Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
462 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13131613 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#11718277 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #13131143 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13130993 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13129917 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #13129892 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13127968 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #11719629 | — | 2 | 1 | no | — |
| 9 | D13×#135 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#88166 | C22 | 1 | 1 | yes | characteristic |
| 11 | #11719166 | — | 2 | 1 | no | — |
| 12 | #11719142 | — | 2 | 1 | no | — |
| 13 | #11719140 | — | 2 | 1 | no | — |
| 14 | #11719111 | — | 2 | 1 | no | — |
| 15 | #11719108 | — | 2 | 2 | no | — |
| 16 | #11719103 | — | 2 | 1 | no | — |
| 17 | C2×#88104 | C22 | 1 | 1 | yes | characteristic |
| 18 | #11719092 | C22 | 1 | 1 | yes | characteristic |
| 19 | #11719089 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×D13⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 21 | C13×#509 | C4 | 1 | 1 | yes | characteristic, complemented |
| 22 | #11718856 | C4 | 1 | 1 | yes | characteristic, complemented |
| 23 | #11718808 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #11718577 | — | 2 | 1 | no | — |
| 25 | #11718576 | — | 2 | 1 | no | — |
| 26 | #11718573 | — | 2 | 1 | no | — |
| 27 | #11718572 | — | 2 | 1 | no | — |
| 28 | #11718570 | C4 | 1 | 1 | yes | characteristic, complemented |
| 29 | D13×M32 | C22 | 1 | 1 | yes | characteristic |
| 30 | #11718280 | — | 2 | 1 | no | — |
| 31 | #11718277 | — | 2 | 2 | no | — |
| 32 | #11718276 | — | 2 | 1 | no | — |
| 33 | #41×D13 | — | 2 | 1 | no | — |
| 34 | C2×#6129 | — | 2 | 1 | no | — |
| 35 | #88240 | — | 2 | 2 | no | — |
| 36 | #88238 | — | 2 | 2 | no | — |
| 37 | #88238 | — | 4 | 2 | no | — |
| 38 | #88237 | — | 2 | 1 | no | — |
| 39 | #88237 | D4 | 1 | 1 | yes | characteristic |
| 40 | D13⋊M16 | — | 4 | 1 | no | — |
| 41 | D13⋊M16 | D4 | 1 | 1 | yes | characteristic |
| 42 | C2×#6118 | — | 2 | 1 | no | — |
| 43 | C2×#6118 | — | 4 | 1 | no | — |
| 44 | C13×#135 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | C2×C13×D8 | C2×C4 | 1 | 1 | yes | characteristic |
| 46 | #88204 | — | 2 | 1 | no | — |
| 47 | C2×#6105 | — | 2 | 1 | no | — |
| 48 | #88173 | D4 | 1 | 1 | yes | characteristic |
| 49 | Q16×D13 | D4 | 1 | 1 | yes | characteristic |
| 50 | #88170 | — | 2 | 1 | no | — |
| 51 | SD16×D13 | — | 2 | 1 | no | — |
| 52 | #88166 | — | 2 | 1 | no | — |
| 53 | #88166 | — | 2 | 1 | no | — |
| 54 | #88166 | — | 2 | 1 | no | — |
| 55 | #88166 | — | 2 | 1 | no | — |
| 56 | #88166 | D4 | 1 | 1 | yes | characteristic |
| 57 | D8×D13 | D4 | 1 | 1 | yes | characteristic |
| 58 | C2×Dic52 | C2×C4 | 1 | 1 | yes | characteristic |
| 59 | #88158 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | C2×C8×D13 | C23 | 1 | 1 | yes | characteristic |
| 61 | #88119 | — | 4 | 2 | no | — |
| 62 | #88118 | — | 2 | 2 | no | — |
| 63 | #88116 | — | 2 | 2 | no | — |
| 64 | #88116 | — | 4 | 1 | no | — |
| 65 | #88116 | — | 4 | 1 | no | — |
| 66 | C2×#6092 | — | 2 | 1 | no | — |
| 67 | #88104 | — | 2 | 1 | no | — |
| 68 | #88104 | D4 | 1 | 2 | yes | — |
| 69 | #88102 | — | 2 | 1 | no | — |
| 70 | #88101 | — | 2 | 1 | no | — |
| 71 | #88100 | — | 2 | 1 | no | — |
| 72 | C8×#261 | — | 2 | 1 | no | — |
| 73 | D13⋊C16 | — | 2 | 1 | no | — |
| 74 | D13⋊C16 | — | 2 | 1 | no | — |
| 75 | C13×SD32 | — | 2 | 1 | no | — |
| 76 | C13×D16 | — | 2 | 1 | no | — |
| 77 | C13×M32 | C2×C4 | 1 | 1 | yes | characteristic |
| 78 | #88069 | — | 2 | 1 | no | — |
| 79 | #88067 | — | 2 | 1 | no | — |
| 80 | #88067 | — | 2 | 1 | no | — |
| 81 | #88066 | — | 2 | 1 | no | — |
| 82 | #88052 | C2×C4 | 1 | 1 | yes | characteristic |
| 83 | Dic104 | — | 2 | 1 | no | — |
| 84 | #88040 | — | 2 | 1 | no | — |
| 85 | #88038 | — | 2 | 1 | no | — |
| 86 | C16×D13 | — | 2 | 1 | no | — |
| 87 | #13021 | — | 13 | 1 | no | maximal, Sylow |
| 88 | C13×#41 | — | 2 | 1 | no | — |
| 89 | C2×D4×C13 | — | 2 | 1 | no | — |
| 90 | C2×C22⋊D13 | — | 4 | 1 | no | — |
| 91 | C22×Dic13 | — | 4 | 1 | no | — |
| 92 | #6131 | — | 2 | 1 | no | — |
| 93 | Q8×D13 | — | 2 | 1 | no | — |
| 94 | #6129 | — | 2 | 1 | no | — |
| 95 | #6129 | — | 4 | 1 | no | — |
| 96 | #6129 | — | 4 | 1 | no | — |
| 97 | #6129 | — | 4 | 1 | no | — |
| 98 | #6129 | — | 4 | 1 | no | — |
| 99 | #6129 | — | 4 | 1 | no | — |
| 100 | D4×D13 | — | 2 | 1 | no | — |
| 101 | D4×D13 | — | 4 | 1 | no | — |
| 102 | #6127 | — | 2 | 1 | no | — |
| 103 | #6127 | — | 4 | 1 | no | — |
| 104 | C2×C4×D13 | — | 4 | 1 | no | — |
| 105 | C2×C4×D13 | C2×D4 | 1 | 1 | yes | characteristic |
| 106 | C2×Dic26 | — | 2 | 1 | no | — |
| 107 | C22⋊#261 | — | 2 | 1 | no | — |
| 108 | C22⋊#261 | — | 4 | 1 | no | — |
| 109 | #6122 | — | 2 | 1 | no | — |
| 110 | #6122 | — | 4 | 2 | no | — |
| 111 | C2×#1057 | — | 4 | 2 | no | — |
| 112 | C2×#1057 | — | 4 | 1 | no | — |
| 113 | C4⋊#261 | — | 2 | 1 | no | — |
| 114 | C4⋊#261 | — | 4 | 1 | no | — |
| 115 | C4×#261 | — | 2 | 1 | no | — |
| 116 | C4×#261 | — | 4 | 1 | no | — |
| 117 | #6118 | — | 2 | 2 | no | — |
| 118 | #6118 | — | 4 | 2 | no | — |
| 119 | #6118 | — | 4 | 1 | no | — |
| 120 | #6118 | D8 | 1 | 1 | yes | characteristic |
| 121 | #6118 | D8 | 1 | 1 | yes | characteristic |
| 122 | D13⋊C8 | — | 2 | 1 | no | — |
| 123 | D13⋊C8 | — | 4 | 2 | no | — |
| 124 | C13×Q16 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 125 | C13×SD16 | — | 2 | 1 | no | — |
| 126 | C13×D8 | — | 2 | 1 | no | — |
| 127 | C13×D8 | — | 2 | 1 | no | — |
| 128 | C13×D8 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 129 | C2×C8×C13 | C22×C4 | 1 | 1 | yes | characteristic |
| 130 | #6107 | — | 2 | 1 | no | — |
| 131 | #6106 | — | 2 | 1 | no | — |
| 132 | #6105 | — | 2 | 1 | no | — |
| 133 | #6105 | — | 4 | 1 | no | — |
| 134 | #6105 | — | 4 | 1 | no | — |
| 135 | #6104 | — | 2 | 1 | no | — |
| 136 | C2×#1055 | #41 | 1 | 1 | yes | characteristic |
| 137 | Dic52 | — | 2 | 1 | no | — |
| 138 | Dic52 | — | 2 | 1 | no | — |
| 139 | Dic52 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 140 | D104 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 141 | #6095 | — | 2 | 1 | no | — |
| 142 | C8×D13 | C2×D4 | 1 | 1 | yes | characteristic |
| 143 | C8×D13 | C2×D4 | 1 | 1 | yes | characteristic |
| 144 | C8×D13 | C2×D4 | 1 | 1 | yes | characteristic |
| 145 | C8×D13 | #41 | 1 | 1 | yes | characteristic |
| 146 | #6092 | — | 4 | 1 | no | — |
| 147 | C13×C16 | — | 2 | 1 | no | — |
| 148 | #6090 | — | 2 | 1 | no | — |
| 149 | #3414 | — | 13 | 1 | no | — |
| 150 | #2957 | — | 13 | 1 | no | — |
| 151 | C2×#359 | — | 13 | 1 | no | — |
| 152 | #2138 | — | 13 | 1 | no | — |
| 153 | #1976 | — | 13 | 1 | no | — |
| 154 | #1389 | — | 13 | 1 | no | — |
| 155 | #1379 | — | 13 | 1 | no | — |
| 156 | C23×C13 | — | 4 | 1 | no | — |
| 157 | C22×D13 | — | 4 | 1 | no | — |
| 158 | C22×D13 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 159 | C2×#261 | — | 4 | 1 | no | — |
| 160 | C2×#261 | — | 8 | 1 | no | — |
| 161 | Q8×C13 | — | 2 | 1 | no | — |
| 162 | D4×C13 | — | 2 | 1 | no | — |
| 163 | D4×C13 | — | 4 | 1 | no | — |
| 164 | D4×C13 | — | 4 | 1 | no | — |
| 165 | D4×C13 | — | 4 | 1 | no | — |
| 166 | C2×C4×C13 | — | 4 | 1 | no | — |
| 167 | C2×C4×C13 | C4×D4 | 1 | 1 | yes | characteristic |
| 168 | C22⋊D13 | — | 4 | 1 | no | — |
| 169 | C22⋊D13 | — | 4 | 1 | no | — |
| 170 | C22⋊D13 | — | 4 | 1 | no | — |
| 171 | C22⋊D13 | — | 8 | 1 | no | — |
| 172 | C22⋊D13 | — | 8 | 1 | no | — |
| 173 | C2×Dic13 | — | 4 | 1 | no | — |
| 174 | C2×Dic13 | — | 4 | 1 | no | — |
| 175 | C2×Dic13 | — | 8 | 1 | no | — |
| 176 | C2×Dic13 | — | 8 | 1 | no | — |
| 177 | C2×Dic13 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 178 | D52 | — | 2 | 1 | no | — |
| 179 | D52 | — | 4 | 1 | no | — |
| 180 | C4×D13 | — | 4 | 1 | no | — |
| 181 | C4×D13 | — | 4 | 1 | no | — |
| 182 | C4×D13 | — | 4 | 1 | no | — |
| 183 | C4×D13 | #120 | 1 | 1 | yes | characteristic |
| 184 | C4×D13 | #121 | 1 | 1 | yes | characteristic |
| 185 | C4×D13 | C2×D8 | 1 | 1 | yes | characteristic |
| 186 | C4×D13 | #135 | 1 | 1 | yes | characteristic |
| 187 | Dic26 | — | 2 | 1 | no | — |
| 188 | Dic26 | — | 4 | 1 | no | — |
| 189 | Dic26 | — | 4 | 1 | no | — |
| 190 | Dic26 | — | 4 | 1 | no | — |
| 191 | #1057 | — | 2 | 1 | no | — |
| 192 | #1057 | — | 2 | 1 | no | — |
| 193 | #1057 | — | 4 | 2 | no | — |
| 194 | C8×C13 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 195 | C8×C13 | C4×D4 | 1 | 1 | yes | characteristic |
| 196 | #1055 | #121 | 1 | 1 | yes | characteristic |
| 197 | #1055 | #123 | 1 | 1 | yes | characteristic |
| 198 | C2×#135 | — | 13 | 1 | no | — |
| 199 | C2×#135 | — | 13 | 1 | no | — |
| 200 | #568 | — | 26 | 1 | no | — |
| 201 | #510 | — | 13 | 1 | no | — |
| 202 | #510 | — | 13 | 1 | no | — |
| 203 | #510 | — | 26 | 1 | no | — |
| 204 | #509 | — | 13 | 1 | no | — |
| 205 | #509 | — | 26 | 1 | no | — |
| 206 | #509 | #261 | 1 | 1 | yes | characteristic, complemented |
| 207 | #508 | — | 26 | 1 | no | — |
| 208 | #508 | — | 26 | 1 | no | — |
| 209 | C2×M32 | — | 13 | 1 | no | — |
| 210 | C22×C16 | — | 13 | 1 | no | — |
| 211 | #444 | — | 26 | 2 | no | — |
| 212 | #443 | — | 26 | 1 | no | — |
| 213 | #443 | — | 26 | 1 | no | — |
| 214 | C2×#108 | — | 13 | 1 | no | — |
| 215 | #427 | — | 13 | 1 | no | — |
| 216 | #421 | — | 26 | 1 | no | — |
| 217 | #421 | — | 26 | 1 | no | — |
| 218 | #410 | — | 26 | 1 | no | — |
| 219 | #405 | — | 13 | 1 | no | — |
| 220 | #359 | — | 26 | 2 | no | — |
| 221 | #358 | — | 26 | 1 | no | — |
| 222 | #357 | — | 26 | 1 | no | — |
| 223 | C22×C13 | — | 4 | 1 | no | — |
| 224 | C22×C13 | — | 8 | 1 | no | — |
| 225 | C22×C13 | — | 16 | 1 | no | — |
| 226 | C22×C13 | #442 | 1 | 1 | yes | characteristic |
| 227 | C2×D13 | — | 4 | 1 | no | — |
| 228 | C2×D13 | — | 4 | 1 | no | — |
| 229 | C2×D13 | — | 16 | 1 | no | — |
| 230 | C2×D13 | #449 | 1 | 1 | yes | characteristic |
| 231 | C2×D13 | #459 | 1 | 1 | yes | characteristic |
| 232 | #261 | — | 8 | 1 | no | — |
| 233 | #261 | — | 16 | 1 | no | — |
| 234 | C4×C13 | — | 4 | 1 | no | — |
| 235 | C4×C13 | #386 | 1 | 1 | yes | characteristic |
| 236 | C4×C13 | C4×D8 | 1 | 1 | yes | characteristic |
| 237 | Dic13 | — | 4 | 1 | no | — |
| 238 | Dic13 | — | 8 | 1 | no | — |
| 239 | Dic13 | #447 | 1 | 1 | yes | characteristic |
| 240 | Dic13 | #463 | 1 | 1 | yes | characteristic |
| 241 | C2×#41 | — | 26 | 1 | no | — |
| 242 | C2×#41 | — | 26 | 1 | no | — |
| 243 | #135 | — | 13 | 1 | no | — |
| 244 | #135 | — | 13 | 1 | no | — |
| 245 | #135 | — | 13 | 1 | no | — |
| 246 | #135 | — | 26 | 1 | no | — |
| 247 | #135 | — | 26 | 1 | no | — |
| 248 | #135 | — | 26 | 1 | no | — |
| 249 | #135 | — | 26 | 1 | no | — |
| 250 | #135 | — | 26 | 1 | no | — |
| 251 | #135 | — | 26 | 1 | no | — |
| 252 | #135 | C2×#261 | 1 | 1 | yes | characteristic |
| 253 | C2×Q16 | — | 13 | 1 | no | — |
| 254 | C2×Q16 | — | 13 | 1 | no | — |
| 255 | C2×SD16 | — | 26 | 1 | no | — |
| 256 | C2×SD16 | — | 26 | 1 | no | — |
| 257 | C2×D8 | — | 13 | 1 | no | — |
| 258 | C2×D8 | C2×#261 | 1 | 1 | yes | characteristic |
| 259 | #131 | — | 26 | 2 | no | — |
| 260 | #131 | — | 26 | 2 | no | — |
| 261 | #131 | — | 52 | 2 | no | — |
| 262 | C2×M16 | — | 13 | 1 | no | — |
| 263 | C2×M16 | — | 26 | 1 | no | — |
| 264 | C2×M16 | — | 52 | 1 | no | — |
| 265 | C2×M16 | — | 52 | 1 | no | — |
| 266 | C22×C8 | — | 13 | 1 | no | — |
| 267 | #117 | — | 13 | 1 | no | — |
| 268 | #117 | — | 26 | 1 | no | — |
| 269 | Q32 | — | 26 | 1 | no | — |
| 270 | Q32 | — | 26 | 1 | no | — |
| 271 | SD32 | — | 2 | 1 | no | — |
| 272 | SD32 | — | 26 | 1 | no | — |
| 273 | SD32 | — | 26 | 1 | no | — |
| 274 | SD32 | — | 26 | 1 | no | — |
| 275 | D16 | — | 2 | 1 | no | — |
| 276 | D16 | — | 26 | 1 | no | — |
| 277 | M32 | — | 13 | 1 | no | — |
| 278 | M32 | — | 26 | 1 | no | — |
| 279 | M32 | C2×#261 | 1 | 1 | yes | characteristic |
| 280 | C2×C16 | — | 26 | 1 | no | — |
| 281 | C2×C16 | — | 26 | 1 | no | — |
| 282 | C2×C16 | — | 26 | 1 | no | — |
| 283 | C2×C16 | — | 26 | 1 | no | — |
| 284 | #108 | — | 13 | 2 | no | — |
| 285 | #108 | — | 26 | 1 | no | — |
| 286 | #107 | — | 26 | 1 | no | — |
| 287 | #106 | — | 26 | 1 | no | — |
| 288 | #104 | — | 26 | 2 | no | — |
| 289 | #104 | — | 26 | 2 | no | — |
| 290 | #104 | — | 52 | 1 | no | — |
| 291 | #104 | — | 52 | 1 | no | — |
| 292 | #99 | — | 52 | 2 | no | — |
| 293 | #97 | — | 26 | 1 | no | — |
| 294 | C4×C8 | — | 26 | 1 | no | — |
| 295 | C2×C13 | — | 2 | 1 | no | — |
| 296 | C2×C13 | — | 8 | 1 | no | — |
| 297 | C2×C13 | — | 16 | 1 | no | — |
| 298 | C2×C13 | #1879 | 1 | 1 | yes | characteristic |
| 299 | D13 | — | 2 | 1 | no | — |
| 300 | D13 | — | 2 | 1 | no | — |
| 301 | D13 | — | 8 | 1 | no | — |
| 302 | #41 | — | 2 | 1 | no | — |
| 303 | #41 | — | 26 | 1 | no | — |
| 304 | #41 | — | 26 | 1 | no | — |
| 305 | #41 | — | 26 | 1 | no | — |
| 306 | #41 | — | 52 | 1 | no | — |
| 307 | #41 | — | 52 | 1 | no | — |
| 308 | #41 | — | 52 | 1 | no | — |
| 309 | #41 | — | 52 | 1 | no | — |
| 310 | #41 | — | 52 | 1 | no | — |
| 311 | #41 | — | 52 | 1 | no | — |
| 312 | C2×Q8 | — | 26 | 1 | no | — |
| 313 | C2×Q8 | — | 26 | 1 | no | — |
| 314 | C2×D4 | — | 2 | 1 | no | — |
| 315 | C2×D4 | — | 26 | 1 | no | — |
| 316 | C2×D4 | — | 52 | 1 | no | — |
| 317 | C2×D4 | — | 52 | 1 | no | — |
| 318 | C22×C4 | — | 13 | 1 | no | — |
| 319 | C22×C4 | — | 52 | 1 | no | — |
| 320 | C22×C4 | — | 52 | 1 | no | — |
| 321 | Q16 | — | 13 | 1 | no | — |
| 322 | Q16 | — | 26 | 1 | no | — |
| 323 | Q16 | — | 26 | 1 | no | — |
| 324 | Q16 | — | 26 | 1 | no | — |
| 325 | Q16 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 326 | SD16 | — | 2 | 1 | no | — |
| 327 | SD16 | — | 26 | 1 | no | — |
| 328 | SD16 | — | 26 | 1 | no | — |
| 329 | SD16 | — | 26 | 1 | no | — |
| 330 | SD16 | — | 52 | 1 | no | — |
| 331 | SD16 | — | 52 | 1 | no | — |
| 332 | D8 | — | 2 | 1 | no | — |
| 333 | D8 | — | 2 | 1 | no | — |
| 334 | D8 | — | 13 | 1 | no | — |
| 335 | D8 | — | 26 | 1 | no | — |
| 336 | D8 | C22⋊#261 | 1 | 1 | yes | characteristic |
| 337 | M16 | — | 13 | 1 | no | — |
| 338 | M16 | — | 13 | 1 | no | — |
| 339 | M16 | — | 26 | 1 | no | — |
| 340 | M16 | — | 26 | 2 | no | — |
| 341 | M16 | — | 52 | 2 | no | — |
| 342 | M16 | — | 52 | 2 | no | — |
| 343 | M16 | — | 52 | 1 | no | — |
| 344 | C2×C8 | — | 13 | 1 | no | — |
| 345 | C2×C8 | — | 13 | 1 | no | — |
| 346 | C2×C8 | — | 13 | 1 | no | — |
| 347 | C2×C8 | — | 13 | 1 | no | — |
| 348 | C2×C8 | — | 13 | 1 | no | — |
| 349 | C2×C8 | — | 26 | 1 | no | — |
| 350 | C2×C8 | — | 52 | 2 | no | — |
| 351 | C2×C8 | — | 52 | 2 | no | — |
| 352 | C2×C8 | — | 52 | 1 | no | — |
| 353 | C2×C8 | C22×#261 | 1 | 1 | yes | characteristic |
| 354 | C4⋊C4 | — | 26 | 1 | no | — |
| 355 | C4⋊C4 | — | 52 | 1 | no | — |
| 356 | C22⋊C4 | — | 26 | 1 | no | — |
| 357 | C22⋊C4 | — | 52 | 1 | no | — |
| 358 | C42 | — | 26 | 1 | no | — |
| 359 | C42 | — | 52 | 1 | no | — |
| 360 | C16 | — | 2 | 1 | no | — |
| 361 | C16 | — | 26 | 1 | no | — |
| 362 | C16 | — | 52 | 1 | no | — |
| 363 | C13 | #13021 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 364 | C23 | — | 4 | 1 | no | — |
| 365 | C23 | — | 13 | 1 | no | — |
| 366 | C23 | — | 52 | 1 | no | — |
| 367 | Q8 | — | 2 | 1 | no | — |
| 368 | Q8 | — | 26 | 1 | no | — |
| 369 | Q8 | — | 52 | 1 | no | — |
| 370 | Q8 | — | 52 | 1 | no | — |
| 371 | Q8 | — | 52 | 1 | no | — |
| 372 | D4 | — | 2 | 1 | no | — |
| 373 | D4 | — | 4 | 1 | no | — |
| 374 | D4 | — | 4 | 1 | no | — |
| 375 | D4 | — | 4 | 1 | no | — |
| 376 | D4 | — | 26 | 1 | no | — |
| 377 | D4 | — | 52 | 1 | no | — |
| 378 | D4 | — | 52 | 1 | no | — |
| 379 | D4 | — | 52 | 1 | no | — |
| 380 | D4 | — | 52 | 1 | no | — |
| 381 | D4 | — | 104 | 1 | no | — |
| 382 | D4 | — | 104 | 1 | no | — |
| 383 | C2×C4 | — | 4 | 1 | no | — |
| 384 | C2×C4 | — | 13 | 1 | no | — |
| 385 | C2×C4 | — | 13 | 1 | no | — |
| 386 | C2×C4 | — | 13 | 1 | no | — |
| 387 | C2×C4 | — | 13 | 1 | no | — |
| 388 | C2×C4 | — | 13 | 1 | no | — |
| 389 | C2×C4 | — | 52 | 1 | no | — |
| 390 | C2×C4 | — | 52 | 1 | no | — |
| 391 | C2×C4 | — | 52 | 1 | no | — |
| 392 | C2×C4 | — | 52 | 1 | no | — |
| 393 | C2×C4 | — | 52 | 1 | no | — |
| 394 | C2×C4 | — | 52 | 1 | no | — |
| 395 | C2×C4 | — | 104 | 1 | no | — |
| 396 | C2×C4 | — | 104 | 1 | no | — |
| 397 | C2×C4 | — | 104 | 1 | no | — |
| 398 | C2×C4 | D4×#261 | 1 | 1 | yes | characteristic |
| 399 | C8 | — | 13 | 1 | no | — |
| 400 | C8 | — | 13 | 1 | no | — |
| 401 | C8 | — | 26 | 1 | no | — |
| 402 | C8 | — | 26 | 1 | no | — |
| 403 | C8 | — | 52 | 2 | no | — |
| 404 | C8 | D4×#261 | 1 | 1 | yes | characteristic |
| 405 | C8 | C2×C22⋊#261 | 1 | 1 | yes | characteristic |
| 406 | C22 | — | 4 | 1 | no | — |
| 407 | C22 | — | 8 | 1 | no | — |
| 408 | C22 | — | 13 | 1 | no | — |
| 409 | C22 | — | 13 | 1 | no | — |
| 410 | C22 | — | 16 | 1 | no | — |
| 411 | C22 | — | 52 | 1 | no | — |
| 412 | C22 | — | 52 | 1 | no | — |
| 413 | C22 | — | 208 | 1 | no | — |
| 414 | C22 | #11719102 | 1 | 1 | yes | characteristic |
| 415 | C4 | — | 4 | 1 | no | — |
| 416 | C4 | — | 13 | 1 | no | — |
| 417 | C4 | — | 13 | 1 | no | — |
| 418 | C4 | — | 52 | 1 | no | — |
| 419 | C4 | — | 104 | 1 | no | — |
| 420 | C4 | — | 104 | 1 | no | — |
| 421 | C4 | — | 208 | 1 | no | — |
| 422 | C4 | D8×#261 | 1 | 1 | yes | characteristic |
| 423 | C4 | #11719150 | 1 | 1 | yes | characteristic |
| 424 | C2 | — | 2 | 1 | no | — |
| 425 | C2 | — | 8 | 1 | no | — |
| 426 | C2 | — | 16 | 1 | no | — |
| 427 | C2 | — | 26 | 1 | no | — |
| 428 | C2 | — | 26 | 1 | no | — |
| 429 | C2 | — | 104 | 1 | no | — |
| 430 | C2 | #13130831 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13131613 | C2 | semidirect |
| 2. C2×#11718277 | C2 | semidirect |
| 3. #13131143 | C2 | semidirect |
| 4. #13130993 | C2 | semidirect |
| 5. #13129917 | C2 | semidirect |
| 6. #13129892 | C2 | semidirect |
| 21. C13×#509 | C4 | semidirect |
| 22. #11718856 | C4 | semidirect |
| 23. #11718808 | C4 | semidirect |
| 28. #11718570 | C4 | semidirect |
| 206. #509 | #261 | semidirect |
| 363. C13 | #13021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131613 | 2 |
| C2×#11718277 | 2 |
| #13131143 | 2 |
| #13130993 | 2 |
| #13129917 | 2 |
| #13129892 | 2 |
| #13127968 | 2 |
| #13021 | 13 |