← #11753827
Subgroups — #11753827
Order 960.
400 conjugacy classes of subgroups.
The subgroup lattice has 360 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #91778 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C5×#887 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C3×#4035 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #91469 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C4×#1204 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #91379 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #91379 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #91339 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #91334 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #91329 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #91329 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | #91325 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #91324 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #91324 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | #91323 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | #65901 | — | 3 | 1 | no | maximal, Hall |
| 17 | C2×C5×Dic6 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#1204 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#1204 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#1204 | C22 | 1 | 1 | yes | characteristic |
| 21 | C3×C5×C4⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 22 | C4⋊Dic15 | C22 | 1 | 1 | yes | characteristic |
| 23 | #6712 | C22 | 1 | 1 | yes | characteristic |
| 24 | #6712 | C22 | 1 | 1 | yes | characteristic |
| 25 | #6712 | C22 | 1 | 1 | yes | characteristic |
| 26 | #6712 | C22 | 1 | 1 | yes | characteristic |
| 27 | C4×Dic15 | C22 | 1 | 1 | yes | characteristic |
| 28 | C5×Dic3⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 29 | C5×Dic3⋊C4 | C22 | 1 | 1 | yes | characteristic |
| 30 | C4×C5×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 31 | C4×C5×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 32 | C4×C5×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 33 | C3×C4⋊Dic5 | C22 | 1 | 1 | yes | characteristic |
| 34 | C3×#683 | C22 | 1 | 1 | yes | characteristic |
| 35 | C3×#683 | C22 | 1 | 1 | yes | characteristic |
| 36 | C3×#683 | C22 | 1 | 1 | yes | characteristic |
| 37 | C3×#683 | C22 | 1 | 1 | yes | characteristic |
| 38 | C3×C4×Dic5 | C22 | 1 | 1 | yes | characteristic |
| 39 | Dic3⋊Dic5 | C22 | 1 | 1 | yes | characteristic |
| 40 | Dic3⋊Dic5 | C22 | 1 | 1 | yes | characteristic |
| 41 | Dic3⋊Dic5 | C22 | 1 | 1 | yes | characteristic |
| 42 | #6669 | C22 | 1 | 1 | yes | characteristic |
| 43 | #6669 | C22 | 1 | 1 | yes | characteristic |
| 44 | #6669 | C22 | 1 | 1 | yes | characteristic |
| 45 | #6668 | C22 | 1 | 1 | yes | characteristic |
| 46 | #6668 | C22 | 1 | 1 | yes | characteristic |
| 47 | #6668 | C22 | 1 | 1 | yes | characteristic |
| 48 | Dic3×Dic5 | C22 | 1 | 1 | yes | characteristic |
| 49 | Dic3×Dic5 | C22 | 1 | 1 | yes | characteristic |
| 50 | Dic3×Dic5 | C22 | 1 | 1 | yes | characteristic |
| 51 | Dic3×Dic5 | C22 | 1 | 1 | yes | characteristic |
| 52 | #5685 | — | 5 | 1 | no | maximal, Hall |
| 53 | C4×C5×Q8 | — | 3 | 1 | no | — |
| 54 | #4090 | — | 3 | 1 | no | — |
| 55 | #4090 | — | 3 | 1 | no | — |
| 56 | #4035 | — | 3 | 1 | no | — |
| 57 | #4035 | — | 3 | 1 | no | — |
| 58 | #4035 | — | 3 | 1 | no | — |
| 59 | #4035 | D3 | 1 | 1 | yes | characteristic |
| 60 | #4033 | — | 3 | 1 | no | — |
| 61 | #4033 | — | 3 | 1 | no | — |
| 62 | #4016 | — | 3 | 1 | no | — |
| 63 | #4016 | — | 3 | 1 | no | — |
| 64 | #4015 | — | 3 | 1 | no | — |
| 65 | C4×Dic10 | — | 3 | 1 | no | — |
| 66 | C4×Dic10 | — | 3 | 1 | no | — |
| 67 | C4×Dic10 | — | 3 | 1 | no | — |
| 68 | C2×C3×C4×C5 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×C3×C4×C5 | C23 | 1 | 1 | yes | characteristic |
| 70 | C2×C3×C4×C5 | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×Dic15 | C23 | 1 | 1 | yes | characteristic |
| 72 | C2×Dic15 | C23 | 1 | 1 | yes | characteristic |
| 73 | C2×Dic15 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×Dic15 | C23 | 1 | 1 | yes | characteristic |
| 75 | C2×C5×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×C5×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 77 | C2×C5×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 78 | C2×C5×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 79 | C5×Dic6 | — | 2 | 2 | no | — |
| 80 | C2×C3×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 81 | C2×C3×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 82 | C2×C3×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 83 | C2×C3×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 84 | #1204 | — | 2 | 2 | no | — |
| 85 | #1204 | — | 2 | 2 | no | — |
| 86 | #1204 | Q8 | 1 | 4 | yes | complemented |
| 87 | C3×#125 | — | 5 | 1 | no | — |
| 88 | #890 | — | 5 | 1 | no | — |
| 89 | #889 | — | 5 | 1 | no | — |
| 90 | #889 | — | 5 | 1 | no | — |
| 91 | #889 | — | 5 | 1 | no | — |
| 92 | #889 | — | 5 | 1 | no | — |
| 93 | #888 | — | 5 | 1 | no | — |
| 94 | #888 | — | 5 | 1 | no | — |
| 95 | #888 | — | 5 | 1 | no | — |
| 96 | #887 | — | 5 | 1 | no | — |
| 97 | #887 | — | 5 | 1 | no | — |
| 98 | #887 | — | 5 | 1 | no | — |
| 99 | #887 | D5 | 1 | 1 | yes | characteristic |
| 100 | C4×Dic6 | — | 5 | 1 | no | — |
| 101 | C4×Dic6 | — | 5 | 1 | no | — |
| 102 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 103 | C2×Dic10 | — | 3 | 1 | no | — |
| 104 | C2×Dic10 | — | 3 | 1 | no | — |
| 105 | C2×Dic10 | — | 3 | 1 | no | — |
| 106 | C5×C4⋊C4 | — | 3 | 1 | no | — |
| 107 | C5×C4⋊C4 | — | 3 | 1 | no | — |
| 108 | C5×C4⋊C4 | C2×D3 | 1 | 1 | yes | characteristic |
| 109 | C42×C5 | — | 3 | 1 | no | — |
| 110 | C42×C5 | — | 3 | 1 | no | — |
| 111 | C42×C5 | — | 3 | 1 | no | — |
| 112 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 113 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 114 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 115 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 116 | C4⋊Dic5 | C2×D3 | 1 | 1 | yes | characteristic |
| 117 | #683 | — | 3 | 1 | no | — |
| 118 | #683 | — | 3 | 1 | no | — |
| 119 | #683 | — | 3 | 1 | no | — |
| 120 | #683 | — | 3 | 1 | no | — |
| 121 | #683 | — | 3 | 1 | no | — |
| 122 | #683 | — | 3 | 1 | no | — |
| 123 | #683 | — | 3 | 1 | no | — |
| 124 | #683 | — | 3 | 1 | no | — |
| 125 | #683 | — | 3 | 1 | no | — |
| 126 | #683 | — | 3 | 1 | no | — |
| 127 | #683 | C2×D3 | 1 | 1 | yes | characteristic |
| 128 | #683 | C2×D3 | 1 | 1 | yes | characteristic |
| 129 | #683 | C2×D3 | 1 | 1 | yes | characteristic |
| 130 | #683 | C2×D3 | 1 | 1 | yes | characteristic |
| 131 | C4×Dic5 | — | 3 | 1 | no | — |
| 132 | C4×Dic5 | — | 3 | 1 | no | — |
| 133 | C4×Dic5 | — | 3 | 1 | no | — |
| 134 | C4×Dic5 | — | 3 | 1 | no | — |
| 135 | C4×Dic5 | — | 3 | 1 | no | — |
| 136 | C4×Dic5 | C2×D3 | 1 | 1 | yes | characteristic |
| 137 | #557 | — | 15 | 1 | no | Sylow |
| 138 | C22×C3×C5 | C24 | 1 | 1 | yes | characteristic |
| 139 | C3×C4×C5 | — | 2 | 1 | no | — |
| 140 | C3×C4×C5 | — | 2 | 1 | no | — |
| 141 | C3×C4×C5 | — | 2 | 1 | no | — |
| 142 | Dic15 | — | 2 | 1 | no | — |
| 143 | Dic15 | — | 2 | 1 | no | — |
| 144 | Dic15 | — | 2 | 1 | no | — |
| 145 | Dic15 | C2×Q8 | 1 | 2 | yes | — |
| 146 | C3×Dic5 | — | 2 | 1 | no | — |
| 147 | C3×Dic5 | — | 2 | 1 | no | — |
| 148 | C3×Dic5 | — | 2 | 1 | no | — |
| 149 | C3×Dic5 | C2×Q8 | 1 | 2 | yes | — |
| 150 | C5×Dic3 | — | 2 | 1 | no | — |
| 151 | C5×Dic3 | — | 2 | 1 | no | — |
| 152 | C5×Dic3 | C2×Q8 | 1 | 2 | yes | — |
| 153 | C5×Dic3 | #41 | 1 | 2 | yes | — |
| 154 | C2×Dic6 | — | 5 | 1 | no | — |
| 155 | C2×Dic6 | — | 5 | 1 | no | — |
| 156 | C2×Dic6 | — | 5 | 1 | no | — |
| 157 | C2×Dic6 | C2×D5 | 1 | 1 | yes | characteristic |
| 158 | C3×C4⋊C4 | — | 5 | 1 | no | — |
| 159 | C3×C4⋊C4 | — | 5 | 1 | no | — |
| 160 | C3×C4⋊C4 | — | 5 | 1 | no | — |
| 161 | C3×C4⋊C4 | — | 5 | 1 | no | — |
| 162 | C3×C4⋊C4 | — | 5 | 1 | no | — |
| 163 | C3×C4⋊C4 | C2×D5 | 1 | 1 | yes | characteristic |
| 164 | C3×C42 | — | 5 | 1 | no | — |
| 165 | C4⋊Dic3 | — | 5 | 1 | no | — |
| 166 | C4⋊Dic3 | — | 5 | 1 | no | — |
| 167 | C4⋊Dic3 | — | 5 | 1 | no | — |
| 168 | C4⋊Dic3 | — | 5 | 1 | no | — |
| 169 | Dic3⋊C4 | — | 5 | 1 | no | — |
| 170 | Dic3⋊C4 | — | 5 | 1 | no | — |
| 171 | Dic3⋊C4 | — | 5 | 1 | no | — |
| 172 | Dic3⋊C4 | — | 5 | 1 | no | — |
| 173 | Dic3⋊C4 | — | 5 | 1 | no | — |
| 174 | Dic3⋊C4 | — | 5 | 1 | no | — |
| 175 | Dic3⋊C4 | — | 5 | 1 | no | — |
| 176 | Dic3⋊C4 | — | 5 | 1 | no | — |
| 177 | Dic3⋊C4 | — | 5 | 1 | no | — |
| 178 | Dic3⋊C4 | — | 5 | 1 | no | — |
| 179 | Dic3⋊C4 | C2×D5 | 1 | 1 | yes | characteristic |
| 180 | Dic3⋊C4 | C2×D5 | 1 | 1 | yes | characteristic |
| 181 | C4×Dic3 | — | 5 | 1 | no | — |
| 182 | C4×Dic3 | — | 5 | 1 | no | — |
| 183 | C4×Dic3 | — | 5 | 1 | no | — |
| 184 | C4×Dic3 | — | 5 | 1 | no | — |
| 185 | C4×Dic3 | — | 5 | 1 | no | — |
| 186 | C4×Dic3 | C2×D5 | 1 | 1 | yes | characteristic |
| 187 | C4×Dic3 | C2×D5 | 1 | 1 | yes | characteristic |
| 188 | C4×Dic3 | C2×D5 | 1 | 1 | yes | characteristic |
| 189 | C5×Q8 | — | 6 | 2 | no | — |
| 190 | C2×C4×C5 | — | 3 | 1 | no | — |
| 191 | C2×C4×C5 | — | 3 | 1 | no | — |
| 192 | C2×C4×C5 | — | 3 | 1 | no | — |
| 193 | C2×C4×C5 | — | 3 | 1 | no | — |
| 194 | C2×C4×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 195 | C2×C4×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 196 | C2×C4×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 197 | C2×Dic5 | — | 3 | 1 | no | — |
| 198 | C2×Dic5 | — | 3 | 1 | no | — |
| 199 | C2×Dic5 | — | 3 | 1 | no | — |
| 200 | C2×Dic5 | — | 3 | 1 | no | — |
| 201 | C2×Dic5 | C22×D3 | 1 | 1 | yes | characteristic |
| 202 | C2×Dic5 | C22×D3 | 1 | 1 | yes | characteristic |
| 203 | C2×Dic5 | C22×D3 | 1 | 1 | yes | characteristic |
| 204 | C2×Dic5 | C22×D3 | 1 | 1 | yes | characteristic |
| 205 | Dic10 | — | 3 | 4 | no | — |
| 206 | Dic10 | — | 6 | 2 | no | — |
| 207 | Dic10 | — | 6 | 2 | no | — |
| 208 | C4⋊Q8 | — | 15 | 1 | no | — |
| 209 | C4⋊Q8 | — | 15 | 1 | no | — |
| 210 | C4⋊Q8 | — | 15 | 1 | no | — |
| 211 | #125 | — | 5 | 1 | no | — |
| 212 | #125 | — | 15 | 1 | no | — |
| 213 | #125 | — | 15 | 1 | no | — |
| 214 | #125 | — | 15 | 1 | no | — |
| 215 | #125 | — | 15 | 1 | no | — |
| 216 | #125 | — | 15 | 1 | no | — |
| 217 | C4×Q8 | — | 3 | 1 | no | — |
| 218 | C4×Q8 | — | 15 | 1 | no | — |
| 219 | C4×Q8 | — | 15 | 1 | no | — |
| 220 | C4×Q8 | — | 15 | 1 | no | — |
| 221 | C4×Q8 | — | 15 | 1 | no | — |
| 222 | C4×Q8 | — | 15 | 1 | no | — |
| 223 | C2×C3×C5 | C22×Q8 | 1 | 1 | yes | characteristic |
| 224 | C2×C3×C5 | C2×#41 | 1 | 1 | yes | characteristic |
| 225 | C2×C3×C5 | 2−1+4 | 1 | 1 | yes | characteristic |
| 226 | C2×C3×C4 | — | 5 | 1 | no | — |
| 227 | C2×C3×C4 | — | 5 | 1 | no | — |
| 228 | C2×C3×C4 | — | 5 | 1 | no | — |
| 229 | C2×C3×C4 | — | 5 | 1 | no | — |
| 230 | C2×C3×C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 231 | C2×C3×C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 232 | C2×C3×C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 233 | C2×Dic3 | — | 5 | 1 | no | — |
| 234 | C2×Dic3 | — | 5 | 1 | no | — |
| 235 | C2×Dic3 | — | 5 | 1 | no | — |
| 236 | C2×Dic3 | — | 5 | 1 | no | — |
| 237 | C2×Dic3 | C22×D5 | 1 | 1 | yes | characteristic |
| 238 | C2×Dic3 | C22×D5 | 1 | 1 | yes | characteristic |
| 239 | C2×Dic3 | C22×D5 | 1 | 1 | yes | characteristic |
| 240 | C2×Dic3 | C22×D5 | 1 | 1 | yes | characteristic |
| 241 | Dic6 | — | 2 | 2 | no | — |
| 242 | Dic6 | — | 5 | 4 | no | — |
| 243 | Dic6 | — | 10 | 2 | no | — |
| 244 | Dic6 | — | 10 | 2 | no | — |
| 245 | C22×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 246 | C4×C5 | — | 2 | 1 | no | — |
| 247 | C4×C5 | — | 2 | 1 | no | — |
| 248 | C4×C5 | — | 2 | 1 | no | — |
| 249 | C4×C5 | — | 3 | 2 | no | — |
| 250 | C4×C5 | — | 3 | 2 | no | — |
| 251 | C4×C5 | — | 6 | 1 | no | — |
| 252 | C4×C5 | — | 6 | 1 | no | — |
| 253 | Dic5 | — | 2 | 1 | no | — |
| 254 | Dic5 | — | 2 | 1 | no | — |
| 255 | Dic5 | — | 2 | 1 | no | — |
| 256 | Dic5 | — | 3 | 2 | no | — |
| 257 | Dic5 | — | 6 | 1 | no | — |
| 258 | Dic5 | — | 6 | 1 | no | — |
| 259 | Dic5 | — | 6 | 1 | no | — |
| 260 | Dic5 | D3×Q8 | 1 | 2 | yes | — |
| 261 | C2×Q8 | — | 3 | 1 | no | — |
| 262 | C2×Q8 | — | 15 | 1 | no | — |
| 263 | C2×Q8 | — | 15 | 1 | no | — |
| 264 | C2×Q8 | — | 15 | 1 | no | — |
| 265 | C4⋊C4 | — | 3 | 1 | no | — |
| 266 | C4⋊C4 | — | 3 | 1 | no | — |
| 267 | C4⋊C4 | — | 5 | 1 | no | — |
| 268 | C4⋊C4 | — | 5 | 1 | no | — |
| 269 | C4⋊C4 | — | 5 | 1 | no | — |
| 270 | C4⋊C4 | — | 5 | 1 | no | — |
| 271 | C4⋊C4 | — | 5 | 1 | no | — |
| 272 | C4⋊C4 | — | 15 | 1 | no | — |
| 273 | C4⋊C4 | — | 15 | 1 | no | — |
| 274 | C4⋊C4 | — | 15 | 1 | no | — |
| 275 | C4⋊C4 | — | 15 | 1 | no | — |
| 276 | C4⋊C4 | — | 15 | 1 | no | — |
| 277 | C4⋊C4 | — | 15 | 1 | no | — |
| 278 | C4⋊C4 | — | 15 | 1 | no | — |
| 279 | C4⋊C4 | — | 15 | 1 | no | — |
| 280 | C4⋊C4 | — | 15 | 1 | no | — |
| 281 | C4⋊C4 | — | 15 | 1 | no | — |
| 282 | C4⋊C4 | — | 15 | 1 | no | — |
| 283 | C4⋊C4 | — | 15 | 1 | no | — |
| 284 | C4⋊C4 | — | 15 | 1 | no | — |
| 285 | C4⋊C4 | — | 15 | 1 | no | — |
| 286 | C4⋊C4 | D3×D5 | 1 | 1 | yes | characteristic |
| 287 | C42 | — | 3 | 1 | no | — |
| 288 | C42 | — | 3 | 1 | no | — |
| 289 | C42 | — | 3 | 1 | no | — |
| 290 | C42 | — | 5 | 1 | no | — |
| 291 | C42 | — | 15 | 1 | no | — |
| 292 | C42 | — | 15 | 1 | no | — |
| 293 | C42 | — | 15 | 1 | no | — |
| 294 | C42 | — | 15 | 1 | no | — |
| 295 | C42 | — | 15 | 1 | no | — |
| 296 | C3×C5 | #557 | 1 | 1 | yes | characteristic, complemented, Hall |
| 297 | C22×C3 | C23×D5 | 1 | 1 | yes | characteristic |
| 298 | C3×C4 | — | 2 | 1 | no | — |
| 299 | C3×C4 | — | 2 | 1 | no | — |
| 300 | C3×C4 | — | 2 | 1 | no | — |
| 301 | C3×C4 | — | 5 | 2 | no | — |
| 302 | C3×C4 | — | 10 | 1 | no | — |
| 303 | C3×C4 | — | 10 | 1 | no | — |
| 304 | C3×C4 | — | 10 | 1 | no | — |
| 305 | Dic3 | — | 2 | 1 | no | — |
| 306 | Dic3 | — | 2 | 1 | no | — |
| 307 | Dic3 | — | 5 | 2 | no | — |
| 308 | Dic3 | — | 10 | 1 | no | — |
| 309 | Dic3 | — | 10 | 1 | no | — |
| 310 | Dic3 | — | 10 | 1 | no | — |
| 311 | Dic3 | #709 | 1 | 2 | yes | — |
| 312 | Dic3 | Q8×D5 | 1 | 2 | yes | — |
| 313 | C2×C5 | C2×D3×Q8 | 1 | 1 | yes | characteristic |
| 314 | C2×C5 | D3×#41 | 1 | 1 | yes | characteristic |
| 315 | C2×C5 | #1010 | 1 | 1 | yes | characteristic |
| 316 | Q8 | — | 6 | 2 | no | — |
| 317 | Q8 | — | 15 | 4 | no | — |
| 318 | Q8 | — | 30 | 2 | no | — |
| 319 | Q8 | — | 30 | 2 | no | — |
| 320 | C2×C4 | — | 3 | 1 | no | — |
| 321 | C2×C4 | — | 3 | 1 | no | — |
| 322 | C2×C4 | — | 3 | 1 | no | — |
| 323 | C2×C4 | — | 3 | 1 | no | — |
| 324 | C2×C4 | — | 5 | 1 | no | — |
| 325 | C2×C4 | — | 5 | 1 | no | — |
| 326 | C2×C4 | — | 5 | 1 | no | — |
| 327 | C2×C4 | — | 5 | 1 | no | — |
| 328 | C2×C4 | — | 15 | 1 | no | — |
| 329 | C2×C4 | — | 15 | 1 | no | — |
| 330 | C2×C4 | — | 15 | 1 | no | — |
| 331 | C2×C4 | — | 15 | 1 | no | — |
| 332 | C2×C4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 333 | C2×C4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 334 | C2×C4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 335 | C2×C3 | C2×#709 | 1 | 1 | yes | characteristic |
| 336 | C2×C3 | C2×Q8×D5 | 1 | 1 | yes | characteristic |
| 337 | C2×C3 | #4150 | 1 | 1 | yes | characteristic |
| 338 | C5 | #5685 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 339 | C22 | C22×D3×D5 | 1 | 1 | yes | characteristic |
| 340 | C4 | — | 2 | 1 | no | — |
| 341 | C4 | — | 2 | 1 | no | — |
| 342 | C4 | — | 2 | 1 | no | — |
| 343 | C4 | — | 3 | 2 | no | — |
| 344 | C4 | — | 3 | 2 | no | — |
| 345 | C4 | — | 5 | 2 | no | — |
| 346 | C4 | — | 6 | 1 | no | — |
| 347 | C4 | — | 6 | 1 | no | — |
| 348 | C4 | — | 10 | 1 | no | — |
| 349 | C4 | — | 10 | 1 | no | — |
| 350 | C4 | — | 10 | 1 | no | — |
| 351 | C4 | — | 15 | 2 | no | — |
| 352 | C4 | — | 30 | 1 | no | — |
| 353 | C4 | — | 30 | 1 | no | — |
| 354 | C4 | — | 30 | 1 | no | — |
| 355 | C3 | #65901 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 356 | C2 | D3×#709 | 1 | 1 | yes | characteristic |
| 357 | C2 | #92020 | 1 | 1 | yes | characteristic |
| 358 | C2 | D3×Q8×D5 | 1 | 1 | yes | characteristic |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta