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Extensions 1→N→G→Q→1 with N=C20 and Q=C2×Dic3

Direct product G=N×Q with N=C20 and Q=C2×Dic3
dρLabelID
Dic3×C2×C20480Dic3xC2xC20480,801

Semidirect products G=N:Q with N=C20 and Q=C2×Dic3
extensionφ:Q→Aut NdρLabelID
C20⋊(C2×Dic3) = D4×C3⋊F5φ: C2×Dic3/C3 → C2×C4 ⊆ Aut C20608C20:(C2xDic3)480,1067
C20⋊2(C2×Dic3) = C2×C60⋊C4φ: C2×Dic3/C6 → C4 ⊆ Aut C20120C20:2(C2xDic3)480,1064
C20⋊3(C2×Dic3) = C2×C4×C3⋊F5φ: C2×Dic3/C6 → C4 ⊆ Aut C20120C20:3(C2xDic3)480,1063
C20⋊4(C2×Dic3) = D5×C4⋊Dic3φ: C2×Dic3/C6 → C22 ⊆ Aut C20240C20:4(C2xDic3)480,488
C20⋊5(C2×Dic3) = D20⋊8Dic3φ: C2×Dic3/C6 → C22 ⊆ Aut C20240C20:5(C2xDic3)480,510
C20⋊6(C2×Dic3) = D4×Dic15φ: C2×Dic3/C6 → C22 ⊆ Aut C20240C20:6(C2xDic3)480,899
C20⋊7(C2×Dic3) = Dic3×D20φ: C2×Dic3/Dic3 → C2 ⊆ Aut C20240C20:7(C2xDic3)480,501
C20⋊8(C2×Dic3) = C4×D5×Dic3φ: C2×Dic3/Dic3 → C2 ⊆ Aut C20240C20:8(C2xDic3)480,467
C20⋊9(C2×Dic3) = C5×D4×Dic3φ: C2×Dic3/Dic3 → C2 ⊆ Aut C20240C20:9(C2xDic3)480,813
C20⋊10(C2×Dic3) = C2×C60⋊5C4φ: C2×Dic3/C2×C6 → C2 ⊆ Aut C20480C20:10(C2xDic3)480,890
C20⋊11(C2×Dic3) = C2×C4×Dic15φ: C2×Dic3/C2×C6 → C2 ⊆ Aut C20480C20:11(C2xDic3)480,887
C20⋊12(C2×Dic3) = C10×C4⋊Dic3φ: C2×Dic3/C2×C6 → C2 ⊆ Aut C20480C20:12(C2xDic3)480,804

Non-split extensions G=N.Q with N=C20 and Q=C2×Dic3
extensionφ:Q→Aut NdρLabelID
C20.1(C2×Dic3) = D20⋊Dic3φ: C2×Dic3/C3 → C2×C4 ⊆ Aut C201208C20.1(C2xDic3)480,312
C20.2(C2×Dic3) = Dic10⋊Dic3φ: C2×Dic3/C3 → C2×C4 ⊆ Aut C201208C20.2(C2xDic3)480,313
C20.3(C2×Dic3) = Dic10⋊2Dic3φ: C2×Dic3/C3 → C2×C4 ⊆ Aut C201208C20.3(C2xDic3)480,314
C20.4(C2×Dic3) = D20⋊2Dic3φ: C2×Dic3/C3 → C2×C4 ⊆ Aut C201208C20.4(C2xDic3)480,315
C20.5(C2×Dic3) = Dic10.Dic3φ: C2×Dic3/C3 → C2×C4 ⊆ Aut C202408C20.5(C2xDic3)480,1066
C20.6(C2×Dic3) = D20.Dic3φ: C2×Dic3/C3 → C2×C4 ⊆ Aut C202408C20.6(C2xDic3)480,1068
C20.7(C2×Dic3) = Q8×C3⋊F5φ: C2×Dic3/C3 → C2×C4 ⊆ Aut C201208C20.7(C2xDic3)480,1069
C20.8(C2×Dic3) = C120⋊C4φ: C2×Dic3/C6 → C4 ⊆ Aut C201204C20.8(C2xDic3)480,298
C20.9(C2×Dic3) = D5.D24φ: C2×Dic3/C6 → C4 ⊆ Aut C201204C20.9(C2xDic3)480,299
C20.10(C2×Dic3) = C40.Dic3φ: C2×Dic3/C6 → C4 ⊆ Aut C202404C20.10(C2xDic3)480,300
C20.11(C2×Dic3) = C24.1F5φ: C2×Dic3/C6 → C4 ⊆ Aut C202404C20.11(C2xDic3)480,301
C20.12(C2×Dic3) = C2×C12.F5φ: C2×Dic3/C6 → C4 ⊆ Aut C20240C20.12(C2xDic3)480,1061
C20.13(C2×Dic3) = C60.59(C2×C4)φ: C2×Dic3/C6 → C4 ⊆ Aut C201204C20.13(C2xDic3)480,1062
C20.14(C2×Dic3) = C24.F5φ: C2×Dic3/C6 → C4 ⊆ Aut C202404C20.14(C2xDic3)480,294
C20.15(C2×Dic3) = C120.C4φ: C2×Dic3/C6 → C4 ⊆ Aut C202404C20.15(C2xDic3)480,295
C20.16(C2×Dic3) = C8×C3⋊F5φ: C2×Dic3/C6 → C4 ⊆ Aut C201204C20.16(C2xDic3)480,296
C20.17(C2×Dic3) = C24⋊F5φ: C2×Dic3/C6 → C4 ⊆ Aut C201204C20.17(C2xDic3)480,297
C20.18(C2×Dic3) = C2×C15⋊C16φ: C2×Dic3/C6 → C4 ⊆ Aut C20480C20.18(C2xDic3)480,302
C20.19(C2×Dic3) = C60.C8φ: C2×Dic3/C6 → C4 ⊆ Aut C202404C20.19(C2xDic3)480,303
C20.20(C2×Dic3) = C2×C60.C4φ: C2×Dic3/C6 → C4 ⊆ Aut C20240C20.20(C2xDic3)480,1060
C20.21(C2×Dic3) = (C2×C12)⋊6F5φ: C2×Dic3/C6 → C4 ⊆ Aut C201204C20.21(C2xDic3)480,1065
C20.22(C2×Dic3) = C30.D8φ: C2×Dic3/C6 → C22 ⊆ Aut C20240C20.22(C2xDic3)480,40
C20.23(C2×Dic3) = C30.Q16φ: C2×Dic3/C6 → C22 ⊆ Aut C20480C20.23(C2xDic3)480,46
C20.24(C2×Dic3) = C60.96D4φ: C2×Dic3/C6 → C22 ⊆ Aut C201204C20.24(C2xDic3)480,52
C20.25(C2×Dic3) = C60.7Q8φ: C2×Dic3/C6 → C22 ⊆ Aut C20480C20.25(C2xDic3)480,61
C20.26(C2×Dic3) = C60.8Q8φ: C2×Dic3/C6 → C22 ⊆ Aut C20480C20.26(C2xDic3)480,64
C20.27(C2×Dic3) = C60.105D4φ: C2×Dic3/C6 → C22 ⊆ Aut C202404C20.27(C2xDic3)480,67
C20.28(C2×Dic3) = D4⋊Dic15φ: C2×Dic3/C6 → C22 ⊆ Aut C20240C20.28(C2xDic3)480,192
C20.29(C2×Dic3) = Q8⋊2Dic15φ: C2×Dic3/C6 → C22 ⊆ Aut C20480C20.29(C2xDic3)480,195
C20.30(C2×Dic3) = Q8⋊3Dic15φ: C2×Dic3/C6 → C22 ⊆ Aut C201204C20.30(C2xDic3)480,197
C20.31(C2×Dic3) = D5×C4.Dic3φ: C2×Dic3/C6 → C22 ⊆ Aut C201204C20.31(C2xDic3)480,358
C20.32(C2×Dic3) = D20.2Dic3φ: C2×Dic3/C6 → C22 ⊆ Aut C202404C20.32(C2xDic3)480,360
C20.33(C2×Dic3) = Dic15⋊6Q8φ: C2×Dic3/C6 → C22 ⊆ Aut C20480C20.33(C2xDic3)480,407
C20.34(C2×Dic3) = (C4×D5)⋊Dic3φ: C2×Dic3/C6 → C22 ⊆ Aut C20240C20.34(C2xDic3)480,434
C20.35(C2×Dic3) = Q8×Dic15φ: C2×Dic3/C6 → C22 ⊆ Aut C20480C20.35(C2xDic3)480,910
C20.36(C2×Dic3) = D4.Dic15φ: C2×Dic3/C6 → C22 ⊆ Aut C202404C20.36(C2xDic3)480,913
C20.37(C2×Dic3) = C6.D40φ: C2×Dic3/Dic3 → C2 ⊆ Aut C20240C20.37(C2xDic3)480,41
C20.38(C2×Dic3) = C6.Dic20φ: C2×Dic3/Dic3 → C2 ⊆ Aut C20480C20.38(C2xDic3)480,47
C20.39(C2×Dic3) = C60.97D4φ: C2×Dic3/Dic3 → C2 ⊆ Aut C201204C20.39(C2xDic3)480,53
C20.40(C2×Dic3) = D20.3Dic3φ: C2×Dic3/Dic3 → C2 ⊆ Aut C202404C20.40(C2xDic3)480,359
C20.41(C2×Dic3) = Dic3×Dic10φ: C2×Dic3/Dic3 → C2 ⊆ Aut C20480C20.41(C2xDic3)480,406
C20.42(C2×Dic3) = D5×C3⋊C16φ: C2×Dic3/Dic3 → C2 ⊆ Aut C202404C20.42(C2xDic3)480,7
C20.43(C2×Dic3) = C40.51D6φ: C2×Dic3/Dic3 → C2 ⊆ Aut C202404C20.43(C2xDic3)480,10
C20.44(C2×Dic3) = Dic3×C5⋊2C8φ: C2×Dic3/Dic3 → C2 ⊆ Aut C20480C20.44(C2xDic3)480,26
C20.45(C2×Dic3) = Dic15⋊4C8φ: C2×Dic3/Dic3 → C2 ⊆ Aut C20480C20.45(C2xDic3)480,27
C20.46(C2×Dic3) = C30.22C42φ: C2×Dic3/Dic3 → C2 ⊆ Aut C20480C20.46(C2xDic3)480,29
C20.47(C2×Dic3) = C30.23C42φ: C2×Dic3/Dic3 → C2 ⊆ Aut C20480C20.47(C2xDic3)480,30
C20.48(C2×Dic3) = C2×D5×C3⋊C8φ: C2×Dic3/Dic3 → C2 ⊆ Aut C20240C20.48(C2xDic3)480,357
C20.49(C2×Dic3) = C2×C20.32D6φ: C2×Dic3/Dic3 → C2 ⊆ Aut C20240C20.49(C2xDic3)480,369
C20.50(C2×Dic3) = (D5×C12)⋊C4φ: C2×Dic3/Dic3 → C2 ⊆ Aut C20240C20.50(C2xDic3)480,433
C20.51(C2×Dic3) = C5×D4⋊Dic3φ: C2×Dic3/Dic3 → C2 ⊆ Aut C20240C20.51(C2xDic3)480,151
C20.52(C2×Dic3) = C5×Q8⋊2Dic3φ: C2×Dic3/Dic3 → C2 ⊆ Aut C20480C20.52(C2xDic3)480,154
C20.53(C2×Dic3) = C5×Q8⋊3Dic3φ: C2×Dic3/Dic3 → C2 ⊆ Aut C201204C20.53(C2xDic3)480,156
C20.54(C2×Dic3) = C5×Q8×Dic3φ: C2×Dic3/Dic3 → C2 ⊆ Aut C20480C20.54(C2xDic3)480,824
C20.55(C2×Dic3) = C5×D4.Dic3φ: C2×Dic3/Dic3 → C2 ⊆ Aut C202404C20.55(C2xDic3)480,827
C20.56(C2×Dic3) = C120⋊10C4φ: C2×Dic3/C2×C6 → C2 ⊆ Aut C20480C20.56(C2xDic3)480,177
C20.57(C2×Dic3) = C120⋊9C4φ: C2×Dic3/C2×C6 → C2 ⊆ Aut C20480C20.57(C2xDic3)480,178
C20.58(C2×Dic3) = C4.18D60φ: C2×Dic3/C2×C6 → C2 ⊆ Aut C202402C20.58(C2xDic3)480,179
C20.59(C2×Dic3) = C2×C60.7C4φ: C2×Dic3/C2×C6 → C2 ⊆ Aut C20240C20.59(C2xDic3)480,886
C20.60(C2×Dic3) = C2×C15⋊3C16φ: C2×Dic3/C2×C6 → C2 ⊆ Aut C20480C20.60(C2xDic3)480,171
C20.61(C2×Dic3) = C60.7C8φ: C2×Dic3/C2×C6 → C2 ⊆ Aut C202402C20.61(C2xDic3)480,172
C20.62(C2×Dic3) = C8×Dic15φ: C2×Dic3/C2×C6 → C2 ⊆ Aut C20480C20.62(C2xDic3)480,173
C20.63(C2×Dic3) = C120⋊13C4φ: C2×Dic3/C2×C6 → C2 ⊆ Aut C20480C20.63(C2xDic3)480,175
C20.64(C2×Dic3) = C22×C15⋊3C8φ: C2×Dic3/C2×C6 → C2 ⊆ Aut C20480C20.64(C2xDic3)480,885
C20.65(C2×Dic3) = C23.26D30φ: C2×Dic3/C2×C6 → C2 ⊆ Aut C20240C20.65(C2xDic3)480,891
C20.66(C2×Dic3) = C5×C8⋊Dic3φ: C2×Dic3/C2×C6 → C2 ⊆ Aut C20480C20.66(C2xDic3)480,136
C20.67(C2×Dic3) = C5×C24⋊1C4φ: C2×Dic3/C2×C6 → C2 ⊆ Aut C20480C20.67(C2xDic3)480,137
C20.68(C2×Dic3) = C5×C24.C4φ: C2×Dic3/C2×C6 → C2 ⊆ Aut C202402C20.68(C2xDic3)480,138
C20.69(C2×Dic3) = C10×C4.Dic3φ: C2×Dic3/C2×C6 → C2 ⊆ Aut C20240C20.69(C2xDic3)480,800
C20.70(C2×Dic3) = C5×C23.26D6φ: C2×Dic3/C2×C6 → C2 ⊆ Aut C20240C20.70(C2xDic3)480,805
C20.71(C2×Dic3) = C10×C3⋊C16central extension (φ=1)480C20.71(C2xDic3)480,130
C20.72(C2×Dic3) = C5×C12.C8central extension (φ=1)2402C20.72(C2xDic3)480,131
C20.73(C2×Dic3) = Dic3×C40central extension (φ=1)480C20.73(C2xDic3)480,132
C20.74(C2×Dic3) = C5×C24⋊C4central extension (φ=1)480C20.74(C2xDic3)480,134
C20.75(C2×Dic3) = C2×C10×C3⋊C8central extension (φ=1)480C20.75(C2xDic3)480,799

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