# Extensions 1→N→G→Q→1 with N=C23 and Q=S3×D5

Direct product G=N×Q with N=C23 and Q=S3×D5
dρLabelID
S3×C23×D5120S3xC2^3xD5480,1207

Semidirect products G=N:Q with N=C23 and Q=S3×D5
extensionφ:Q→Aut NdρLabelID
C23⋊(S3×D5) = C2×D5×S4φ: S3×D5/D5S3 ⊆ Aut C23306+C2^3:(S3xD5)480,1193
C232(S3×D5) = D308D4φ: S3×D5/C15C22 ⊆ Aut C23120C2^3:2(S3xD5)480,653
C233(S3×D5) = C15⋊2+ 1+4φ: S3×D5/C15C22 ⊆ Aut C231204C2^3:3(S3xD5)480,1125
C234(S3×D5) = C2×S3×C5⋊D4φ: S3×D5/C5×S3C2 ⊆ Aut C23120C2^3:4(S3xD5)480,1123
C235(S3×D5) = C2×D5×C3⋊D4φ: S3×D5/C3×D5C2 ⊆ Aut C23120C2^3:5(S3xD5)480,1122
C236(S3×D5) = C2×D10⋊D6φ: S3×D5/D15C2 ⊆ Aut C23120C2^3:6(S3xD5)480,1124

Non-split extensions G=N.Q with N=C23 and Q=S3×D5
extensionφ:Q→Aut NdρLabelID
C23.1(S3×D5) = A4⋊Dic10φ: S3×D5/D5S3 ⊆ Aut C231206-C2^3.1(S3xD5)480,975
C23.2(S3×D5) = Dic5×S4φ: S3×D5/D5S3 ⊆ Aut C23606-C2^3.2(S3xD5)480,976
C23.3(S3×D5) = Dic52S4φ: S3×D5/D5S3 ⊆ Aut C23606C2^3.3(S3xD5)480,977
C23.4(S3×D5) = Dic5⋊S4φ: S3×D5/D5S3 ⊆ Aut C23606C2^3.4(S3xD5)480,978
C23.5(S3×D5) = D5×A4⋊C4φ: S3×D5/D5S3 ⊆ Aut C23606C2^3.5(S3xD5)480,979
C23.6(S3×D5) = D10⋊S4φ: S3×D5/D5S3 ⊆ Aut C23606C2^3.6(S3xD5)480,980
C23.7(S3×D5) = A4⋊D20φ: S3×D5/D5S3 ⊆ Aut C23606+C2^3.7(S3xD5)480,981
C23.8(S3×D5) = (C2×C6).D20φ: S3×D5/C15C22 ⊆ Aut C231204C2^3.8(S3xD5)480,71
C23.9(S3×D5) = C158(C23⋊C4)φ: S3×D5/C15C22 ⊆ Aut C231204C2^3.9(S3xD5)480,72
C23.10(S3×D5) = C159(C23⋊C4)φ: S3×D5/C15C22 ⊆ Aut C231204C2^3.10(S3xD5)480,73
C23.11(S3×D5) = C23.D5⋊S3φ: S3×D5/C15C22 ⊆ Aut C23240C2^3.11(S3xD5)480,601
C23.12(S3×D5) = Dic15.19D4φ: S3×D5/C15C22 ⊆ Aut C23240C2^3.12(S3xD5)480,602
C23.13(S3×D5) = C23.13(S3×D5)φ: S3×D5/C15C22 ⊆ Aut C23240C2^3.13(S3xD5)480,606
C23.14(S3×D5) = C23.14(S3×D5)φ: S3×D5/C15C22 ⊆ Aut C23240C2^3.14(S3xD5)480,607
C23.15(S3×D5) = D306D4φ: S3×D5/C15C22 ⊆ Aut C23240C2^3.15(S3xD5)480,609
C23.16(S3×D5) = C6.(D4×D5)φ: S3×D5/C15C22 ⊆ Aut C23240C2^3.16(S3xD5)480,610
C23.17(S3×D5) = C23.17(S3×D5)φ: S3×D5/C15C22 ⊆ Aut C23240C2^3.17(S3xD5)480,624
C23.18(S3×D5) = (C6×D5)⋊D4φ: S3×D5/C15C22 ⊆ Aut C23240C2^3.18(S3xD5)480,625
C23.19(S3×D5) = Dic153D4φ: S3×D5/C15C22 ⊆ Aut C23240C2^3.19(S3xD5)480,626
C23.20(S3×D5) = (S3×C10).D4φ: S3×D5/C15C22 ⊆ Aut C23240C2^3.20(S3xD5)480,631
C23.21(S3×D5) = D307D4φ: S3×D5/C15C22 ⊆ Aut C23240C2^3.21(S3xD5)480,633
C23.22(S3×D5) = Dic154D4φ: S3×D5/C15C22 ⊆ Aut C23240C2^3.22(S3xD5)480,634
C23.23(S3×D5) = D30.16D4φ: S3×D5/C15C22 ⊆ Aut C23240C2^3.23(S3xD5)480,638
C23.24(S3×D5) = (S3×C10)⋊D4φ: S3×D5/C15C22 ⊆ Aut C23240C2^3.24(S3xD5)480,641
C23.25(S3×D5) = Dic155D4φ: S3×D5/C15C22 ⊆ Aut C23240C2^3.25(S3xD5)480,643
C23.26(S3×D5) = C23.26(S3×D5)φ: S3×D5/C5×S3C2 ⊆ Aut C23240C2^3.26(S3xD5)480,605
C23.27(S3×D5) = (C2×C30).D4φ: S3×D5/C5×S3C2 ⊆ Aut C23240C2^3.27(S3xD5)480,612
C23.28(S3×D5) = C10.(C2×D12)φ: S3×D5/C5×S3C2 ⊆ Aut C23240C2^3.28(S3xD5)480,618
C23.29(S3×D5) = Dic3×C5⋊D4φ: S3×D5/C5×S3C2 ⊆ Aut C23240C2^3.29(S3xD5)480,629
C23.30(S3×D5) = S3×C23.D5φ: S3×D5/C5×S3C2 ⊆ Aut C23120C2^3.30(S3xD5)480,630
C23.31(S3×D5) = C1528(C4×D4)φ: S3×D5/C5×S3C2 ⊆ Aut C23240C2^3.31(S3xD5)480,632
C23.32(S3×D5) = C15⋊C22≀C2φ: S3×D5/C5×S3C2 ⊆ Aut C23120C2^3.32(S3xD5)480,644
C23.33(S3×D5) = (C2×C6)⋊D20φ: S3×D5/C5×S3C2 ⊆ Aut C23240C2^3.33(S3xD5)480,645
C23.34(S3×D5) = (C2×C10)⋊11D12φ: S3×D5/C5×S3C2 ⊆ Aut C23120C2^3.34(S3xD5)480,646
C23.35(S3×D5) = (C2×C10)⋊8Dic6φ: S3×D5/C5×S3C2 ⊆ Aut C23240C2^3.35(S3xD5)480,651
C23.36(S3×D5) = C2×Dic5.D6φ: S3×D5/C5×S3C2 ⊆ Aut C23240C2^3.36(S3xD5)480,1113
C23.37(S3×D5) = (C6×Dic5)⋊7C4φ: S3×D5/C3×D5C2 ⊆ Aut C23240C2^3.37(S3xD5)480,604
C23.38(S3×D5) = C30.(C2×D4)φ: S3×D5/C3×D5C2 ⊆ Aut C23240C2^3.38(S3xD5)480,615
C23.39(S3×D5) = C6.D4⋊D5φ: S3×D5/C3×D5C2 ⊆ Aut C23240C2^3.39(S3xD5)480,622
C23.40(S3×D5) = D5×C6.D4φ: S3×D5/C3×D5C2 ⊆ Aut C23120C2^3.40(S3xD5)480,623
C23.41(S3×D5) = Dic5×C3⋊D4φ: S3×D5/C3×D5C2 ⊆ Aut C23240C2^3.41(S3xD5)480,627
C23.42(S3×D5) = C1526(C4×D4)φ: S3×D5/C3×D5C2 ⊆ Aut C23240C2^3.42(S3xD5)480,628
C23.43(S3×D5) = (C2×C30)⋊D4φ: S3×D5/C3×D5C2 ⊆ Aut C23120C2^3.43(S3xD5)480,639
C23.44(S3×D5) = (C2×C6)⋊8D20φ: S3×D5/C3×D5C2 ⊆ Aut C23120C2^3.44(S3xD5)480,640
C23.45(S3×D5) = (C2×C10)⋊4D12φ: S3×D5/C3×D5C2 ⊆ Aut C23240C2^3.45(S3xD5)480,642
C23.46(S3×D5) = (C2×C30)⋊Q8φ: S3×D5/C3×D5C2 ⊆ Aut C23240C2^3.46(S3xD5)480,650
C23.47(S3×D5) = C2×Dic3.D10φ: S3×D5/C3×D5C2 ⊆ Aut C23240C2^3.47(S3xD5)480,1116
C23.48(S3×D5) = C23.48(S3×D5)φ: S3×D5/D15C2 ⊆ Aut C23240C2^3.48(S3xD5)480,608
C23.49(S3×D5) = C6.(C2×D20)φ: S3×D5/D15C2 ⊆ Aut C23240C2^3.49(S3xD5)480,613
C23.50(S3×D5) = (C2×C10).D12φ: S3×D5/D15C2 ⊆ Aut C23240C2^3.50(S3xD5)480,619
C23.51(S3×D5) = Dic1516D4φ: S3×D5/D15C2 ⊆ Aut C23240C2^3.51(S3xD5)480,635
C23.52(S3×D5) = Dic1517D4φ: S3×D5/D15C2 ⊆ Aut C23240C2^3.52(S3xD5)480,636
C23.53(S3×D5) = D30.45D4φ: S3×D5/D15C2 ⊆ Aut C23120C2^3.53(S3xD5)480,637
C23.54(S3×D5) = Dic1518D4φ: S3×D5/D15C2 ⊆ Aut C23240C2^3.54(S3xD5)480,647
C23.55(S3×D5) = D3018D4φ: S3×D5/D15C2 ⊆ Aut C23120C2^3.55(S3xD5)480,648
C23.56(S3×D5) = D3019D4φ: S3×D5/D15C2 ⊆ Aut C23120C2^3.56(S3xD5)480,649
C23.57(S3×D5) = Dic15.48D4φ: S3×D5/D15C2 ⊆ Aut C23240C2^3.57(S3xD5)480,652
C23.58(S3×D5) = C2×C30.C23φ: S3×D5/D15C2 ⊆ Aut C23240C2^3.58(S3xD5)480,1114
C23.59(S3×D5) = C30.24C42central extension (φ=1)480C2^3.59(S3xD5)480,70
C23.60(S3×D5) = C2×Dic3×Dic5central extension (φ=1)480C2^3.60(S3xD5)480,603
C23.61(S3×D5) = C2×D10⋊Dic3central extension (φ=1)240C2^3.61(S3xD5)480,611
C23.62(S3×D5) = C2×D6⋊Dic5central extension (φ=1)240C2^3.62(S3xD5)480,614
C23.63(S3×D5) = C2×D304C4central extension (φ=1)240C2^3.63(S3xD5)480,616
C23.64(S3×D5) = C2×C30.Q8central extension (φ=1)480C2^3.64(S3xD5)480,617
C23.65(S3×D5) = C2×Dic155C4central extension (φ=1)480C2^3.65(S3xD5)480,620
C23.66(S3×D5) = C2×C6.Dic10central extension (φ=1)480C2^3.66(S3xD5)480,621
C23.67(S3×D5) = C22×D5×Dic3central extension (φ=1)240C2^3.67(S3xD5)480,1112
C23.68(S3×D5) = C22×S3×Dic5central extension (φ=1)240C2^3.68(S3xD5)480,1115
C23.69(S3×D5) = C22×D30.C2central extension (φ=1)240C2^3.69(S3xD5)480,1117
C23.70(S3×D5) = C22×C15⋊D4central extension (φ=1)240C2^3.70(S3xD5)480,1118
C23.71(S3×D5) = C22×C3⋊D20central extension (φ=1)240C2^3.71(S3xD5)480,1119
C23.72(S3×D5) = C22×C5⋊D12central extension (φ=1)240C2^3.72(S3xD5)480,1120
C23.73(S3×D5) = C22×C15⋊Q8central extension (φ=1)480C2^3.73(S3xD5)480,1121

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