Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1102 conjugacy classes of subgroups.
The subgroup lattice has 638 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13129605 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #13127972 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13127970 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13124499 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13116788 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #13116783 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | C2×#11718080 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #13116456 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×C13×#360 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #11719648 | — | 2 | 1 | no | — |
| 11 | C2×C13×#135 | C22 | 1 | 1 | yes | characteristic |
| 12 | #11719527 | — | 2 | 1 | no | — |
| 13 | #11719476 | — | 2 | 1 | no | — |
| 14 | #11719475 | — | 2 | 2 | no | — |
| 15 | #11719474 | — | 2 | 1 | no | — |
| 16 | #11719473 | C22 | 1 | 4 | yes | — |
| 17 | D13×#135 | — | 2 | 2 | no | — |
| 18 | #11719471 | — | 2 | 1 | no | — |
| 19 | #11719467 | — | 2 | 2 | no | — |
| 20 | #11719462 | — | 2 | 1 | no | — |
| 21 | C2×#88158 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#88158 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C2×#88155 | C22 | 1 | 1 | yes | characteristic |
| 24 | #11719215 | — | 2 | 1 | no | — |
| 25 | C2×C13×M32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C2×C13×#106 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #11718856 | C22 | 1 | 2 | yes | complemented |
| 28 | #11718855 | — | 2 | 2 | no | — |
| 29 | #11718854 | C22 | 1 | 2 | yes | complemented |
| 30 | #11718840 | — | 2 | 1 | no | — |
| 31 | #11718808 | — | 2 | 1 | no | — |
| 32 | C2×#88052 | C22 | 1 | 1 | yes | characteristic, complemented |
| 33 | #11718627 | — | 2 | 1 | no | — |
| 34 | #11718570 | — | 2 | 1 | no | — |
| 35 | #11718570 | C22 | 1 | 2 | yes | complemented |
| 36 | #11718569 | — | 2 | 1 | no | — |
| 37 | #11718569 | C22 | 1 | 2 | yes | complemented |
| 38 | #11718565 | — | 2 | 2 | no | — |
| 39 | #11718529 | C22 | 1 | 2 | yes | complemented |
| 40 | #11718526 | C22 | 1 | 2 | yes | complemented |
| 41 | #11718525 | — | 2 | 2 | no | — |
| 42 | C13×#360 | C22 | 1 | 4 | yes | complemented |
| 43 | #11718106 | C22 | 1 | 4 | yes | complemented |
| 44 | #11718080 | C22 | 1 | 4 | yes | complemented |
| 45 | C2×C13×#41 | — | 2 | 1 | no | — |
| 46 | #88257 | — | 2 | 2 | no | — |
| 47 | #88257 | — | 4 | 1 | no | — |
| 48 | #88256 | — | 2 | 2 | no | — |
| 49 | #88256 | — | 4 | 1 | no | — |
| 50 | #41×D13 | — | 2 | 4 | no | — |
| 51 | #41×D13 | — | 4 | 2 | no | — |
| 52 | #88254 | — | 2 | 2 | no | — |
| 53 | #88251 | — | 2 | 2 | no | — |
| 54 | #88251 | — | 4 | 2 | no | — |
| 55 | C2×#6127 | — | 2 | 1 | no | — |
| 56 | C2×#6127 | — | 2 | 1 | no | — |
| 57 | C2×#6127 | — | 4 | 2 | no | — |
| 58 | C2×#6127 | D4 | 1 | 1 | yes | characteristic |
| 59 | C13×#135 | — | 2 | 1 | no | — |
| 60 | C13×#135 | — | 2 | 1 | no | — |
| 61 | C13×#135 | D4 | 1 | 2 | yes | complemented |
| 62 | C13×#135 | C23 | 1 | 2 | yes | — |
| 63 | C2×C13×Q16 | D4 | 1 | 1 | yes | characteristic, complemented |
| 64 | C2×C13×SD16 | — | 2 | 1 | no | — |
| 65 | C2×C13×D8 | D4 | 1 | 1 | yes | characteristic, complemented |
| 66 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×C13×C4⋊C4 | — | 2 | 1 | no | — |
| 68 | #88205 | — | 2 | 2 | no | — |
| 69 | #88204 | — | 2 | 4 | no | — |
| 70 | #88203 | — | 2 | 2 | no | — |
| 71 | #88196 | — | 2 | 2 | no | — |
| 72 | #88186 | — | 2 | 2 | no | — |
| 73 | #88184 | — | 4 | 2 | no | — |
| 74 | C2×#6099 | D4 | 1 | 1 | yes | characteristic |
| 75 | #88173 | — | 2 | 2 | no | — |
| 76 | #88172 | — | 2 | 4 | no | — |
| 77 | Q16×D13 | — | 2 | 2 | no | — |
| 78 | #88170 | — | 2 | 4 | no | — |
| 79 | #88169 | — | 2 | 4 | no | — |
| 80 | #88168 | — | 2 | 4 | no | — |
| 81 | SD16×D13 | — | 2 | 4 | no | — |
| 82 | #88166 | — | 2 | 2 | no | — |
| 83 | #88165 | — | 2 | 4 | no | — |
| 84 | D8×D13 | — | 2 | 2 | no | — |
| 85 | C2×Dic52 | D4 | 1 | 1 | yes | characteristic, complemented |
| 86 | C2×Dic52 | C23 | 1 | 1 | yes | characteristic |
| 87 | #88158 | — | 2 | 1 | no | — |
| 88 | #88158 | — | 2 | 1 | no | — |
| 89 | #88158 | — | 2 | 1 | no | — |
| 90 | #88158 | — | 2 | 1 | no | — |
| 91 | #88158 | — | 2 | 1 | no | — |
| 92 | #88158 | — | 2 | 1 | no | — |
| 93 | #88158 | D4 | 1 | 2 | yes | complemented |
| 94 | #88158 | C23 | 1 | 2 | yes | — |
| 95 | C2×D104 | D4 | 1 | 1 | yes | characteristic, complemented |
| 96 | C2×D104 | C23 | 1 | 1 | yes | characteristic |
| 97 | C2×#6095 | — | 2 | 1 | no | — |
| 98 | C2×#6095 | — | 2 | 1 | no | — |
| 99 | #88155 | — | 2 | 1 | no | — |
| 100 | #88155 | — | 2 | 1 | no | — |
| 101 | #88155 | — | 2 | 1 | no | — |
| 102 | #88155 | — | 2 | 1 | no | — |
| 103 | C2×#6094 | C23 | 1 | 2 | yes | — |
| 104 | C2×C8×D13 | D4 | 1 | 2 | yes | — |
| 105 | #88151 | — | 2 | 2 | no | — |
| 106 | #88151 | — | 4 | 1 | no | — |
| 107 | #88149 | — | 2 | 2 | no | — |
| 108 | #88149 | — | 4 | 1 | no | — |
| 109 | C13×M32 | — | 2 | 1 | no | — |
| 110 | C13×M32 | C23 | 1 | 2 | yes | — |
| 111 | C2×C13×C16 | — | 2 | 1 | no | — |
| 112 | C13×#106 | — | 2 | 1 | no | — |
| 113 | C13×#106 | C23 | 1 | 2 | yes | — |
| 114 | #88069 | — | 2 | 2 | no | — |
| 115 | #88068 | — | 2 | 2 | no | — |
| 116 | #88067 | — | 2 | 2 | no | — |
| 117 | #88066 | — | 2 | 2 | no | — |
| 118 | #88052 | — | 2 | 1 | no | — |
| 119 | #88052 | C23 | 1 | 2 | yes | — |
| 120 | C2×#6090 | — | 2 | 1 | no | — |
| 121 | #88050 | — | 2 | 2 | no | — |
| 122 | #88049 | — | 2 | 2 | no | — |
| 123 | Dic104 | — | 2 | 2 | no | — |
| 124 | #88040 | — | 2 | 2 | no | — |
| 125 | #88040 | — | 2 | 2 | no | — |
| 126 | D208 | — | 2 | 2 | no | — |
| 127 | #33533 | — | 13 | 1 | no | maximal, Sylow |
| 128 | C13×#41 | — | 2 | 2 | no | — |
| 129 | C13×#41 | — | 2 | 2 | no | — |
| 130 | C13×#41 | — | 4 | 1 | no | — |
| 131 | C13×#41 | — | 4 | 1 | no | — |
| 132 | C2×Q8×C13 | — | 2 | 1 | no | — |
| 133 | C2×D4×C13 | — | 2 | 1 | no | — |
| 134 | C2×D4×C13 | — | 4 | 1 | no | — |
| 135 | C22×C4×C13 | — | 4 | 1 | no | — |
| 136 | C22×C4×C13 | — | 4 | 1 | no | — |
| 137 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 138 | C2×C22⋊D13 | — | 4 | 4 | no | — |
| 139 | C2×C22⋊D13 | — | 4 | 1 | no | — |
| 140 | C2×C22⋊D13 | — | 4 | 1 | no | — |
| 141 | C2×C22⋊D13 | D8 | 1 | 2 | yes | — |
| 142 | #6131 | — | 2 | 4 | no | — |
| 143 | #6131 | — | 4 | 2 | no | — |
| 144 | Q8×D13 | — | 2 | 4 | no | — |
| 145 | Q8×D13 | — | 4 | 2 | no | — |
| 146 | #6129 | — | 2 | 4 | no | — |
| 147 | #6129 | — | 4 | 2 | no | — |
| 148 | #6129 | — | 4 | 4 | no | — |
| 149 | #6129 | — | 4 | 4 | no | — |
| 150 | D4×D13 | — | 2 | 4 | no | — |
| 151 | D4×D13 | — | 4 | 2 | no | — |
| 152 | D4×D13 | — | 4 | 4 | no | — |
| 153 | D4×D13 | — | 4 | 4 | no | — |
| 154 | #6127 | — | 2 | 1 | no | — |
| 155 | #6127 | — | 2 | 1 | no | — |
| 156 | #6127 | — | 2 | 1 | no | — |
| 157 | #6127 | — | 2 | 1 | no | — |
| 158 | #6127 | — | 2 | 2 | no | — |
| 159 | #6127 | — | 2 | 2 | no | — |
| 160 | #6127 | — | 4 | 2 | no | — |
| 161 | #6127 | — | 4 | 4 | no | — |
| 162 | #6127 | — | 4 | 2 | no | — |
| 163 | #6127 | — | 4 | 4 | no | — |
| 164 | #6127 | — | 4 | 1 | no | — |
| 165 | #6127 | — | 4 | 1 | no | — |
| 166 | #6127 | — | 4 | 1 | no | — |
| 167 | #6127 | — | 4 | 1 | no | — |
| 168 | #6127 | — | 4 | 1 | no | — |
| 169 | #6127 | — | 4 | 1 | no | — |
| 170 | C2×D52 | — | 2 | 1 | no | — |
| 171 | C2×D52 | — | 2 | 1 | no | — |
| 172 | C2×D52 | — | 4 | 2 | no | — |
| 173 | C2×D52 | — | 4 | 2 | no | — |
| 174 | C2×D52 | D8 | 1 | 1 | yes | characteristic |
| 175 | C2×C4×D13 | — | 4 | 4 | no | — |
| 176 | C2×C4×D13 | — | 4 | 1 | no | — |
| 177 | C2×C4×D13 | — | 4 | 1 | no | — |
| 178 | C2×C4×D13 | C2×D4 | 1 | 2 | yes | — |
| 179 | C2×Dic26 | — | 2 | 1 | no | — |
| 180 | C2×Dic26 | — | 2 | 1 | no | — |
| 181 | C2×Dic26 | — | 4 | 2 | no | — |
| 182 | C2×Dic26 | D8 | 1 | 1 | yes | characteristic |
| 183 | C13×Q16 | — | 2 | 1 | no | — |
| 184 | C13×Q16 | C2×D4 | 1 | 2 | yes | — |
| 185 | C13×SD16 | — | 2 | 2 | no | — |
| 186 | C13×SD16 | — | 2 | 2 | no | — |
| 187 | C13×D8 | — | 2 | 1 | no | — |
| 188 | C13×D8 | C2×D4 | 1 | 2 | yes | — |
| 189 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 194 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 195 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 196 | C13×C4⋊C4 | — | 4 | 1 | no | — |
| 197 | #6107 | — | 2 | 4 | no | — |
| 198 | #6106 | — | 2 | 4 | no | — |
| 199 | #6105 | — | 2 | 4 | no | — |
| 200 | #6104 | — | 2 | 4 | no | — |
| 201 | #6103 | — | 4 | 2 | no | — |
| 202 | #6103 | — | 4 | 2 | no | — |
| 203 | C4⋊Dic13 | — | 4 | 2 | no | — |
| 204 | #6099 | — | 2 | 1 | no | — |
| 205 | #6099 | — | 2 | 1 | no | — |
| 206 | C2×#1055 | C2×D4 | 1 | 2 | yes | — |
| 207 | Dic52 | — | 2 | 1 | no | — |
| 208 | Dic52 | — | 2 | 1 | no | — |
| 209 | Dic52 | — | 2 | 1 | no | — |
| 210 | Dic52 | C2×D4 | 1 | 2 | yes | — |
| 211 | D104 | — | 2 | 1 | no | — |
| 212 | D104 | — | 2 | 1 | no | — |
| 213 | D104 | — | 2 | 1 | no | — |
| 214 | D104 | C2×D4 | 1 | 2 | yes | — |
| 215 | #6095 | — | 2 | 2 | no | — |
| 216 | #6095 | — | 2 | 2 | no | — |
| 217 | #6095 | — | 4 | 1 | no | — |
| 218 | #6095 | — | 4 | 1 | no | — |
| 219 | #6094 | — | 2 | 2 | no | — |
| 220 | #6094 | — | 2 | 2 | no | — |
| 221 | C8×D13 | — | 2 | 2 | no | — |
| 222 | C8×D13 | — | 2 | 2 | no | — |
| 223 | C13×C16 | — | 2 | 2 | no | — |
| 224 | #6090 | — | 2 | 2 | no | — |
| 225 | #3584 | — | 13 | 1 | no | — |
| 226 | #3414 | — | 13 | 1 | no | — |
| 227 | #3414 | — | 13 | 1 | no | — |
| 228 | #3060 | — | 13 | 1 | no | — |
| 229 | #2191 | — | 13 | 4 | no | — |
| 230 | #2190 | — | 13 | 4 | no | — |
| 231 | C2×#360 | — | 13 | 1 | no | — |
| 232 | C2×#360 | D13 | 1 | 1 | yes | characteristic, complemented |
| 233 | #2115 | — | 13 | 1 | no | — |
| 234 | C23×C13 | — | 4 | 1 | no | — |
| 235 | C23×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 236 | C22×D13 | — | 4 | 4 | no | — |
| 237 | C22×D13 | — | 4 | 1 | no | — |
| 238 | C22×D13 | — | 4 | 1 | no | — |
| 239 | C22×D13 | C2×D8 | 1 | 2 | yes | — |
| 240 | Q8×C13 | — | 2 | 2 | no | — |
| 241 | Q8×C13 | — | 4 | 1 | no | — |
| 242 | D4×C13 | — | 2 | 2 | no | — |
| 243 | D4×C13 | — | 4 | 2 | no | — |
| 244 | D4×C13 | — | 4 | 2 | no | — |
| 245 | D4×C13 | — | 4 | 1 | no | — |
| 246 | C2×C4×C13 | — | 4 | 1 | no | — |
| 247 | C2×C4×C13 | — | 4 | 2 | no | — |
| 248 | C2×C4×C13 | — | 4 | 2 | no | — |
| 249 | C2×C4×C13 | — | 4 | 2 | no | — |
| 250 | C2×C4×C13 | — | 16 | 1 | no | — |
| 251 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 252 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 253 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 254 | C2×C4×C13 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 255 | C2×C4×C13 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 256 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 257 | C22⋊D13 | — | 2 | 2 | no | — |
| 258 | C22⋊D13 | — | 2 | 2 | no | — |
| 259 | C22⋊D13 | — | 4 | 4 | no | — |
| 260 | C22⋊D13 | — | 4 | 4 | no | — |
| 261 | C22⋊D13 | — | 4 | 2 | no | — |
| 262 | C22⋊D13 | — | 4 | 2 | no | — |
| 263 | C22⋊D13 | — | 8 | 1 | no | — |
| 264 | C22⋊D13 | — | 8 | 1 | no | — |
| 265 | C2×Dic13 | — | 4 | 4 | no | — |
| 266 | C2×Dic13 | — | 4 | 1 | no | — |
| 267 | C2×Dic13 | — | 4 | 1 | no | — |
| 268 | C2×Dic13 | C2×D8 | 1 | 2 | yes | — |
| 269 | D52 | — | 2 | 2 | no | — |
| 270 | D52 | — | 2 | 1 | no | — |
| 271 | D52 | — | 2 | 1 | no | — |
| 272 | D52 | — | 4 | 4 | no | — |
| 273 | D52 | — | 4 | 1 | no | — |
| 274 | D52 | — | 4 | 1 | no | — |
| 275 | D52 | — | 4 | 1 | no | — |
| 276 | D52 | — | 16 | 2 | no | — |
| 277 | C4×D13 | — | 2 | 2 | no | — |
| 278 | C4×D13 | — | 2 | 2 | no | — |
| 279 | C4×D13 | — | 4 | 4 | no | — |
| 280 | C4×D13 | — | 4 | 4 | no | — |
| 281 | C4×D13 | — | 4 | 2 | no | — |
| 282 | C4×D13 | — | 4 | 2 | no | — |
| 283 | C4×D13 | — | 8 | 1 | no | — |
| 284 | C4×D13 | — | 8 | 1 | no | — |
| 285 | Dic26 | — | 2 | 1 | no | — |
| 286 | Dic26 | — | 2 | 1 | no | — |
| 287 | Dic26 | — | 2 | 2 | no | — |
| 288 | Dic26 | — | 4 | 4 | no | — |
| 289 | Dic26 | — | 4 | 1 | no | — |
| 290 | Dic26 | — | 4 | 1 | no | — |
| 291 | Dic26 | — | 4 | 1 | no | — |
| 292 | C8×C13 | #120 | 1 | 1 | yes | characteristic |
| 293 | C8×C13 | #120 | 1 | 1 | yes | characteristic |
| 294 | C8×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 295 | C8×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 296 | #1055 | — | 2 | 2 | no | — |
| 297 | #585 | — | 26 | 1 | no | — |
| 298 | #578 | — | 26 | 1 | no | — |
| 299 | #578 | — | 26 | 1 | no | — |
| 300 | #577 | — | 26 | 2 | no | — |
| 301 | #577 | — | 26 | 2 | no | — |
| 302 | #576 | — | 26 | 1 | no | — |
| 303 | #576 | — | 26 | 1 | no | — |
| 304 | #575 | — | 13 | 4 | no | — |
| 305 | #575 | — | 26 | 1 | no | — |
| 306 | C2×#135 | — | 13 | 1 | no | — |
| 307 | C2×#135 | — | 13 | 1 | no | — |
| 308 | C2×#135 | — | 26 | 2 | no | — |
| 309 | C2×#135 | C2×D13 | 1 | 1 | yes | characteristic |
| 310 | C2×#131 | — | 13 | 1 | no | — |
| 311 | #537 | — | 26 | 1 | no | — |
| 312 | #510 | — | 13 | 2 | no | — |
| 313 | #510 | — | 13 | 2 | no | — |
| 314 | #510 | — | 26 | 1 | no | — |
| 315 | #510 | — | 26 | 1 | no | — |
| 316 | #509 | — | 13 | 2 | no | — |
| 317 | #509 | — | 13 | 2 | no | — |
| 318 | #509 | — | 26 | 1 | no | — |
| 319 | #509 | — | 26 | 1 | no | — |
| 320 | #508 | — | 26 | 2 | no | — |
| 321 | #508 | — | 26 | 2 | no | — |
| 322 | C2×M32 | — | 13 | 1 | no | — |
| 323 | C2×M32 | C2×D13 | 1 | 1 | yes | characteristic, complemented |
| 324 | #470 | — | 13 | 2 | no | — |
| 325 | #469 | — | 13 | 2 | no | — |
| 326 | #465 | — | 26 | 2 | no | — |
| 327 | C2×#106 | C2×D13 | 1 | 1 | yes | characteristic, complemented |
| 328 | #417 | — | 26 | 1 | no | — |
| 329 | #360 | — | 13 | 4 | no | — |
| 330 | #360 | C2×D13 | 1 | 4 | yes | complemented |
| 331 | #349 | — | 13 | 4 | no | — |
| 332 | C22×C13 | — | 4 | 1 | no | — |
| 333 | C22×C13 | — | 4 | 2 | no | — |
| 334 | C22×C13 | — | 16 | 1 | no | — |
| 335 | C22×C13 | #447 | 1 | 1 | yes | characteristic |
| 336 | C22×C13 | #447 | 1 | 1 | yes | characteristic |
| 337 | C22×C13 | C22×D8 | 1 | 1 | yes | characteristic |
| 338 | C2×D13 | — | 2 | 2 | no | — |
| 339 | C2×D13 | — | 4 | 2 | no | — |
| 340 | C2×D13 | — | 4 | 2 | no | — |
| 341 | C2×D13 | — | 8 | 1 | no | — |
| 342 | C2×D13 | — | 8 | 1 | no | — |
| 343 | C2×D13 | — | 8 | 1 | no | — |
| 344 | C2×D13 | — | 16 | 4 | no | — |
| 345 | C2×D13 | — | 16 | 1 | no | — |
| 346 | C4×C13 | — | 4 | 2 | no | — |
| 347 | C4×C13 | — | 8 | 2 | no | — |
| 348 | C4×C13 | #447 | 1 | 1 | yes | characteristic |
| 349 | C4×C13 | #447 | 1 | 1 | yes | characteristic |
| 350 | C4×C13 | C2×#120 | 1 | 1 | yes | characteristic |
| 351 | C4×C13 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 352 | Dic13 | — | 2 | 2 | no | — |
| 353 | Dic13 | — | 4 | 2 | no | — |
| 354 | Dic13 | — | 8 | 1 | no | — |
| 355 | 2−1+4 | — | 26 | 2 | no | — |
| 356 | 2−1+4 | — | 26 | 2 | no | — |
| 357 | 2−1+4 | — | 52 | 1 | no | — |
| 358 | H(5,𝔽2) | — | 26 | 2 | no | — |
| 359 | H(5,𝔽2) | — | 26 | 2 | no | — |
| 360 | H(5,𝔽2) | — | 52 | 2 | no | — |
| 361 | H(5,𝔽2) | — | 52 | 1 | no | — |
| 362 | C2×#41 | — | 2 | 1 | no | — |
| 363 | C2×#41 | — | 13 | 1 | no | — |
| 364 | C2×#41 | — | 26 | 4 | no | — |
| 365 | C2×#41 | — | 26 | 1 | no | — |
| 366 | C2×#41 | — | 26 | 1 | no | — |
| 367 | C2×#41 | — | 52 | 2 | no | — |
| 368 | C2×#41 | — | 52 | 2 | no | — |
| 369 | #137 | — | 26 | 4 | no | — |
| 370 | #137 | — | 26 | 2 | no | — |
| 371 | #137 | — | 26 | 2 | no | — |
| 372 | #137 | — | 26 | 4 | no | — |
| 373 | AGL(1,ℤ/8) | — | 26 | 4 | no | — |
| 374 | AGL(1,ℤ/8) | — | 26 | 2 | no | — |
| 375 | AGL(1,ℤ/8) | — | 26 | 2 | no | — |
| 376 | AGL(1,ℤ/8) | — | 26 | 4 | no | — |
| 377 | #135 | — | 2 | 1 | no | — |
| 378 | #135 | — | 2 | 1 | no | — |
| 379 | #135 | — | 13 | 2 | no | — |
| 380 | #135 | — | 13 | 2 | no | — |
| 381 | #135 | — | 26 | 4 | no | — |
| 382 | #135 | — | 26 | 2 | no | — |
| 383 | #135 | — | 26 | 4 | no | — |
| 384 | #135 | — | 26 | 2 | no | — |
| 385 | #135 | — | 26 | 1 | no | — |
| 386 | #135 | — | 26 | 1 | no | — |
| 387 | #135 | — | 26 | 1 | no | — |
| 388 | #135 | — | 26 | 1 | no | — |
| 389 | #135 | — | 26 | 1 | no | — |
| 390 | #135 | — | 26 | 1 | no | — |
| 391 | #135 | D52 | 1 | 2 | yes | complemented |
| 392 | #135 | C22×D13 | 1 | 2 | yes | — |
| 393 | C2×Q16 | — | 13 | 1 | no | — |
| 394 | C2×Q16 | — | 13 | 1 | no | — |
| 395 | C2×Q16 | — | 26 | 2 | no | — |
| 396 | C2×Q16 | D52 | 1 | 1 | yes | characteristic, complemented |
| 397 | C2×SD16 | — | 2 | 1 | no | — |
| 398 | C2×SD16 | — | 26 | 4 | no | — |
| 399 | C2×SD16 | — | 26 | 1 | no | — |
| 400 | C2×SD16 | — | 26 | 1 | no | — |
| 401 | C2×D8 | — | 13 | 1 | no | — |
| 402 | C2×D8 | — | 13 | 1 | no | — |
| 403 | C2×D8 | — | 26 | 2 | no | — |
| 404 | C2×D8 | D52 | 1 | 1 | yes | characteristic, complemented |
| 405 | #131 | — | 26 | 1 | no | — |
| 406 | #131 | — | 26 | 1 | no | — |
| 407 | #131 | — | 26 | 1 | no | — |
| 408 | #131 | — | 26 | 1 | no | — |
| 409 | C2×M16 | — | 13 | 1 | no | — |
| 410 | C2×M16 | — | 13 | 2 | no | — |
| 411 | C22×C8 | — | 13 | 2 | no | — |
| 412 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 413 | C22⋊Q8 | — | 26 | 2 | no | — |
| 414 | C22⋊Q8 | — | 52 | 1 | no | — |
| 415 | #121 | — | 26 | 2 | no | — |
| 416 | #121 | — | 52 | 1 | no | — |
| 417 | #121 | — | 52 | 2 | no | — |
| 418 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 419 | Q32 | — | 26 | 2 | no | — |
| 420 | Q32 | — | 26 | 2 | no | — |
| 421 | SD32 | — | 26 | 2 | no | — |
| 422 | SD32 | — | 26 | 2 | no | — |
| 423 | SD32 | — | 26 | 2 | no | — |
| 424 | SD32 | — | 26 | 2 | no | — |
| 425 | D16 | — | 26 | 2 | no | — |
| 426 | D16 | — | 26 | 2 | no | — |
| 427 | M32 | — | 2 | 1 | no | — |
| 428 | M32 | — | 13 | 2 | no | — |
| 429 | M32 | — | 26 | 1 | no | — |
| 430 | M32 | C22×D13 | 1 | 2 | yes | — |
| 431 | C2×C16 | — | 2 | 1 | no | — |
| 432 | C2×C16 | — | 26 | 1 | no | — |
| 433 | #106 | — | 2 | 1 | no | — |
| 434 | #106 | C22×D13 | 1 | 2 | yes | — |
| 435 | #103 | — | 26 | 2 | no | — |
| 436 | #102 | — | 26 | 2 | no | — |
| 437 | C2×C13 | — | 2 | 1 | no | — |
| 438 | C2×C13 | — | 2 | 1 | no | — |
| 439 | C2×C13 | — | 2 | 1 | no | — |
| 440 | C2×C13 | — | 8 | 2 | no | — |
| 441 | C2×C13 | C2×#447 | 1 | 1 | yes | characteristic |
| 442 | D13 | — | 4 | 2 | no | — |
| 443 | D13 | — | 8 | 2 | no | — |
| 444 | D13 | — | 16 | 1 | no | — |
| 445 | #41 | — | 2 | 2 | no | — |
| 446 | #41 | — | 2 | 2 | no | — |
| 447 | #41 | — | 4 | 1 | no | — |
| 448 | #41 | — | 4 | 1 | no | — |
| 449 | #41 | — | 26 | 1 | no | — |
| 450 | #41 | — | 26 | 1 | no | — |
| 451 | #41 | — | 26 | 1 | no | — |
| 452 | #41 | — | 26 | 1 | no | — |
| 453 | #41 | — | 26 | 4 | no | — |
| 454 | #41 | — | 26 | 4 | no | — |
| 455 | #41 | — | 26 | 2 | no | — |
| 456 | #41 | — | 26 | 2 | no | — |
| 457 | #41 | — | 52 | 4 | no | — |
| 458 | #41 | — | 52 | 4 | no | — |
| 459 | #41 | — | 52 | 2 | no | — |
| 460 | #41 | — | 52 | 2 | no | — |
| 461 | #41 | — | 52 | 4 | no | — |
| 462 | #41 | — | 52 | 4 | no | — |
| 463 | #41 | — | 52 | 2 | no | — |
| 464 | #41 | — | 52 | 2 | no | — |
| 465 | #41 | — | 52 | 1 | no | — |
| 466 | #41 | — | 52 | 1 | no | — |
| 467 | #41 | — | 52 | 1 | no | — |
| 468 | #41 | — | 52 | 1 | no | — |
| 469 | #41 | — | 52 | 1 | no | — |
| 470 | #41 | — | 52 | 1 | no | — |
| 471 | C2×Q8 | — | 2 | 1 | no | — |
| 472 | C2×Q8 | — | 13 | 1 | no | — |
| 473 | C2×Q8 | — | 26 | 4 | no | — |
| 474 | C2×Q8 | — | 26 | 1 | no | — |
| 475 | C2×Q8 | — | 26 | 1 | no | — |
| 476 | C2×Q8 | — | 52 | 2 | no | — |
| 477 | C2×Q8 | — | 52 | 2 | no | — |
| 478 | C2×D4 | — | 2 | 1 | no | — |
| 479 | C2×D4 | — | 4 | 1 | no | — |
| 480 | C2×D4 | — | 13 | 2 | no | — |
| 481 | C2×D4 | — | 13 | 1 | no | — |
| 482 | C2×D4 | — | 26 | 4 | no | — |
| 483 | C2×D4 | — | 26 | 1 | no | — |
| 484 | C2×D4 | — | 26 | 1 | no | — |
| 485 | C2×D4 | — | 52 | 2 | no | — |
| 486 | C2×D4 | — | 52 | 2 | no | — |
| 487 | C2×D4 | — | 52 | 4 | no | — |
| 488 | C2×D4 | — | 52 | 2 | no | — |
| 489 | C2×D4 | — | 52 | 4 | no | — |
| 490 | C2×D4 | — | 52 | 4 | no | — |
| 491 | C2×D4 | — | 52 | 1 | no | — |
| 492 | C2×D4 | — | 52 | 1 | no | — |
| 493 | C22×C4 | — | 4 | 1 | no | — |
| 494 | C22×C4 | — | 4 | 1 | no | — |
| 495 | C22×C4 | — | 13 | 2 | no | — |
| 496 | C22×C4 | — | 52 | 4 | no | — |
| 497 | C22×C4 | — | 52 | 1 | no | — |
| 498 | C22×C4 | — | 52 | 1 | no | — |
| 499 | C22×C4 | D4×D13 | 1 | 1 | yes | characteristic |
| 500 | Q16 | — | 2 | 1 | no | — |
| 501 | Q16 | — | 13 | 2 | no | — |
| 502 | Q16 | — | 26 | 4 | no | — |
| 503 | Q16 | — | 26 | 1 | no | — |
| 504 | Q16 | — | 26 | 1 | no | — |
| 505 | Q16 | — | 26 | 1 | no | — |
| 506 | Q16 | C2×D52 | 1 | 2 | yes | — |
| 507 | SD16 | — | 2 | 2 | no | — |
| 508 | SD16 | — | 2 | 2 | no | — |
| 509 | SD16 | — | 26 | 4 | no | — |
| 510 | SD16 | — | 26 | 4 | no | — |
| 511 | SD16 | — | 26 | 2 | no | — |
| 512 | SD16 | — | 26 | 2 | no | — |
| 513 | SD16 | — | 52 | 1 | no | — |
| 514 | SD16 | — | 52 | 1 | no | — |
| 515 | D8 | — | 2 | 1 | no | — |
| 516 | D8 | — | 13 | 2 | no | — |
| 517 | D8 | — | 26 | 4 | no | — |
| 518 | D8 | — | 26 | 1 | no | — |
| 519 | D8 | — | 26 | 1 | no | — |
| 520 | D8 | — | 26 | 1 | no | — |
| 521 | D8 | C2×D52 | 1 | 2 | yes | — |
| 522 | M16 | — | 26 | 1 | no | — |
| 523 | M16 | — | 26 | 1 | no | — |
| 524 | M16 | — | 26 | 2 | no | — |
| 525 | M16 | — | 26 | 2 | no | — |
| 526 | C2×C8 | — | 13 | 2 | no | — |
| 527 | C2×C8 | — | 26 | 2 | no | — |
| 528 | C2×C8 | — | 26 | 2 | no | — |
| 529 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 530 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 531 | C2×C8 | D4×D13 | 1 | 1 | yes | characteristic |
| 532 | C2×C8 | D4×D13 | 1 | 1 | yes | characteristic |
| 533 | C2×C8 | D4×D13 | 1 | 1 | yes | characteristic |
| 534 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 535 | C4⋊C4 | — | 2 | 2 | no | — |
| 536 | C4⋊C4 | — | 4 | 1 | no | — |
| 537 | C4⋊C4 | — | 52 | 2 | no | — |
| 538 | C22⋊C4 | — | 52 | 2 | no | — |
| 539 | C22⋊C4 | — | 52 | 2 | no | — |
| 540 | C16 | — | 2 | 2 | no | — |
| 541 | C16 | — | 26 | 2 | no | — |
| 542 | C13 | #33533 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 543 | C23 | — | 4 | 1 | no | — |
| 544 | C23 | — | 13 | 2 | no | — |
| 545 | C23 | — | 52 | 4 | no | — |
| 546 | C23 | — | 52 | 1 | no | — |
| 547 | C23 | — | 52 | 1 | no | — |
| 548 | C23 | D8×D13 | 1 | 1 | yes | characteristic |
| 549 | Q8 | — | 2 | 2 | no | — |
| 550 | Q8 | — | 4 | 1 | no | — |
| 551 | Q8 | — | 26 | 1 | no | — |
| 552 | Q8 | — | 26 | 1 | no | — |
| 553 | Q8 | — | 26 | 2 | no | — |
| 554 | Q8 | — | 52 | 4 | no | — |
| 555 | Q8 | — | 52 | 1 | no | — |
| 556 | Q8 | — | 52 | 1 | no | — |
| 557 | Q8 | — | 52 | 1 | no | — |
| 558 | D4 | — | 2 | 2 | no | — |
| 559 | D4 | — | 4 | 2 | no | — |
| 560 | D4 | — | 4 | 2 | no | — |
| 561 | D4 | — | 4 | 1 | no | — |
| 562 | D4 | — | 26 | 2 | no | — |
| 563 | D4 | — | 26 | 2 | no | — |
| 564 | D4 | — | 26 | 2 | no | — |
| 565 | D4 | — | 26 | 1 | no | — |
| 566 | D4 | — | 26 | 1 | no | — |
| 567 | D4 | — | 52 | 4 | no | — |
| 568 | D4 | — | 52 | 4 | no | — |
| 569 | D4 | — | 52 | 4 | no | — |
| 570 | D4 | — | 52 | 2 | no | — |
| 571 | D4 | — | 52 | 2 | no | — |
| 572 | D4 | — | 52 | 1 | no | — |
| 573 | D4 | — | 52 | 1 | no | — |
| 574 | D4 | — | 52 | 1 | no | — |
| 575 | D4 | — | 104 | 1 | no | — |
| 576 | D4 | — | 104 | 1 | no | — |
| 577 | D4 | — | 208 | 2 | no | — |
| 578 | C2×C4 | — | 4 | 1 | no | — |
| 579 | C2×C4 | — | 4 | 2 | no | — |
| 580 | C2×C4 | — | 4 | 2 | no | — |
| 581 | C2×C4 | — | 4 | 2 | no | — |
| 582 | C2×C4 | — | 13 | 2 | no | — |
| 583 | C2×C4 | — | 16 | 1 | no | — |
| 584 | C2×C4 | — | 26 | 2 | no | — |
| 585 | C2×C4 | — | 26 | 2 | no | — |
| 586 | C2×C4 | — | 52 | 4 | no | — |
| 587 | C2×C4 | — | 52 | 4 | no | — |
| 588 | C2×C4 | — | 52 | 4 | no | — |
| 589 | C2×C4 | — | 52 | 1 | no | — |
| 590 | C2×C4 | — | 52 | 2 | no | — |
| 591 | C2×C4 | — | 52 | 2 | no | — |
| 592 | C2×C4 | — | 52 | 1 | no | — |
| 593 | C2×C4 | — | 104 | 1 | no | — |
| 594 | C2×C4 | — | 104 | 1 | no | — |
| 595 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 596 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 597 | C2×C4 | D8×D13 | 1 | 1 | yes | characteristic |
| 598 | C2×C4 | #88168 | 1 | 1 | yes | characteristic |
| 599 | C2×C4 | #88168 | 1 | 1 | yes | characteristic |
| 600 | C2×C4 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 601 | C8 | — | 26 | 2 | no | — |
| 602 | C8 | #88136 | 1 | 1 | yes | characteristic |
| 603 | C8 | #88136 | 1 | 1 | yes | characteristic |
| 604 | C8 | C22×D52 | 1 | 1 | yes | characteristic |
| 605 | C8 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 606 | C22 | — | 4 | 1 | no | — |
| 607 | C22 | — | 4 | 2 | no | — |
| 608 | C22 | — | 16 | 1 | no | — |
| 609 | C22 | — | 26 | 2 | no | — |
| 610 | C22 | — | 52 | 2 | no | — |
| 611 | C22 | — | 52 | 2 | no | — |
| 612 | C22 | — | 104 | 1 | no | — |
| 613 | C22 | — | 104 | 1 | no | — |
| 614 | C22 | — | 104 | 1 | no | — |
| 615 | C22 | — | 208 | 1 | no | — |
| 616 | C22 | — | 208 | 4 | no | — |
| 617 | C22 | #11718434 | 1 | 1 | yes | characteristic |
| 618 | C22 | #11718434 | 1 | 1 | yes | characteristic |
| 619 | C22 | C2×D8×D13 | 1 | 1 | yes | characteristic |
| 620 | C4 | — | 4 | 2 | no | — |
| 621 | C4 | — | 8 | 2 | no | — |
| 622 | C4 | — | 26 | 2 | no | — |
| 623 | C4 | — | 52 | 2 | no | — |
| 624 | C4 | — | 104 | 1 | no | — |
| 625 | C4 | #11718434 | 1 | 1 | yes | characteristic |
| 626 | C4 | #11718434 | 1 | 1 | yes | characteristic |
| 627 | C4 | C2×#88136 | 1 | 1 | yes | characteristic |
| 628 | C4 | C2×#88168 | 1 | 1 | yes | characteristic |
| 629 | C2 | — | 2 | 1 | no | — |
| 630 | C2 | — | 2 | 1 | no | — |
| 631 | C2 | — | 2 | 1 | no | — |
| 632 | C2 | — | 8 | 2 | no | — |
| 633 | C2 | — | 52 | 2 | no | — |
| 634 | C2 | — | 104 | 2 | no | — |
| 635 | C2 | — | 208 | 1 | no | — |
| 636 | C2 | C2×#11718434 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13129605 | C2 | semidirect |
| 2. #13127972 | C2 | semidirect |
| 3. #13127970 | C2 | semidirect |
| 4. #13124499 | C2 | semidirect |
| 5. #13116788 | C2 | semidirect |
| 6. #13116783 | C2 | semidirect |
| 7. C2×#11718080 | C2 | semidirect |
| 8. #13116456 | C2 | semidirect |
| 9. C2×C13×#360 | C2 | semidirect |
| 22. C2×#88158 | C22 | semidirect |
| 25. C2×C13×M32 | C22 | semidirect |
| 26. C2×C13×#106 | C22 | semidirect |
| 27. #11718856 | C22 | semidirect |
| 29. #11718854 | C22 | semidirect |
| 32. C2×#88052 | C22 | semidirect |
| 35. #11718570 | C22 | semidirect |
| 37. #11718569 | C22 | semidirect |
| 39. #11718529 | C22 | semidirect |
| 40. #11718526 | C22 | semidirect |
| 42. C13×#360 | C22 | semidirect |
| 43. #11718106 | C22 | semidirect |
| 44. #11718080 | C22 | semidirect |
| 61. C13×#135 | D4 | semidirect |
| 63. C2×C13×Q16 | D4 | semidirect |
| 65. C2×C13×D8 | D4 | semidirect |
| 85. C2×Dic52 | D4 | semidirect |
| 93. #88158 | D4 | semidirect |
| 95. C2×D104 | D4 | semidirect |
| 232. C2×#360 | D13 | semidirect |
| 323. C2×M32 | C2×D13 | semidirect |
| 327. C2×#106 | C2×D13 | semidirect |
| 330. #360 | C2×D13 | semidirect |
| 391. #135 | D52 | semidirect |
| 396. C2×Q16 | D52 | semidirect |
| 404. C2×D8 | D52 | semidirect |
| 542. C13 | #33533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13129605 | 2 |
| #13127972 | 2 |
| #13127970 | 2 |
| #13124499 | 2 |
| #13116788 | 2 |
| #13116783 | 2 |
| C2×#11718080 | 2 |
| #13116456 | 2 |
| C2×C13×#360 | 2 |
| #33533 | 13 |