# Extensions 1→N→G→Q→1 with N=C23 and Q=C6×D5

Direct product G=N×Q with N=C23 and Q=C6×D5
dρLabelID
D5×C23×C6240D5xC2^3xC6480,1210

Semidirect products G=N:Q with N=C23 and Q=C6×D5
extensionφ:Q→Aut NdρLabelID
C231(C6×D5) = C3×C23⋊D10φ: C6×D5/C15C22 ⊆ Aut C23120C2^3:1(C6xD5)480,730
C232(C6×D5) = C3×D46D10φ: C6×D5/C15C22 ⊆ Aut C231204C2^3:2(C6xD5)480,1141
C233(C6×D5) = C22×D5×A4φ: C6×D5/D10C3 ⊆ Aut C2360C2^3:3(C6xD5)480,1202
C234(C6×D5) = C6×D4×D5φ: C6×D5/C3×D5C2 ⊆ Aut C23120C2^3:4(C6xD5)480,1139
C235(C6×D5) = C2×C6×C5⋊D4φ: C6×D5/C30C2 ⊆ Aut C23240C2^3:5(C6xD5)480,1149

Non-split extensions G=N.Q with N=C23 and Q=C6×D5
extensionφ:Q→Aut NdρLabelID
C23.1(C6×D5) = C3×C23.1D10φ: C6×D5/C15C22 ⊆ Aut C231204C2^3.1(C6xD5)480,84
C23.2(C6×D5) = C3×C23⋊Dic5φ: C6×D5/C15C22 ⊆ Aut C231204C2^3.2(C6xD5)480,112
C23.3(C6×D5) = C3×C23.D10φ: C6×D5/C15C22 ⊆ Aut C23240C2^3.3(C6xD5)480,672
C23.4(C6×D5) = C3×D10.12D4φ: C6×D5/C15C22 ⊆ Aut C23240C2^3.4(C6xD5)480,676
C23.5(C6×D5) = C3×D10⋊D4φ: C6×D5/C15C22 ⊆ Aut C23240C2^3.5(C6xD5)480,677
C23.6(C6×D5) = C3×Dic5.5D4φ: C6×D5/C15C22 ⊆ Aut C23240C2^3.6(C6xD5)480,678
C23.7(C6×D5) = C3×C20.17D4φ: C6×D5/C15C22 ⊆ Aut C23240C2^3.7(C6xD5)480,729
C23.8(C6×D5) = C3×C202D4φ: C6×D5/C15C22 ⊆ Aut C23240C2^3.8(C6xD5)480,731
C23.9(C6×D5) = C3×C20⋊D4φ: C6×D5/C15C22 ⊆ Aut C23240C2^3.9(C6xD5)480,733
C23.10(C6×D5) = A4×Dic10φ: C6×D5/D10C3 ⊆ Aut C231206-C2^3.10(C6xD5)480,1035
C23.11(C6×D5) = C4×D5×A4φ: C6×D5/D10C3 ⊆ Aut C23606C2^3.11(C6xD5)480,1036
C23.12(C6×D5) = A4×D20φ: C6×D5/D10C3 ⊆ Aut C23606+C2^3.12(C6xD5)480,1037
C23.13(C6×D5) = C2×A4×Dic5φ: C6×D5/D10C3 ⊆ Aut C23120C2^3.13(C6xD5)480,1044
C23.14(C6×D5) = A4×C5⋊D4φ: C6×D5/D10C3 ⊆ Aut C23606C2^3.14(C6xD5)480,1045
C23.15(C6×D5) = C3×C23.11D10φ: C6×D5/C3×D5C2 ⊆ Aut C23240C2^3.15(C6xD5)480,670
C23.16(C6×D5) = C3×Dic5.14D4φ: C6×D5/C3×D5C2 ⊆ Aut C23240C2^3.16(C6xD5)480,671
C23.17(C6×D5) = C3×D5×C22⋊C4φ: C6×D5/C3×D5C2 ⊆ Aut C23120C2^3.17(C6xD5)480,673
C23.18(C6×D5) = C3×Dic54D4φ: C6×D5/C3×D5C2 ⊆ Aut C23240C2^3.18(C6xD5)480,674
C23.19(C6×D5) = C3×C22⋊D20φ: C6×D5/C3×D5C2 ⊆ Aut C23120C2^3.19(C6xD5)480,675
C23.20(C6×D5) = C3×C22.D20φ: C6×D5/C3×D5C2 ⊆ Aut C23240C2^3.20(C6xD5)480,679
C23.21(C6×D5) = C3×D4×Dic5φ: C6×D5/C3×D5C2 ⊆ Aut C23240C2^3.21(C6xD5)480,727
C23.22(C6×D5) = C3×C23.18D10φ: C6×D5/C3×D5C2 ⊆ Aut C23240C2^3.22(C6xD5)480,728
C23.23(C6×D5) = C3×Dic5⋊D4φ: C6×D5/C3×D5C2 ⊆ Aut C23240C2^3.23(C6xD5)480,732
C23.24(C6×D5) = C6×D42D5φ: C6×D5/C3×D5C2 ⊆ Aut C23240C2^3.24(C6xD5)480,1140
C23.25(C6×D5) = C3×C20.48D4φ: C6×D5/C30C2 ⊆ Aut C23240C2^3.25(C6xD5)480,717
C23.26(C6×D5) = C3×C23.21D10φ: C6×D5/C30C2 ⊆ Aut C23240C2^3.26(C6xD5)480,719
C23.27(C6×D5) = C12×C5⋊D4φ: C6×D5/C30C2 ⊆ Aut C23240C2^3.27(C6xD5)480,721
C23.28(C6×D5) = C3×C23.23D10φ: C6×D5/C30C2 ⊆ Aut C23240C2^3.28(C6xD5)480,722
C23.29(C6×D5) = C3×C207D4φ: C6×D5/C30C2 ⊆ Aut C23240C2^3.29(C6xD5)480,723
C23.30(C6×D5) = C3×C242D5φ: C6×D5/C30C2 ⊆ Aut C23120C2^3.30(C6xD5)480,746
C23.31(C6×D5) = C6×C4○D20φ: C6×D5/C30C2 ⊆ Aut C23240C2^3.31(C6xD5)480,1138
C23.32(C6×D5) = C3×C10.10C42central extension (φ=1)480C2^3.32(C6xD5)480,109
C23.33(C6×D5) = Dic5×C2×C12central extension (φ=1)480C2^3.33(C6xD5)480,715
C23.34(C6×D5) = C6×C10.D4central extension (φ=1)480C2^3.34(C6xD5)480,716
C23.35(C6×D5) = C6×C4⋊Dic5central extension (φ=1)480C2^3.35(C6xD5)480,718
C23.36(C6×D5) = C6×D10⋊C4central extension (φ=1)240C2^3.36(C6xD5)480,720
C23.37(C6×D5) = C6×C23.D5central extension (φ=1)240C2^3.37(C6xD5)480,745
C23.38(C6×D5) = C2×C6×Dic10central extension (φ=1)480C2^3.38(C6xD5)480,1135
C23.39(C6×D5) = D5×C22×C12central extension (φ=1)240C2^3.39(C6xD5)480,1136
C23.40(C6×D5) = C2×C6×D20central extension (φ=1)240C2^3.40(C6xD5)480,1137
C23.41(C6×D5) = Dic5×C22×C6central extension (φ=1)480C2^3.41(C6xD5)480,1148

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