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

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

Semidirect products G=N:Q with N=C12 and Q=C2×C20
extensionφ:Q→Aut NdρLabelID
C12⋊1(C2×C20) = C5×S3×C4⋊C4φ: C2×C20/C10 → C22 ⊆ Aut C12240C12:1(C2xC20)480,770
C12⋊2(C2×C20) = C5×Dic3⋊5D4φ: C2×C20/C10 → C22 ⊆ Aut C12240C12:2(C2xC20)480,772
C12⋊3(C2×C20) = C5×D4×Dic3φ: C2×C20/C10 → C22 ⊆ Aut C12240C12:3(C2xC20)480,813
C12⋊4(C2×C20) = C20×D12φ: C2×C20/C20 → C2 ⊆ Aut C12240C12:4(C2xC20)480,752
C12⋊5(C2×C20) = S3×C4×C20φ: C2×C20/C20 → C2 ⊆ Aut C12240C12:5(C2xC20)480,750
C12⋊6(C2×C20) = D4×C60φ: C2×C20/C20 → C2 ⊆ Aut C12240C12:6(C2xC20)480,923
C12⋊7(C2×C20) = C10×C4⋊Dic3φ: C2×C20/C2×C10 → C2 ⊆ Aut C12480C12:7(C2xC20)480,804
C12⋊8(C2×C20) = Dic3×C2×C20φ: C2×C20/C2×C10 → C2 ⊆ Aut C12480C12:8(C2xC20)480,801
C12⋊9(C2×C20) = C4⋊C4×C30φ: C2×C20/C2×C10 → C2 ⊆ Aut C12480C12:9(C2xC20)480,921

Non-split extensions G=N.Q with N=C12 and Q=C2×C20
extensionφ:Q→Aut NdρLabelID
C12.1(C2×C20) = C5×C6.Q16φ: C2×C20/C10 → C22 ⊆ Aut C12480C12.1(C2xC20)480,126
C12.2(C2×C20) = C5×C12.Q8φ: C2×C20/C10 → C22 ⊆ Aut C12480C12.2(C2xC20)480,127
C12.3(C2×C20) = C5×C6.D8φ: C2×C20/C10 → C22 ⊆ Aut C12240C12.3(C2xC20)480,128
C12.4(C2×C20) = C5×C6.SD16φ: C2×C20/C10 → C22 ⊆ Aut C12480C12.4(C2xC20)480,129
C12.5(C2×C20) = C5×C12.53D4φ: C2×C20/C10 → C22 ⊆ Aut C122404C12.5(C2xC20)480,141
C12.6(C2×C20) = C5×D12⋊C4φ: C2×C20/C10 → C22 ⊆ Aut C121204C12.6(C2xC20)480,144
C12.7(C2×C20) = C5×D4⋊Dic3φ: C2×C20/C10 → C22 ⊆ Aut C12240C12.7(C2xC20)480,151
C12.8(C2×C20) = C5×Q8⋊2Dic3φ: C2×C20/C10 → C22 ⊆ Aut C12480C12.8(C2xC20)480,154
C12.9(C2×C20) = C5×Q8⋊3Dic3φ: C2×C20/C10 → C22 ⊆ Aut C121204C12.9(C2xC20)480,156
C12.10(C2×C20) = C5×Dic6⋊C4φ: C2×C20/C10 → C22 ⊆ Aut C12480C12.10(C2xC20)480,766
C12.11(C2×C20) = C5×C4⋊C4⋊7S3φ: C2×C20/C10 → C22 ⊆ Aut C12240C12.11(C2xC20)480,771
C12.12(C2×C20) = C5×S3×M4(2)φ: C2×C20/C10 → C22 ⊆ Aut C121204C12.12(C2xC20)480,785
C12.13(C2×C20) = C5×D12.C4φ: C2×C20/C10 → C22 ⊆ Aut C122404C12.13(C2xC20)480,786
C12.14(C2×C20) = C5×Q8×Dic3φ: C2×C20/C10 → C22 ⊆ Aut C12480C12.14(C2xC20)480,824
C12.15(C2×C20) = C5×D4.Dic3φ: C2×C20/C10 → C22 ⊆ Aut C122404C12.15(C2xC20)480,827
C12.16(C2×C20) = C5×C42⋊4S3φ: C2×C20/C20 → C2 ⊆ Aut C121202C12.16(C2xC20)480,124
C12.17(C2×C20) = C5×C2.Dic12φ: C2×C20/C20 → C2 ⊆ Aut C12480C12.17(C2xC20)480,135
C12.18(C2×C20) = C5×C2.D24φ: C2×C20/C20 → C2 ⊆ Aut C12240C12.18(C2xC20)480,140
C12.19(C2×C20) = C20×Dic6φ: C2×C20/C20 → C2 ⊆ Aut C12480C12.19(C2xC20)480,747
C12.20(C2×C20) = C5×C8○D12φ: C2×C20/C20 → C2 ⊆ Aut C122402C12.20(C2xC20)480,780
C12.21(C2×C20) = S3×C80φ: C2×C20/C20 → C2 ⊆ Aut C122402C12.21(C2xC20)480,116
C12.22(C2×C20) = C5×D6.C8φ: C2×C20/C20 → C2 ⊆ Aut C122402C12.22(C2xC20)480,117
C12.23(C2×C20) = C20×C3⋊C8φ: C2×C20/C20 → C2 ⊆ Aut C12480C12.23(C2xC20)480,121
C12.24(C2×C20) = C5×C42.S3φ: C2×C20/C20 → C2 ⊆ Aut C12480C12.24(C2xC20)480,122
C12.25(C2×C20) = Dic3×C40φ: C2×C20/C20 → C2 ⊆ Aut C12480C12.25(C2xC20)480,132
C12.26(C2×C20) = C5×C42⋊2S3φ: C2×C20/C20 → C2 ⊆ Aut C12240C12.26(C2xC20)480,751
C12.27(C2×C20) = S3×C2×C40φ: C2×C20/C20 → C2 ⊆ Aut C12240C12.27(C2xC20)480,778
C12.28(C2×C20) = C10×C8⋊S3φ: C2×C20/C20 → C2 ⊆ Aut C12240C12.28(C2xC20)480,779
C12.29(C2×C20) = C15×D4⋊C4φ: C2×C20/C20 → C2 ⊆ Aut C12240C12.29(C2xC20)480,205
C12.30(C2×C20) = C15×Q8⋊C4φ: C2×C20/C20 → C2 ⊆ Aut C12480C12.30(C2xC20)480,206
C12.31(C2×C20) = C15×C4≀C2φ: C2×C20/C20 → C2 ⊆ Aut C121202C12.31(C2xC20)480,207
C12.32(C2×C20) = Q8×C60φ: C2×C20/C20 → C2 ⊆ Aut C12480C12.32(C2xC20)480,924
C12.33(C2×C20) = C15×C8○D4φ: C2×C20/C20 → C2 ⊆ Aut C122402C12.33(C2xC20)480,936
C12.34(C2×C20) = C5×C8⋊Dic3φ: C2×C20/C2×C10 → C2 ⊆ Aut C12480C12.34(C2xC20)480,136
C12.35(C2×C20) = C5×C24⋊1C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C12480C12.35(C2xC20)480,137
C12.36(C2×C20) = C5×C24.C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C122402C12.36(C2xC20)480,138
C12.37(C2×C20) = C10×C4.Dic3φ: C2×C20/C2×C10 → C2 ⊆ Aut C12240C12.37(C2xC20)480,800
C12.38(C2×C20) = C10×C3⋊C16φ: C2×C20/C2×C10 → C2 ⊆ Aut C12480C12.38(C2xC20)480,130
C12.39(C2×C20) = C5×C12.C8φ: C2×C20/C2×C10 → C2 ⊆ Aut C122402C12.39(C2xC20)480,131
C12.40(C2×C20) = C5×C24⋊C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C12480C12.40(C2xC20)480,134
C12.41(C2×C20) = C2×C10×C3⋊C8φ: C2×C20/C2×C10 → C2 ⊆ Aut C12480C12.41(C2xC20)480,799
C12.42(C2×C20) = C5×C23.26D6φ: C2×C20/C2×C10 → C2 ⊆ Aut C12240C12.42(C2xC20)480,805
C12.43(C2×C20) = C15×C4.Q8φ: C2×C20/C2×C10 → C2 ⊆ Aut C12480C12.43(C2xC20)480,209
C12.44(C2×C20) = C15×C2.D8φ: C2×C20/C2×C10 → C2 ⊆ Aut C12480C12.44(C2xC20)480,210
C12.45(C2×C20) = C15×C8.C4φ: C2×C20/C2×C10 → C2 ⊆ Aut C122402C12.45(C2xC20)480,211
C12.46(C2×C20) = C15×C42⋊C2φ: C2×C20/C2×C10 → C2 ⊆ Aut C12240C12.46(C2xC20)480,922
C12.47(C2×C20) = M4(2)×C30φ: C2×C20/C2×C10 → C2 ⊆ Aut C12240C12.47(C2xC20)480,935
C12.48(C2×C20) = C15×C8⋊C4central extension (φ=1)480C12.48(C2xC20)480,200
C12.49(C2×C20) = C15×M5(2)central extension (φ=1)2402C12.49(C2xC20)480,213

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