# Extensions 1→N→G→Q→1 with N=C4 and Q=S3×C2×C10

Direct product G=N×Q with N=C4 and Q=S3×C2×C10
dρLabelID
S3×C22×C20240S3xC2^2xC20480,1151

Semidirect products G=N:Q with N=C4 and Q=S3×C2×C10
extensionφ:Q→Aut NdρLabelID
C41(S3×C2×C10) = S3×D4×C10φ: S3×C2×C10/S3×C10C2 ⊆ Aut C4120C4:1(S3xC2xC10)480,1154
C42(S3×C2×C10) = C2×C10×D12φ: S3×C2×C10/C2×C30C2 ⊆ Aut C4240C4:2(S3xC2xC10)480,1152

Non-split extensions G=N.Q with N=C4 and Q=S3×C2×C10
extensionφ:Q→Aut NdρLabelID
C4.1(S3×C2×C10) = C5×S3×D8φ: S3×C2×C10/S3×C10C2 ⊆ Aut C41204C4.1(S3xC2xC10)480,789
C4.2(S3×C2×C10) = C5×D8⋊S3φ: S3×C2×C10/S3×C10C2 ⊆ Aut C41204C4.2(S3xC2xC10)480,790
C4.3(S3×C2×C10) = C5×D83S3φ: S3×C2×C10/S3×C10C2 ⊆ Aut C42404C4.3(S3xC2xC10)480,791
C4.4(S3×C2×C10) = C5×S3×SD16φ: S3×C2×C10/S3×C10C2 ⊆ Aut C41204C4.4(S3xC2xC10)480,792
C4.5(S3×C2×C10) = C5×Q83D6φ: S3×C2×C10/S3×C10C2 ⊆ Aut C41204C4.5(S3xC2xC10)480,793
C4.6(S3×C2×C10) = C5×D4.D6φ: S3×C2×C10/S3×C10C2 ⊆ Aut C42404C4.6(S3xC2xC10)480,794
C4.7(S3×C2×C10) = C5×Q8.7D6φ: S3×C2×C10/S3×C10C2 ⊆ Aut C42404C4.7(S3xC2xC10)480,795
C4.8(S3×C2×C10) = C5×S3×Q16φ: S3×C2×C10/S3×C10C2 ⊆ Aut C42404C4.8(S3xC2xC10)480,796
C4.9(S3×C2×C10) = C5×Q16⋊S3φ: S3×C2×C10/S3×C10C2 ⊆ Aut C42404C4.9(S3xC2xC10)480,797
C4.10(S3×C2×C10) = C5×D24⋊C2φ: S3×C2×C10/S3×C10C2 ⊆ Aut C42404C4.10(S3xC2xC10)480,798
C4.11(S3×C2×C10) = C10×D4⋊S3φ: S3×C2×C10/S3×C10C2 ⊆ Aut C4240C4.11(S3xC2xC10)480,810
C4.12(S3×C2×C10) = C5×D126C22φ: S3×C2×C10/S3×C10C2 ⊆ Aut C41204C4.12(S3xC2xC10)480,811
C4.13(S3×C2×C10) = C10×D4.S3φ: S3×C2×C10/S3×C10C2 ⊆ Aut C4240C4.13(S3xC2xC10)480,812
C4.14(S3×C2×C10) = C10×Q82S3φ: S3×C2×C10/S3×C10C2 ⊆ Aut C4240C4.14(S3xC2xC10)480,820
C4.15(S3×C2×C10) = C5×Q8.11D6φ: S3×C2×C10/S3×C10C2 ⊆ Aut C42404C4.15(S3xC2xC10)480,821
C4.16(S3×C2×C10) = C10×C3⋊Q16φ: S3×C2×C10/S3×C10C2 ⊆ Aut C4480C4.16(S3xC2xC10)480,822
C4.17(S3×C2×C10) = C5×D4⋊D6φ: S3×C2×C10/S3×C10C2 ⊆ Aut C41204C4.17(S3xC2xC10)480,828
C4.18(S3×C2×C10) = C5×Q8.13D6φ: S3×C2×C10/S3×C10C2 ⊆ Aut C42404C4.18(S3xC2xC10)480,829
C4.19(S3×C2×C10) = C5×Q8.14D6φ: S3×C2×C10/S3×C10C2 ⊆ Aut C42404C4.19(S3xC2xC10)480,830
C4.20(S3×C2×C10) = C10×D42S3φ: S3×C2×C10/S3×C10C2 ⊆ Aut C4240C4.20(S3xC2xC10)480,1155
C4.21(S3×C2×C10) = C5×D46D6φ: S3×C2×C10/S3×C10C2 ⊆ Aut C41204C4.21(S3xC2xC10)480,1156
C4.22(S3×C2×C10) = S3×Q8×C10φ: S3×C2×C10/S3×C10C2 ⊆ Aut C4240C4.22(S3xC2xC10)480,1157
C4.23(S3×C2×C10) = C10×Q83S3φ: S3×C2×C10/S3×C10C2 ⊆ Aut C4240C4.23(S3xC2xC10)480,1158
C4.24(S3×C2×C10) = C5×Q8.15D6φ: S3×C2×C10/S3×C10C2 ⊆ Aut C42404C4.24(S3xC2xC10)480,1159
C4.25(S3×C2×C10) = C5×S3×C4○D4φ: S3×C2×C10/S3×C10C2 ⊆ Aut C41204C4.25(S3xC2xC10)480,1160
C4.26(S3×C2×C10) = C5×D4○D12φ: S3×C2×C10/S3×C10C2 ⊆ Aut C41204C4.26(S3xC2xC10)480,1161
C4.27(S3×C2×C10) = C5×Q8○D12φ: S3×C2×C10/S3×C10C2 ⊆ Aut C42404C4.27(S3xC2xC10)480,1162
C4.28(S3×C2×C10) = C10×C24⋊C2φ: S3×C2×C10/C2×C30C2 ⊆ Aut C4240C4.28(S3xC2xC10)480,781
C4.29(S3×C2×C10) = C10×D24φ: S3×C2×C10/C2×C30C2 ⊆ Aut C4240C4.29(S3xC2xC10)480,782
C4.30(S3×C2×C10) = C5×C4○D24φ: S3×C2×C10/C2×C30C2 ⊆ Aut C42402C4.30(S3xC2xC10)480,783
C4.31(S3×C2×C10) = C10×Dic12φ: S3×C2×C10/C2×C30C2 ⊆ Aut C4480C4.31(S3xC2xC10)480,784
C4.32(S3×C2×C10) = C5×C8⋊D6φ: S3×C2×C10/C2×C30C2 ⊆ Aut C41204C4.32(S3xC2xC10)480,787
C4.33(S3×C2×C10) = C5×C8.D6φ: S3×C2×C10/C2×C30C2 ⊆ Aut C42404C4.33(S3xC2xC10)480,788
C4.34(S3×C2×C10) = C2×C10×Dic6φ: S3×C2×C10/C2×C30C2 ⊆ Aut C4480C4.34(S3xC2xC10)480,1150
C4.35(S3×C2×C10) = S3×C2×C40central extension (φ=1)240C4.35(S3xC2xC10)480,778
C4.36(S3×C2×C10) = C10×C8⋊S3central extension (φ=1)240C4.36(S3xC2xC10)480,779
C4.37(S3×C2×C10) = C5×C8○D12central extension (φ=1)2402C4.37(S3xC2xC10)480,780
C4.38(S3×C2×C10) = C5×S3×M4(2)central extension (φ=1)1204C4.38(S3xC2xC10)480,785
C4.39(S3×C2×C10) = C5×D12.C4central extension (φ=1)2404C4.39(S3xC2xC10)480,786
C4.40(S3×C2×C10) = C2×C10×C3⋊C8central extension (φ=1)480C4.40(S3xC2xC10)480,799
C4.41(S3×C2×C10) = C10×C4.Dic3central extension (φ=1)240C4.41(S3xC2xC10)480,800
C4.42(S3×C2×C10) = C5×D4.Dic3central extension (φ=1)2404C4.42(S3xC2xC10)480,827
C4.43(S3×C2×C10) = C10×C4○D12central extension (φ=1)240C4.43(S3xC2xC10)480,1153

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