D4/C6 → C22 ⊆ Aut C201204C20.12(C3xD4)480,701
C20.13(C3×D4) = C3×C8.D10φ: C3×D4/C6 → C22 ⊆ Aut C202404C20.13(C3xD4)480,702
C20.14(C3×D4) = C6×D4⋊D5φ: C3×D4/C6 → C22 ⊆ Aut C20240C20.14(C3xD4)480,724
C20.15(C3×D4) = C3×D4.D10φ: C3×D4/C6 → C22 ⊆ Aut C201204C20.15(C3xD4)480,725
C20.16(C3×D4) = C6×D4.D5φ: C3×D4/C6 → C22 ⊆ Aut C20240C20.16(C3xD4)480,726
C20.17(C3×D4) = C3×C20.17D4φ: C3×D4/C6 → C22 ⊆ Aut C20240C20.17(C3xD4)480,729
C20.18(C3×D4) = C6×Q8⋊D5φ: C3×D4/C6 → C22 ⊆ Aut C20240C20.18(C3xD4)480,734
C20.19(C3×D4) = C3×C20.C23φ: C3×D4/C6 → C22 ⊆ Aut C202404C20.19(C3xD4)480,735
C20.20(C3×D4) = C6×C5⋊Q16φ: C3×D4/C6 → C22 ⊆ Aut C20480C20.20(C3xD4)480,736
C20.21(C3×D4) = C3×Dic5⋊Q8φ: C3×D4/C6 → C22 ⊆ Aut C20480C20.21(C3xD4)480,737
C20.22(C3×D4) = C3×D10⋊3Q8φ: C3×D4/C6 → C22 ⊆ Aut C20240C20.22(C3xD4)480,739
C20.23(C3×D4) = C3×C20.23D4φ: C3×D4/C6 → C22 ⊆ Aut C20240C20.23(C3xD4)480,740
C20.24(C3×D4) = C3×D80φ: C3×D4/C12 → C2 ⊆ Aut C202402C20.24(C3xD4)480,77
C20.25(C3×D4) = C3×C16⋊D5φ: C3×D4/C12 → C2 ⊆ Aut C202402C20.25(C3xD4)480,78
C20.26(C3×D4) = C3×Dic40φ: C3×D4/C12 → C2 ⊆ Aut C204802C20.26(C3xD4)480,79
C20.27(C3×D4) = C3×C20⋊2Q8φ: C3×D4/C12 → C2 ⊆ Aut C20480C20.27(C3xD4)480,662
C20.28(C3×D4) = C3×C4.D20φ: C3×D4/C12 → C2 ⊆ Aut C20240C20.28(C3xD4)480,668
C20.29(C3×D4) = C6×C40⋊C2φ: C3×D4/C12 → C2 ⊆ Aut C20240C20.29(C3xD4)480,695
C20.30(C3×D4) = C6×D40φ: C3×D4/C12 → C2 ⊆ Aut C20240C20.30(C3xD4)480,696
C20.31(C3×D4) = C6×Dic20φ: C3×D4/C12 → C2 ⊆ Aut C20480C20.31(C3xD4)480,698
C20.32(C3×D4) = C3×C20⋊3C8φ: C3×D4/C12 → C2 ⊆ Aut C20480C20.32(C3xD4)480,82
C20.33(C3×D4) = C3×D20⋊4C4φ: C3×D4/C12 → C2 ⊆ Aut C201202C20.33(C3xD4)480,83
C20.34(C3×D4) = C3×C40.6C4φ: C3×D4/C12 → C2 ⊆ Aut C202402C20.34(C3xD4)480,97
C20.35(C3×D4) = C3×D40⋊7C2φ: C3×D4/C12 → C2 ⊆ Aut C202402C20.35(C3xD4)480,697
C20.36(C3×D4) = C15×D16φ: C3×D4/C12 → C2 ⊆ Aut C202402C20.36(C3xD4)480,214
C20.37(C3×D4) = C15×SD32φ: C3×D4/C12 → C2 ⊆ Aut C202402C20.37(C3xD4)480,215
C20.38(C3×D4) = C15×Q32φ: C3×D4/C12 → C2 ⊆ Aut C204802C20.38(C3xD4)480,216
C20.39(C3×D4) = C15×C4.4D4φ: C3×D4/C12 → C2 ⊆ Aut C20240C20.39(C3xD4)480,929
C20.40(C3×D4) = C15×C4⋊Q8φ: C3×D4/C12 → C2 ⊆ Aut C20480C20.40(C3xD4)480,933
C20.41(C3×D4) = D8×C30φ: C3×D4/C12 → C2 ⊆ Aut C20240C20.41(C3xD4)480,937
C20.42(C3×D4) = SD16×C30φ: C3×D4/C12 → C2 ⊆ Aut C20240C20.42(C3xD4)480,938
C20.43(C3×D4) = Q16×C30φ: C3×D4/C12 → C2 ⊆ Aut C20480C20.43(C3xD4)480,939
C20.44(C3×D4) = C3×C20.44D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C20480C20.44(C3xD4)480,94
C20.45(C3×D4) = C3×D20⋊5C4φ: C3×D4/C2×C6 → C2 ⊆ Aut C20240C20.45(C3xD4)480,99
C20.46(C3×D4) = C3×C20.46D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C201204C20.46(C3xD4)480,101
C20.47(C3×D4) = C3×C4.12D20φ: C3×D4/C2×C6 → C2 ⊆ Aut C202404C20.47(C3xD4)480,102
C20.48(C3×D4) = C3×C20.48D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C20240C20.48(C3xD4)480,717
C20.49(C3×D4) = C3×D4⋊D10φ: C3×D4/C2×C6 → C2 ⊆ Aut C201204C20.49(C3xD4)480,742
C20.50(C3×D4) = C3×D4.9D10φ: C3×D4/C2×C6 → C2 ⊆ Aut C202404C20.50(C3xD4)480,744
C20.51(C3×D4) = C3×C20.8Q8φ: C3×D4/C2×C6 → C2 ⊆ Aut C20480C20.51(C3xD4)480,92
C20.52(C3×D4) = C3×D10⋊1C8φ: C3×D4/C2×C6 → C2 ⊆ Aut C20240C20.52(C3xD4)480,98
C20.53(C3×D4) = C3×C20.53D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C202404C20.53(C3xD4)480,100
C20.54(C3×D4) = C3×D20⋊7C4φ: C3×D4/C2×C6 → C2 ⊆ Aut C201204C20.54(C3xD4)480,103
C20.55(C3×D4) = C3×C20.55D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C20240C20.55(C3xD4)480,108
C20.56(C3×D4) = C3×D4⋊2Dic5φ: C3×D4/C2×C6 → C2 ⊆ Aut C201204C20.56(C3xD4)480,115
C20.57(C3×D4) = C3×D4.8D10φ: C3×D4/C2×C6 → C2 ⊆ Aut C202404C20.57(C3xD4)480,743
C20.58(C3×D4) = C15×C4.D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C201204C20.58(C3xD4)480,203
C20.59(C3×D4) = C15×C4.10D4φ: C3×D4/C2×C6 → C2 ⊆ Aut C202404C20.59(C3xD4)480,204
C20.60(C3×D4) = C15×D4⋊C4φ: C3×D4/C2×C6 → C2 ⊆ Aut C20240C20.60(C3xD4)480,205
C20.61(C3×D4) = C15×Q8⋊C4φ: C3×D4/C2×C6 → C2 ⊆ Aut C20480C20.61(C3xD4)480,206
C20.62(C3×D4) = C15×C22⋊Q8φ: C3×D4/C2×C6 → C2 ⊆ Aut C20240C20.62(C3xD4)480,927
C20.63(C3×D4) = C15×C8⋊C22φ: C3×D4/C2×C6 → C2 ⊆ Aut C201204C20.63(C3xD4)480,941
C20.64(C3×D4) = C15×C8.C22φ: C3×D4/C2×C6 → C2 ⊆ Aut C202404C20.64(C3xD4)480,942
C20.65(C3×D4) = C15×C22⋊C8central extension (φ=1)240C20.65(C3xD4)480,201
C20.66(C3×D4) = C15×C4≀C2central extension (φ=1)1202C20.66(C3xD4)480,207
C20.67(C3×D4) = C15×C4⋊C8central extension (φ=1)480C20.67(C3xD4)480,208
C20.68(C3×D4) = C15×C8.C4central extension (φ=1)2402C20.68(C3xD4)480,211
C20.69(C3×D4) = C15×C4○D8central extension (φ=1)2402C20.69(C3xD4)480,940

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