# Extensions 1→N→G→Q→1 with N=C5×Dic3 and Q=C23

Direct product G=N×Q with N=C5×Dic3 and Q=C23
dρLabelID
Dic3×C22×C10480Dic3xC2^2xC10480,1163

Semidirect products G=N:Q with N=C5×Dic3 and Q=C23
extensionφ:Q→Out NdρLabelID
(C5×Dic3)⋊1C23 = S3×D4×D5φ: C23/C2C22 ⊆ Out C5×Dic3608+(C5xDic3):1C2^3480,1097
(C5×Dic3)⋊2C23 = C2×D5×C3⋊D4φ: C23/C2C22 ⊆ Out C5×Dic3120(C5xDic3):2C2^3480,1122
(C5×Dic3)⋊3C23 = C2×D10⋊D6φ: C23/C2C22 ⊆ Out C5×Dic3120(C5xDic3):3C2^3480,1124
(C5×Dic3)⋊4C23 = S3×C2×C4×D5φ: C23/C22C2 ⊆ Out C5×Dic3120(C5xDic3):4C2^3480,1086
(C5×Dic3)⋊5C23 = C2×S3×D20φ: C23/C22C2 ⊆ Out C5×Dic3120(C5xDic3):5C2^3480,1088
(C5×Dic3)⋊6C23 = C22×D5×Dic3φ: C23/C22C2 ⊆ Out C5×Dic3240(C5xDic3):6C2^3480,1112
(C5×Dic3)⋊7C23 = C22×D30.C2φ: C23/C22C2 ⊆ Out C5×Dic3240(C5xDic3):7C2^3480,1117
(C5×Dic3)⋊8C23 = C22×C3⋊D20φ: C23/C22C2 ⊆ Out C5×Dic3240(C5xDic3):8C2^3480,1119
(C5×Dic3)⋊9C23 = S3×D4×C10φ: C23/C22C2 ⊆ Out C5×Dic3120(C5xDic3):9C2^3480,1154
(C5×Dic3)⋊10C23 = C2×C10×C3⋊D4φ: C23/C22C2 ⊆ Out C5×Dic3240(C5xDic3):10C2^3480,1164
(C5×Dic3)⋊11C23 = S3×C22×C20φ: trivial image240(C5xDic3):11C2^3480,1151

Non-split extensions G=N.Q with N=C5×Dic3 and Q=C23
extensionφ:Q→Out NdρLabelID
(C5×Dic3).1C23 = C2×D5×Dic6φ: C23/C2C22 ⊆ Out C5×Dic3240(C5xDic3).1C2^3480,1073
(C5×Dic3).2C23 = C2×D20⋊S3φ: C23/C2C22 ⊆ Out C5×Dic3240(C5xDic3).2C2^3480,1075
(C5×Dic3).3C23 = D20.38D6φ: C23/C2C22 ⊆ Out C5×Dic32404(C5xDic3).3C2^3480,1076
(C5×Dic3).4C23 = D20.39D6φ: C23/C2C22 ⊆ Out C5×Dic32404-(C5xDic3).4C2^3480,1077
(C5×Dic3).5C23 = C30.C24φ: C23/C2C22 ⊆ Out C5×Dic32404(C5xDic3).5C2^3480,1080
(C5×Dic3).6C23 = C2×D15⋊Q8φ: C23/C2C22 ⊆ Out C5×Dic3240(C5xDic3).6C2^3480,1082
(C5×Dic3).7C23 = C2×C12.28D10φ: C23/C2C22 ⊆ Out C5×Dic3240(C5xDic3).7C2^3480,1085
(C5×Dic3).8C23 = D5×C4○D12φ: C23/C2C22 ⊆ Out C5×Dic31204(C5xDic3).8C2^3480,1090
(C5×Dic3).9C23 = D2024D6φ: C23/C2C22 ⊆ Out C5×Dic31204(C5xDic3).9C2^3480,1092
(C5×Dic3).10C23 = D2025D6φ: C23/C2C22 ⊆ Out C5×Dic31204(C5xDic3).10C2^3480,1093
(C5×Dic3).11C23 = D2029D6φ: C23/C2C22 ⊆ Out C5×Dic31204+(C5xDic3).11C2^3480,1095
(C5×Dic3).12C23 = C15⋊2- 1+4φ: C23/C2C22 ⊆ Out C5×Dic32408-(C5xDic3).12C2^3480,1096
(C5×Dic3).13C23 = D5×D42S3φ: C23/C2C22 ⊆ Out C5×Dic31208-(C5xDic3).13C2^3480,1098
(C5×Dic3).14C23 = S3×D42D5φ: C23/C2C22 ⊆ Out C5×Dic31208-(C5xDic3).14C2^3480,1099
(C5×Dic3).15C23 = D30.C23φ: C23/C2C22 ⊆ Out C5×Dic31208+(C5xDic3).15C2^3480,1100
(C5×Dic3).16C23 = D2013D6φ: C23/C2C22 ⊆ Out C5×Dic31208-(C5xDic3).16C2^3480,1101
(C5×Dic3).17C23 = D1214D10φ: C23/C2C22 ⊆ Out C5×Dic31208+(C5xDic3).17C2^3480,1103
(C5×Dic3).18C23 = D20.29D6φ: C23/C2C22 ⊆ Out C5×Dic32408-(C5xDic3).18C2^3480,1104
(C5×Dic3).19C23 = C30.33C24φ: C23/C2C22 ⊆ Out C5×Dic32408+(C5xDic3).19C2^3480,1105
(C5×Dic3).20C23 = S3×Q8×D5φ: C23/C2C22 ⊆ Out C5×Dic31208-(C5xDic3).20C2^3480,1107
(C5×Dic3).21C23 = S3×Q82D5φ: C23/C2C22 ⊆ Out C5×Dic31208+(C5xDic3).21C2^3480,1109
(C5×Dic3).22C23 = C2×C30.C23φ: C23/C2C22 ⊆ Out C5×Dic3240(C5xDic3).22C2^3480,1114
(C5×Dic3).23C23 = C2×Dic3.D10φ: C23/C2C22 ⊆ Out C5×Dic3240(C5xDic3).23C2^3480,1116
(C5×Dic3).24C23 = C15⋊2+ 1+4φ: C23/C2C22 ⊆ Out C5×Dic31204(C5xDic3).24C2^3480,1125
(C5×Dic3).25C23 = C2×D205S3φ: C23/C22C2 ⊆ Out C5×Dic3240(C5xDic3).25C2^3480,1074
(C5×Dic3).26C23 = C2×S3×Dic10φ: C23/C22C2 ⊆ Out C5×Dic3240(C5xDic3).26C2^3480,1078
(C5×Dic3).27C23 = C2×D60⋊C2φ: C23/C22C2 ⊆ Out C5×Dic3240(C5xDic3).27C2^3480,1081
(C5×Dic3).28C23 = C2×D6.D10φ: C23/C22C2 ⊆ Out C5×Dic3240(C5xDic3).28C2^3480,1083
(C5×Dic3).29C23 = S3×C4○D20φ: C23/C22C2 ⊆ Out C5×Dic31204(C5xDic3).29C2^3480,1091
(C5×Dic3).30C23 = D2014D6φ: C23/C22C2 ⊆ Out C5×Dic31208+(C5xDic3).30C2^3480,1102
(C5×Dic3).31C23 = D12.29D10φ: C23/C22C2 ⊆ Out C5×Dic32408-(C5xDic3).31C2^3480,1106
(C5×Dic3).32C23 = D5×Q83S3φ: C23/C22C2 ⊆ Out C5×Dic31208+(C5xDic3).32C2^3480,1108
(C5×Dic3).33C23 = D2016D6φ: C23/C22C2 ⊆ Out C5×Dic31208-(C5xDic3).33C2^3480,1110
(C5×Dic3).34C23 = D2017D6φ: C23/C22C2 ⊆ Out C5×Dic31208+(C5xDic3).34C2^3480,1111
(C5×Dic3).35C23 = C2×Dic5.D6φ: C23/C22C2 ⊆ Out C5×Dic3240(C5xDic3).35C2^3480,1113
(C5×Dic3).36C23 = C22×C15⋊Q8φ: C23/C22C2 ⊆ Out C5×Dic3480(C5xDic3).36C2^3480,1121
(C5×Dic3).37C23 = C2×C10×Dic6φ: C23/C22C2 ⊆ Out C5×Dic3480(C5xDic3).37C2^3480,1150
(C5×Dic3).38C23 = C10×C4○D12φ: C23/C22C2 ⊆ Out C5×Dic3240(C5xDic3).38C2^3480,1153
(C5×Dic3).39C23 = C10×D42S3φ: C23/C22C2 ⊆ Out C5×Dic3240(C5xDic3).39C2^3480,1155
(C5×Dic3).40C23 = C5×D46D6φ: C23/C22C2 ⊆ Out C5×Dic31204(C5xDic3).40C2^3480,1156
(C5×Dic3).41C23 = S3×Q8×C10φ: C23/C22C2 ⊆ Out C5×Dic3240(C5xDic3).41C2^3480,1157
(C5×Dic3).42C23 = C5×Q8.15D6φ: C23/C22C2 ⊆ Out C5×Dic32404(C5xDic3).42C2^3480,1159
(C5×Dic3).43C23 = C5×S3×C4○D4φ: C23/C22C2 ⊆ Out C5×Dic31204(C5xDic3).43C2^3480,1160
(C5×Dic3).44C23 = C5×D4○D12φ: C23/C22C2 ⊆ Out C5×Dic31204(C5xDic3).44C2^3480,1161
(C5×Dic3).45C23 = C5×Q8○D12φ: C23/C22C2 ⊆ Out C5×Dic32404(C5xDic3).45C2^3480,1162
(C5×Dic3).46C23 = C10×Q83S3φ: trivial image240(C5xDic3).46C2^3480,1158

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