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Extensions 1→N→G→Q→1 with N=C6 and Q=C5×C4○D4

Direct product G=N×Q with N=C6 and Q=C5×C4○D4
dρLabelID
C4○D4×C30240C4oD4xC30480,1183

Semidirect products G=N:Q with N=C6 and Q=C5×C4○D4
extensionφ:Q→Aut NdρLabelID
C6⋊1(C5×C4○D4) = C10×C4○D12φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C6240C6:1(C5xC4oD4)480,1153
C6⋊2(C5×C4○D4) = C10×D4⋊2S3φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C6240C6:2(C5xC4oD4)480,1155
C6⋊3(C5×C4○D4) = C10×Q8⋊3S3φ: C5×C4○D4/C5×Q8 → C2 ⊆ Aut C6240C6:3(C5xC4oD4)480,1158

Non-split extensions G=N.Q with N=C6 and Q=C5×C4○D4
extensionφ:Q→Aut NdρLabelID
C6.1(C5×C4○D4) = C20×Dic6φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C6480C6.1(C5xC4oD4)480,747
C6.2(C5×C4○D4) = C5×C12.6Q8φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C6480C6.2(C5xC4oD4)480,749
C6.3(C5×C4○D4) = C5×C42⋊2S3φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C6240C6.3(C5xC4oD4)480,751
C6.4(C5×C4○D4) = C20×D12φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C6240C6.4(C5xC4oD4)480,752
C6.5(C5×C4○D4) = C5×C42⋊7S3φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C6240C6.5(C5xC4oD4)480,754
C6.6(C5×C4○D4) = C5×C42⋊3S3φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C6240C6.6(C5xC4oD4)480,755
C6.7(C5×C4○D4) = C5×C23.9D6φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C6240C6.7(C5xC4oD4)480,762
C6.8(C5×C4○D4) = C5×Dic3⋊D4φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C6240C6.8(C5xC4oD4)480,763
C6.9(C5×C4○D4) = C5×C23.11D6φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C6240C6.9(C5xC4oD4)480,764
C6.10(C5×C4○D4) = C5×Dic3.Q8φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C6480C6.10(C5xC4oD4)480,768
C6.11(C5×C4○D4) = C5×D6.D4φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C6240C6.11(C5xC4oD4)480,773
C6.12(C5×C4○D4) = C5×D6⋊Q8φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C6240C6.12(C5xC4oD4)480,775
C6.13(C5×C4○D4) = C5×C12.48D4φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C6240C6.13(C5xC4oD4)480,803
C6.14(C5×C4○D4) = C5×C23.26D6φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C6240C6.14(C5xC4oD4)480,805
C6.15(C5×C4○D4) = C20×C3⋊D4φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C6240C6.15(C5xC4oD4)480,807
C6.16(C5×C4○D4) = C5×C23.28D6φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C6240C6.16(C5xC4oD4)480,808
C6.17(C5×C4○D4) = C5×C12⋊7D4φ: C5×C4○D4/C2×C20 → C2 ⊆ Aut C6240C6.17(C5xC4oD4)480,809
C6.18(C5×C4○D4) = C5×C23.16D6φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C6240C6.18(C5xC4oD4)480,756
C6.19(C5×C4○D4) = C5×Dic3.D4φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C6240C6.19(C5xC4oD4)480,757
C6.20(C5×C4○D4) = C5×C23.8D6φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C6240C6.20(C5xC4oD4)480,758
C6.21(C5×C4○D4) = C5×Dic3⋊4D4φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C6240C6.21(C5xC4oD4)480,760
C6.22(C5×C4○D4) = C5×C23.21D6φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C6240C6.22(C5xC4oD4)480,765
C6.23(C5×C4○D4) = C5×Dic6⋊C4φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C6480C6.23(C5xC4oD4)480,766
C6.24(C5×C4○D4) = C5×C4.Dic6φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C6480C6.24(C5xC4oD4)480,769
C6.25(C5×C4○D4) = C5×C4⋊C4⋊7S3φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C6240C6.25(C5xC4oD4)480,771
C6.26(C5×C4○D4) = C5×C4.D12φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C6240C6.26(C5xC4oD4)480,776
C6.27(C5×C4○D4) = C5×D4×Dic3φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C6240C6.27(C5xC4oD4)480,813
C6.28(C5×C4○D4) = C5×C23.23D6φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C6240C6.28(C5xC4oD4)480,814
C6.29(C5×C4○D4) = C5×C23.12D6φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C6240C6.29(C5xC4oD4)480,815
C6.30(C5×C4○D4) = C5×D6⋊3D4φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C6240C6.30(C5xC4oD4)480,817
C6.31(C5×C4○D4) = C5×C23.14D6φ: C5×C4○D4/C5×D4 → C2 ⊆ Aut C6240C6.31(C5xC4oD4)480,818
C6.32(C5×C4○D4) = C5×Dic3⋊5D4φ: C5×C4○D4/C5×Q8 → C2 ⊆ Aut C6240C6.32(C5xC4oD4)480,772
C6.33(C5×C4○D4) = C5×C12⋊D4φ: C5×C4○D4/C5×Q8 → C2 ⊆ Aut C6240C6.33(C5xC4oD4)480,774
C6.34(C5×C4○D4) = C5×C4⋊C4⋊S3φ: C5×C4○D4/C5×Q8 → C2 ⊆ Aut C6240C6.34(C5xC4oD4)480,777
C6.35(C5×C4○D4) = C5×Q8×Dic3φ: C5×C4○D4/C5×Q8 → C2 ⊆ Aut C6480C6.35(C5xC4oD4)480,824
C6.36(C5×C4○D4) = C5×D6⋊3Q8φ: C5×C4○D4/C5×Q8 → C2 ⊆ Aut C6240C6.36(C5xC4oD4)480,825
C6.37(C5×C4○D4) = C5×C12.23D4φ: C5×C4○D4/C5×Q8 → C2 ⊆ Aut C6240C6.37(C5xC4oD4)480,826
C6.38(C5×C4○D4) = C15×C42⋊C2central extension (φ=1)240C6.38(C5xC4oD4)480,922
C6.39(C5×C4○D4) = D4×C60central extension (φ=1)240C6.39(C5xC4oD4)480,923
C6.40(C5×C4○D4) = Q8×C60central extension (φ=1)480C6.40(C5xC4oD4)480,924
C6.41(C5×C4○D4) = C15×C4⋊D4central extension (φ=1)240C6.41(C5xC4oD4)480,926
C6.42(C5×C4○D4) = C15×C22⋊Q8central extension (φ=1)240C6.42(C5xC4oD4)480,927
C6.43(C5×C4○D4) = C15×C22.D4central extension (φ=1)240C6.43(C5xC4oD4)480,928
C6.44(C5×C4○D4) = C15×C4.4D4central extension (φ=1)240C6.44(C5xC4oD4)480,929
C6.45(C5×C4○D4) = C15×C42.C2central extension (φ=1)480C6.45(C5xC4oD4)480,930
C6.46(C5×C4○D4) = C15×C42⋊2C2central extension (φ=1)240C6.46(C5xC4oD4)480,931

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