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Extensions 1→N→G→Q→1 with N=C10 and Q=C23⋊C4

Direct product G=N×Q with N=C10 and Q=C23⋊C4
dρLabelID
C10×C23⋊C480C10xC2^3:C4320,910

Semidirect products G=N:Q with N=C10 and Q=C23⋊C4
extensionφ:Q→Aut NdρLabelID
C10⋊1(C23⋊C4) = C2×D10.D4φ: C23⋊C4/C2×C4 → C4 ⊆ Aut C1080C10:1(C2^3:C4)320,1082
C10⋊2(C23⋊C4) = C2×C23⋊F5φ: C23⋊C4/C23 → C4 ⊆ Aut C1080C10:2(C2^3:C4)320,1134
C10⋊3(C23⋊C4) = C2×C23.1D10φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C1080C10:3(C2^3:C4)320,581
C10⋊4(C23⋊C4) = C2×C23⋊Dic5φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C1080C10:4(C2^3:C4)320,846

Non-split extensions G=N.Q with N=C10 and Q=C23⋊C4
extensionφ:Q→Aut NdρLabelID
C10.1(C23⋊C4) = C42⋊F5φ: C23⋊C4/C2×C4 → C4 ⊆ Aut C10404+C10.1(C2^3:C4)320,191
C10.2(C23⋊C4) = C42⋊2F5φ: C23⋊C4/C2×C4 → C4 ⊆ Aut C10804C10.2(C2^3:C4)320,192
C10.3(C23⋊C4) = C42.F5φ: C23⋊C4/C2×C4 → C4 ⊆ Aut C10804-C10.3(C2^3:C4)320,193
C10.4(C23⋊C4) = C42.2F5φ: C23⋊C4/C2×C4 → C4 ⊆ Aut C10804C10.4(C2^3:C4)320,194
C10.5(C23⋊C4) = C5⋊C2≀C4φ: C23⋊C4/C2×C4 → C4 ⊆ Aut C10408+C10.5(C2^3:C4)320,202
C10.6(C23⋊C4) = C22⋊C4⋊F5φ: C23⋊C4/C2×C4 → C4 ⊆ Aut C10808-C10.6(C2^3:C4)320,203
C10.7(C23⋊C4) = D10.1D8φ: C23⋊C4/C2×C4 → C4 ⊆ Aut C1080C10.7(C2^3:C4)320,206
C10.8(C23⋊C4) = D10.1Q16φ: C23⋊C4/C2×C4 → C4 ⊆ Aut C1080C10.8(C2^3:C4)320,207
C10.9(C23⋊C4) = (C2×C20)⋊1C8φ: C23⋊C4/C2×C4 → C4 ⊆ Aut C10160C10.9(C2^3:C4)320,251
C10.10(C23⋊C4) = C5⋊(C23⋊C8)φ: C23⋊C4/C2×C4 → C4 ⊆ Aut C1080C10.10(C2^3:C4)320,253
C10.11(C23⋊C4) = C22⋊F5⋊C4φ: C23⋊C4/C2×C4 → C4 ⊆ Aut C1080C10.11(C2^3:C4)320,255
C10.12(C23⋊C4) = (C22×C4).F5φ: C23⋊C4/C23 → C4 ⊆ Aut C10160C10.12(C2^3:C4)320,252
C10.13(C23⋊C4) = (C22×C4)⋊F5φ: C23⋊C4/C23 → C4 ⊆ Aut C10804C10.13(C2^3:C4)320,254
C10.14(C23⋊C4) = D10.SD16φ: C23⋊C4/C23 → C4 ⊆ Aut C1080C10.14(C2^3:C4)320,258
C10.15(C23⋊C4) = (C2×D4)⋊F5φ: C23⋊C4/C23 → C4 ⊆ Aut C10408+C10.15(C2^3:C4)320,260
C10.16(C23⋊C4) = (D4×C10).C4φ: C23⋊C4/C23 → C4 ⊆ Aut C10808-C10.16(C2^3:C4)320,261
C10.17(C23⋊C4) = D10.Q16φ: C23⋊C4/C23 → C4 ⊆ Aut C1080C10.17(C2^3:C4)320,264
C10.18(C23⋊C4) = (C2×Q8)⋊F5φ: C23⋊C4/C23 → C4 ⊆ Aut C10808+C10.18(C2^3:C4)320,266
C10.19(C23⋊C4) = (Q8×C10).C4φ: C23⋊C4/C23 → C4 ⊆ Aut C10808-C10.19(C2^3:C4)320,267
C10.20(C23⋊C4) = C24.F5φ: C23⋊C4/C23 → C4 ⊆ Aut C1080C10.20(C2^3:C4)320,271
C10.21(C23⋊C4) = C24⋊2F5φ: C23⋊C4/C23 → C4 ⊆ Aut C10404C10.21(C2^3:C4)320,272
C10.22(C23⋊C4) = (C2×D20)⋊C4φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C1080C10.22(C2^3:C4)320,9
C10.23(C23⋊C4) = C4⋊Dic5⋊C4φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C1080C10.23(C2^3:C4)320,10
C10.24(C23⋊C4) = C23.30D20φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C1080C10.24(C2^3:C4)320,25
C10.25(C23⋊C4) = C5⋊3(C23⋊C8)φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C1080C10.25(C2^3:C4)320,26
C10.26(C23⋊C4) = (C2×Dic5)⋊C8φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C10160C10.26(C2^3:C4)320,27
C10.27(C23⋊C4) = C22.2D40φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C1080C10.27(C2^3:C4)320,28
C10.28(C23⋊C4) = C5⋊3C2≀C4φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C10408+C10.28(C2^3:C4)320,29
C10.29(C23⋊C4) = (C2×C20).D4φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C10808-C10.29(C2^3:C4)320,30
C10.30(C23⋊C4) = C23.D20φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C10808-C10.30(C2^3:C4)320,31
C10.31(C23⋊C4) = C23.2D20φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C10408+C10.31(C2^3:C4)320,32
C10.32(C23⋊C4) = C23.3D20φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C10408+C10.32(C2^3:C4)320,33
C10.33(C23⋊C4) = C23.4D20φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C10808-C10.33(C2^3:C4)320,34
C10.34(C23⋊C4) = (C2×C4).D20φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C10808+C10.34(C2^3:C4)320,35
C10.35(C23⋊C4) = (C2×Q8).D10φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C10808-C10.35(C2^3:C4)320,36
C10.36(C23⋊C4) = C24.2D10φ: C23⋊C4/C22⋊C4 → C2 ⊆ Aut C1080C10.36(C2^3:C4)320,85
C10.37(C23⋊C4) = C24.Dic5φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C1080C10.37(C2^3:C4)320,83
C10.38(C23⋊C4) = C24.D10φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C1080C10.38(C2^3:C4)320,84
C10.39(C23⋊C4) = (C2×C20)⋊C8φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C10160C10.39(C2^3:C4)320,86
C10.40(C23⋊C4) = C24⋊2Dic5φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C10404C10.40(C2^3:C4)320,94
C10.41(C23⋊C4) = C4⋊C4⋊Dic5φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C1080C10.41(C2^3:C4)320,95
C10.42(C23⋊C4) = C10.29C4≀C2φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C1080C10.42(C2^3:C4)320,96
C10.43(C23⋊C4) = (C22×C20)⋊C4φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C10804C10.43(C2^3:C4)320,97
C10.44(C23⋊C4) = C42⋊Dic5φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C10804C10.44(C2^3:C4)320,99
C10.45(C23⋊C4) = C42.Dic5φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C10804C10.45(C2^3:C4)320,100
C10.46(C23⋊C4) = C42⋊3Dic5φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C10404C10.46(C2^3:C4)320,103
C10.47(C23⋊C4) = C42.3Dic5φ: C23⋊C4/C2×D4 → C2 ⊆ Aut C10804C10.47(C2^3:C4)320,106
C10.48(C23⋊C4) = C5×C23⋊C8central extension (φ=1)80C10.48(C2^3:C4)320,128
C10.49(C23⋊C4) = C5×C22.M4(2)central extension (φ=1)160C10.49(C2^3:C4)320,129
C10.50(C23⋊C4) = C5×C22.SD16central extension (φ=1)80C10.50(C2^3:C4)320,132
C10.51(C23⋊C4) = C5×C23.31D4central extension (φ=1)80C10.51(C2^3:C4)320,133
C10.52(C23⋊C4) = C5×C23.9D4central extension (φ=1)80C10.52(C2^3:C4)320,147
C10.53(C23⋊C4) = C5×C2≀C4central extension (φ=1)404C10.53(C2^3:C4)320,156
C10.54(C23⋊C4) = C5×C23.D4central extension (φ=1)804C10.54(C2^3:C4)320,157
C10.55(C23⋊C4) = C5×C42⋊C4central extension (φ=1)404C10.55(C2^3:C4)320,158
C10.56(C23⋊C4) = C5×C42⋊3C4central extension (φ=1)804C10.56(C2^3:C4)320,159
C10.57(C23⋊C4) = C5×C42.C4central extension (φ=1)804C10.57(C2^3:C4)320,160
C10.58(C23⋊C4) = C5×C42.3C4central extension (φ=1)804C10.58(C2^3:C4)320,161

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