# Extensions 1→N→G→Q→1 with N=D30 and Q=C23

Direct product G=N×Q with N=D30 and Q=C23
dρLabelID
C24×D15240C2^4xD15480,1212

Semidirect products G=N:Q with N=D30 and Q=C23
extensionφ:Q→Out NdρLabelID
D301C23 = C2×D5×D12φ: C23/C2C22 ⊆ Out D30120D30:1C2^3480,1087
D302C23 = C2×S3×D20φ: C23/C2C22 ⊆ Out D30120D30:2C2^3480,1088
D303C23 = S3×D4×D5φ: C23/C2C22 ⊆ Out D30608+D30:3C2^3480,1097
D304C23 = C2×D5×C3⋊D4φ: C23/C2C22 ⊆ Out D30120D30:4C2^3480,1122
D305C23 = C2×S3×C5⋊D4φ: C23/C2C22 ⊆ Out D30120D30:5C2^3480,1123
D306C23 = C22×D60φ: C23/C22C2 ⊆ Out D30240D30:6C2^3480,1167
D307C23 = C2×D4×D15φ: C23/C22C2 ⊆ Out D30120D30:7C2^3480,1169
D308C23 = C22×C157D4φ: C23/C22C2 ⊆ Out D30240D30:8C2^3480,1179
D309C23 = C22×C3⋊D20φ: C23/C22C2 ⊆ Out D30240D30:9C2^3480,1119
D3010C23 = C22×C5⋊D12φ: C23/C22C2 ⊆ Out D30240D30:10C2^3480,1120
D3011C23 = C2×D10⋊D6φ: C23/C22C2 ⊆ Out D30120D30:11C2^3480,1124
D3012C23 = S3×C23×D5φ: C23/C22C2 ⊆ Out D30120D30:12C2^3480,1207

Non-split extensions G=N.Q with N=D30 and Q=C23
extensionφ:Q→Out NdρLabelID
D30.1C23 = D20.38D6φ: C23/C2C22 ⊆ Out D302404D30.1C2^3480,1076
D30.2C23 = C30.C24φ: C23/C2C22 ⊆ Out D302404D30.2C2^3480,1080
D30.3C23 = C2×D60⋊C2φ: C23/C2C22 ⊆ Out D30240D30.3C2^3480,1081
D30.4C23 = C2×C12.28D10φ: C23/C2C22 ⊆ Out D30240D30.4C2^3480,1085
D30.5C23 = D5×C4○D12φ: C23/C2C22 ⊆ Out D301204D30.5C2^3480,1090
D30.6C23 = S3×C4○D20φ: C23/C2C22 ⊆ Out D301204D30.6C2^3480,1091
D30.7C23 = D2025D6φ: C23/C2C22 ⊆ Out D301204D30.7C2^3480,1093
D30.8C23 = D2026D6φ: C23/C2C22 ⊆ Out D301204D30.8C2^3480,1094
D30.9C23 = D2029D6φ: C23/C2C22 ⊆ Out D301204+D30.9C2^3480,1095
D30.10C23 = C15⋊2- 1+4φ: C23/C2C22 ⊆ Out D302408-D30.10C2^3480,1096
D30.11C23 = D5×D42S3φ: C23/C2C22 ⊆ Out D301208-D30.11C2^3480,1098
D30.12C23 = S3×D42D5φ: C23/C2C22 ⊆ Out D301208-D30.12C2^3480,1099
D30.13C23 = D30.C23φ: C23/C2C22 ⊆ Out D301208+D30.13C2^3480,1100
D30.14C23 = D2013D6φ: C23/C2C22 ⊆ Out D301208-D30.14C2^3480,1101
D30.15C23 = D2014D6φ: C23/C2C22 ⊆ Out D301208+D30.15C2^3480,1102
D30.16C23 = D1214D10φ: C23/C2C22 ⊆ Out D301208+D30.16C2^3480,1103
D30.17C23 = C30.33C24φ: C23/C2C22 ⊆ Out D302408+D30.17C2^3480,1105
D30.18C23 = D5×Q83S3φ: C23/C2C22 ⊆ Out D301208+D30.18C2^3480,1108
D30.19C23 = S3×Q82D5φ: C23/C2C22 ⊆ Out D301208+D30.19C2^3480,1109
D30.20C23 = D2017D6φ: C23/C2C22 ⊆ Out D301208+D30.20C2^3480,1111
D30.21C23 = C2×Dic5.D6φ: C23/C2C22 ⊆ Out D30240D30.21C2^3480,1113
D30.22C23 = C2×Dic3.D10φ: C23/C2C22 ⊆ Out D30240D30.22C2^3480,1116
D30.23C23 = C15⋊2+ 1+4φ: C23/C2C22 ⊆ Out D301204D30.23C2^3480,1125
D30.24C23 = C2×D6011C2φ: C23/C22C2 ⊆ Out D30240D30.24C2^3480,1168
D30.25C23 = C2×D42D15φ: C23/C22C2 ⊆ Out D30240D30.25C2^3480,1170
D30.26C23 = D46D30φ: C23/C22C2 ⊆ Out D301204D30.26C2^3480,1171
D30.27C23 = C2×Q83D15φ: C23/C22C2 ⊆ Out D30240D30.27C2^3480,1173
D30.28C23 = Q8.15D30φ: C23/C22C2 ⊆ Out D302404D30.28C2^3480,1174
D30.29C23 = C4○D4×D15φ: C23/C22C2 ⊆ Out D301204D30.29C2^3480,1175
D30.30C23 = D48D30φ: C23/C22C2 ⊆ Out D301204+D30.30C2^3480,1176
D30.31C23 = D4.10D30φ: C23/C22C2 ⊆ Out D302404-D30.31C2^3480,1177
D30.32C23 = C2×D20⋊S3φ: C23/C22C2 ⊆ Out D30240D30.32C2^3480,1075
D30.33C23 = C2×D12⋊D5φ: C23/C22C2 ⊆ Out D30240D30.33C2^3480,1079
D30.34C23 = C2×D15⋊Q8φ: C23/C22C2 ⊆ Out D30240D30.34C2^3480,1082
D30.35C23 = C2×D6.D10φ: C23/C22C2 ⊆ Out D30240D30.35C2^3480,1083
D30.36C23 = S3×C2×C4×D5φ: C23/C22C2 ⊆ Out D30120D30.36C2^3480,1086
D30.37C23 = C2×C20⋊D6φ: C23/C22C2 ⊆ Out D30120D30.37C2^3480,1089
D30.38C23 = D2024D6φ: C23/C22C2 ⊆ Out D301204D30.38C2^3480,1092
D30.39C23 = D20.29D6φ: C23/C22C2 ⊆ Out D302408-D30.39C2^3480,1104
D30.40C23 = D12.29D10φ: C23/C22C2 ⊆ Out D302408-D30.40C2^3480,1106
D30.41C23 = S3×Q8×D5φ: C23/C22C2 ⊆ Out D301208-D30.41C2^3480,1107
D30.42C23 = D2016D6φ: C23/C22C2 ⊆ Out D301208-D30.42C2^3480,1110
D30.43C23 = C22×D30.C2φ: C23/C22C2 ⊆ Out D30240D30.43C2^3480,1117
D30.44C23 = C22×C4×D15φ: trivial image240D30.44C2^3480,1166
D30.45C23 = C2×Q8×D15φ: trivial image240D30.45C2^3480,1172

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