# Extensions 1→N→G→Q→1 with N=C30 and Q=C24

Direct product G=N×Q with N=C30 and Q=C24
dρLabelID
C24×C30480C2^4xC30480,1213

Semidirect products G=N:Q with N=C30 and Q=C24
extensionφ:Q→Aut NdρLabelID
C30⋊C24 = S3×C23×D5φ: C24/C22C22 ⊆ Aut C30120C30:C2^4480,1207
C302C24 = C24×D15φ: C24/C23C2 ⊆ Aut C30240C30:2C2^4480,1212
C303C24 = D5×C23×C6φ: C24/C23C2 ⊆ Aut C30240C30:3C2^4480,1210
C304C24 = S3×C23×C10φ: C24/C23C2 ⊆ Aut C30240C30:4C2^4480,1211

Non-split extensions G=N.Q with N=C30 and Q=C24
extensionφ:Q→Aut NdρLabelID
C30.1C24 = C2×D5×Dic6φ: C24/C22C22 ⊆ Aut C30240C30.1C2^4480,1073
C30.2C24 = C2×D205S3φ: C24/C22C22 ⊆ Aut C30240C30.2C2^4480,1074
C30.3C24 = C2×D20⋊S3φ: C24/C22C22 ⊆ Aut C30240C30.3C2^4480,1075
C30.4C24 = D20.38D6φ: C24/C22C22 ⊆ Aut C302404C30.4C2^4480,1076
C30.5C24 = D20.39D6φ: C24/C22C22 ⊆ Aut C302404-C30.5C2^4480,1077
C30.6C24 = C2×S3×Dic10φ: C24/C22C22 ⊆ Aut C30240C30.6C2^4480,1078
C30.7C24 = C2×D12⋊D5φ: C24/C22C22 ⊆ Aut C30240C30.7C2^4480,1079
C30.8C24 = C30.C24φ: C24/C22C22 ⊆ Aut C302404C30.8C2^4480,1080
C30.9C24 = C2×D60⋊C2φ: C24/C22C22 ⊆ Aut C30240C30.9C2^4480,1081
C30.10C24 = C2×D15⋊Q8φ: C24/C22C22 ⊆ Aut C30240C30.10C2^4480,1082
C30.11C24 = C2×D6.D10φ: C24/C22C22 ⊆ Aut C30240C30.11C2^4480,1083
C30.12C24 = C2×D125D5φ: C24/C22C22 ⊆ Aut C30240C30.12C2^4480,1084
C30.13C24 = C2×C12.28D10φ: C24/C22C22 ⊆ Aut C30240C30.13C2^4480,1085
C30.14C24 = S3×C2×C4×D5φ: C24/C22C22 ⊆ Aut C30120C30.14C2^4480,1086
C30.15C24 = C2×D5×D12φ: C24/C22C22 ⊆ Aut C30120C30.15C2^4480,1087
C30.16C24 = C2×S3×D20φ: C24/C22C22 ⊆ Aut C30120C30.16C2^4480,1088
C30.17C24 = C2×C20⋊D6φ: C24/C22C22 ⊆ Aut C30120C30.17C2^4480,1089
C30.18C24 = D5×C4○D12φ: C24/C22C22 ⊆ Aut C301204C30.18C2^4480,1090
C30.19C24 = S3×C4○D20φ: C24/C22C22 ⊆ Aut C301204C30.19C2^4480,1091
C30.20C24 = D2024D6φ: C24/C22C22 ⊆ Aut C301204C30.20C2^4480,1092
C30.21C24 = D2025D6φ: C24/C22C22 ⊆ Aut C301204C30.21C2^4480,1093
C30.22C24 = D2026D6φ: C24/C22C22 ⊆ Aut C301204C30.22C2^4480,1094
C30.23C24 = D2029D6φ: C24/C22C22 ⊆ Aut C301204+C30.23C2^4480,1095
C30.24C24 = C15⋊2- 1+4φ: C24/C22C22 ⊆ Aut C302408-C30.24C2^4480,1096
C30.25C24 = S3×D4×D5φ: C24/C22C22 ⊆ Aut C30608+C30.25C2^4480,1097
C30.26C24 = D5×D42S3φ: C24/C22C22 ⊆ Aut C301208-C30.26C2^4480,1098
C30.27C24 = S3×D42D5φ: C24/C22C22 ⊆ Aut C301208-C30.27C2^4480,1099
C30.28C24 = D30.C23φ: C24/C22C22 ⊆ Aut C301208+C30.28C2^4480,1100
C30.29C24 = D2013D6φ: C24/C22C22 ⊆ Aut C301208-C30.29C2^4480,1101
C30.30C24 = D2014D6φ: C24/C22C22 ⊆ Aut C301208+C30.30C2^4480,1102
C30.31C24 = D1214D10φ: C24/C22C22 ⊆ Aut C301208+C30.31C2^4480,1103
C30.32C24 = D20.29D6φ: C24/C22C22 ⊆ Aut C302408-C30.32C2^4480,1104
C30.33C24 = C30.33C24φ: C24/C22C22 ⊆ Aut C302408+C30.33C2^4480,1105
C30.34C24 = D12.29D10φ: C24/C22C22 ⊆ Aut C302408-C30.34C2^4480,1106
C30.35C24 = S3×Q8×D5φ: C24/C22C22 ⊆ Aut C301208-C30.35C2^4480,1107
C30.36C24 = D5×Q83S3φ: C24/C22C22 ⊆ Aut C301208+C30.36C2^4480,1108
C30.37C24 = S3×Q82D5φ: C24/C22C22 ⊆ Aut C301208+C30.37C2^4480,1109
C30.38C24 = D2016D6φ: C24/C22C22 ⊆ Aut C301208-C30.38C2^4480,1110
C30.39C24 = D2017D6φ: C24/C22C22 ⊆ Aut C301208+C30.39C2^4480,1111
C30.40C24 = C22×D5×Dic3φ: C24/C22C22 ⊆ Aut C30240C30.40C2^4480,1112
C30.41C24 = C2×Dic5.D6φ: C24/C22C22 ⊆ Aut C30240C30.41C2^4480,1113
C30.42C24 = C2×C30.C23φ: C24/C22C22 ⊆ Aut C30240C30.42C2^4480,1114
C30.43C24 = C22×S3×Dic5φ: C24/C22C22 ⊆ Aut C30240C30.43C2^4480,1115
C30.44C24 = C2×Dic3.D10φ: C24/C22C22 ⊆ Aut C30240C30.44C2^4480,1116
C30.45C24 = C22×D30.C2φ: C24/C22C22 ⊆ Aut C30240C30.45C2^4480,1117
C30.46C24 = C22×C15⋊D4φ: C24/C22C22 ⊆ Aut C30240C30.46C2^4480,1118
C30.47C24 = C22×C3⋊D20φ: C24/C22C22 ⊆ Aut C30240C30.47C2^4480,1119
C30.48C24 = C22×C5⋊D12φ: C24/C22C22 ⊆ Aut C30240C30.48C2^4480,1120
C30.49C24 = C22×C15⋊Q8φ: C24/C22C22 ⊆ Aut C30480C30.49C2^4480,1121
C30.50C24 = C2×D5×C3⋊D4φ: C24/C22C22 ⊆ Aut C30120C30.50C2^4480,1122
C30.51C24 = C2×S3×C5⋊D4φ: C24/C22C22 ⊆ Aut C30120C30.51C2^4480,1123
C30.52C24 = C2×D10⋊D6φ: C24/C22C22 ⊆ Aut C30120C30.52C2^4480,1124
C30.53C24 = C15⋊2+ 1+4φ: C24/C22C22 ⊆ Aut C301204C30.53C2^4480,1125
C30.54C24 = C22×Dic30φ: C24/C23C2 ⊆ Aut C30480C30.54C2^4480,1165
C30.55C24 = C22×C4×D15φ: C24/C23C2 ⊆ Aut C30240C30.55C2^4480,1166
C30.56C24 = C22×D60φ: C24/C23C2 ⊆ Aut C30240C30.56C2^4480,1167
C30.57C24 = C2×D6011C2φ: C24/C23C2 ⊆ Aut C30240C30.57C2^4480,1168
C30.58C24 = C2×D4×D15φ: C24/C23C2 ⊆ Aut C30120C30.58C2^4480,1169
C30.59C24 = C2×D42D15φ: C24/C23C2 ⊆ Aut C30240C30.59C2^4480,1170
C30.60C24 = D46D30φ: C24/C23C2 ⊆ Aut C301204C30.60C2^4480,1171
C30.61C24 = C2×Q8×D15φ: C24/C23C2 ⊆ Aut C30240C30.61C2^4480,1172
C30.62C24 = C2×Q83D15φ: C24/C23C2 ⊆ Aut C30240C30.62C2^4480,1173
C30.63C24 = Q8.15D30φ: C24/C23C2 ⊆ Aut C302404C30.63C2^4480,1174
C30.64C24 = C4○D4×D15φ: C24/C23C2 ⊆ Aut C301204C30.64C2^4480,1175
C30.65C24 = D48D30φ: C24/C23C2 ⊆ Aut C301204+C30.65C2^4480,1176
C30.66C24 = D4.10D30φ: C24/C23C2 ⊆ Aut C302404-C30.66C2^4480,1177
C30.67C24 = C23×Dic15φ: C24/C23C2 ⊆ Aut C30480C30.67C2^4480,1178
C30.68C24 = C22×C157D4φ: C24/C23C2 ⊆ Aut C30240C30.68C2^4480,1179
C30.69C24 = C2×C6×Dic10φ: C24/C23C2 ⊆ Aut C30480C30.69C2^4480,1135
C30.70C24 = D5×C22×C12φ: C24/C23C2 ⊆ Aut C30240C30.70C2^4480,1136
C30.71C24 = C2×C6×D20φ: C24/C23C2 ⊆ Aut C30240C30.71C2^4480,1137
C30.72C24 = C6×C4○D20φ: C24/C23C2 ⊆ Aut C30240C30.72C2^4480,1138
C30.73C24 = C6×D4×D5φ: C24/C23C2 ⊆ Aut C30120C30.73C2^4480,1139
C30.74C24 = C6×D42D5φ: C24/C23C2 ⊆ Aut C30240C30.74C2^4480,1140
C30.75C24 = C3×D46D10φ: C24/C23C2 ⊆ Aut C301204C30.75C2^4480,1141
C30.76C24 = C6×Q8×D5φ: C24/C23C2 ⊆ Aut C30240C30.76C2^4480,1142
C30.77C24 = C6×Q82D5φ: C24/C23C2 ⊆ Aut C30240C30.77C2^4480,1143
C30.78C24 = C3×Q8.10D10φ: C24/C23C2 ⊆ Aut C302404C30.78C2^4480,1144
C30.79C24 = C3×D5×C4○D4φ: C24/C23C2 ⊆ Aut C301204C30.79C2^4480,1145
C30.80C24 = C3×D48D10φ: C24/C23C2 ⊆ Aut C301204C30.80C2^4480,1146
C30.81C24 = C3×D4.10D10φ: C24/C23C2 ⊆ Aut C302404C30.81C2^4480,1147
C30.82C24 = Dic5×C22×C6φ: C24/C23C2 ⊆ Aut C30480C30.82C2^4480,1148
C30.83C24 = C2×C6×C5⋊D4φ: C24/C23C2 ⊆ Aut C30240C30.83C2^4480,1149
C30.84C24 = C2×C10×Dic6φ: C24/C23C2 ⊆ Aut C30480C30.84C2^4480,1150
C30.85C24 = S3×C22×C20φ: C24/C23C2 ⊆ Aut C30240C30.85C2^4480,1151
C30.86C24 = C2×C10×D12φ: C24/C23C2 ⊆ Aut C30240C30.86C2^4480,1152
C30.87C24 = C10×C4○D12φ: C24/C23C2 ⊆ Aut C30240C30.87C2^4480,1153
C30.88C24 = S3×D4×C10φ: C24/C23C2 ⊆ Aut C30120C30.88C2^4480,1154
C30.89C24 = C10×D42S3φ: C24/C23C2 ⊆ Aut C30240C30.89C2^4480,1155
C30.90C24 = C5×D46D6φ: C24/C23C2 ⊆ Aut C301204C30.90C2^4480,1156
C30.91C24 = S3×Q8×C10φ: C24/C23C2 ⊆ Aut C30240C30.91C2^4480,1157
C30.92C24 = C10×Q83S3φ: C24/C23C2 ⊆ Aut C30240C30.92C2^4480,1158
C30.93C24 = C5×Q8.15D6φ: C24/C23C2 ⊆ Aut C302404C30.93C2^4480,1159
C30.94C24 = C5×S3×C4○D4φ: C24/C23C2 ⊆ Aut C301204C30.94C2^4480,1160
C30.95C24 = C5×D4○D12φ: C24/C23C2 ⊆ Aut C301204C30.95C2^4480,1161
C30.96C24 = C5×Q8○D12φ: C24/C23C2 ⊆ Aut C302404C30.96C2^4480,1162
C30.97C24 = Dic3×C22×C10φ: C24/C23C2 ⊆ Aut C30480C30.97C2^4480,1163
C30.98C24 = C2×C10×C3⋊D4φ: C24/C23C2 ⊆ Aut C30240C30.98C2^4480,1164
C30.99C24 = D4×C2×C30central extension (φ=1)240C30.99C2^4480,1181
C30.100C24 = Q8×C2×C30central extension (φ=1)480C30.100C2^4480,1182
C30.101C24 = C4○D4×C30central extension (φ=1)240C30.101C2^4480,1183
C30.102C24 = C15×2+ 1+4central extension (φ=1)1204C30.102C2^4480,1184
C30.103C24 = C15×2- 1+4central extension (φ=1)2404C30.103C2^4480,1185

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