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

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

Semidirect products G=N:Q with N=S3×C10 and Q=C23
extensionφ:Q→Out NdρLabelID
(S3×C10)⋊1C23 = C2×D5×D12φ: C23/C2C22 ⊆ Out S3×C10120(S3xC10):1C2^3480,1087
(S3×C10)⋊2C23 = C2×C20⋊D6φ: C23/C2C22 ⊆ Out S3×C10120(S3xC10):2C2^3480,1089
(S3×C10)⋊3C23 = S3×D4×D5φ: C23/C2C22 ⊆ Out S3×C10608+(S3xC10):3C2^3480,1097
(S3×C10)⋊4C23 = C2×D5×C3⋊D4φ: C23/C2C22 ⊆ Out S3×C10120(S3xC10):4C2^3480,1122
(S3×C10)⋊5C23 = C2×D10⋊D6φ: C23/C2C22 ⊆ Out S3×C10120(S3xC10):5C2^3480,1124
(S3×C10)⋊6C23 = C22×C15⋊D4φ: C23/C22C2 ⊆ Out S3×C10240(S3xC10):6C2^3480,1118
(S3×C10)⋊7C23 = C22×C5⋊D12φ: C23/C22C2 ⊆ Out S3×C10240(S3xC10):7C2^3480,1120
(S3×C10)⋊8C23 = C2×S3×C5⋊D4φ: C23/C22C2 ⊆ Out S3×C10120(S3xC10):8C2^3480,1123
(S3×C10)⋊9C23 = S3×C23×D5φ: C23/C22C2 ⊆ Out S3×C10120(S3xC10):9C2^3480,1207
(S3×C10)⋊10C23 = C2×C10×D12φ: C23/C22C2 ⊆ Out S3×C10240(S3xC10):10C2^3480,1152
(S3×C10)⋊11C23 = S3×D4×C10φ: C23/C22C2 ⊆ Out S3×C10120(S3xC10):11C2^3480,1154
(S3×C10)⋊12C23 = C2×C10×C3⋊D4φ: C23/C22C2 ⊆ Out S3×C10240(S3xC10):12C2^3480,1164

Non-split extensions G=N.Q with N=S3×C10 and Q=C23
extensionφ:Q→Out NdρLabelID
(S3×C10).1C23 = D20.39D6φ: C23/C2C22 ⊆ Out S3×C102404-(S3xC10).1C2^3480,1077
(S3×C10).2C23 = C2×D12⋊D5φ: C23/C2C22 ⊆ Out S3×C10240(S3xC10).2C2^3480,1079
(S3×C10).3C23 = C30.C24φ: C23/C2C22 ⊆ Out S3×C102404(S3xC10).3C2^3480,1080
(S3×C10).4C23 = C2×D125D5φ: C23/C2C22 ⊆ Out S3×C10240(S3xC10).4C2^3480,1084
(S3×C10).5C23 = D5×C4○D12φ: C23/C2C22 ⊆ Out S3×C101204(S3xC10).5C2^3480,1090
(S3×C10).6C23 = D2024D6φ: C23/C2C22 ⊆ Out S3×C101204(S3xC10).6C2^3480,1092
(S3×C10).7C23 = D2025D6φ: C23/C2C22 ⊆ Out S3×C101204(S3xC10).7C2^3480,1093
(S3×C10).8C23 = D2026D6φ: C23/C2C22 ⊆ Out S3×C101204(S3xC10).8C2^3480,1094
(S3×C10).9C23 = D2029D6φ: C23/C2C22 ⊆ Out S3×C101204+(S3xC10).9C2^3480,1095
(S3×C10).10C23 = C15⋊2- 1+4φ: C23/C2C22 ⊆ Out S3×C102408-(S3xC10).10C2^3480,1096
(S3×C10).11C23 = D5×D42S3φ: C23/C2C22 ⊆ Out S3×C101208-(S3xC10).11C2^3480,1098
(S3×C10).12C23 = S3×D42D5φ: C23/C2C22 ⊆ Out S3×C101208-(S3xC10).12C2^3480,1099
(S3×C10).13C23 = D30.C23φ: C23/C2C22 ⊆ Out S3×C101208+(S3xC10).13C2^3480,1100
(S3×C10).14C23 = D2013D6φ: C23/C2C22 ⊆ Out S3×C101208-(S3xC10).14C2^3480,1101
(S3×C10).15C23 = D2014D6φ: C23/C2C22 ⊆ Out S3×C101208+(S3xC10).15C2^3480,1102
(S3×C10).16C23 = D1214D10φ: C23/C2C22 ⊆ Out S3×C101208+(S3xC10).16C2^3480,1103
(S3×C10).17C23 = D12.29D10φ: C23/C2C22 ⊆ Out S3×C102408-(S3xC10).17C2^3480,1106
(S3×C10).18C23 = D5×Q83S3φ: C23/C2C22 ⊆ Out S3×C101208+(S3xC10).18C2^3480,1108
(S3×C10).19C23 = D2016D6φ: C23/C2C22 ⊆ Out S3×C101208-(S3xC10).19C2^3480,1110
(S3×C10).20C23 = D2017D6φ: C23/C2C22 ⊆ Out S3×C101208+(S3xC10).20C2^3480,1111
(S3×C10).21C23 = C2×C30.C23φ: C23/C2C22 ⊆ Out S3×C10240(S3xC10).21C2^3480,1114
(S3×C10).22C23 = C2×Dic3.D10φ: C23/C2C22 ⊆ Out S3×C10240(S3xC10).22C2^3480,1116
(S3×C10).23C23 = C15⋊2+ 1+4φ: C23/C2C22 ⊆ Out S3×C101204(S3xC10).23C2^3480,1125
(S3×C10).24C23 = C2×D205S3φ: C23/C22C2 ⊆ Out S3×C10240(S3xC10).24C2^3480,1074
(S3×C10).25C23 = C2×S3×Dic10φ: C23/C22C2 ⊆ Out S3×C10240(S3xC10).25C2^3480,1078
(S3×C10).26C23 = C2×D60⋊C2φ: C23/C22C2 ⊆ Out S3×C10240(S3xC10).26C2^3480,1081
(S3×C10).27C23 = C2×D6.D10φ: C23/C22C2 ⊆ Out S3×C10240(S3xC10).27C2^3480,1083
(S3×C10).28C23 = S3×C2×C4×D5φ: C23/C22C2 ⊆ Out S3×C10120(S3xC10).28C2^3480,1086
(S3×C10).29C23 = C2×S3×D20φ: C23/C22C2 ⊆ Out S3×C10120(S3xC10).29C2^3480,1088
(S3×C10).30C23 = S3×C4○D20φ: C23/C22C2 ⊆ Out S3×C101204(S3xC10).30C2^3480,1091
(S3×C10).31C23 = D20.29D6φ: C23/C22C2 ⊆ Out S3×C102408-(S3xC10).31C2^3480,1104
(S3×C10).32C23 = C30.33C24φ: C23/C22C2 ⊆ Out S3×C102408+(S3xC10).32C2^3480,1105
(S3×C10).33C23 = S3×Q8×D5φ: C23/C22C2 ⊆ Out S3×C101208-(S3xC10).33C2^3480,1107
(S3×C10).34C23 = S3×Q82D5φ: C23/C22C2 ⊆ Out S3×C101208+(S3xC10).34C2^3480,1109
(S3×C10).35C23 = C22×S3×Dic5φ: C23/C22C2 ⊆ Out S3×C10240(S3xC10).35C2^3480,1115
(S3×C10).36C23 = C10×C4○D12φ: C23/C22C2 ⊆ Out S3×C10240(S3xC10).36C2^3480,1153
(S3×C10).37C23 = C10×D42S3φ: C23/C22C2 ⊆ Out S3×C10240(S3xC10).37C2^3480,1155
(S3×C10).38C23 = C5×D46D6φ: C23/C22C2 ⊆ Out S3×C101204(S3xC10).38C2^3480,1156
(S3×C10).39C23 = C10×Q83S3φ: C23/C22C2 ⊆ Out S3×C10240(S3xC10).39C2^3480,1158
(S3×C10).40C23 = C5×Q8.15D6φ: C23/C22C2 ⊆ Out S3×C102404(S3xC10).40C2^3480,1159
(S3×C10).41C23 = C5×S3×C4○D4φ: C23/C22C2 ⊆ Out S3×C101204(S3xC10).41C2^3480,1160
(S3×C10).42C23 = C5×D4○D12φ: C23/C22C2 ⊆ Out S3×C101204(S3xC10).42C2^3480,1161
(S3×C10).43C23 = C5×Q8○D12φ: C23/C22C2 ⊆ Out S3×C102404(S3xC10).43C2^3480,1162
(S3×C10).44C23 = S3×C22×C20φ: trivial image240(S3xC10).44C2^3480,1151
(S3×C10).45C23 = S3×Q8×C10φ: trivial image240(S3xC10).45C2^3480,1157

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