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

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

Semidirect products G=N:Q with N=C10 and Q=S3×C23
extensionφ:Q→Aut NdρLabelID
C101(S3×C23) = S3×C23×D5φ: S3×C23/C22×S3C2 ⊆ Aut C10120C10:1(S3xC2^3)480,1207
C102(S3×C23) = C24×D15φ: S3×C23/C22×C6C2 ⊆ Aut C10240C10:2(S3xC2^3)480,1212

Non-split extensions G=N.Q with N=C10 and Q=S3×C23
extensionφ:Q→Aut NdρLabelID
C10.1(S3×C23) = C2×D5×Dic6φ: S3×C23/C22×S3C2 ⊆ Aut C10240C10.1(S3xC2^3)480,1073
C10.2(S3×C23) = C2×D205S3φ: S3×C23/C22×S3C2 ⊆ Aut C10240C10.2(S3xC2^3)480,1074
C10.3(S3×C23) = C2×D20⋊S3φ: S3×C23/C22×S3C2 ⊆ Aut C10240C10.3(S3xC2^3)480,1075
C10.4(S3×C23) = D20.38D6φ: S3×C23/C22×S3C2 ⊆ Aut C102404C10.4(S3xC2^3)480,1076
C10.5(S3×C23) = D20.39D6φ: S3×C23/C22×S3C2 ⊆ Aut C102404-C10.5(S3xC2^3)480,1077
C10.6(S3×C23) = C2×S3×Dic10φ: S3×C23/C22×S3C2 ⊆ Aut C10240C10.6(S3xC2^3)480,1078
C10.7(S3×C23) = C2×D12⋊D5φ: S3×C23/C22×S3C2 ⊆ Aut C10240C10.7(S3xC2^3)480,1079
C10.8(S3×C23) = C30.C24φ: S3×C23/C22×S3C2 ⊆ Aut C102404C10.8(S3xC2^3)480,1080
C10.9(S3×C23) = C2×D60⋊C2φ: S3×C23/C22×S3C2 ⊆ Aut C10240C10.9(S3xC2^3)480,1081
C10.10(S3×C23) = C2×D15⋊Q8φ: S3×C23/C22×S3C2 ⊆ Aut C10240C10.10(S3xC2^3)480,1082
C10.11(S3×C23) = C2×D6.D10φ: S3×C23/C22×S3C2 ⊆ Aut C10240C10.11(S3xC2^3)480,1083
C10.12(S3×C23) = C2×D125D5φ: S3×C23/C22×S3C2 ⊆ Aut C10240C10.12(S3xC2^3)480,1084
C10.13(S3×C23) = C2×C12.28D10φ: S3×C23/C22×S3C2 ⊆ Aut C10240C10.13(S3xC2^3)480,1085
C10.14(S3×C23) = S3×C2×C4×D5φ: S3×C23/C22×S3C2 ⊆ Aut C10120C10.14(S3xC2^3)480,1086
C10.15(S3×C23) = C2×D5×D12φ: S3×C23/C22×S3C2 ⊆ Aut C10120C10.15(S3xC2^3)480,1087
C10.16(S3×C23) = C2×S3×D20φ: S3×C23/C22×S3C2 ⊆ Aut C10120C10.16(S3xC2^3)480,1088
C10.17(S3×C23) = C2×C20⋊D6φ: S3×C23/C22×S3C2 ⊆ Aut C10120C10.17(S3xC2^3)480,1089
C10.18(S3×C23) = D5×C4○D12φ: S3×C23/C22×S3C2 ⊆ Aut C101204C10.18(S3xC2^3)480,1090
C10.19(S3×C23) = S3×C4○D20φ: S3×C23/C22×S3C2 ⊆ Aut C101204C10.19(S3xC2^3)480,1091
C10.20(S3×C23) = D2024D6φ: S3×C23/C22×S3C2 ⊆ Aut C101204C10.20(S3xC2^3)480,1092
C10.21(S3×C23) = D2025D6φ: S3×C23/C22×S3C2 ⊆ Aut C101204C10.21(S3xC2^3)480,1093
C10.22(S3×C23) = D2026D6φ: S3×C23/C22×S3C2 ⊆ Aut C101204C10.22(S3xC2^3)480,1094
C10.23(S3×C23) = D2029D6φ: S3×C23/C22×S3C2 ⊆ Aut C101204+C10.23(S3xC2^3)480,1095
C10.24(S3×C23) = C15⋊2- 1+4φ: S3×C23/C22×S3C2 ⊆ Aut C102408-C10.24(S3xC2^3)480,1096
C10.25(S3×C23) = S3×D4×D5φ: S3×C23/C22×S3C2 ⊆ Aut C10608+C10.25(S3xC2^3)480,1097
C10.26(S3×C23) = D5×D42S3φ: S3×C23/C22×S3C2 ⊆ Aut C101208-C10.26(S3xC2^3)480,1098
C10.27(S3×C23) = S3×D42D5φ: S3×C23/C22×S3C2 ⊆ Aut C101208-C10.27(S3xC2^3)480,1099
C10.28(S3×C23) = D30.C23φ: S3×C23/C22×S3C2 ⊆ Aut C101208+C10.28(S3xC2^3)480,1100
C10.29(S3×C23) = D2013D6φ: S3×C23/C22×S3C2 ⊆ Aut C101208-C10.29(S3xC2^3)480,1101
C10.30(S3×C23) = D2014D6φ: S3×C23/C22×S3C2 ⊆ Aut C101208+C10.30(S3xC2^3)480,1102
C10.31(S3×C23) = D1214D10φ: S3×C23/C22×S3C2 ⊆ Aut C101208+C10.31(S3xC2^3)480,1103
C10.32(S3×C23) = D20.29D6φ: S3×C23/C22×S3C2 ⊆ Aut C102408-C10.32(S3xC2^3)480,1104
C10.33(S3×C23) = C30.33C24φ: S3×C23/C22×S3C2 ⊆ Aut C102408+C10.33(S3xC2^3)480,1105
C10.34(S3×C23) = D12.29D10φ: S3×C23/C22×S3C2 ⊆ Aut C102408-C10.34(S3xC2^3)480,1106
C10.35(S3×C23) = S3×Q8×D5φ: S3×C23/C22×S3C2 ⊆ Aut C101208-C10.35(S3xC2^3)480,1107
C10.36(S3×C23) = D5×Q83S3φ: S3×C23/C22×S3C2 ⊆ Aut C101208+C10.36(S3xC2^3)480,1108
C10.37(S3×C23) = S3×Q82D5φ: S3×C23/C22×S3C2 ⊆ Aut C101208+C10.37(S3xC2^3)480,1109
C10.38(S3×C23) = D2016D6φ: S3×C23/C22×S3C2 ⊆ Aut C101208-C10.38(S3xC2^3)480,1110
C10.39(S3×C23) = D2017D6φ: S3×C23/C22×S3C2 ⊆ Aut C101208+C10.39(S3xC2^3)480,1111
C10.40(S3×C23) = C22×D5×Dic3φ: S3×C23/C22×S3C2 ⊆ Aut C10240C10.40(S3xC2^3)480,1112
C10.41(S3×C23) = C2×Dic5.D6φ: S3×C23/C22×S3C2 ⊆ Aut C10240C10.41(S3xC2^3)480,1113
C10.42(S3×C23) = C2×C30.C23φ: S3×C23/C22×S3C2 ⊆ Aut C10240C10.42(S3xC2^3)480,1114
C10.43(S3×C23) = C22×S3×Dic5φ: S3×C23/C22×S3C2 ⊆ Aut C10240C10.43(S3xC2^3)480,1115
C10.44(S3×C23) = C2×Dic3.D10φ: S3×C23/C22×S3C2 ⊆ Aut C10240C10.44(S3xC2^3)480,1116
C10.45(S3×C23) = C22×D30.C2φ: S3×C23/C22×S3C2 ⊆ Aut C10240C10.45(S3xC2^3)480,1117
C10.46(S3×C23) = C22×C15⋊D4φ: S3×C23/C22×S3C2 ⊆ Aut C10240C10.46(S3xC2^3)480,1118
C10.47(S3×C23) = C22×C3⋊D20φ: S3×C23/C22×S3C2 ⊆ Aut C10240C10.47(S3xC2^3)480,1119
C10.48(S3×C23) = C22×C5⋊D12φ: S3×C23/C22×S3C2 ⊆ Aut C10240C10.48(S3xC2^3)480,1120
C10.49(S3×C23) = C22×C15⋊Q8φ: S3×C23/C22×S3C2 ⊆ Aut C10480C10.49(S3xC2^3)480,1121
C10.50(S3×C23) = C2×D5×C3⋊D4φ: S3×C23/C22×S3C2 ⊆ Aut C10120C10.50(S3xC2^3)480,1122
C10.51(S3×C23) = C2×S3×C5⋊D4φ: S3×C23/C22×S3C2 ⊆ Aut C10120C10.51(S3xC2^3)480,1123
C10.52(S3×C23) = C2×D10⋊D6φ: S3×C23/C22×S3C2 ⊆ Aut C10120C10.52(S3xC2^3)480,1124
C10.53(S3×C23) = C15⋊2+ 1+4φ: S3×C23/C22×S3C2 ⊆ Aut C101204C10.53(S3xC2^3)480,1125
C10.54(S3×C23) = C22×Dic30φ: S3×C23/C22×C6C2 ⊆ Aut C10480C10.54(S3xC2^3)480,1165
C10.55(S3×C23) = C22×C4×D15φ: S3×C23/C22×C6C2 ⊆ Aut C10240C10.55(S3xC2^3)480,1166
C10.56(S3×C23) = C22×D60φ: S3×C23/C22×C6C2 ⊆ Aut C10240C10.56(S3xC2^3)480,1167
C10.57(S3×C23) = C2×D6011C2φ: S3×C23/C22×C6C2 ⊆ Aut C10240C10.57(S3xC2^3)480,1168
C10.58(S3×C23) = C2×D4×D15φ: S3×C23/C22×C6C2 ⊆ Aut C10120C10.58(S3xC2^3)480,1169
C10.59(S3×C23) = C2×D42D15φ: S3×C23/C22×C6C2 ⊆ Aut C10240C10.59(S3xC2^3)480,1170
C10.60(S3×C23) = D46D30φ: S3×C23/C22×C6C2 ⊆ Aut C101204C10.60(S3xC2^3)480,1171
C10.61(S3×C23) = C2×Q8×D15φ: S3×C23/C22×C6C2 ⊆ Aut C10240C10.61(S3xC2^3)480,1172
C10.62(S3×C23) = C2×Q83D15φ: S3×C23/C22×C6C2 ⊆ Aut C10240C10.62(S3xC2^3)480,1173
C10.63(S3×C23) = Q8.15D30φ: S3×C23/C22×C6C2 ⊆ Aut C102404C10.63(S3xC2^3)480,1174
C10.64(S3×C23) = C4○D4×D15φ: S3×C23/C22×C6C2 ⊆ Aut C101204C10.64(S3xC2^3)480,1175
C10.65(S3×C23) = D48D30φ: S3×C23/C22×C6C2 ⊆ Aut C101204+C10.65(S3xC2^3)480,1176
C10.66(S3×C23) = D4.10D30φ: S3×C23/C22×C6C2 ⊆ Aut C102404-C10.66(S3xC2^3)480,1177
C10.67(S3×C23) = C23×Dic15φ: S3×C23/C22×C6C2 ⊆ Aut C10480C10.67(S3xC2^3)480,1178
C10.68(S3×C23) = C22×C157D4φ: S3×C23/C22×C6C2 ⊆ Aut C10240C10.68(S3xC2^3)480,1179
C10.69(S3×C23) = C2×C10×Dic6central extension (φ=1)480C10.69(S3xC2^3)480,1150
C10.70(S3×C23) = S3×C22×C20central extension (φ=1)240C10.70(S3xC2^3)480,1151
C10.71(S3×C23) = C2×C10×D12central extension (φ=1)240C10.71(S3xC2^3)480,1152
C10.72(S3×C23) = C10×C4○D12central extension (φ=1)240C10.72(S3xC2^3)480,1153
C10.73(S3×C23) = S3×D4×C10central extension (φ=1)120C10.73(S3xC2^3)480,1154
C10.74(S3×C23) = C10×D42S3central extension (φ=1)240C10.74(S3xC2^3)480,1155
C10.75(S3×C23) = C5×D46D6central extension (φ=1)1204C10.75(S3xC2^3)480,1156
C10.76(S3×C23) = S3×Q8×C10central extension (φ=1)240C10.76(S3xC2^3)480,1157
C10.77(S3×C23) = C10×Q83S3central extension (φ=1)240C10.77(S3xC2^3)480,1158
C10.78(S3×C23) = C5×Q8.15D6central extension (φ=1)2404C10.78(S3xC2^3)480,1159
C10.79(S3×C23) = C5×S3×C4○D4central extension (φ=1)1204C10.79(S3xC2^3)480,1160
C10.80(S3×C23) = C5×D4○D12central extension (φ=1)1204C10.80(S3xC2^3)480,1161
C10.81(S3×C23) = C5×Q8○D12central extension (φ=1)2404C10.81(S3xC2^3)480,1162
C10.82(S3×C23) = Dic3×C22×C10central extension (φ=1)480C10.82(S3xC2^3)480,1163
C10.83(S3×C23) = C2×C10×C3⋊D4central extension (φ=1)240C10.83(S3xC2^3)480,1164

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