# Extensions 1→N→G→Q→1 with N=C23 and Q=S3×C10

Direct product G=N×Q with N=C23 and Q=S3×C10
dρLabelID
S3×C23×C10240S3xC2^3xC10480,1211

Semidirect products G=N:Q with N=C23 and Q=S3×C10
extensionφ:Q→Aut NdρLabelID
C23⋊(S3×C10) = C2×C10×S4φ: S3×C10/C10S3 ⊆ Aut C2360C2^3:(S3xC10)480,1198
C232(S3×C10) = C5×C232D6φ: S3×C10/C15C22 ⊆ Aut C23120C2^3:2(S3xC10)480,816
C233(S3×C10) = C5×D46D6φ: S3×C10/C15C22 ⊆ Aut C231204C2^3:3(S3xC10)480,1156
C234(S3×C10) = S3×D4×C10φ: S3×C10/C5×S3C2 ⊆ Aut C23120C2^3:4(S3xC10)480,1154
C235(S3×C10) = C2×C10×C3⋊D4φ: S3×C10/C30C2 ⊆ Aut C23240C2^3:5(S3xC10)480,1164

Non-split extensions G=N.Q with N=C23 and Q=S3×C10
extensionφ:Q→Aut NdρLabelID
C23.1(S3×C10) = C5×A4⋊Q8φ: S3×C10/C10S3 ⊆ Aut C231206C2^3.1(S3xC10)480,1013
C23.2(S3×C10) = C20×S4φ: S3×C10/C10S3 ⊆ Aut C23603C2^3.2(S3xC10)480,1014
C23.3(S3×C10) = C5×C4⋊S4φ: S3×C10/C10S3 ⊆ Aut C23606C2^3.3(S3xC10)480,1015
C23.4(S3×C10) = C10×A4⋊C4φ: S3×C10/C10S3 ⊆ Aut C23120C2^3.4(S3xC10)480,1022
C23.5(S3×C10) = C5×A4⋊D4φ: S3×C10/C10S3 ⊆ Aut C23606C2^3.5(S3xC10)480,1023
C23.6(S3×C10) = C5×C23.6D6φ: S3×C10/C15C22 ⊆ Aut C231204C2^3.6(S3xC10)480,125
C23.7(S3×C10) = C5×C23.7D6φ: S3×C10/C15C22 ⊆ Aut C231204C2^3.7(S3xC10)480,153
C23.8(S3×C10) = C5×C23.8D6φ: S3×C10/C15C22 ⊆ Aut C23240C2^3.8(S3xC10)480,758
C23.9(S3×C10) = C5×C23.9D6φ: S3×C10/C15C22 ⊆ Aut C23240C2^3.9(S3xC10)480,762
C23.10(S3×C10) = C5×Dic3⋊D4φ: S3×C10/C15C22 ⊆ Aut C23240C2^3.10(S3xC10)480,763
C23.11(S3×C10) = C5×C23.11D6φ: S3×C10/C15C22 ⊆ Aut C23240C2^3.11(S3xC10)480,764
C23.12(S3×C10) = C5×C23.12D6φ: S3×C10/C15C22 ⊆ Aut C23240C2^3.12(S3xC10)480,815
C23.13(S3×C10) = C5×D63D4φ: S3×C10/C15C22 ⊆ Aut C23240C2^3.13(S3xC10)480,817
C23.14(S3×C10) = C5×C23.14D6φ: S3×C10/C15C22 ⊆ Aut C23240C2^3.14(S3xC10)480,818
C23.15(S3×C10) = C5×C123D4φ: S3×C10/C15C22 ⊆ Aut C23240C2^3.15(S3xC10)480,819
C23.16(S3×C10) = C5×C23.16D6φ: S3×C10/C5×S3C2 ⊆ Aut C23240C2^3.16(S3xC10)480,756
C23.17(S3×C10) = C5×Dic3.D4φ: S3×C10/C5×S3C2 ⊆ Aut C23240C2^3.17(S3xC10)480,757
C23.18(S3×C10) = C5×S3×C22⋊C4φ: S3×C10/C5×S3C2 ⊆ Aut C23120C2^3.18(S3xC10)480,759
C23.19(S3×C10) = C5×Dic34D4φ: S3×C10/C5×S3C2 ⊆ Aut C23240C2^3.19(S3xC10)480,760
C23.20(S3×C10) = C5×D6⋊D4φ: S3×C10/C5×S3C2 ⊆ Aut C23120C2^3.20(S3xC10)480,761
C23.21(S3×C10) = C5×C23.21D6φ: S3×C10/C5×S3C2 ⊆ Aut C23240C2^3.21(S3xC10)480,765
C23.22(S3×C10) = C5×D4×Dic3φ: S3×C10/C5×S3C2 ⊆ Aut C23240C2^3.22(S3xC10)480,813
C23.23(S3×C10) = C5×C23.23D6φ: S3×C10/C5×S3C2 ⊆ Aut C23240C2^3.23(S3xC10)480,814
C23.24(S3×C10) = C10×D42S3φ: S3×C10/C5×S3C2 ⊆ Aut C23240C2^3.24(S3xC10)480,1155
C23.25(S3×C10) = C5×C12.48D4φ: S3×C10/C30C2 ⊆ Aut C23240C2^3.25(S3xC10)480,803
C23.26(S3×C10) = C5×C23.26D6φ: S3×C10/C30C2 ⊆ Aut C23240C2^3.26(S3xC10)480,805
C23.27(S3×C10) = C20×C3⋊D4φ: S3×C10/C30C2 ⊆ Aut C23240C2^3.27(S3xC10)480,807
C23.28(S3×C10) = C5×C23.28D6φ: S3×C10/C30C2 ⊆ Aut C23240C2^3.28(S3xC10)480,808
C23.29(S3×C10) = C5×C127D4φ: S3×C10/C30C2 ⊆ Aut C23240C2^3.29(S3xC10)480,809
C23.30(S3×C10) = C5×C244S3φ: S3×C10/C30C2 ⊆ Aut C23120C2^3.30(S3xC10)480,832
C23.31(S3×C10) = C10×C4○D12φ: S3×C10/C30C2 ⊆ Aut C23240C2^3.31(S3xC10)480,1153
C23.32(S3×C10) = C5×C6.C42central extension (φ=1)480C2^3.32(S3xC10)480,150
C23.33(S3×C10) = Dic3×C2×C20central extension (φ=1)480C2^3.33(S3xC10)480,801
C23.34(S3×C10) = C10×Dic3⋊C4central extension (φ=1)480C2^3.34(S3xC10)480,802
C23.35(S3×C10) = C10×C4⋊Dic3central extension (φ=1)480C2^3.35(S3xC10)480,804
C23.36(S3×C10) = C10×D6⋊C4central extension (φ=1)240C2^3.36(S3xC10)480,806
C23.37(S3×C10) = C10×C6.D4central extension (φ=1)240C2^3.37(S3xC10)480,831
C23.38(S3×C10) = C2×C10×Dic6central extension (φ=1)480C2^3.38(S3xC10)480,1150
C23.39(S3×C10) = S3×C22×C20central extension (φ=1)240C2^3.39(S3xC10)480,1151
C23.40(S3×C10) = C2×C10×D12central extension (φ=1)240C2^3.40(S3xC10)480,1152
C23.41(S3×C10) = Dic3×C22×C10central extension (φ=1)480C2^3.41(S3xC10)480,1163

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