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Extensions 1→N→G→Q→1 with N=C20 and Q=C2×C12

Direct product G=N×Q with N=C20 and Q=C2×C12
dρLabelID
C2×C4×C60480C2xC4xC60480,919

Semidirect products G=N:Q with N=C20 and Q=C2×C12
extensionφ:Q→Aut NdρLabelID
C20⋊(C2×C12) = C3×D4×F5φ: C2×C12/C3 → C2×C4 ⊆ Aut C20608C20:(C2xC12)480,1054
C20⋊2(C2×C12) = C6×C4⋊F5φ: C2×C12/C6 → C4 ⊆ Aut C20120C20:2(C2xC12)480,1051
C20⋊3(C2×C12) = F5×C2×C12φ: C2×C12/C6 → C4 ⊆ Aut C20120C20:3(C2xC12)480,1050
C20⋊4(C2×C12) = C3×D5×C4⋊C4φ: C2×C12/C6 → C22 ⊆ Aut C20240C20:4(C2xC12)480,684
C20⋊5(C2×C12) = C3×D20⋊8C4φ: C2×C12/C6 → C22 ⊆ Aut C20240C20:5(C2xC12)480,686
C20⋊6(C2×C12) = C3×D4×Dic5φ: C2×C12/C6 → C22 ⊆ Aut C20240C20:6(C2xC12)480,727
C20⋊7(C2×C12) = C12×D20φ: C2×C12/C12 → C2 ⊆ Aut C20240C20:7(C2xC12)480,666
C20⋊8(C2×C12) = D5×C4×C12φ: C2×C12/C12 → C2 ⊆ Aut C20240C20:8(C2xC12)480,664
C20⋊9(C2×C12) = D4×C60φ: C2×C12/C12 → C2 ⊆ Aut C20240C20:9(C2xC12)480,923
C20⋊10(C2×C12) = C6×C4⋊Dic5φ: C2×C12/C2×C6 → C2 ⊆ Aut C20480C20:10(C2xC12)480,718
C20⋊11(C2×C12) = Dic5×C2×C12φ: C2×C12/C2×C6 → C2 ⊆ Aut C20480C20:11(C2xC12)480,715
C20⋊12(C2×C12) = C4⋊C4×C30φ: C2×C12/C2×C6 → C2 ⊆ Aut C20480C20:12(C2xC12)480,921

Non-split extensions G=N.Q with N=C20 and Q=C2×C12
extensionφ:Q→Aut NdρLabelID
C20.1(C2×C12) = C3×D20⋊C4φ: C2×C12/C3 → C2×C4 ⊆ Aut C201208C20.1(C2xC12)480,287
C20.2(C2×C12) = C3×D4⋊F5φ: C2×C12/C3 → C2×C4 ⊆ Aut C201208C20.2(C2xC12)480,288
C20.3(C2×C12) = C3×Q8⋊F5φ: C2×C12/C3 → C2×C4 ⊆ Aut C201208C20.3(C2xC12)480,289
C20.4(C2×C12) = C3×Q8⋊2F5φ: C2×C12/C3 → C2×C4 ⊆ Aut C201208C20.4(C2xC12)480,290
C20.5(C2×C12) = C3×D4.F5φ: C2×C12/C3 → C2×C4 ⊆ Aut C202408C20.5(C2xC12)480,1053
C20.6(C2×C12) = C3×Q8.F5φ: C2×C12/C3 → C2×C4 ⊆ Aut C202408C20.6(C2xC12)480,1055
C20.7(C2×C12) = C3×Q8×F5φ: C2×C12/C3 → C2×C4 ⊆ Aut C201208C20.7(C2xC12)480,1056
C20.8(C2×C12) = C3×C40⋊C4φ: C2×C12/C6 → C4 ⊆ Aut C201204C20.8(C2xC12)480,273
C20.9(C2×C12) = C3×D5.D8φ: C2×C12/C6 → C4 ⊆ Aut C201204C20.9(C2xC12)480,274
C20.10(C2×C12) = C3×C40.C4φ: C2×C12/C6 → C4 ⊆ Aut C202404C20.10(C2xC12)480,275
C20.11(C2×C12) = C3×D10.Q8φ: C2×C12/C6 → C4 ⊆ Aut C202404C20.11(C2xC12)480,276
C20.12(C2×C12) = C6×C4.F5φ: C2×C12/C6 → C4 ⊆ Aut C20240C20.12(C2xC12)480,1048
C20.13(C2×C12) = C3×D5⋊C16φ: C2×C12/C6 → C4 ⊆ Aut C202404C20.13(C2xC12)480,269
C20.14(C2×C12) = C3×C8.F5φ: C2×C12/C6 → C4 ⊆ Aut C202404C20.14(C2xC12)480,270
C20.15(C2×C12) = F5×C24φ: C2×C12/C6 → C4 ⊆ Aut C201204C20.15(C2xC12)480,271
C20.16(C2×C12) = C3×C8⋊F5φ: C2×C12/C6 → C4 ⊆ Aut C201204C20.16(C2xC12)480,272
C20.17(C2×C12) = C6×C5⋊C16φ: C2×C12/C6 → C4 ⊆ Aut C20480C20.17(C2xC12)480,277
C20.18(C2×C12) = C3×C20.C8φ: C2×C12/C6 → C4 ⊆ Aut C202404C20.18(C2xC12)480,278
C20.19(C2×C12) = C6×D5⋊C8φ: C2×C12/C6 → C4 ⊆ Aut C20240C20.19(C2xC12)480,1047
C20.20(C2×C12) = C3×D5⋊M4(2)φ: C2×C12/C6 → C4 ⊆ Aut C201204C20.20(C2xC12)480,1049
C20.21(C2×C12) = C3×D10.C23φ: C2×C12/C6 → C4 ⊆ Aut C201204C20.21(C2xC12)480,1052
C20.22(C2×C12) = C3×C10.D8φ: C2×C12/C6 → C22 ⊆ Aut C20480C20.22(C2xC12)480,85
C20.23(C2×C12) = C3×C20.Q8φ: C2×C12/C6 → C22 ⊆ Aut C20480C20.23(C2xC12)480,86
C20.24(C2×C12) = C3×D20⋊6C4φ: C2×C12/C6 → C22 ⊆ Aut C20240C20.24(C2xC12)480,87
C20.25(C2×C12) = C3×C10.Q16φ: C2×C12/C6 → C22 ⊆ Aut C20480C20.25(C2xC12)480,88
C20.26(C2×C12) = C3×C20.53D4φ: C2×C12/C6 → C22 ⊆ Aut C202404C20.26(C2xC12)480,100
C20.27(C2×C12) = C3×D20⋊7C4φ: C2×C12/C6 → C22 ⊆ Aut C201204C20.27(C2xC12)480,103
C20.28(C2×C12) = C3×D4⋊Dic5φ: C2×C12/C6 → C22 ⊆ Aut C20240C20.28(C2xC12)480,110
C20.29(C2×C12) = C3×Q8⋊Dic5φ: C2×C12/C6 → C22 ⊆ Aut C20480C20.29(C2xC12)480,113
C20.30(C2×C12) = C3×D4⋊2Dic5φ: C2×C12/C6 → C22 ⊆ Aut C201204C20.30(C2xC12)480,115
C20.31(C2×C12) = C3×Dic5⋊3Q8φ: C2×C12/C6 → C22 ⊆ Aut C20480C20.31(C2xC12)480,680
C20.32(C2×C12) = C3×C4⋊C4⋊7D5φ: C2×C12/C6 → C22 ⊆ Aut C20240C20.32(C2xC12)480,685
C20.33(C2×C12) = C3×D5×M4(2)φ: C2×C12/C6 → C22 ⊆ Aut C201204C20.33(C2xC12)480,699
C20.34(C2×C12) = C3×D20.2C4φ: C2×C12/C6 → C22 ⊆ Aut C202404C20.34(C2xC12)480,700
C20.35(C2×C12) = C3×Q8×Dic5φ: C2×C12/C6 → C22 ⊆ Aut C20480C20.35(C2xC12)480,738
C20.36(C2×C12) = C3×D4.Dic5φ: C2×C12/C6 → C22 ⊆ Aut C202404C20.36(C2xC12)480,741
C20.37(C2×C12) = C3×D20⋊4C4φ: C2×C12/C12 → C2 ⊆ Aut C201202C20.37(C2xC12)480,83
C20.38(C2×C12) = C3×C20.44D4φ: C2×C12/C12 → C2 ⊆ Aut C20480C20.38(C2xC12)480,94
C20.39(C2×C12) = C3×D20⋊5C4φ: C2×C12/C12 → C2 ⊆ Aut C20240C20.39(C2xC12)480,99
C20.40(C2×C12) = C12×Dic10φ: C2×C12/C12 → C2 ⊆ Aut C20480C20.40(C2xC12)480,661
C20.41(C2×C12) = C3×D20.3C4φ: C2×C12/C12 → C2 ⊆ Aut C202402C20.41(C2xC12)480,694
C20.42(C2×C12) = D5×C48φ: C2×C12/C12 → C2 ⊆ Aut C202402C20.42(C2xC12)480,75
C20.43(C2×C12) = C3×C80⋊C2φ: C2×C12/C12 → C2 ⊆ Aut C202402C20.43(C2xC12)480,76
C20.44(C2×C12) = C12×C5⋊2C8φ: C2×C12/C12 → C2 ⊆ Aut C20480C20.44(C2xC12)480,80
C20.45(C2×C12) = C3×C42.D5φ: C2×C12/C12 → C2 ⊆ Aut C20480C20.45(C2xC12)480,81
C20.46(C2×C12) = Dic5×C24φ: C2×C12/C12 → C2 ⊆ Aut C20480C20.46(C2xC12)480,91
C20.47(C2×C12) = C3×C42⋊D5φ: C2×C12/C12 → C2 ⊆ Aut C20240C20.47(C2xC12)480,665
C20.48(C2×C12) = D5×C2×C24φ: C2×C12/C12 → C2 ⊆ Aut C20240C20.48(C2xC12)480,692
C20.49(C2×C12) = C6×C8⋊D5φ: C2×C12/C12 → C2 ⊆ Aut C20240C20.49(C2xC12)480,693
C20.50(C2×C12) = C15×D4⋊C4φ: C2×C12/C12 → C2 ⊆ Aut C20240C20.50(C2xC12)480,205
C20.51(C2×C12) = C15×Q8⋊C4φ: C2×C12/C12 → C2 ⊆ Aut C20480C20.51(C2xC12)480,206
C20.52(C2×C12) = C15×C4≀C2φ: C2×C12/C12 → C2 ⊆ Aut C201202C20.52(C2xC12)480,207
C20.53(C2×C12) = Q8×C60φ: C2×C12/C12 → C2 ⊆ Aut C20480C20.53(C2xC12)480,924
C20.54(C2×C12) = C15×C8○D4φ: C2×C12/C12 → C2 ⊆ Aut C202402C20.54(C2xC12)480,936
C20.55(C2×C12) = C3×C40⋊6C4φ: C2×C12/C2×C6 → C2 ⊆ Aut C20480C20.55(C2xC12)480,95
C20.56(C2×C12) = C3×C40⋊5C4φ: C2×C12/C2×C6 → C2 ⊆ Aut C20480C20.56(C2xC12)480,96
C20.57(C2×C12) = C3×C40.6C4φ: C2×C12/C2×C6 → C2 ⊆ Aut C202402C20.57(C2xC12)480,97
C20.58(C2×C12) = C6×C4.Dic5φ: C2×C12/C2×C6 → C2 ⊆ Aut C20240C20.58(C2xC12)480,714
C20.59(C2×C12) = C3×C23.21D10φ: C2×C12/C2×C6 → C2 ⊆ Aut C20240C20.59(C2xC12)480,719
C20.60(C2×C12) = C6×C5⋊2C16φ: C2×C12/C2×C6 → C2 ⊆ Aut C20480C20.60(C2xC12)480,89
C20.61(C2×C12) = C3×C20.4C8φ: C2×C12/C2×C6 → C2 ⊆ Aut C202402C20.61(C2xC12)480,90
C20.62(C2×C12) = C3×C40⋊8C4φ: C2×C12/C2×C6 → C2 ⊆ Aut C20480C20.62(C2xC12)480,93
C20.63(C2×C12) = C2×C6×C5⋊2C8φ: C2×C12/C2×C6 → C2 ⊆ Aut C20480C20.63(C2xC12)480,713
C20.64(C2×C12) = C15×C4.Q8φ: C2×C12/C2×C6 → C2 ⊆ Aut C20480C20.64(C2xC12)480,209
C20.65(C2×C12) = C15×C2.D8φ: C2×C12/C2×C6 → C2 ⊆ Aut C20480C20.65(C2xC12)480,210
C20.66(C2×C12) = C15×C8.C4φ: C2×C12/C2×C6 → C2 ⊆ Aut C202402C20.66(C2xC12)480,211
C20.67(C2×C12) = C15×C42⋊C2φ: C2×C12/C2×C6 → C2 ⊆ Aut C20240C20.67(C2xC12)480,922
C20.68(C2×C12) = M4(2)×C30φ: C2×C12/C2×C6 → C2 ⊆ Aut C20240C20.68(C2xC12)480,935
C20.69(C2×C12) = C15×C8⋊C4central extension (φ=1)480C20.69(C2xC12)480,200
C20.70(C2×C12) = C15×M5(2)central extension (φ=1)2402C20.70(C2xC12)480,213

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