# Extensions 1→N→G→Q→1 with N=C12 and Q=C22×C10

Direct product G=N×Q with N=C12 and Q=C22×C10
dρLabelID
C23×C60480C2^3xC60480,1180

Semidirect products G=N:Q with N=C12 and Q=C22×C10
extensionφ:Q→Aut NdρLabelID
C12⋊(C22×C10) = S3×D4×C10φ: C22×C10/C10C22 ⊆ Aut C12120C12:(C2^2xC10)480,1154
C122(C22×C10) = C2×C10×D12φ: C22×C10/C2×C10C2 ⊆ Aut C12240C12:2(C2^2xC10)480,1152
C123(C22×C10) = S3×C22×C20φ: C22×C10/C2×C10C2 ⊆ Aut C12240C12:3(C2^2xC10)480,1151
C124(C22×C10) = D4×C2×C30φ: C22×C10/C2×C10C2 ⊆ Aut C12240C12:4(C2^2xC10)480,1181

Non-split extensions G=N.Q with N=C12 and Q=C22×C10
extensionφ:Q→Aut NdρLabelID
C12.1(C22×C10) = C5×S3×D8φ: C22×C10/C10C22 ⊆ Aut C121204C12.1(C2^2xC10)480,789
C12.2(C22×C10) = C5×D8⋊S3φ: C22×C10/C10C22 ⊆ Aut C121204C12.2(C2^2xC10)480,790
C12.3(C22×C10) = C5×D83S3φ: C22×C10/C10C22 ⊆ Aut C122404C12.3(C2^2xC10)480,791
C12.4(C22×C10) = C5×S3×SD16φ: C22×C10/C10C22 ⊆ Aut C121204C12.4(C2^2xC10)480,792
C12.5(C22×C10) = C5×Q83D6φ: C22×C10/C10C22 ⊆ Aut C121204C12.5(C2^2xC10)480,793
C12.6(C22×C10) = C5×D4.D6φ: C22×C10/C10C22 ⊆ Aut C122404C12.6(C2^2xC10)480,794
C12.7(C22×C10) = C5×Q8.7D6φ: C22×C10/C10C22 ⊆ Aut C122404C12.7(C2^2xC10)480,795
C12.8(C22×C10) = C5×S3×Q16φ: C22×C10/C10C22 ⊆ Aut C122404C12.8(C2^2xC10)480,796
C12.9(C22×C10) = C5×Q16⋊S3φ: C22×C10/C10C22 ⊆ Aut C122404C12.9(C2^2xC10)480,797
C12.10(C22×C10) = C5×D24⋊C2φ: C22×C10/C10C22 ⊆ Aut C122404C12.10(C2^2xC10)480,798
C12.11(C22×C10) = C10×D4⋊S3φ: C22×C10/C10C22 ⊆ Aut C12240C12.11(C2^2xC10)480,810
C12.12(C22×C10) = C5×D126C22φ: C22×C10/C10C22 ⊆ Aut C121204C12.12(C2^2xC10)480,811
C12.13(C22×C10) = C10×D4.S3φ: C22×C10/C10C22 ⊆ Aut C12240C12.13(C2^2xC10)480,812
C12.14(C22×C10) = C10×Q82S3φ: C22×C10/C10C22 ⊆ Aut C12240C12.14(C2^2xC10)480,820
C12.15(C22×C10) = C5×Q8.11D6φ: C22×C10/C10C22 ⊆ Aut C122404C12.15(C2^2xC10)480,821
C12.16(C22×C10) = C10×C3⋊Q16φ: C22×C10/C10C22 ⊆ Aut C12480C12.16(C2^2xC10)480,822
C12.17(C22×C10) = C5×D4⋊D6φ: C22×C10/C10C22 ⊆ Aut C121204C12.17(C2^2xC10)480,828
C12.18(C22×C10) = C5×Q8.13D6φ: C22×C10/C10C22 ⊆ Aut C122404C12.18(C2^2xC10)480,829
C12.19(C22×C10) = C5×Q8.14D6φ: C22×C10/C10C22 ⊆ Aut C122404C12.19(C2^2xC10)480,830
C12.20(C22×C10) = C10×D42S3φ: C22×C10/C10C22 ⊆ Aut C12240C12.20(C2^2xC10)480,1155
C12.21(C22×C10) = C5×D46D6φ: C22×C10/C10C22 ⊆ Aut C121204C12.21(C2^2xC10)480,1156
C12.22(C22×C10) = S3×Q8×C10φ: C22×C10/C10C22 ⊆ Aut C12240C12.22(C2^2xC10)480,1157
C12.23(C22×C10) = C10×Q83S3φ: C22×C10/C10C22 ⊆ Aut C12240C12.23(C2^2xC10)480,1158
C12.24(C22×C10) = C5×Q8.15D6φ: C22×C10/C10C22 ⊆ Aut C122404C12.24(C2^2xC10)480,1159
C12.25(C22×C10) = C5×S3×C4○D4φ: C22×C10/C10C22 ⊆ Aut C121204C12.25(C2^2xC10)480,1160
C12.26(C22×C10) = C5×D4○D12φ: C22×C10/C10C22 ⊆ Aut C121204C12.26(C2^2xC10)480,1161
C12.27(C22×C10) = C5×Q8○D12φ: C22×C10/C10C22 ⊆ Aut C122404C12.27(C2^2xC10)480,1162
C12.28(C22×C10) = C10×C24⋊C2φ: C22×C10/C2×C10C2 ⊆ Aut C12240C12.28(C2^2xC10)480,781
C12.29(C22×C10) = C10×D24φ: C22×C10/C2×C10C2 ⊆ Aut C12240C12.29(C2^2xC10)480,782
C12.30(C22×C10) = C5×C4○D24φ: C22×C10/C2×C10C2 ⊆ Aut C122402C12.30(C2^2xC10)480,783
C12.31(C22×C10) = C10×Dic12φ: C22×C10/C2×C10C2 ⊆ Aut C12480C12.31(C2^2xC10)480,784
C12.32(C22×C10) = C5×C8⋊D6φ: C22×C10/C2×C10C2 ⊆ Aut C121204C12.32(C2^2xC10)480,787
C12.33(C22×C10) = C5×C8.D6φ: C22×C10/C2×C10C2 ⊆ Aut C122404C12.33(C2^2xC10)480,788
C12.34(C22×C10) = C2×C10×Dic6φ: C22×C10/C2×C10C2 ⊆ Aut C12480C12.34(C2^2xC10)480,1150
C12.35(C22×C10) = S3×C2×C40φ: C22×C10/C2×C10C2 ⊆ Aut C12240C12.35(C2^2xC10)480,778
C12.36(C22×C10) = C10×C8⋊S3φ: C22×C10/C2×C10C2 ⊆ Aut C12240C12.36(C2^2xC10)480,779
C12.37(C22×C10) = C5×C8○D12φ: C22×C10/C2×C10C2 ⊆ Aut C122402C12.37(C2^2xC10)480,780
C12.38(C22×C10) = C5×S3×M4(2)φ: C22×C10/C2×C10C2 ⊆ Aut C121204C12.38(C2^2xC10)480,785
C12.39(C22×C10) = C5×D12.C4φ: C22×C10/C2×C10C2 ⊆ Aut C122404C12.39(C2^2xC10)480,786
C12.40(C22×C10) = C2×C10×C3⋊C8φ: C22×C10/C2×C10C2 ⊆ Aut C12480C12.40(C2^2xC10)480,799
C12.41(C22×C10) = C10×C4.Dic3φ: C22×C10/C2×C10C2 ⊆ Aut C12240C12.41(C2^2xC10)480,800
C12.42(C22×C10) = C5×D4.Dic3φ: C22×C10/C2×C10C2 ⊆ Aut C122404C12.42(C2^2xC10)480,827
C12.43(C22×C10) = C10×C4○D12φ: C22×C10/C2×C10C2 ⊆ Aut C12240C12.43(C2^2xC10)480,1153
C12.44(C22×C10) = D8×C30φ: C22×C10/C2×C10C2 ⊆ Aut C12240C12.44(C2^2xC10)480,937
C12.45(C22×C10) = SD16×C30φ: C22×C10/C2×C10C2 ⊆ Aut C12240C12.45(C2^2xC10)480,938
C12.46(C22×C10) = Q16×C30φ: C22×C10/C2×C10C2 ⊆ Aut C12480C12.46(C2^2xC10)480,939
C12.47(C22×C10) = C15×C4○D8φ: C22×C10/C2×C10C2 ⊆ Aut C122402C12.47(C2^2xC10)480,940
C12.48(C22×C10) = C15×C8⋊C22φ: C22×C10/C2×C10C2 ⊆ Aut C121204C12.48(C2^2xC10)480,941
C12.49(C22×C10) = C15×C8.C22φ: C22×C10/C2×C10C2 ⊆ Aut C122404C12.49(C2^2xC10)480,942
C12.50(C22×C10) = Q8×C2×C30φ: C22×C10/C2×C10C2 ⊆ Aut C12480C12.50(C2^2xC10)480,1182
C12.51(C22×C10) = C15×2+ 1+4φ: C22×C10/C2×C10C2 ⊆ Aut C121204C12.51(C2^2xC10)480,1184
C12.52(C22×C10) = C15×2- 1+4φ: C22×C10/C2×C10C2 ⊆ Aut C122404C12.52(C2^2xC10)480,1185
C12.53(C22×C10) = M4(2)×C30central extension (φ=1)240C12.53(C2^2xC10)480,935
C12.54(C22×C10) = C15×C8○D4central extension (φ=1)2402C12.54(C2^2xC10)480,936
C12.55(C22×C10) = C4○D4×C30central extension (φ=1)240C12.55(C2^2xC10)480,1183

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