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Extensions 1→N→G→Q→1 with N=C10 and Q=C3×C4○D4

Direct product G=N×Q with N=C10 and Q=C3×C4○D4
dρLabelID
C4○D4×C30240C4oD4xC30480,1183

Semidirect products G=N:Q with N=C10 and Q=C3×C4○D4
extensionφ:Q→Aut NdρLabelID
C10⋊1(C3×C4○D4) = C6×C4○D20φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C10240C10:1(C3xC4oD4)480,1138
C10⋊2(C3×C4○D4) = C6×D4⋊2D5φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C10240C10:2(C3xC4oD4)480,1140
C10⋊3(C3×C4○D4) = C6×Q8⋊2D5φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C10240C10:3(C3xC4oD4)480,1143

Non-split extensions G=N.Q with N=C10 and Q=C3×C4○D4
extensionφ:Q→Aut NdρLabelID
C10.1(C3×C4○D4) = C12×Dic10φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C10480C10.1(C3xC4oD4)480,661
C10.2(C3×C4○D4) = C3×C20.6Q8φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C10480C10.2(C3xC4oD4)480,663
C10.3(C3×C4○D4) = C3×C42⋊D5φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C10240C10.3(C3xC4oD4)480,665
C10.4(C3×C4○D4) = C12×D20φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C10240C10.4(C3xC4oD4)480,666
C10.5(C3×C4○D4) = C3×C4.D20φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C10240C10.5(C3xC4oD4)480,668
C10.6(C3×C4○D4) = C3×C42⋊2D5φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C10240C10.6(C3xC4oD4)480,669
C10.7(C3×C4○D4) = C3×D10.12D4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C10240C10.7(C3xC4oD4)480,676
C10.8(C3×C4○D4) = C3×D10⋊D4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C10240C10.8(C3xC4oD4)480,677
C10.9(C3×C4○D4) = C3×Dic5.5D4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C10240C10.9(C3xC4oD4)480,678
C10.10(C3×C4○D4) = C3×Dic5.Q8φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C10480C10.10(C3xC4oD4)480,682
C10.11(C3×C4○D4) = C3×D10.13D4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C10240C10.11(C3xC4oD4)480,687
C10.12(C3×C4○D4) = C3×D10⋊Q8φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C10240C10.12(C3xC4oD4)480,689
C10.13(C3×C4○D4) = C3×C20.48D4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C10240C10.13(C3xC4oD4)480,717
C10.14(C3×C4○D4) = C3×C23.21D10φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C10240C10.14(C3xC4oD4)480,719
C10.15(C3×C4○D4) = C12×C5⋊D4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C10240C10.15(C3xC4oD4)480,721
C10.16(C3×C4○D4) = C3×C23.23D10φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C10240C10.16(C3xC4oD4)480,722
C10.17(C3×C4○D4) = C3×C20⋊7D4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C10240C10.17(C3xC4oD4)480,723
C10.18(C3×C4○D4) = C3×C23.11D10φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C10240C10.18(C3xC4oD4)480,670
C10.19(C3×C4○D4) = C3×Dic5.14D4φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C10240C10.19(C3xC4oD4)480,671
C10.20(C3×C4○D4) = C3×C23.D10φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C10240C10.20(C3xC4oD4)480,672
C10.21(C3×C4○D4) = C3×Dic5⋊4D4φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C10240C10.21(C3xC4oD4)480,674
C10.22(C3×C4○D4) = C3×C22.D20φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C10240C10.22(C3xC4oD4)480,679
C10.23(C3×C4○D4) = C3×Dic5⋊3Q8φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C10480C10.23(C3xC4oD4)480,680
C10.24(C3×C4○D4) = C3×C4⋊C4⋊7D5φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C10240C10.24(C3xC4oD4)480,685
C10.25(C3×C4○D4) = C3×D10⋊2Q8φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C10240C10.25(C3xC4oD4)480,690
C10.26(C3×C4○D4) = C3×C4⋊C4⋊D5φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C10240C10.26(C3xC4oD4)480,691
C10.27(C3×C4○D4) = C3×D4×Dic5φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C10240C10.27(C3xC4oD4)480,727
C10.28(C3×C4○D4) = C3×C23.18D10φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C10240C10.28(C3xC4oD4)480,728
C10.29(C3×C4○D4) = C3×C20.17D4φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C10240C10.29(C3xC4oD4)480,729
C10.30(C3×C4○D4) = C3×C20⋊2D4φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C10240C10.30(C3xC4oD4)480,731
C10.31(C3×C4○D4) = C3×Dic5⋊D4φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C10240C10.31(C3xC4oD4)480,732
C10.32(C3×C4○D4) = C3×C4.Dic10φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C10480C10.32(C3xC4oD4)480,683
C10.33(C3×C4○D4) = C3×D20⋊8C4φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C10240C10.33(C3xC4oD4)480,686
C10.34(C3×C4○D4) = C3×C4⋊D20φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C10240C10.34(C3xC4oD4)480,688
C10.35(C3×C4○D4) = C3×Q8×Dic5φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C10480C10.35(C3xC4oD4)480,738
C10.36(C3×C4○D4) = C3×D10⋊3Q8φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C10240C10.36(C3xC4oD4)480,739
C10.37(C3×C4○D4) = C3×C20.23D4φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C10240C10.37(C3xC4oD4)480,740
C10.38(C3×C4○D4) = C15×C42⋊C2central extension (φ=1)240C10.38(C3xC4oD4)480,922
C10.39(C3×C4○D4) = D4×C60central extension (φ=1)240C10.39(C3xC4oD4)480,923
C10.40(C3×C4○D4) = Q8×C60central extension (φ=1)480C10.40(C3xC4oD4)480,924
C10.41(C3×C4○D4) = C15×C4⋊D4central extension (φ=1)240C10.41(C3xC4oD4)480,926
C10.42(C3×C4○D4) = C15×C22⋊Q8central extension (φ=1)240C10.42(C3xC4oD4)480,927
C10.43(C3×C4○D4) = C15×C22.D4central extension (φ=1)240C10.43(C3xC4oD4)480,928
C10.44(C3×C4○D4) = C15×C4.4D4central extension (φ=1)240C10.44(C3xC4oD4)480,929
C10.45(C3×C4○D4) = C15×C42.C2central extension (φ=1)480C10.45(C3xC4oD4)480,930
C10.46(C3×C4○D4) = C15×C42⋊2C2central extension (φ=1)240C10.46(C3xC4oD4)480,931

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