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Extensions 1→N→G→Q→1 with N=C6 and Q=C23×D5

Direct product G=N×Q with N=C6 and Q=C23×D5
dρLabelID
D5×C23×C6240D5xC2^3xC6480,1210

Semidirect products G=N:Q with N=C6 and Q=C23×D5
extensionφ:Q→Aut NdρLabelID
C6⋊1(C23×D5) = S3×C23×D5φ: C23×D5/C22×D5 → C2 ⊆ Aut C6120C6:1(C2^3xD5)480,1207
C6⋊2(C23×D5) = C24×D15φ: C23×D5/C22×C10 → C2 ⊆ Aut C6240C6:2(C2^3xD5)480,1212

Non-split extensions G=N.Q with N=C6 and Q=C23×D5
extensionφ:Q→Aut NdρLabelID
C6.1(C23×D5) = C2×D5×Dic6φ: C23×D5/C22×D5 → C2 ⊆ Aut C6240C6.1(C2^3xD5)480,1073
C6.2(C23×D5) = C2×D20⋊5S3φ: C23×D5/C22×D5 → C2 ⊆ Aut C6240C6.2(C2^3xD5)480,1074
C6.3(C23×D5) = C2×D20⋊S3φ: C23×D5/C22×D5 → C2 ⊆ Aut C6240C6.3(C2^3xD5)480,1075
C6.4(C23×D5) = D20.38D6φ: C23×D5/C22×D5 → C2 ⊆ Aut C62404C6.4(C2^3xD5)480,1076
C6.5(C23×D5) = D20.39D6φ: C23×D5/C22×D5 → C2 ⊆ Aut C62404-C6.5(C2^3xD5)480,1077
C6.6(C23×D5) = C2×S3×Dic10φ: C23×D5/C22×D5 → C2 ⊆ Aut C6240C6.6(C2^3xD5)480,1078
C6.7(C23×D5) = C2×D12⋊D5φ: C23×D5/C22×D5 → C2 ⊆ Aut C6240C6.7(C2^3xD5)480,1079
C6.8(C23×D5) = C30.C24φ: C23×D5/C22×D5 → C2 ⊆ Aut C62404C6.8(C2^3xD5)480,1080
C6.9(C23×D5) = C2×D60⋊C2φ: C23×D5/C22×D5 → C2 ⊆ Aut C6240C6.9(C2^3xD5)480,1081
C6.10(C23×D5) = C2×D15⋊Q8φ: C23×D5/C22×D5 → C2 ⊆ Aut C6240C6.10(C2^3xD5)480,1082
C6.11(C23×D5) = C2×D6.D10φ: C23×D5/C22×D5 → C2 ⊆ Aut C6240C6.11(C2^3xD5)480,1083
C6.12(C23×D5) = C2×D12⋊5D5φ: C23×D5/C22×D5 → C2 ⊆ Aut C6240C6.12(C2^3xD5)480,1084
C6.13(C23×D5) = C2×C12.28D10φ: C23×D5/C22×D5 → C2 ⊆ Aut C6240C6.13(C2^3xD5)480,1085
C6.14(C23×D5) = S3×C2×C4×D5φ: C23×D5/C22×D5 → C2 ⊆ Aut C6120C6.14(C2^3xD5)480,1086
C6.15(C23×D5) = C2×D5×D12φ: C23×D5/C22×D5 → C2 ⊆ Aut C6120C6.15(C2^3xD5)480,1087
C6.16(C23×D5) = C2×S3×D20φ: C23×D5/C22×D5 → C2 ⊆ Aut C6120C6.16(C2^3xD5)480,1088
C6.17(C23×D5) = C2×C20⋊D6φ: C23×D5/C22×D5 → C2 ⊆ Aut C6120C6.17(C2^3xD5)480,1089
C6.18(C23×D5) = D5×C4○D12φ: C23×D5/C22×D5 → C2 ⊆ Aut C61204C6.18(C2^3xD5)480,1090
C6.19(C23×D5) = S3×C4○D20φ: C23×D5/C22×D5 → C2 ⊆ Aut C61204C6.19(C2^3xD5)480,1091
C6.20(C23×D5) = D20⋊24D6φ: C23×D5/C22×D5 → C2 ⊆ Aut C61204C6.20(C2^3xD5)480,1092
C6.21(C23×D5) = D20⋊25D6φ: C23×D5/C22×D5 → C2 ⊆ Aut C61204C6.21(C2^3xD5)480,1093
C6.22(C23×D5) = D20⋊26D6φ: C23×D5/C22×D5 → C2 ⊆ Aut C61204C6.22(C2^3xD5)480,1094
C6.23(C23×D5) = D20⋊29D6φ: C23×D5/C22×D5 → C2 ⊆ Aut C61204+C6.23(C2^3xD5)480,1095
C6.24(C23×D5) = C15⋊2- 1+4φ: C23×D5/C22×D5 → C2 ⊆ Aut C62408-C6.24(C2^3xD5)480,1096
C6.25(C23×D5) = S3×D4×D5φ: C23×D5/C22×D5 → C2 ⊆ Aut C6608+C6.25(C2^3xD5)480,1097
C6.26(C23×D5) = D5×D4⋊2S3φ: C23×D5/C22×D5 → C2 ⊆ Aut C61208-C6.26(C2^3xD5)480,1098
C6.27(C23×D5) = S3×D4⋊2D5φ: C23×D5/C22×D5 → C2 ⊆ Aut C61208-C6.27(C2^3xD5)480,1099
C6.28(C23×D5) = D30.C23φ: C23×D5/C22×D5 → C2 ⊆ Aut C61208+C6.28(C2^3xD5)480,1100
C6.29(C23×D5) = D20⋊13D6φ: C23×D5/C22×D5 → C2 ⊆ Aut C61208-C6.29(C2^3xD5)480,1101
C6.30(C23×D5) = D20⋊14D6φ: C23×D5/C22×D5 → C2 ⊆ Aut C61208+C6.30(C2^3xD5)480,1102
C6.31(C23×D5) = D12⋊14D10φ: C23×D5/C22×D5 → C2 ⊆ Aut C61208+C6.31(C2^3xD5)480,1103
C6.32(C23×D5) = D20.29D6φ: C23×D5/C22×D5 → C2 ⊆ Aut C62408-C6.32(C2^3xD5)480,1104
C6.33(C23×D5) = C30.33C24φ: C23×D5/C22×D5 → C2 ⊆ Aut C62408+C6.33(C2^3xD5)480,1105
C6.34(C23×D5) = D12.29D10φ: C23×D5/C22×D5 → C2 ⊆ Aut C62408-C6.34(C2^3xD5)480,1106
C6.35(C23×D5) = S3×Q8×D5φ: C23×D5/C22×D5 → C2 ⊆ Aut C61208-C6.35(C2^3xD5)480,1107
C6.36(C23×D5) = D5×Q8⋊3S3φ: C23×D5/C22×D5 → C2 ⊆ Aut C61208+C6.36(C2^3xD5)480,1108
C6.37(C23×D5) = S3×Q8⋊2D5φ: C23×D5/C22×D5 → C2 ⊆ Aut C61208+C6.37(C2^3xD5)480,1109
C6.38(C23×D5) = D20⋊16D6φ: C23×D5/C22×D5 → C2 ⊆ Aut C61208-C6.38(C2^3xD5)480,1110
C6.39(C23×D5) = D20⋊17D6φ: C23×D5/C22×D5 → C2 ⊆ Aut C61208+C6.39(C2^3xD5)480,1111
C6.40(C23×D5) = C22×D5×Dic3φ: C23×D5/C22×D5 → C2 ⊆ Aut C6240C6.40(C2^3xD5)480,1112
C6.41(C23×D5) = C2×Dic5.D6φ: C23×D5/C22×D5 → C2 ⊆ Aut C6240C6.41(C2^3xD5)480,1113
C6.42(C23×D5) = C2×C30.C23φ: C23×D5/C22×D5 → C2 ⊆ Aut C6240C6.42(C2^3xD5)480,1114
C6.43(C23×D5) = C22×S3×Dic5φ: C23×D5/C22×D5 → C2 ⊆ Aut C6240C6.43(C2^3xD5)480,1115
C6.44(C23×D5) = C2×Dic3.D10φ: C23×D5/C22×D5 → C2 ⊆ Aut C6240C6.44(C2^3xD5)480,1116
C6.45(C23×D5) = C22×D30.C2φ: C23×D5/C22×D5 → C2 ⊆ Aut C6240C6.45(C2^3xD5)480,1117
C6.46(C23×D5) = C22×C15⋊D4φ: C23×D5/C22×D5 → C2 ⊆ Aut C6240C6.46(C2^3xD5)480,1118
C6.47(C23×D5) = C22×C3⋊D20φ: C23×D5/C22×D5 → C2 ⊆ Aut C6240C6.47(C2^3xD5)480,1119
C6.48(C23×D5) = C22×C5⋊D12φ: C23×D5/C22×D5 → C2 ⊆ Aut C6240C6.48(C2^3xD5)480,1120
C6.49(C23×D5) = C22×C15⋊Q8φ: C23×D5/C22×D5 → C2 ⊆ Aut C6480C6.49(C2^3xD5)480,1121
C6.50(C23×D5) = C2×D5×C3⋊D4φ: C23×D5/C22×D5 → C2 ⊆ Aut C6120C6.50(C2^3xD5)480,1122
C6.51(C23×D5) = C2×S3×C5⋊D4φ: C23×D5/C22×D5 → C2 ⊆ Aut C6120C6.51(C2^3xD5)480,1123
C6.52(C23×D5) = C2×D10⋊D6φ: C23×D5/C22×D5 → C2 ⊆ Aut C6120C6.52(C2^3xD5)480,1124
C6.53(C23×D5) = C15⋊2+ 1+4φ: C23×D5/C22×D5 → C2 ⊆ Aut C61204C6.53(C2^3xD5)480,1125
C6.54(C23×D5) = C22×Dic30φ: C23×D5/C22×C10 → C2 ⊆ Aut C6480C6.54(C2^3xD5)480,1165
C6.55(C23×D5) = C22×C4×D15φ: C23×D5/C22×C10 → C2 ⊆ Aut C6240C6.55(C2^3xD5)480,1166
C6.56(C23×D5) = C22×D60φ: C23×D5/C22×C10 → C2 ⊆ Aut C6240C6.56(C2^3xD5)480,1167
C6.57(C23×D5) = C2×D60⋊11C2φ: C23×D5/C22×C10 → C2 ⊆ Aut C6240C6.57(C2^3xD5)480,1168
C6.58(C23×D5) = C2×D4×D15φ: C23×D5/C22×C10 → C2 ⊆ Aut C6120C6.58(C2^3xD5)480,1169
C6.59(C23×D5) = C2×D4⋊2D15φ: C23×D5/C22×C10 → C2 ⊆ Aut C6240C6.59(C2^3xD5)480,1170
C6.60(C23×D5) = D4⋊6D30φ: C23×D5/C22×C10 → C2 ⊆ Aut C61204C6.60(C2^3xD5)480,1171
C6.61(C23×D5) = C2×Q8×D15φ: C23×D5/C22×C10 → C2 ⊆ Aut C6240C6.61(C2^3xD5)480,1172
C6.62(C23×D5) = C2×Q8⋊3D15φ: C23×D5/C22×C10 → C2 ⊆ Aut C6240C6.62(C2^3xD5)480,1173
C6.63(C23×D5) = Q8.15D30φ: C23×D5/C22×C10 → C2 ⊆ Aut C62404C6.63(C2^3xD5)480,1174
C6.64(C23×D5) = C4○D4×D15φ: C23×D5/C22×C10 → C2 ⊆ Aut C61204C6.64(C2^3xD5)480,1175
C6.65(C23×D5) = D4⋊8D30φ: C23×D5/C22×C10 → C2 ⊆ Aut C61204+C6.65(C2^3xD5)480,1176
C6.66(C23×D5) = D4.10D30φ: C23×D5/C22×C10 → C2 ⊆ Aut C62404-C6.66(C2^3xD5)480,1177
C6.67(C23×D5) = C23×Dic15φ: C23×D5/C22×C10 → C2 ⊆ Aut C6480C6.67(C2^3xD5)480,1178
C6.68(C23×D5) = C22×C15⋊7D4φ: C23×D5/C22×C10 → C2 ⊆ Aut C6240C6.68(C2^3xD5)480,1179
C6.69(C23×D5) = C2×C6×Dic10central extension (φ=1)480C6.69(C2^3xD5)480,1135
C6.70(C23×D5) = D5×C22×C12central extension (φ=1)240C6.70(C2^3xD5)480,1136
C6.71(C23×D5) = C2×C6×D20central extension (φ=1)240C6.71(C2^3xD5)480,1137
C6.72(C23×D5) = C6×C4○D20central extension (φ=1)240C6.72(C2^3xD5)480,1138
C6.73(C23×D5) = C6×D4×D5central extension (φ=1)120C6.73(C2^3xD5)480,1139
C6.74(C23×D5) = C6×D4⋊2D5central extension (φ=1)240C6.74(C2^3xD5)480,1140
C6.75(C23×D5) = C3×D4⋊6D10central extension (φ=1)1204C6.75(C2^3xD5)480,1141
C6.76(C23×D5) = C6×Q8×D5central extension (φ=1)240C6.76(C2^3xD5)480,1142
C6.77(C23×D5) = C6×Q8⋊2D5central extension (φ=1)240C6.77(C2^3xD5)480,1143
C6.78(C23×D5) = C3×Q8.10D10central extension (φ=1)2404C6.78(C2^3xD5)480,1144
C6.79(C23×D5) = C3×D5×C4○D4central extension (φ=1)1204C6.79(C2^3xD5)480,1145
C6.80(C23×D5) = C3×D4⋊8D10central extension (φ=1)1204C6.80(C2^3xD5)480,1146
C6.81(C23×D5) = C3×D4.10D10central extension (φ=1)2404C6.81(C2^3xD5)480,1147
C6.82(C23×D5) = Dic5×C22×C6central extension (φ=1)480C6.82(C2^3xD5)480,1148
C6.83(C23×D5) = C2×C6×C5⋊D4central extension (φ=1)240C6.83(C2^3xD5)480,1149

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