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Extensions 1→N→G→Q→1 with N=C6 and Q=C22×C20

Direct product G=N×Q with N=C6 and Q=C22×C20
dρLabelID
C23×C60480C2^3xC60480,1180

Semidirect products G=N:Q with N=C6 and Q=C22×C20
extensionφ:Q→Aut NdρLabelID
C6⋊1(C22×C20) = S3×C22×C20φ: C22×C20/C2×C20 → C2 ⊆ Aut C6240C6:1(C2^2xC20)480,1151
C6⋊2(C22×C20) = Dic3×C22×C10φ: C22×C20/C22×C10 → C2 ⊆ Aut C6480C6:2(C2^2xC20)480,1163

Non-split extensions G=N.Q with N=C6 and Q=C22×C20
extensionφ:Q→Aut NdρLabelID
C6.1(C22×C20) = C20×Dic6φ: C22×C20/C2×C20 → C2 ⊆ Aut C6480C6.1(C2^2xC20)480,747
C6.2(C22×C20) = S3×C4×C20φ: C22×C20/C2×C20 → C2 ⊆ Aut C6240C6.2(C2^2xC20)480,750
C6.3(C22×C20) = C5×C42⋊2S3φ: C22×C20/C2×C20 → C2 ⊆ Aut C6240C6.3(C2^2xC20)480,751
C6.4(C22×C20) = C20×D12φ: C22×C20/C2×C20 → C2 ⊆ Aut C6240C6.4(C2^2xC20)480,752
C6.5(C22×C20) = C5×C23.16D6φ: C22×C20/C2×C20 → C2 ⊆ Aut C6240C6.5(C2^2xC20)480,756
C6.6(C22×C20) = C5×S3×C22⋊C4φ: C22×C20/C2×C20 → C2 ⊆ Aut C6120C6.6(C2^2xC20)480,759
C6.7(C22×C20) = C5×Dic3⋊4D4φ: C22×C20/C2×C20 → C2 ⊆ Aut C6240C6.7(C2^2xC20)480,760
C6.8(C22×C20) = C5×Dic6⋊C4φ: C22×C20/C2×C20 → C2 ⊆ Aut C6480C6.8(C2^2xC20)480,766
C6.9(C22×C20) = C5×S3×C4⋊C4φ: C22×C20/C2×C20 → C2 ⊆ Aut C6240C6.9(C2^2xC20)480,770
C6.10(C22×C20) = C5×C4⋊C4⋊7S3φ: C22×C20/C2×C20 → C2 ⊆ Aut C6240C6.10(C2^2xC20)480,771
C6.11(C22×C20) = C5×Dic3⋊5D4φ: C22×C20/C2×C20 → C2 ⊆ Aut C6240C6.11(C2^2xC20)480,772
C6.12(C22×C20) = S3×C2×C40φ: C22×C20/C2×C20 → C2 ⊆ Aut C6240C6.12(C2^2xC20)480,778
C6.13(C22×C20) = C10×C8⋊S3φ: C22×C20/C2×C20 → C2 ⊆ Aut C6240C6.13(C2^2xC20)480,779
C6.14(C22×C20) = C5×C8○D12φ: C22×C20/C2×C20 → C2 ⊆ Aut C62402C6.14(C2^2xC20)480,780
C6.15(C22×C20) = C5×S3×M4(2)φ: C22×C20/C2×C20 → C2 ⊆ Aut C61204C6.15(C2^2xC20)480,785
C6.16(C22×C20) = C5×D12.C4φ: C22×C20/C2×C20 → C2 ⊆ Aut C62404C6.16(C2^2xC20)480,786
C6.17(C22×C20) = C10×Dic3⋊C4φ: C22×C20/C2×C20 → C2 ⊆ Aut C6480C6.17(C2^2xC20)480,802
C6.18(C22×C20) = C10×D6⋊C4φ: C22×C20/C2×C20 → C2 ⊆ Aut C6240C6.18(C2^2xC20)480,806
C6.19(C22×C20) = C20×C3⋊D4φ: C22×C20/C2×C20 → C2 ⊆ Aut C6240C6.19(C2^2xC20)480,807
C6.20(C22×C20) = C2×C10×C3⋊C8φ: C22×C20/C22×C10 → C2 ⊆ Aut C6480C6.20(C2^2xC20)480,799
C6.21(C22×C20) = C10×C4.Dic3φ: C22×C20/C22×C10 → C2 ⊆ Aut C6240C6.21(C2^2xC20)480,800
C6.22(C22×C20) = Dic3×C2×C20φ: C22×C20/C22×C10 → C2 ⊆ Aut C6480C6.22(C2^2xC20)480,801
C6.23(C22×C20) = C10×C4⋊Dic3φ: C22×C20/C22×C10 → C2 ⊆ Aut C6480C6.23(C2^2xC20)480,804
C6.24(C22×C20) = C5×C23.26D6φ: C22×C20/C22×C10 → C2 ⊆ Aut C6240C6.24(C2^2xC20)480,805
C6.25(C22×C20) = C5×D4×Dic3φ: C22×C20/C22×C10 → C2 ⊆ Aut C6240C6.25(C2^2xC20)480,813
C6.26(C22×C20) = C5×Q8×Dic3φ: C22×C20/C22×C10 → C2 ⊆ Aut C6480C6.26(C2^2xC20)480,824
C6.27(C22×C20) = C5×D4.Dic3φ: C22×C20/C22×C10 → C2 ⊆ Aut C62404C6.27(C2^2xC20)480,827
C6.28(C22×C20) = C10×C6.D4φ: C22×C20/C22×C10 → C2 ⊆ Aut C6240C6.28(C2^2xC20)480,831
C6.29(C22×C20) = C22⋊C4×C30central extension (φ=1)240C6.29(C2^2xC20)480,920
C6.30(C22×C20) = C4⋊C4×C30central extension (φ=1)480C6.30(C2^2xC20)480,921
C6.31(C22×C20) = C15×C42⋊C2central extension (φ=1)240C6.31(C2^2xC20)480,922
C6.32(C22×C20) = D4×C60central extension (φ=1)240C6.32(C2^2xC20)480,923
C6.33(C22×C20) = Q8×C60central extension (φ=1)480C6.33(C2^2xC20)480,924
C6.34(C22×C20) = M4(2)×C30central extension (φ=1)240C6.34(C2^2xC20)480,935
C6.35(C22×C20) = C15×C8○D4central extension (φ=1)2402C6.35(C2^2xC20)480,936

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