Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1090 conjugacy classes of subgroups.
The subgroup lattice has 588 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #13129605 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#11718570 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#11718856 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #13124492 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #13116788 | C2 | 1 | 8 | yes | maximal, complemented |
| 6 | #13116571 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #13116456 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C13×#2145 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #11719648 | — | 2 | 1 | no | — |
| 10 | C2×C13×#135 | C22 | 1 | 1 | yes | characteristic |
| 11 | #11719527 | — | 2 | 1 | no | — |
| 12 | #11719476 | — | 2 | 1 | no | — |
| 13 | #11719475 | — | 2 | 2 | no | — |
| 14 | #11719474 | — | 2 | 1 | no | — |
| 15 | #11719473 | C22 | 1 | 4 | yes | — |
| 16 | D13×#135 | — | 2 | 2 | no | — |
| 17 | #11719471 | — | 2 | 1 | no | — |
| 18 | #11719467 | — | 2 | 2 | no | — |
| 19 | #11719462 | — | 2 | 1 | no | — |
| 20 | C22×Dic52 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×#88158 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#88155 | C22 | 1 | 1 | yes | characteristic |
| 23 | #11719231 | — | 2 | 1 | no | — |
| 24 | C2×C13×M32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C13×#427 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #11718856 | — | 2 | 2 | no | — |
| 27 | #11718856 | C22 | 1 | 4 | yes | complemented |
| 28 | C2×#88069 | — | 2 | 1 | no | — |
| 29 | C2×#88067 | — | 2 | 1 | no | — |
| 30 | C2×#88052 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #11718665 | — | 2 | 1 | no | — |
| 32 | #11718570 | — | 2 | 2 | no | — |
| 33 | #11718570 | C22 | 1 | 4 | yes | complemented |
| 34 | C2×Dic104 | — | 2 | 1 | no | — |
| 35 | C2×#88040 | — | 2 | 1 | no | — |
| 36 | #11718548 | — | 2 | 2 | no | — |
| 37 | #11718529 | C22 | 1 | 4 | yes | complemented |
| 38 | C13×#360 | C22 | 1 | 4 | yes | complemented |
| 39 | #11718106 | C22 | 1 | 4 | yes | complemented |
| 40 | #11718080 | C22 | 1 | 4 | yes | complemented |
| 41 | C2×C13×#41 | — | 2 | 1 | no | — |
| 42 | #88257 | — | 2 | 2 | no | — |
| 43 | #88257 | — | 4 | 1 | no | — |
| 44 | #88256 | — | 2 | 2 | no | — |
| 45 | #88256 | — | 4 | 1 | no | — |
| 46 | #41×D13 | — | 2 | 4 | no | — |
| 47 | #41×D13 | — | 4 | 2 | no | — |
| 48 | #88254 | — | 2 | 2 | no | — |
| 49 | #88251 | — | 2 | 2 | no | — |
| 50 | #88251 | — | 4 | 2 | no | — |
| 51 | C2×#6127 | — | 2 | 1 | no | — |
| 52 | C2×#6127 | — | 4 | 2 | no | — |
| 53 | C2×#6127 | D4 | 1 | 1 | yes | characteristic |
| 54 | C22×Dic26 | — | 2 | 1 | no | — |
| 55 | C13×#135 | — | 2 | 1 | no | — |
| 56 | C13×#135 | — | 2 | 1 | no | — |
| 57 | C13×#135 | D4 | 1 | 2 | yes | — |
| 58 | C13×#135 | C23 | 1 | 2 | yes | — |
| 59 | C2×C13×Q16 | D4 | 1 | 1 | yes | characteristic |
| 60 | C2×C13×SD16 | — | 2 | 1 | no | — |
| 61 | C2×C13×D8 | D4 | 1 | 1 | yes | characteristic |
| 62 | C22×C8×C13 | C23 | 1 | 1 | yes | characteristic |
| 63 | C13×#117 | — | 2 | 1 | no | — |
| 64 | #88205 | — | 2 | 2 | no | — |
| 65 | #88204 | — | 2 | 4 | no | — |
| 66 | #88203 | — | 2 | 2 | no | — |
| 67 | #88196 | — | 2 | 2 | no | — |
| 68 | #88186 | — | 2 | 2 | no | — |
| 69 | C2×#6099 | D4 | 1 | 1 | yes | characteristic |
| 70 | #88173 | — | 2 | 2 | no | — |
| 71 | #88172 | — | 2 | 4 | no | — |
| 72 | Q16×D13 | — | 2 | 2 | no | — |
| 73 | #88170 | — | 2 | 4 | no | — |
| 74 | #88169 | — | 2 | 4 | no | — |
| 75 | #88168 | — | 2 | 4 | no | — |
| 76 | SD16×D13 | — | 2 | 4 | no | — |
| 77 | #88166 | — | 2 | 2 | no | — |
| 78 | #88165 | — | 2 | 4 | no | — |
| 79 | D8×D13 | — | 2 | 2 | no | — |
| 80 | C2×Dic52 | — | 2 | 1 | no | — |
| 81 | C2×Dic52 | — | 2 | 1 | no | — |
| 82 | C2×Dic52 | — | 2 | 1 | no | — |
| 83 | C2×Dic52 | — | 2 | 1 | no | — |
| 84 | C2×Dic52 | — | 2 | 1 | no | — |
| 85 | C2×Dic52 | D4 | 1 | 1 | yes | characteristic |
| 86 | C2×Dic52 | C23 | 1 | 2 | yes | — |
| 87 | #88158 | — | 2 | 1 | no | — |
| 88 | #88158 | — | 2 | 1 | no | — |
| 89 | #88158 | D4 | 1 | 2 | yes | — |
| 90 | #88158 | C23 | 1 | 2 | yes | — |
| 91 | C2×D104 | D4 | 1 | 1 | yes | characteristic |
| 92 | C2×#6095 | — | 2 | 1 | no | — |
| 93 | #88155 | — | 2 | 1 | no | — |
| 94 | #88155 | — | 2 | 1 | no | — |
| 95 | #88155 | — | 2 | 1 | no | — |
| 96 | #88155 | — | 2 | 1 | no | — |
| 97 | C2×#6094 | C23 | 1 | 2 | yes | — |
| 98 | C2×C8×D13 | D4 | 1 | 2 | yes | — |
| 99 | #88151 | — | 2 | 4 | no | — |
| 100 | #88140 | — | 4 | 2 | no | — |
| 101 | #88129 | — | 4 | 1 | no | — |
| 102 | #88123 | — | 4 | 1 | no | — |
| 103 | C13×M32 | — | 2 | 1 | no | — |
| 104 | C13×M32 | C23 | 1 | 2 | yes | — |
| 105 | C2×C13×C16 | — | 2 | 1 | no | — |
| 106 | C13×#107 | — | 2 | 1 | no | — |
| 107 | C13×#106 | C23 | 1 | 2 | yes | — |
| 108 | #88069 | — | 2 | 4 | no | — |
| 109 | #88067 | — | 2 | 4 | no | — |
| 110 | #88052 | — | 2 | 1 | no | — |
| 111 | #88052 | C23 | 1 | 2 | yes | — |
| 112 | C2×#6090 | — | 2 | 1 | no | — |
| 113 | #88050 | — | 2 | 4 | no | — |
| 114 | Dic104 | — | 2 | 4 | no | — |
| 115 | #88040 | — | 2 | 4 | no | — |
| 116 | #33532 | — | 13 | 1 | no | maximal, Sylow |
| 117 | C13×#41 | — | 2 | 2 | no | — |
| 118 | C13×#41 | — | 2 | 2 | no | — |
| 119 | C13×#41 | — | 4 | 1 | no | — |
| 120 | C13×#41 | — | 4 | 1 | no | — |
| 121 | C2×Q8×C13 | — | 2 | 1 | no | — |
| 122 | C2×D4×C13 | — | 2 | 1 | no | — |
| 123 | C2×D4×C13 | — | 4 | 1 | no | — |
| 124 | C22×C4×C13 | — | 4 | 1 | no | — |
| 125 | C22×C4×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 126 | C2×C22⋊D13 | — | 4 | 4 | no | — |
| 127 | C2×C22⋊D13 | — | 4 | 1 | no | — |
| 128 | C2×C22⋊D13 | D8 | 1 | 2 | yes | — |
| 129 | C22×Dic13 | — | 4 | 1 | no | — |
| 130 | #6131 | — | 2 | 4 | no | — |
| 131 | #6131 | — | 4 | 2 | no | — |
| 132 | Q8×D13 | — | 2 | 4 | no | — |
| 133 | Q8×D13 | — | 4 | 2 | no | — |
| 134 | #6129 | — | 2 | 4 | no | — |
| 135 | #6129 | — | 4 | 2 | no | — |
| 136 | #6129 | — | 4 | 4 | no | — |
| 137 | #6129 | — | 4 | 4 | no | — |
| 138 | D4×D13 | — | 2 | 4 | no | — |
| 139 | D4×D13 | — | 4 | 2 | no | — |
| 140 | D4×D13 | — | 4 | 4 | no | — |
| 141 | D4×D13 | — | 4 | 4 | no | — |
| 142 | #6127 | — | 2 | 1 | no | — |
| 143 | #6127 | — | 2 | 1 | no | — |
| 144 | #6127 | — | 2 | 1 | no | — |
| 145 | #6127 | — | 2 | 1 | no | — |
| 146 | #6127 | — | 2 | 2 | no | — |
| 147 | #6127 | — | 2 | 2 | no | — |
| 148 | #6127 | — | 4 | 2 | no | — |
| 149 | #6127 | — | 4 | 4 | no | — |
| 150 | #6127 | — | 4 | 2 | no | — |
| 151 | #6127 | — | 4 | 4 | no | — |
| 152 | #6127 | — | 4 | 1 | no | — |
| 153 | #6127 | — | 4 | 1 | no | — |
| 154 | C2×D52 | — | 2 | 1 | no | — |
| 155 | C2×D52 | — | 4 | 2 | no | — |
| 156 | C2×D52 | D8 | 1 | 1 | yes | characteristic |
| 157 | C2×C4×D13 | — | 4 | 4 | no | — |
| 158 | C2×C4×D13 | — | 4 | 1 | no | — |
| 159 | C2×C4×D13 | C2×D4 | 1 | 2 | yes | — |
| 160 | C2×Dic26 | — | 2 | 1 | no | — |
| 161 | C2×Dic26 | — | 2 | 2 | no | — |
| 162 | C2×Dic26 | — | 4 | 2 | no | — |
| 163 | C2×Dic26 | — | 4 | 1 | no | — |
| 164 | C2×Dic26 | — | 4 | 1 | no | — |
| 165 | C2×Dic26 | — | 4 | 1 | no | — |
| 166 | C2×Dic26 | — | 4 | 1 | no | — |
| 167 | C2×Dic26 | — | 4 | 1 | no | — |
| 168 | C2×Dic26 | D8 | 1 | 1 | yes | characteristic |
| 169 | C13×Q16 | — | 2 | 1 | no | — |
| 170 | C13×Q16 | C2×D4 | 1 | 2 | yes | — |
| 171 | C13×SD16 | — | 2 | 2 | no | — |
| 172 | C13×SD16 | — | 2 | 2 | no | — |
| 173 | C13×D8 | — | 2 | 1 | no | — |
| 174 | C13×D8 | C2×D4 | 1 | 2 | yes | — |
| 175 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 178 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | C2×C8×C13 | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | C2×C8×C13 | C24 | 1 | 1 | yes | characteristic |
| 181 | C13×C4⋊C4 | — | 2 | 2 | no | — |
| 182 | C13×C22⋊C4 | — | 4 | 1 | no | — |
| 183 | C42×C13 | — | 4 | 1 | no | — |
| 184 | #6107 | — | 2 | 4 | no | — |
| 185 | #6106 | — | 2 | 4 | no | — |
| 186 | #6105 | — | 2 | 4 | no | — |
| 187 | #6104 | — | 2 | 4 | no | — |
| 188 | #6103 | — | 4 | 4 | no | — |
| 189 | C4⋊Dic13 | — | 4 | 4 | no | — |
| 190 | #6099 | — | 2 | 1 | no | — |
| 191 | #6099 | — | 2 | 1 | no | — |
| 192 | C2×#1055 | C2×D4 | 1 | 2 | yes | — |
| 193 | Dic52 | — | 2 | 1 | no | — |
| 194 | Dic52 | — | 2 | 2 | no | — |
| 195 | Dic52 | — | 2 | 2 | no | — |
| 196 | Dic52 | — | 4 | 1 | no | — |
| 197 | Dic52 | — | 4 | 1 | no | — |
| 198 | Dic52 | C2×D4 | 1 | 2 | yes | — |
| 199 | D104 | — | 2 | 1 | no | — |
| 200 | D104 | C2×D4 | 1 | 2 | yes | — |
| 201 | #6095 | — | 2 | 2 | no | — |
| 202 | #6095 | — | 2 | 2 | no | — |
| 203 | #6094 | — | 2 | 2 | no | — |
| 204 | #6094 | — | 2 | 2 | no | — |
| 205 | C8×D13 | — | 2 | 2 | no | — |
| 206 | C8×D13 | — | 2 | 2 | no | — |
| 207 | C13×C16 | — | 2 | 2 | no | — |
| 208 | #6090 | — | 2 | 2 | no | — |
| 209 | #3584 | — | 13 | 1 | no | — |
| 210 | C2×#510 | — | 13 | 1 | no | — |
| 211 | C2×#510 | — | 13 | 1 | no | — |
| 212 | #3059 | — | 13 | 1 | no | — |
| 213 | #2191 | — | 13 | 8 | no | — |
| 214 | #2145 | — | 13 | 1 | no | — |
| 215 | #2145 | D13 | 1 | 1 | yes | characteristic, complemented |
| 216 | #2115 | — | 13 | 1 | no | — |
| 217 | C23×C13 | — | 4 | 1 | no | — |
| 218 | C23×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 219 | C22×D13 | — | 4 | 4 | no | — |
| 220 | C22×D13 | — | 4 | 1 | no | — |
| 221 | C22×D13 | C2×D8 | 1 | 2 | yes | — |
| 222 | Q8×C13 | — | 2 | 2 | no | — |
| 223 | Q8×C13 | — | 4 | 1 | no | — |
| 224 | D4×C13 | — | 2 | 2 | no | — |
| 225 | D4×C13 | — | 4 | 2 | no | — |
| 226 | D4×C13 | — | 4 | 2 | no | — |
| 227 | D4×C13 | — | 4 | 1 | no | — |
| 228 | C2×C4×C13 | — | 4 | 1 | no | — |
| 229 | C2×C4×C13 | — | 4 | 2 | no | — |
| 230 | C2×C4×C13 | — | 4 | 2 | no | — |
| 231 | C2×C4×C13 | — | 4 | 2 | no | — |
| 232 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 233 | C2×C4×C13 | #120 | 1 | 1 | yes | characteristic |
| 234 | C2×C4×C13 | C2×D8 | 1 | 1 | yes | characteristic |
| 235 | C2×C4×C13 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 236 | C2×C4×C13 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 237 | C2×C4×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 238 | C22⋊D13 | — | 2 | 2 | no | — |
| 239 | C22⋊D13 | — | 2 | 2 | no | — |
| 240 | C22⋊D13 | — | 4 | 4 | no | — |
| 241 | C22⋊D13 | — | 4 | 4 | no | — |
| 242 | C22⋊D13 | — | 4 | 2 | no | — |
| 243 | C22⋊D13 | — | 4 | 2 | no | — |
| 244 | C2×Dic13 | — | 4 | 4 | no | — |
| 245 | C2×Dic13 | — | 4 | 1 | no | — |
| 246 | C2×Dic13 | — | 4 | 2 | no | — |
| 247 | C2×Dic13 | — | 8 | 1 | no | — |
| 248 | C2×Dic13 | — | 8 | 1 | no | — |
| 249 | C2×Dic13 | C2×D8 | 1 | 2 | yes | — |
| 250 | D52 | — | 2 | 2 | no | — |
| 251 | D52 | — | 2 | 1 | no | — |
| 252 | D52 | — | 2 | 1 | no | — |
| 253 | D52 | — | 4 | 4 | no | — |
| 254 | D52 | — | 4 | 1 | no | — |
| 255 | C4×D13 | — | 2 | 2 | no | — |
| 256 | C4×D13 | — | 2 | 2 | no | — |
| 257 | C4×D13 | — | 4 | 4 | no | — |
| 258 | C4×D13 | — | 4 | 4 | no | — |
| 259 | C4×D13 | — | 4 | 2 | no | — |
| 260 | C4×D13 | — | 4 | 2 | no | — |
| 261 | Dic26 | — | 2 | 1 | no | — |
| 262 | Dic26 | — | 2 | 1 | no | — |
| 263 | Dic26 | — | 2 | 2 | no | — |
| 264 | Dic26 | — | 4 | 4 | no | — |
| 265 | Dic26 | — | 4 | 1 | no | — |
| 266 | Dic26 | — | 4 | 2 | no | — |
| 267 | Dic26 | — | 4 | 2 | no | — |
| 268 | Dic26 | — | 8 | 1 | no | — |
| 269 | Dic26 | — | 8 | 1 | no | — |
| 270 | C8×C13 | #120 | 1 | 1 | yes | characteristic |
| 271 | C8×C13 | #120 | 1 | 1 | yes | characteristic |
| 272 | C8×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 273 | C8×C13 | C22×D4 | 1 | 1 | yes | characteristic |
| 274 | #1055 | — | 2 | 2 | no | — |
| 275 | #585 | — | 26 | 1 | no | — |
| 276 | #578 | — | 26 | 1 | no | — |
| 277 | #578 | — | 26 | 1 | no | — |
| 278 | #577 | — | 26 | 2 | no | — |
| 279 | #577 | — | 26 | 2 | no | — |
| 280 | #576 | — | 26 | 1 | no | — |
| 281 | #576 | — | 26 | 1 | no | — |
| 282 | #575 | — | 13 | 4 | no | — |
| 283 | #575 | — | 26 | 1 | no | — |
| 284 | C2×#135 | — | 13 | 1 | no | — |
| 285 | C2×#135 | — | 26 | 2 | no | — |
| 286 | C2×#135 | C2×D13 | 1 | 1 | yes | characteristic |
| 287 | C22×Q16 | — | 13 | 1 | no | — |
| 288 | C2×#131 | — | 13 | 1 | no | — |
| 289 | #536 | — | 26 | 1 | no | — |
| 290 | #510 | — | 13 | 4 | no | — |
| 291 | #510 | — | 13 | 4 | no | — |
| 292 | #510 | — | 26 | 2 | no | — |
| 293 | #510 | — | 26 | 2 | no | — |
| 294 | C2×Q32 | — | 26 | 1 | no | — |
| 295 | C2×Q32 | — | 26 | 1 | no | — |
| 296 | C2×SD32 | — | 26 | 1 | no | — |
| 297 | C2×SD32 | — | 26 | 1 | no | — |
| 298 | C2×M32 | — | 13 | 1 | no | — |
| 299 | C2×M32 | C2×D13 | 1 | 1 | yes | characteristic, complemented |
| 300 | #470 | — | 13 | 4 | no | — |
| 301 | #467 | — | 26 | 2 | no | — |
| 302 | #427 | C2×D13 | 1 | 1 | yes | characteristic, complemented |
| 303 | #419 | — | 26 | 1 | no | — |
| 304 | #360 | — | 13 | 4 | no | — |
| 305 | #360 | C2×D13 | 1 | 4 | yes | complemented |
| 306 | #349 | — | 13 | 4 | no | — |
| 307 | C22×C13 | — | 4 | 1 | no | — |
| 308 | C22×C13 | — | 4 | 2 | no | — |
| 309 | C22×C13 | — | 16 | 1 | no | — |
| 310 | C22×C13 | #447 | 1 | 1 | yes | characteristic |
| 311 | C22×C13 | #447 | 1 | 1 | yes | characteristic |
| 312 | C22×C13 | C22×D8 | 1 | 1 | yes | characteristic |
| 313 | C2×D13 | — | 2 | 2 | no | — |
| 314 | C2×D13 | — | 4 | 2 | no | — |
| 315 | C2×D13 | — | 4 | 2 | no | — |
| 316 | C2×D13 | — | 16 | 4 | no | — |
| 317 | C2×D13 | — | 16 | 1 | no | — |
| 318 | C4×C13 | — | 4 | 2 | no | — |
| 319 | C4×C13 | — | 8 | 2 | no | — |
| 320 | C4×C13 | #447 | 1 | 1 | yes | characteristic |
| 321 | C4×C13 | #447 | 1 | 1 | yes | characteristic |
| 322 | C4×C13 | C2×#120 | 1 | 1 | yes | characteristic |
| 323 | C4×C13 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 324 | Dic13 | — | 2 | 2 | no | — |
| 325 | Dic13 | — | 4 | 2 | no | — |
| 326 | Dic13 | — | 8 | 2 | no | — |
| 327 | 2−1+4 | — | 26 | 2 | no | — |
| 328 | 2−1+4 | — | 26 | 2 | no | — |
| 329 | 2−1+4 | — | 52 | 1 | no | — |
| 330 | H(5,𝔽2) | — | 26 | 2 | no | — |
| 331 | H(5,𝔽2) | — | 26 | 2 | no | — |
| 332 | H(5,𝔽2) | — | 52 | 2 | no | — |
| 333 | H(5,𝔽2) | — | 52 | 1 | no | — |
| 334 | C2×#41 | — | 2 | 1 | no | — |
| 335 | C2×#41 | — | 13 | 1 | no | — |
| 336 | C2×#41 | — | 26 | 4 | no | — |
| 337 | C2×#41 | — | 26 | 1 | no | — |
| 338 | C2×#41 | — | 52 | 2 | no | — |
| 339 | C2×#41 | — | 52 | 2 | no | — |
| 340 | C22×Q8 | — | 26 | 1 | no | — |
| 341 | #137 | — | 26 | 4 | no | — |
| 342 | #137 | — | 26 | 2 | no | — |
| 343 | #137 | — | 26 | 2 | no | — |
| 344 | #137 | — | 26 | 4 | no | — |
| 345 | AGL(1,ℤ/8) | — | 26 | 4 | no | — |
| 346 | AGL(1,ℤ/8) | — | 26 | 2 | no | — |
| 347 | AGL(1,ℤ/8) | — | 26 | 2 | no | — |
| 348 | AGL(1,ℤ/8) | — | 26 | 4 | no | — |
| 349 | #135 | — | 2 | 1 | no | — |
| 350 | #135 | — | 2 | 1 | no | — |
| 351 | #135 | — | 13 | 2 | no | — |
| 352 | #135 | — | 13 | 2 | no | — |
| 353 | #135 | — | 26 | 4 | no | — |
| 354 | #135 | — | 26 | 2 | no | — |
| 355 | #135 | — | 26 | 4 | no | — |
| 356 | #135 | — | 26 | 2 | no | — |
| 357 | #135 | — | 26 | 1 | no | — |
| 358 | #135 | — | 26 | 1 | no | — |
| 359 | #135 | D52 | 1 | 2 | yes | — |
| 360 | #135 | C22×D13 | 1 | 2 | yes | — |
| 361 | C2×Q16 | — | 13 | 1 | no | — |
| 362 | C2×Q16 | — | 13 | 2 | no | — |
| 363 | C2×Q16 | — | 26 | 2 | no | — |
| 364 | C2×Q16 | — | 26 | 1 | no | — |
| 365 | C2×Q16 | — | 26 | 1 | no | — |
| 366 | C2×Q16 | — | 26 | 1 | no | — |
| 367 | C2×Q16 | — | 26 | 1 | no | — |
| 368 | C2×Q16 | — | 26 | 1 | no | — |
| 369 | C2×Q16 | D52 | 1 | 1 | yes | characteristic |
| 370 | C2×SD16 | — | 2 | 1 | no | — |
| 371 | C2×SD16 | — | 26 | 4 | no | — |
| 372 | C2×SD16 | — | 26 | 1 | no | — |
| 373 | C2×D8 | — | 13 | 1 | no | — |
| 374 | C2×D8 | — | 26 | 2 | no | — |
| 375 | C2×D8 | D52 | 1 | 1 | yes | characteristic |
| 376 | #131 | — | 26 | 1 | no | — |
| 377 | #131 | — | 26 | 1 | no | — |
| 378 | #131 | — | 26 | 1 | no | — |
| 379 | #131 | — | 26 | 1 | no | — |
| 380 | C2×M16 | — | 13 | 1 | no | — |
| 381 | C2×M16 | — | 13 | 2 | no | — |
| 382 | C22×C8 | — | 13 | 2 | no | — |
| 383 | C22×C8 | C22×D13 | 1 | 1 | yes | characteristic |
| 384 | C4⋊Q8 | — | 52 | 1 | no | — |
| 385 | #124 | — | 52 | 1 | no | — |
| 386 | #123 | — | 52 | 2 | no | — |
| 387 | C22⋊Q8 | — | 26 | 4 | no | — |
| 388 | #117 | — | 2 | 1 | no | — |
| 389 | Q32 | — | 26 | 4 | no | — |
| 390 | Q32 | — | 26 | 4 | no | — |
| 391 | SD32 | — | 26 | 4 | no | — |
| 392 | SD32 | — | 26 | 4 | no | — |
| 393 | M32 | — | 2 | 1 | no | — |
| 394 | M32 | — | 13 | 2 | no | — |
| 395 | M32 | — | 26 | 1 | no | — |
| 396 | M32 | C22×D13 | 1 | 2 | yes | — |
| 397 | C2×C16 | — | 2 | 1 | no | — |
| 398 | C2×C16 | — | 26 | 1 | no | — |
| 399 | #107 | — | 2 | 1 | no | — |
| 400 | #106 | C22×D13 | 1 | 2 | yes | — |
| 401 | #103 | — | 26 | 4 | no | — |
| 402 | C2×C13 | — | 2 | 1 | no | — |
| 403 | C2×C13 | — | 2 | 1 | no | — |
| 404 | C2×C13 | — | 2 | 1 | no | — |
| 405 | C2×C13 | — | 8 | 2 | no | — |
| 406 | C2×C13 | C2×#447 | 1 | 1 | yes | characteristic |
| 407 | D13 | — | 4 | 2 | no | — |
| 408 | D13 | — | 8 | 2 | no | — |
| 409 | #41 | — | 2 | 2 | no | — |
| 410 | #41 | — | 2 | 2 | no | — |
| 411 | #41 | — | 4 | 1 | no | — |
| 412 | #41 | — | 4 | 1 | no | — |
| 413 | #41 | — | 26 | 1 | no | — |
| 414 | #41 | — | 26 | 1 | no | — |
| 415 | #41 | — | 26 | 1 | no | — |
| 416 | #41 | — | 26 | 1 | no | — |
| 417 | #41 | — | 26 | 4 | no | — |
| 418 | #41 | — | 26 | 4 | no | — |
| 419 | #41 | — | 26 | 2 | no | — |
| 420 | #41 | — | 26 | 2 | no | — |
| 421 | #41 | — | 52 | 4 | no | — |
| 422 | #41 | — | 52 | 4 | no | — |
| 423 | #41 | — | 52 | 2 | no | — |
| 424 | #41 | — | 52 | 2 | no | — |
| 425 | #41 | — | 52 | 4 | no | — |
| 426 | #41 | — | 52 | 4 | no | — |
| 427 | #41 | — | 52 | 2 | no | — |
| 428 | #41 | — | 52 | 2 | no | — |
| 429 | #41 | — | 52 | 1 | no | — |
| 430 | #41 | — | 52 | 1 | no | — |
| 431 | C2×Q8 | — | 2 | 1 | no | — |
| 432 | C2×Q8 | — | 13 | 1 | no | — |
| 433 | C2×Q8 | — | 26 | 4 | no | — |
| 434 | C2×Q8 | — | 26 | 1 | no | — |
| 435 | C2×Q8 | — | 26 | 2 | no | — |
| 436 | C2×Q8 | — | 52 | 2 | no | — |
| 437 | C2×Q8 | — | 52 | 2 | no | — |
| 438 | C2×Q8 | — | 52 | 1 | no | — |
| 439 | C2×Q8 | — | 52 | 1 | no | — |
| 440 | C2×Q8 | — | 52 | 1 | no | — |
| 441 | C2×Q8 | — | 52 | 1 | no | — |
| 442 | C2×Q8 | — | 52 | 1 | no | — |
| 443 | C2×D4 | — | 2 | 1 | no | — |
| 444 | C2×D4 | — | 4 | 1 | no | — |
| 445 | C2×D4 | — | 13 | 2 | no | — |
| 446 | C2×D4 | — | 13 | 1 | no | — |
| 447 | C2×D4 | — | 26 | 4 | no | — |
| 448 | C2×D4 | — | 26 | 1 | no | — |
| 449 | C2×D4 | — | 52 | 2 | no | — |
| 450 | C2×D4 | — | 52 | 4 | no | — |
| 451 | C2×D4 | — | 52 | 2 | no | — |
| 452 | C2×D4 | — | 52 | 4 | no | — |
| 453 | C2×D4 | — | 52 | 4 | no | — |
| 454 | C2×D4 | — | 52 | 1 | no | — |
| 455 | C22×C4 | — | 4 | 1 | no | — |
| 456 | C22×C4 | — | 13 | 2 | no | — |
| 457 | C22×C4 | — | 52 | 4 | no | — |
| 458 | C22×C4 | — | 52 | 1 | no | — |
| 459 | C22×C4 | — | 52 | 1 | no | — |
| 460 | C22×C4 | D4×D13 | 1 | 1 | yes | characteristic |
| 461 | Q16 | — | 2 | 1 | no | — |
| 462 | Q16 | — | 13 | 2 | no | — |
| 463 | Q16 | — | 26 | 4 | no | — |
| 464 | Q16 | — | 26 | 1 | no | — |
| 465 | Q16 | — | 26 | 2 | no | — |
| 466 | Q16 | — | 26 | 2 | no | — |
| 467 | Q16 | — | 52 | 1 | no | — |
| 468 | Q16 | — | 52 | 1 | no | — |
| 469 | Q16 | C2×D52 | 1 | 2 | yes | — |
| 470 | SD16 | — | 2 | 2 | no | — |
| 471 | SD16 | — | 2 | 2 | no | — |
| 472 | SD16 | — | 26 | 4 | no | — |
| 473 | SD16 | — | 26 | 4 | no | — |
| 474 | SD16 | — | 26 | 2 | no | — |
| 475 | SD16 | — | 26 | 2 | no | — |
| 476 | D8 | — | 2 | 1 | no | — |
| 477 | D8 | — | 13 | 2 | no | — |
| 478 | D8 | — | 26 | 4 | no | — |
| 479 | D8 | — | 26 | 1 | no | — |
| 480 | D8 | C2×D52 | 1 | 2 | yes | — |
| 481 | M16 | — | 26 | 1 | no | — |
| 482 | M16 | — | 26 | 1 | no | — |
| 483 | M16 | — | 26 | 2 | no | — |
| 484 | M16 | — | 26 | 2 | no | — |
| 485 | C2×C8 | — | 13 | 2 | no | — |
| 486 | C2×C8 | — | 26 | 2 | no | — |
| 487 | C2×C8 | — | 26 | 2 | no | — |
| 488 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 489 | C2×C8 | C2×D52 | 1 | 1 | yes | characteristic |
| 490 | C2×C8 | D4×D13 | 1 | 1 | yes | characteristic |
| 491 | C2×C8 | D4×D13 | 1 | 1 | yes | characteristic |
| 492 | C2×C8 | D4×D13 | 1 | 1 | yes | characteristic |
| 493 | C2×C8 | C23×D13 | 1 | 1 | yes | characteristic |
| 494 | C4⋊C4 | — | 2 | 2 | no | — |
| 495 | C4⋊C4 | — | 52 | 4 | no | — |
| 496 | C22⋊C4 | — | 4 | 1 | no | — |
| 497 | C22⋊C4 | — | 52 | 4 | no | — |
| 498 | C42 | — | 4 | 1 | no | — |
| 499 | C16 | — | 2 | 2 | no | — |
| 500 | C16 | — | 26 | 2 | no | — |
| 501 | C13 | #33532 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 502 | C23 | — | 4 | 1 | no | — |
| 503 | C23 | — | 13 | 2 | no | — |
| 504 | C23 | — | 52 | 4 | no | — |
| 505 | C23 | — | 52 | 1 | no | — |
| 506 | C23 | D8×D13 | 1 | 1 | yes | characteristic |
| 507 | Q8 | — | 2 | 2 | no | — |
| 508 | Q8 | — | 4 | 1 | no | — |
| 509 | Q8 | — | 26 | 1 | no | — |
| 510 | Q8 | — | 26 | 1 | no | — |
| 511 | Q8 | — | 26 | 2 | no | — |
| 512 | Q8 | — | 52 | 4 | no | — |
| 513 | Q8 | — | 52 | 1 | no | — |
| 514 | Q8 | — | 52 | 2 | no | — |
| 515 | Q8 | — | 52 | 2 | no | — |
| 516 | Q8 | — | 104 | 1 | no | — |
| 517 | Q8 | — | 104 | 1 | no | — |
| 518 | D4 | — | 2 | 2 | no | — |
| 519 | D4 | — | 4 | 2 | no | — |
| 520 | D4 | — | 4 | 2 | no | — |
| 521 | D4 | — | 4 | 1 | no | — |
| 522 | D4 | — | 26 | 2 | no | — |
| 523 | D4 | — | 26 | 2 | no | — |
| 524 | D4 | — | 26 | 2 | no | — |
| 525 | D4 | — | 26 | 1 | no | — |
| 526 | D4 | — | 26 | 1 | no | — |
| 527 | D4 | — | 52 | 4 | no | — |
| 528 | D4 | — | 52 | 4 | no | — |
| 529 | D4 | — | 52 | 4 | no | — |
| 530 | D4 | — | 52 | 2 | no | — |
| 531 | D4 | — | 52 | 2 | no | — |
| 532 | D4 | — | 52 | 1 | no | — |
| 533 | C2×C4 | — | 4 | 1 | no | — |
| 534 | C2×C4 | — | 4 | 2 | no | — |
| 535 | C2×C4 | — | 4 | 2 | no | — |
| 536 | C2×C4 | — | 4 | 2 | no | — |
| 537 | C2×C4 | — | 13 | 2 | no | — |
| 538 | C2×C4 | — | 26 | 2 | no | — |
| 539 | C2×C4 | — | 26 | 2 | no | — |
| 540 | C2×C4 | — | 52 | 4 | no | — |
| 541 | C2×C4 | — | 52 | 4 | no | — |
| 542 | C2×C4 | — | 52 | 4 | no | — |
| 543 | C2×C4 | — | 52 | 1 | no | — |
| 544 | C2×C4 | — | 52 | 2 | no | — |
| 545 | C2×C4 | — | 52 | 2 | no | — |
| 546 | C2×C4 | — | 52 | 2 | no | — |
| 547 | C2×C4 | — | 104 | 1 | no | — |
| 548 | C2×C4 | — | 104 | 1 | no | — |
| 549 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 550 | C2×C4 | #88136 | 1 | 1 | yes | characteristic |
| 551 | C2×C4 | D8×D13 | 1 | 1 | yes | characteristic |
| 552 | C2×C4 | #88168 | 1 | 1 | yes | characteristic |
| 553 | C2×C4 | #88168 | 1 | 1 | yes | characteristic |
| 554 | C2×C4 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 555 | C8 | — | 26 | 2 | no | — |
| 556 | C8 | #88136 | 1 | 1 | yes | characteristic |
| 557 | C8 | #88136 | 1 | 1 | yes | characteristic |
| 558 | C8 | C22×D52 | 1 | 1 | yes | characteristic |
| 559 | C8 | C2×D4×D13 | 1 | 1 | yes | characteristic |
| 560 | C22 | — | 4 | 1 | no | — |
| 561 | C22 | — | 4 | 2 | no | — |
| 562 | C22 | — | 16 | 1 | no | — |
| 563 | C22 | — | 26 | 2 | no | — |
| 564 | C22 | — | 52 | 2 | no | — |
| 565 | C22 | — | 52 | 2 | no | — |
| 566 | C22 | — | 208 | 1 | no | — |
| 567 | C22 | — | 208 | 4 | no | — |
| 568 | C22 | #11718434 | 1 | 1 | yes | characteristic |
| 569 | C22 | #11718434 | 1 | 1 | yes | characteristic |
| 570 | C22 | C2×D8×D13 | 1 | 1 | yes | characteristic |
| 571 | C4 | — | 4 | 2 | no | — |
| 572 | C4 | — | 8 | 2 | no | — |
| 573 | C4 | — | 26 | 2 | no | — |
| 574 | C4 | — | 52 | 2 | no | — |
| 575 | C4 | — | 104 | 2 | no | — |
| 576 | C4 | #11718434 | 1 | 1 | yes | characteristic |
| 577 | C4 | #11718434 | 1 | 1 | yes | characteristic |
| 578 | C4 | C2×#88136 | 1 | 1 | yes | characteristic |
| 579 | C4 | C2×#88168 | 1 | 1 | yes | characteristic |
| 580 | C2 | — | 2 | 1 | no | — |
| 581 | C2 | — | 2 | 1 | no | — |
| 582 | C2 | — | 2 | 1 | no | — |
| 583 | C2 | — | 8 | 2 | no | — |
| 584 | C2 | — | 52 | 2 | no | — |
| 585 | C2 | — | 104 | 2 | no | — |
| 586 | C2 | C2×#11718434 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#11718570 | C2 | semidirect |
| 3. C2×#11718856 | C2 | semidirect |
| 4. #13124492 | C2 | semidirect |
| 5. #13116788 | C2 | semidirect |
| 6. #13116571 | C2 | semidirect |
| 7. #13116456 | C2 | semidirect |
| 8. C13×#2145 | C2 | semidirect |
| 20. C22×Dic52 | C22 | semidirect |
| 24. C2×C13×M32 | C22 | semidirect |
| 25. C13×#427 | C22 | semidirect |
| 27. #11718856 | C22 | semidirect |
| 30. C2×#88052 | C22 | semidirect |
| 33. #11718570 | C22 | semidirect |
| 37. #11718529 | C22 | semidirect |
| 38. C13×#360 | C22 | semidirect |
| 39. #11718106 | C22 | semidirect |
| 40. #11718080 | C22 | semidirect |
| 215. #2145 | D13 | semidirect |
| 299. C2×M32 | C2×D13 | semidirect |
| 302. #427 | C2×D13 | semidirect |
| 305. #360 | C2×D13 | semidirect |
| 501. C13 | #33532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13129605 | 2 |
| C2×#11718570 | 2 |
| C2×#11718856 | 2 |
| #13124492 | 2 |
| #13116788 | 2 |
| #13116571 | 2 |
| #13116456 | 2 |
| C13×#2145 | 2 |
| #33532 | 13 |