Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1410 conjugacy classes of subgroups.
The subgroup lattice has 920 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20288492 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20285632 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #493×D53 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20284192 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20273782 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20273780 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #20273778 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #20273771 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #20273770 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #20273768 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #20273767 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #20273381 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #20273164 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #20273096 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C53×#1621 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#13133263 | — | 2 | 1 | no | — |
| 17 | C2×#13133244 | — | 2 | 1 | no | — |
| 18 | C2×D8×D53 | — | 2 | 2 | no | — |
| 19 | #16811295 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #16811292 | — | 2 | 1 | no | — |
| 21 | D4×D212 | — | 2 | 1 | no | — |
| 22 | D4×D212 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #16811258 | — | 2 | 1 | no | — |
| 24 | #16811258 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #16811257 | — | 2 | 2 | no | — |
| 26 | #16811257 | — | 2 | 1 | no | — |
| 27 | #16811189 | — | 2 | 2 | no | — |
| 28 | #16811189 | — | 2 | 1 | no | — |
| 29 | #16811170 | — | 2 | 1 | no | — |
| 30 | #16811170 | C22 | 1 | 1 | yes | characteristic |
| 31 | #127×D53 | — | 2 | 1 | no | — |
| 32 | #127×D53 | C22 | 1 | 1 | yes | characteristic |
| 33 | #127×D53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 34 | C4×#11719949 | C22 | 1 | 1 | yes | characteristic |
| 35 | #16811000 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #16810999 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #16810999 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #16810998 | — | 2 | 1 | no | — |
| 39 | #16810998 | — | 2 | 2 | no | — |
| 40 | #16810968 | — | 2 | 1 | no | — |
| 41 | #16810823 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #16810821 | — | 2 | 1 | no | — |
| 43 | #16810819 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | #16810819 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | #16810818 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | #16810817 | — | 2 | 1 | no | — |
| 47 | #16810815 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | #16810815 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | #16810758 | — | 2 | 1 | no | — |
| 50 | #16810755 | — | 2 | 1 | no | — |
| 51 | #16810675 | C22 | 1 | 1 | yes | characteristic, complemented |
| 52 | #16810645 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | #16810626 | — | 2 | 1 | no | — |
| 54 | C4×C8×D53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | #16810367 | C22 | 1 | 1 | yes | characteristic, complemented |
| 56 | #16810366 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | #16810366 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | Q8⋊#88322 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | #16810352 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | #16810352 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | D4⋊#88322 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | #16810350 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | #16810350 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | C53×#550 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | C53×#493 | C22 | 1 | 1 | yes | characteristic, complemented |
| 66 | C53×#460 | C22 | 1 | 1 | yes | characteristic, complemented |
| 67 | C53×#459 | C22 | 1 | 1 | yes | characteristic, complemented |
| 68 | C53×#331 | C22 | 1 | 1 | yes | characteristic, complemented |
| 69 | C53×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 70 | C53×D4⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 71 | #13133263 | — | 4 | 4 | no | — |
| 72 | #13133263 | — | 4 | 4 | no | — |
| 73 | C2×#11719949 | — | 2 | 1 | no | — |
| 74 | C2×#11719949 | D4 | 1 | 1 | yes | characteristic |
| 75 | C2×#11719945 | — | 2 | 2 | no | — |
| 76 | C2×#11719945 | — | 2 | 1 | no | — |
| 77 | C22×D212 | — | 2 | 2 | no | — |
| 78 | C22×D212 | — | 2 | 1 | no | — |
| 79 | C2×D4×D53 | — | 2 | 2 | no | — |
| 80 | C2×D4×D53 | — | 2 | 2 | no | — |
| 81 | C2×D4×D53 | — | 2 | 2 | no | — |
| 82 | C2×D4×D53 | — | 2 | 1 | no | — |
| 83 | C2×D4×D53 | — | 2 | 1 | no | — |
| 84 | C2×D4×D53 | — | 2 | 1 | no | — |
| 85 | C2×D4×D53 | — | 2 | 1 | no | — |
| 86 | C2×D4×D53 | — | 2 | 1 | no | — |
| 87 | C2×D4×D53 | — | 2 | 1 | no | — |
| 88 | C2×D4×D53 | — | 2 | 1 | no | — |
| 89 | C2×D4×D53 | — | 2 | 1 | no | — |
| 90 | C2×D4×D53 | D4 | 1 | 2 | yes | — |
| 91 | #13133244 | — | 4 | 4 | no | — |
| 92 | C2×#11719924 | — | 2 | 1 | no | — |
| 93 | C2×D424 | — | 2 | 1 | no | — |
| 94 | C2×D424 | — | 2 | 2 | no | — |
| 95 | C2×D424 | — | 2 | 1 | no | — |
| 96 | C2×#11719922 | — | 2 | 2 | no | — |
| 97 | C2×#11719922 | — | 2 | 1 | no | — |
| 98 | C2×#11719922 | — | 2 | 1 | no | — |
| 99 | C2×#11719922 | — | 2 | 2 | no | — |
| 100 | C2×#11719922 | — | 2 | 1 | no | — |
| 101 | D8×D53 | — | 4 | 8 | no | — |
| 102 | C2×#11719912 | — | 2 | 1 | no | — |
| 103 | C2×C8×D53 | — | 2 | 1 | no | — |
| 104 | #13133216 | D4 | 1 | 1 | yes | characteristic |
| 105 | #13133214 | — | 2 | 1 | no | — |
| 106 | #13133214 | C23 | 1 | 1 | yes | characteristic |
| 107 | #13133214 | C23 | 1 | 1 | yes | characteristic |
| 108 | #13133213 | — | 2 | 2 | no | — |
| 109 | #13133213 | — | 2 | 2 | no | — |
| 110 | #13133213 | — | 2 | 1 | no | — |
| 111 | #13133213 | — | 2 | 1 | no | — |
| 112 | #13133213 | — | 2 | 1 | no | — |
| 113 | #13133213 | — | 2 | 1 | no | — |
| 114 | #13133213 | — | 2 | 1 | no | — |
| 115 | #13133213 | D4 | 1 | 1 | yes | characteristic |
| 116 | #13133213 | D4 | 1 | 2 | yes | — |
| 117 | #13133203 | — | 2 | 2 | no | — |
| 118 | #13133203 | — | 2 | 1 | no | — |
| 119 | #13133192 | — | 2 | 1 | no | — |
| 120 | #13133192 | — | 2 | 1 | no | — |
| 121 | #13133192 | — | 2 | 2 | no | — |
| 122 | #13133192 | D4 | 1 | 1 | yes | characteristic |
| 123 | #13133191 | — | 2 | 2 | no | — |
| 124 | #13133191 | — | 2 | 1 | no | — |
| 125 | #13133190 | — | 2 | 2 | no | — |
| 126 | #13133190 | — | 2 | 1 | no | — |
| 127 | #13133188 | — | 2 | 2 | no | — |
| 128 | #13133188 | — | 2 | 1 | no | — |
| 129 | #13133188 | — | 2 | 1 | no | — |
| 130 | #13133188 | D4 | 1 | 1 | yes | characteristic |
| 131 | #13133187 | — | 2 | 2 | no | — |
| 132 | #13133187 | — | 2 | 2 | no | — |
| 133 | #13133187 | — | 2 | 2 | no | — |
| 134 | #13133185 | — | 2 | 2 | no | — |
| 135 | #13133185 | — | 2 | 2 | no | — |
| 136 | #13133185 | — | 2 | 2 | no | — |
| 137 | Q8×Dic53 | D4 | 1 | 1 | yes | characteristic |
| 138 | C4×D212 | — | 2 | 1 | no | — |
| 139 | C4×D212 | — | 2 | 1 | no | — |
| 140 | C4×D212 | C23 | 1 | 1 | yes | characteristic |
| 141 | C4×D212 | C23 | 1 | 1 | yes | characteristic |
| 142 | #13133179 | — | 2 | 1 | no | — |
| 143 | #13133179 | D4 | 1 | 1 | yes | characteristic |
| 144 | C4×C22⋊D53 | — | 2 | 2 | no | — |
| 145 | C4×C22⋊D53 | — | 2 | 1 | no | — |
| 146 | #13133175 | — | 2 | 1 | no | — |
| 147 | #13133175 | D4 | 1 | 1 | yes | characteristic |
| 148 | C42×D53 | — | 2 | 1 | no | — |
| 149 | C42×D53 | C23 | 1 | 1 | yes | characteristic |
| 150 | C4⋊#88322 | C23 | 1 | 1 | yes | characteristic |
| 151 | C4⋊#88322 | C23 | 1 | 1 | yes | characteristic |
| 152 | #13133146 | — | 2 | 1 | no | — |
| 153 | #13133139 | — | 2 | 1 | no | — |
| 154 | #13133139 | — | 2 | 1 | no | — |
| 155 | #13133138 | — | 2 | 1 | no | — |
| 156 | #13133138 | — | 2 | 1 | no | — |
| 157 | #13133137 | — | 2 | 1 | no | — |
| 158 | #13133137 | — | 2 | 1 | no | — |
| 159 | #13133129 | — | 2 | 1 | no | — |
| 160 | C4×#88322 | C23 | 1 | 1 | yes | characteristic |
| 161 | C8×Dic53 | — | 2 | 1 | no | — |
| 162 | C8×Dic53 | — | 2 | 1 | no | — |
| 163 | C2×#41×C53 | — | 2 | 1 | no | — |
| 164 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 165 | C2×D8×C53 | — | 2 | 2 | no | — |
| 166 | C2×D8×C53 | — | 2 | 1 | no | — |
| 167 | #127×C53 | — | 2 | 1 | no | — |
| 168 | #127×C53 | C23 | 1 | 1 | yes | characteristic |
| 169 | #127×C53 | C23 | 1 | 1 | yes | characteristic |
| 170 | #121×C53 | — | 2 | 1 | no | — |
| 171 | #121×C53 | — | 2 | 2 | no | — |
| 172 | C4×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 173 | C4×D4×C53 | — | 2 | 1 | no | — |
| 174 | C4×D4×C53 | C23 | 1 | 1 | yes | characteristic |
| 175 | C4⋊C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 176 | C4⋊C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 177 | #102×C53 | — | 2 | 1 | no | — |
| 178 | #102×C53 | — | 2 | 1 | no | — |
| 179 | C4×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 180 | C23×D53 | — | 2 | 2 | no | — |
| 181 | C23×D53 | — | 2 | 2 | no | — |
| 182 | C23×D53 | — | 2 | 2 | no | — |
| 183 | C23×D53 | — | 4 | 1 | no | — |
| 184 | #41×C53 | — | 4 | 2 | no | — |
| 185 | #41×C53 | — | 4 | 2 | no | — |
| 186 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | C2×D4×C53 | — | 2 | 2 | no | — |
| 188 | C2×D4×C53 | — | 2 | 2 | no | — |
| 189 | C2×D4×C53 | — | 2 | 1 | no | — |
| 190 | C2×D4×C53 | — | 2 | 1 | no | — |
| 191 | C2×D4×C53 | — | 2 | 1 | no | — |
| 192 | C2×D4×C53 | — | 2 | 1 | no | — |
| 193 | C2×D4×C53 | — | 2 | 1 | no | — |
| 194 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 195 | C2×D4×C53 | C2×D4 | 1 | 2 | yes | — |
| 196 | C22×C4×C53 | — | 2 | 2 | no | — |
| 197 | C22×C4×C53 | — | 2 | 1 | no | — |
| 198 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 199 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 200 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 201 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 202 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 203 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 204 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 205 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 206 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 207 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 208 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 209 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 210 | #11719949 | — | 2 | 2 | no | — |
| 211 | #11719949 | — | 4 | 2 | no | — |
| 212 | #11719949 | — | 4 | 2 | no | — |
| 213 | #11719949 | D8 | 1 | 4 | yes | complemented |
| 214 | D4×D53 | — | 4 | 8 | no | — |
| 215 | D4×D53 | — | 4 | 4 | no | — |
| 216 | D4×D53 | — | 4 | 4 | no | — |
| 217 | D4×D53 | — | 4 | 8 | no | — |
| 218 | D4×D53 | — | 4 | 2 | no | — |
| 219 | D4×D53 | — | 4 | 2 | no | — |
| 220 | D4×D53 | — | 4 | 2 | no | — |
| 221 | D4×D53 | — | 4 | 2 | no | — |
| 222 | D4×D53 | — | 4 | 2 | no | — |
| 223 | D4×D53 | — | 4 | 2 | no | — |
| 224 | D4×D53 | — | 8 | 1 | no | — |
| 225 | D4×D53 | — | 8 | 1 | no | — |
| 226 | D4×D53 | — | 8 | 1 | no | — |
| 227 | D4×D53 | — | 8 | 1 | no | — |
| 228 | D4×D53 | — | 8 | 1 | no | — |
| 229 | D4×D53 | — | 8 | 1 | no | — |
| 230 | D4×D53 | — | 8 | 1 | no | — |
| 231 | D4×D53 | — | 8 | 1 | no | — |
| 232 | D4×D53 | — | 8 | 4 | no | — |
| 233 | #11719945 | — | 4 | 8 | no | — |
| 234 | #11719945 | — | 4 | 2 | no | — |
| 235 | #11719945 | — | 4 | 2 | no | — |
| 236 | C2×D212 | — | 2 | 1 | no | — |
| 237 | C2×D212 | — | 2 | 2 | no | — |
| 238 | C2×D212 | — | 2 | 2 | no | — |
| 239 | C2×D212 | — | 2 | 1 | no | — |
| 240 | C2×D212 | — | 2 | 1 | no | — |
| 241 | C2×D212 | — | 2 | 1 | no | — |
| 242 | C2×D212 | — | 2 | 1 | no | — |
| 243 | C2×D212 | — | 2 | 1 | no | — |
| 244 | C2×D212 | — | 2 | 1 | no | — |
| 245 | C2×D212 | — | 2 | 2 | no | — |
| 246 | C2×D212 | — | 4 | 8 | no | — |
| 247 | C2×D212 | — | 4 | 2 | no | — |
| 248 | C2×D212 | — | 4 | 2 | no | — |
| 249 | C2×D212 | C2×D4 | 1 | 1 | yes | characteristic |
| 250 | C2×D212 | C2×D4 | 1 | 1 | yes | characteristic |
| 251 | C2×D212 | C2×D4 | 1 | 2 | yes | — |
| 252 | C2×C4×D53 | — | 2 | 1 | no | — |
| 253 | C2×C4×D53 | — | 2 | 2 | no | — |
| 254 | C2×C4×D53 | — | 2 | 1 | no | — |
| 255 | C2×C4×D53 | — | 2 | 1 | no | — |
| 256 | C2×C4×D53 | — | 2 | 1 | no | — |
| 257 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 258 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 259 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 260 | C2×Dic106 | — | 2 | 1 | no | — |
| 261 | SD16×C53 | — | 4 | 2 | no | — |
| 262 | D8×C53 | — | 4 | 4 | no | — |
| 263 | D8×C53 | — | 8 | 1 | no | — |
| 264 | C2×C8×C53 | — | 2 | 1 | no | — |
| 265 | C2×C8×C53 | — | 2 | 1 | no | — |
| 266 | C2×C8×C53 | — | 2 | 1 | no | — |
| 267 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 268 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 269 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 270 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 271 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 272 | C42×C53 | — | 2 | 1 | no | — |
| 273 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 274 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 275 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 276 | #11719924 | — | 4 | 2 | no | — |
| 277 | #11719922 | — | 4 | 4 | no | — |
| 278 | #11719922 | — | 4 | 4 | no | — |
| 279 | #11719922 | — | 4 | 2 | no | — |
| 280 | #11719922 | — | 8 | 1 | no | — |
| 281 | #11719922 | — | 8 | 1 | no | — |
| 282 | #11719921 | — | 2 | 2 | no | — |
| 283 | #11719921 | — | 2 | 2 | no | — |
| 284 | #11719921 | — | 2 | 1 | no | — |
| 285 | #11719921 | — | 2 | 1 | no | — |
| 286 | #11719921 | — | 2 | 1 | no | — |
| 287 | #11719921 | — | 2 | 1 | no | — |
| 288 | #11719921 | — | 2 | 1 | no | — |
| 289 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 290 | C4⋊Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 291 | C4⋊Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 292 | #11719919 | — | 2 | 1 | no | — |
| 293 | C4×Dic53 | — | 2 | 1 | no | — |
| 294 | C4×Dic53 | — | 2 | 1 | no | — |
| 295 | C4×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 296 | C4×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 297 | C4×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 298 | C2×#88322 | — | 2 | 1 | no | — |
| 299 | C2×#88322 | — | 2 | 1 | no | — |
| 300 | C2×#88322 | — | 2 | 1 | no | — |
| 301 | D424 | — | 4 | 4 | no | — |
| 302 | D424 | — | 4 | 2 | no | — |
| 303 | D424 | — | 8 | 1 | no | — |
| 304 | #11719912 | — | 4 | 2 | no | — |
| 305 | C8×D53 | — | 2 | 4 | no | — |
| 306 | C23×C53 | — | 2 | 1 | no | — |
| 307 | C23×C53 | — | 2 | 2 | no | — |
| 308 | C23×C53 | — | 4 | 1 | no | — |
| 309 | C22×D53 | — | 2 | 1 | no | — |
| 310 | C22×D53 | — | 2 | 1 | no | — |
| 311 | C22×D53 | — | 2 | 2 | no | — |
| 312 | C22×D53 | — | 4 | 4 | no | — |
| 313 | C22×D53 | — | 4 | 4 | no | — |
| 314 | C22×D53 | — | 4 | 4 | no | — |
| 315 | C22×D53 | — | 4 | 1 | no | — |
| 316 | C22×D53 | — | 8 | 2 | no | — |
| 317 | C22×D53 | — | 8 | 2 | no | — |
| 318 | C22×D53 | — | 8 | 2 | no | — |
| 319 | C22×D53 | — | 8 | 2 | no | — |
| 320 | C22×D53 | — | 8 | 2 | no | — |
| 321 | C22×D53 | — | 8 | 2 | no | — |
| 322 | C22×D53 | — | 8 | 2 | no | — |
| 323 | C22×D53 | — | 8 | 2 | no | — |
| 324 | C22×D53 | — | 8 | 2 | no | — |
| 325 | C22×D53 | #120 | 1 | 1 | yes | characteristic |
| 326 | Q8×C53 | — | 2 | 1 | no | — |
| 327 | Q8×C53 | C2×D8 | 1 | 2 | yes | complemented |
| 328 | D4×C53 | — | 2 | 1 | no | — |
| 329 | D4×C53 | — | 2 | 1 | no | — |
| 330 | D4×C53 | — | 4 | 2 | no | — |
| 331 | D4×C53 | — | 4 | 4 | no | — |
| 332 | D4×C53 | — | 4 | 2 | no | — |
| 333 | D4×C53 | — | 4 | 1 | no | — |
| 334 | D4×C53 | — | 4 | 1 | no | — |
| 335 | D4×C53 | — | 4 | 1 | no | — |
| 336 | D4×C53 | — | 4 | 1 | no | — |
| 337 | D4×C53 | — | 4 | 1 | no | — |
| 338 | D4×C53 | — | 4 | 1 | no | — |
| 339 | D4×C53 | — | 4 | 1 | no | — |
| 340 | D4×C53 | — | 4 | 1 | no | — |
| 341 | D4×C53 | — | 8 | 2 | no | — |
| 342 | C2×C4×C53 | — | 2 | 1 | no | — |
| 343 | C2×C4×C53 | — | 2 | 1 | no | — |
| 344 | C2×C4×C53 | — | 2 | 1 | no | — |
| 345 | C2×C4×C53 | — | 4 | 4 | no | — |
| 346 | C2×C4×C53 | — | 4 | 1 | no | — |
| 347 | C2×C4×C53 | — | 4 | 1 | no | — |
| 348 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 349 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 350 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 351 | C22⋊D53 | — | 4 | 4 | no | — |
| 352 | C22⋊D53 | — | 4 | 2 | no | — |
| 353 | C22⋊D53 | — | 4 | 4 | no | — |
| 354 | C22⋊D53 | — | 4 | 2 | no | — |
| 355 | C22⋊D53 | — | 4 | 4 | no | — |
| 356 | C22⋊D53 | — | 4 | 2 | no | — |
| 357 | C22⋊D53 | — | 8 | 2 | no | — |
| 358 | C22⋊D53 | — | 8 | 2 | no | — |
| 359 | C22⋊D53 | — | 8 | 2 | no | — |
| 360 | C22⋊D53 | — | 8 | 2 | no | — |
| 361 | C22⋊D53 | — | 8 | 2 | no | — |
| 362 | C22⋊D53 | — | 8 | 2 | no | — |
| 363 | C2×Dic53 | — | 2 | 1 | no | — |
| 364 | C2×Dic53 | — | 2 | 1 | no | — |
| 365 | C2×Dic53 | #120 | 1 | 1 | yes | characteristic |
| 366 | C2×Dic53 | #120 | 1 | 1 | yes | characteristic |
| 367 | C2×Dic53 | #120 | 1 | 1 | yes | characteristic |
| 368 | D212 | — | 2 | 4 | no | — |
| 369 | D212 | — | 2 | 1 | no | — |
| 370 | D212 | — | 2 | 1 | no | — |
| 371 | D212 | — | 2 | 1 | no | — |
| 372 | D212 | — | 4 | 2 | no | — |
| 373 | D212 | — | 4 | 4 | no | — |
| 374 | D212 | — | 4 | 2 | no | — |
| 375 | D212 | — | 4 | 4 | no | — |
| 376 | D212 | — | 4 | 2 | no | — |
| 377 | D212 | — | 4 | 1 | no | — |
| 378 | D212 | — | 4 | 1 | no | — |
| 379 | D212 | — | 4 | 1 | no | — |
| 380 | D212 | — | 4 | 1 | no | — |
| 381 | D212 | — | 4 | 1 | no | — |
| 382 | D212 | — | 4 | 1 | no | — |
| 383 | D212 | — | 4 | 1 | no | — |
| 384 | D212 | — | 4 | 1 | no | — |
| 385 | D212 | — | 8 | 2 | no | — |
| 386 | D212 | C2×D8 | 1 | 2 | yes | complemented |
| 387 | C4×D53 | — | 2 | 1 | no | — |
| 388 | C4×D53 | — | 2 | 1 | no | — |
| 389 | C4×D53 | — | 2 | 4 | no | — |
| 390 | C4×D53 | — | 2 | 2 | no | — |
| 391 | C4×D53 | — | 4 | 4 | no | — |
| 392 | C4×D53 | — | 4 | 1 | no | — |
| 393 | C4×D53 | — | 4 | 1 | no | — |
| 394 | C4×D53 | — | 4 | 1 | no | — |
| 395 | C4×D53 | — | 4 | 1 | no | — |
| 396 | C4×D53 | — | 4 | 2 | no | — |
| 397 | C4×D53 | C2×D8 | 1 | 2 | yes | — |
| 398 | C4×D53 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 399 | Dic106 | — | 4 | 2 | no | — |
| 400 | C8×C53 | — | 2 | 2 | no | — |
| 401 | C8×C53 | — | 4 | 1 | no | — |
| 402 | C8×C53 | — | 4 | 1 | no | — |
| 403 | #88322 | — | 2 | 2 | no | — |
| 404 | #88322 | — | 4 | 1 | no | — |
| 405 | #88322 | — | 4 | 1 | no | — |
| 406 | #18620 | — | 53 | 1 | no | maximal, Sylow |
| 407 | C22×C53 | — | 4 | 2 | no | — |
| 408 | C22×C53 | — | 4 | 1 | no | — |
| 409 | C22×C53 | — | 4 | 1 | no | — |
| 410 | C22×C53 | — | 4 | 2 | no | — |
| 411 | C22×C53 | — | 4 | 2 | no | — |
| 412 | C22×C53 | — | 4 | 1 | no | — |
| 413 | C22×C53 | — | 8 | 1 | no | — |
| 414 | C22×C53 | — | 8 | 1 | no | — |
| 415 | C22×C53 | — | 8 | 1 | no | — |
| 416 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 417 | C2×D53 | — | 2 | 1 | no | — |
| 418 | C2×D53 | — | 2 | 1 | no | — |
| 419 | C2×D53 | — | 2 | 2 | no | — |
| 420 | C2×D53 | — | 4 | 1 | no | — |
| 421 | C2×D53 | — | 4 | 1 | no | — |
| 422 | C2×D53 | — | 4 | 2 | no | — |
| 423 | C2×D53 | — | 4 | 1 | no | — |
| 424 | C2×D53 | — | 4 | 1 | no | — |
| 425 | C2×D53 | — | 4 | 2 | no | — |
| 426 | C2×D53 | — | 4 | 2 | no | — |
| 427 | C2×D53 | — | 4 | 1 | no | — |
| 428 | C2×D53 | — | 8 | 1 | no | — |
| 429 | C2×D53 | — | 8 | 1 | no | — |
| 430 | C2×D53 | — | 8 | 1 | no | — |
| 431 | C2×D53 | — | 16 | 4 | no | — |
| 432 | C2×D53 | — | 16 | 4 | no | — |
| 433 | C2×D53 | — | 16 | 4 | no | — |
| 434 | C2×D53 | — | 16 | 4 | no | — |
| 435 | C2×D53 | #447 | 1 | 2 | yes | — |
| 436 | C4×C53 | — | 2 | 2 | no | — |
| 437 | C4×C53 | — | 2 | 1 | no | — |
| 438 | C4×C53 | — | 4 | 1 | no | — |
| 439 | C4×C53 | — | 4 | 1 | no | — |
| 440 | C4×C53 | C22×D8 | 1 | 1 | yes | characteristic |
| 441 | C4×C53 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 442 | C4×C53 | #576 | 1 | 1 | yes | characteristic |
| 443 | C4×C53 | #576 | 1 | 1 | yes | characteristic |
| 444 | Dic53 | — | 2 | 1 | no | — |
| 445 | Dic53 | — | 4 | 1 | no | — |
| 446 | Dic53 | — | 4 | 1 | no | — |
| 447 | Dic53 | #447 | 1 | 2 | yes | — |
| 448 | Dic53 | #453 | 1 | 2 | yes | — |
| 449 | #3498 | — | 53 | 1 | no | — |
| 450 | #3205 | — | 53 | 1 | no | — |
| 451 | C2×#493 | — | 53 | 1 | no | — |
| 452 | #3038 | — | 53 | 1 | no | — |
| 453 | #1621 | — | 53 | 1 | no | — |
| 454 | #1621 | — | 53 | 1 | no | — |
| 455 | #1621 | — | 53 | 1 | no | — |
| 456 | #1621 | D53 | 1 | 1 | yes | characteristic, complemented |
| 457 | #1619 | — | 53 | 1 | no | — |
| 458 | #1619 | — | 53 | 1 | no | — |
| 459 | #1619 | — | 53 | 1 | no | — |
| 460 | #1619 | — | 53 | 1 | no | — |
| 461 | #1545 | — | 53 | 1 | no | — |
| 462 | #1492 | — | 53 | 1 | no | — |
| 463 | #1476 | — | 53 | 1 | no | — |
| 464 | C2×C53 | — | 8 | 2 | no | — |
| 465 | C2×C53 | — | 8 | 1 | no | — |
| 466 | C2×C53 | — | 16 | 1 | no | — |
| 467 | C2×C53 | C2×#447 | 1 | 1 | yes | characteristic |
| 468 | C2×C53 | #3008 | 1 | 1 | yes | characteristic |
| 469 | C2×C53 | C2×#453 | 1 | 1 | yes | characteristic |
| 470 | D53 | — | 2 | 2 | no | — |
| 471 | D53 | — | 4 | 2 | no | — |
| 472 | D53 | — | 8 | 1 | no | — |
| 473 | D53 | — | 8 | 2 | no | — |
| 474 | D53 | — | 16 | 1 | no | — |
| 475 | C2×H(5,𝔽2) | — | 106 | 1 | no | — |
| 476 | C2×AGL(1,ℤ/8) | — | 106 | 1 | no | — |
| 477 | C22×D8 | — | 106 | 2 | no | — |
| 478 | #550 | — | 53 | 1 | no | — |
| 479 | #550 | — | 106 | 1 | no | — |
| 480 | #550 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 481 | D42 | — | 53 | 1 | no | — |
| 482 | D42 | — | 53 | 1 | no | — |
| 483 | D42 | — | 106 | 1 | no | — |
| 484 | D42 | — | 106 | 1 | no | — |
| 485 | D42 | — | 106 | 2 | no | — |
| 486 | D42 | — | 106 | 1 | no | — |
| 487 | #535 | — | 106 | 1 | no | — |
| 488 | #535 | — | 106 | 2 | no | — |
| 489 | #532 | — | 53 | 1 | no | — |
| 490 | #532 | — | 106 | 1 | no | — |
| 491 | C2×#127 | — | 53 | 1 | no | — |
| 492 | C2×#127 | — | 53 | 1 | no | — |
| 493 | C2×#127 | — | 106 | 1 | no | — |
| 494 | C4×#41 | — | 53 | 1 | no | — |
| 495 | #493 | — | 53 | 1 | no | — |
| 496 | #493 | — | 53 | 1 | no | — |
| 497 | #493 | — | 53 | 1 | no | — |
| 498 | #493 | — | 106 | 2 | no | — |
| 499 | #493 | — | 106 | 1 | no | — |
| 500 | #493 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 501 | #486 | — | 106 | 1 | no | — |
| 502 | #460 | — | 53 | 1 | no | — |
| 503 | #460 | — | 106 | 1 | no | — |
| 504 | #460 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 505 | #459 | — | 53 | 1 | no | — |
| 506 | #459 | — | 53 | 1 | no | — |
| 507 | #459 | — | 53 | 1 | no | — |
| 508 | #459 | — | 53 | 1 | no | — |
| 509 | #459 | — | 53 | 1 | no | — |
| 510 | #459 | — | 106 | 1 | no | — |
| 511 | #459 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 512 | #447 | — | 106 | 1 | no | — |
| 513 | #447 | — | 106 | 1 | no | — |
| 514 | #431 | — | 53 | 1 | no | — |
| 515 | #423 | — | 53 | 1 | no | — |
| 516 | #418 | — | 106 | 1 | no | — |
| 517 | C2×C4×C8 | — | 53 | 1 | no | — |
| 518 | #331 | — | 53 | 1 | no | — |
| 519 | #331 | — | 53 | 1 | no | — |
| 520 | #331 | — | 53 | 1 | no | — |
| 521 | #331 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 522 | Q8⋊C8 | — | 53 | 1 | no | — |
| 523 | Q8⋊C8 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 524 | D4⋊C8 | — | 53 | 1 | no | — |
| 525 | D4⋊C8 | — | 53 | 1 | no | — |
| 526 | D4⋊C8 | — | 53 | 1 | no | — |
| 527 | D4⋊C8 | — | 53 | 1 | no | — |
| 528 | D4⋊C8 | — | 53 | 1 | no | — |
| 529 | D4⋊C8 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 530 | C53 | #18620 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 531 | H(5,𝔽2) | — | 212 | 4 | no | — |
| 532 | H(5,𝔽2) | — | 212 | 4 | no | — |
| 533 | C2×#41 | — | 2 | 1 | no | — |
| 534 | C2×#41 | — | 53 | 1 | no | — |
| 535 | C2×#41 | — | 106 | 1 | no | — |
| 536 | C2×#41 | — | 106 | 2 | no | — |
| 537 | C2×#41 | — | 106 | 1 | no | — |
| 538 | C22×D4 | — | 53 | 2 | no | — |
| 539 | C22×D4 | — | 106 | 1 | no | — |
| 540 | C22×D4 | — | 106 | 2 | no | — |
| 541 | C22×D4 | — | 106 | 1 | no | — |
| 542 | C22×D4 | — | 106 | 1 | no | — |
| 543 | C22×D4 | — | 106 | 1 | no | — |
| 544 | C22×D4 | — | 106 | 1 | no | — |
| 545 | C22×D4 | — | 106 | 1 | no | — |
| 546 | C22×D4 | — | 106 | 1 | no | — |
| 547 | C22×D4 | — | 106 | 1 | no | — |
| 548 | C22×D4 | — | 106 | 2 | no | — |
| 549 | C22×D4 | — | 106 | 2 | no | — |
| 550 | C22×D4 | — | 106 | 2 | no | — |
| 551 | C22×D4 | — | 106 | 1 | no | — |
| 552 | AGL(1,ℤ/8) | — | 212 | 4 | no | — |
| 553 | C2×SD16 | — | 2 | 1 | no | — |
| 554 | C2×SD16 | — | 106 | 1 | no | — |
| 555 | C2×D8 | — | 2 | 2 | no | — |
| 556 | C2×D8 | — | 2 | 1 | no | — |
| 557 | C2×D8 | — | 106 | 1 | no | — |
| 558 | C2×D8 | — | 106 | 2 | no | — |
| 559 | C2×D8 | — | 106 | 1 | no | — |
| 560 | C2×D8 | — | 106 | 1 | no | — |
| 561 | C2×D8 | — | 106 | 1 | no | — |
| 562 | C2×D8 | — | 106 | 2 | no | — |
| 563 | C2×D8 | — | 106 | 1 | no | — |
| 564 | C2×D8 | — | 106 | 2 | no | — |
| 565 | C2×D8 | — | 212 | 8 | no | — |
| 566 | C2×M16 | — | 106 | 1 | no | — |
| 567 | C22×C8 | — | 106 | 1 | no | — |
| 568 | C4⋊Q8 | — | 53 | 1 | no | — |
| 569 | #127 | — | 2 | 1 | no | — |
| 570 | #127 | — | 53 | 2 | no | — |
| 571 | #127 | — | 53 | 1 | no | — |
| 572 | #127 | — | 53 | 1 | no | — |
| 573 | #127 | — | 53 | 1 | no | — |
| 574 | #127 | — | 106 | 1 | no | — |
| 575 | #127 | — | 106 | 1 | no | — |
| 576 | #127 | — | 106 | 1 | no | — |
| 577 | #127 | — | 106 | 1 | no | — |
| 578 | #127 | — | 106 | 1 | no | — |
| 579 | #127 | — | 106 | 1 | no | — |
| 580 | #127 | — | 106 | 2 | no | — |
| 581 | #127 | — | 106 | 2 | no | — |
| 582 | #127 | C22×D53 | 1 | 1 | yes | characteristic |
| 583 | #127 | C22×D53 | 1 | 1 | yes | characteristic |
| 584 | #124 | — | 106 | 1 | no | — |
| 585 | #124 | — | 106 | 2 | no | — |
| 586 | #121 | — | 2 | 2 | no | — |
| 587 | #121 | — | 2 | 1 | no | — |
| 588 | #121 | — | 53 | 1 | no | — |
| 589 | #121 | — | 53 | 1 | no | — |
| 590 | #121 | — | 106 | 1 | no | — |
| 591 | #121 | — | 106 | 2 | no | — |
| 592 | #121 | — | 106 | 2 | no | — |
| 593 | #121 | — | 106 | 1 | no | — |
| 594 | #121 | — | 106 | 1 | no | — |
| 595 | #121 | — | 106 | 1 | no | — |
| 596 | #121 | — | 106 | 2 | no | — |
| 597 | #121 | — | 106 | 2 | no | — |
| 598 | #121 | — | 106 | 1 | no | — |
| 599 | #121 | — | 106 | 1 | no | — |
| 600 | #120 | — | 106 | 2 | no | — |
| 601 | #120 | — | 106 | 2 | no | — |
| 602 | #120 | — | 106 | 2 | no | — |
| 603 | #120 | — | 106 | 2 | no | — |
| 604 | #120 | — | 106 | 2 | no | — |
| 605 | #120 | — | 106 | 2 | no | — |
| 606 | C4×Q8 | — | 53 | 1 | no | — |
| 607 | C4×Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 608 | C4×D4 | — | 2 | 1 | no | — |
| 609 | C4×D4 | — | 53 | 1 | no | — |
| 610 | C4×D4 | — | 53 | 1 | no | — |
| 611 | C4×D4 | — | 53 | 1 | no | — |
| 612 | C4×D4 | — | 106 | 1 | no | — |
| 613 | C4×D4 | — | 106 | 1 | no | — |
| 614 | C4×D4 | — | 106 | 1 | no | — |
| 615 | C4×D4 | — | 106 | 1 | no | — |
| 616 | C4×D4 | — | 106 | 2 | no | — |
| 617 | C4×D4 | C22×D53 | 1 | 1 | yes | characteristic |
| 618 | #117 | — | 53 | 1 | no | — |
| 619 | #117 | — | 106 | 1 | no | — |
| 620 | C2×C42 | — | 53 | 1 | no | — |
| 621 | C2×C42 | — | 106 | 1 | no | — |
| 622 | C4⋊C8 | — | 53 | 1 | no | — |
| 623 | C4⋊C8 | — | 53 | 1 | no | — |
| 624 | C4⋊C8 | — | 106 | 1 | no | — |
| 625 | C4⋊C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 626 | C4⋊C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 627 | #102 | — | 2 | 1 | no | — |
| 628 | #102 | — | 2 | 1 | no | — |
| 629 | #102 | — | 106 | 1 | no | — |
| 630 | #102 | — | 106 | 1 | no | — |
| 631 | #102 | — | 106 | 1 | no | — |
| 632 | #102 | — | 106 | 1 | no | — |
| 633 | #102 | — | 106 | 1 | no | — |
| 634 | #102 | — | 106 | 1 | no | — |
| 635 | C22⋊C8 | — | 106 | 1 | no | — |
| 636 | C4×C8 | — | 53 | 1 | no | — |
| 637 | C4×C8 | — | 106 | 1 | no | — |
| 638 | C4×C8 | — | 106 | 1 | no | — |
| 639 | C4×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 640 | C24 | — | 106 | 2 | no | — |
| 641 | C24 | — | 106 | 2 | no | — |
| 642 | C24 | — | 106 | 2 | no | — |
| 643 | C24 | — | 212 | 1 | no | — |
| 644 | #41 | — | 4 | 2 | no | — |
| 645 | #41 | — | 4 | 2 | no | — |
| 646 | #41 | — | 53 | 4 | no | — |
| 647 | #41 | — | 106 | 2 | no | — |
| 648 | #41 | — | 212 | 2 | no | — |
| 649 | #41 | — | 212 | 2 | no | — |
| 650 | #41 | — | 212 | 8 | no | — |
| 651 | #41 | — | 212 | 2 | no | — |
| 652 | #41 | — | 212 | 2 | no | — |
| 653 | C2×Q8 | — | 106 | 1 | no | — |
| 654 | C2×Q8 | D4×D53 | 1 | 1 | yes | characteristic |
| 655 | C2×D4 | — | 2 | 2 | no | — |
| 656 | C2×D4 | — | 2 | 2 | no | — |
| 657 | C2×D4 | — | 2 | 1 | no | — |
| 658 | C2×D4 | — | 2 | 1 | no | — |
| 659 | C2×D4 | — | 2 | 1 | no | — |
| 660 | C2×D4 | — | 2 | 1 | no | — |
| 661 | C2×D4 | — | 2 | 1 | no | — |
| 662 | C2×D4 | — | 53 | 1 | no | — |
| 663 | C2×D4 | — | 53 | 1 | no | — |
| 664 | C2×D4 | — | 53 | 2 | no | — |
| 665 | C2×D4 | — | 106 | 1 | no | — |
| 666 | C2×D4 | — | 106 | 2 | no | — |
| 667 | C2×D4 | — | 106 | 1 | no | — |
| 668 | C2×D4 | — | 106 | 2 | no | — |
| 669 | C2×D4 | — | 106 | 2 | no | — |
| 670 | C2×D4 | — | 106 | 2 | no | — |
| 671 | C2×D4 | — | 106 | 1 | no | — |
| 672 | C2×D4 | — | 106 | 2 | no | — |
| 673 | C2×D4 | — | 106 | 1 | no | — |
| 674 | C2×D4 | — | 106 | 2 | no | — |
| 675 | C2×D4 | — | 106 | 2 | no | — |
| 676 | C2×D4 | — | 106 | 2 | no | — |
| 677 | C2×D4 | — | 106 | 1 | no | — |
| 678 | C2×D4 | — | 106 | 2 | no | — |
| 679 | C2×D4 | — | 106 | 1 | no | — |
| 680 | C2×D4 | — | 106 | 1 | no | — |
| 681 | C2×D4 | — | 106 | 1 | no | — |
| 682 | C2×D4 | — | 106 | 1 | no | — |
| 683 | C2×D4 | — | 106 | 1 | no | — |
| 684 | C2×D4 | — | 424 | 1 | no | — |
| 685 | C2×D4 | — | 424 | 1 | no | — |
| 686 | C2×D4 | — | 424 | 1 | no | — |
| 687 | C2×D4 | — | 424 | 1 | no | — |
| 688 | C2×D4 | — | 424 | 1 | no | — |
| 689 | C2×D4 | — | 424 | 1 | no | — |
| 690 | C2×D4 | — | 424 | 1 | no | — |
| 691 | C2×D4 | — | 424 | 1 | no | — |
| 692 | C2×D4 | — | 424 | 4 | no | — |
| 693 | C2×D4 | — | 212 | 2 | no | — |
| 694 | C2×D4 | — | 212 | 8 | no | — |
| 695 | C2×D4 | — | 212 | 2 | no | — |
| 696 | C2×D4 | — | 212 | 2 | no | — |
| 697 | C2×D4 | — | 212 | 2 | no | — |
| 698 | C2×D4 | — | 212 | 2 | no | — |
| 699 | C2×D4 | — | 212 | 2 | no | — |
| 700 | C2×D4 | — | 212 | 1 | no | — |
| 701 | C2×D4 | — | 212 | 1 | no | — |
| 702 | C2×D4 | — | 212 | 1 | no | — |
| 703 | C2×D4 | — | 212 | 4 | no | — |
| 704 | C2×D4 | — | 212 | 8 | no | — |
| 705 | C2×D4 | — | 212 | 4 | no | — |
| 706 | C2×D4 | — | 212 | 2 | no | — |
| 707 | C2×D4 | — | 212 | 8 | no | — |
| 708 | C2×D4 | — | 212 | 2 | no | — |
| 709 | C2×D4 | D4×D53 | 1 | 1 | yes | characteristic |
| 710 | C2×D4 | D4×D53 | 1 | 2 | yes | — |
| 711 | C22×C4 | — | 2 | 2 | no | — |
| 712 | C22×C4 | — | 2 | 1 | no | — |
| 713 | C22×C4 | — | 53 | 1 | no | — |
| 714 | C22×C4 | — | 53 | 1 | no | — |
| 715 | C22×C4 | — | 53 | 1 | no | — |
| 716 | C22×C4 | — | 106 | 1 | no | — |
| 717 | C22×C4 | — | 106 | 1 | no | — |
| 718 | C22×C4 | — | 106 | 2 | no | — |
| 719 | C22×C4 | — | 106 | 1 | no | — |
| 720 | C22×C4 | — | 106 | 1 | no | — |
| 721 | SD16 | — | 4 | 2 | no | — |
| 722 | SD16 | — | 212 | 2 | no | — |
| 723 | D8 | — | 4 | 4 | no | — |
| 724 | D8 | — | 8 | 1 | no | — |
| 725 | D8 | — | 424 | 1 | no | — |
| 726 | D8 | — | 424 | 1 | no | — |
| 727 | D8 | — | 424 | 1 | no | — |
| 728 | D8 | — | 212 | 4 | no | — |
| 729 | D8 | — | 212 | 2 | no | — |
| 730 | D8 | — | 212 | 4 | no | — |
| 731 | D8 | — | 212 | 4 | no | — |
| 732 | D8 | — | 212 | 2 | no | — |
| 733 | M16 | — | 212 | 2 | no | — |
| 734 | C2×C8 | — | 2 | 1 | no | — |
| 735 | C2×C8 | — | 2 | 1 | no | — |
| 736 | C2×C8 | — | 2 | 1 | no | — |
| 737 | C2×C8 | — | 106 | 4 | no | — |
| 738 | C2×C8 | — | 106 | 1 | no | — |
| 739 | C2×C8 | — | 106 | 1 | no | — |
| 740 | C2×C8 | — | 106 | 1 | no | — |
| 741 | C4⋊C4 | — | 2 | 1 | no | — |
| 742 | C4⋊C4 | — | 53 | 1 | no | — |
| 743 | C4⋊C4 | — | 53 | 1 | no | — |
| 744 | C4⋊C4 | — | 106 | 1 | no | — |
| 745 | C4⋊C4 | — | 106 | 1 | no | — |
| 746 | C4⋊C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 747 | C4⋊C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 748 | C22⋊C4 | — | 2 | 2 | no | — |
| 749 | C22⋊C4 | — | 2 | 1 | no | — |
| 750 | C22⋊C4 | — | 106 | 1 | no | — |
| 751 | C22⋊C4 | — | 106 | 1 | no | — |
| 752 | C22⋊C4 | — | 106 | 1 | no | — |
| 753 | C22⋊C4 | — | 106 | 2 | no | — |
| 754 | C22⋊C4 | — | 106 | 2 | no | — |
| 755 | C22⋊C4 | — | 106 | 1 | no | — |
| 756 | C22⋊C4 | — | 106 | 2 | no | — |
| 757 | C22⋊C4 | — | 106 | 1 | no | — |
| 758 | C22⋊C4 | — | 106 | 1 | no | — |
| 759 | C42 | — | 2 | 1 | no | — |
| 760 | C42 | — | 53 | 1 | no | — |
| 761 | C42 | — | 53 | 1 | no | — |
| 762 | C42 | — | 53 | 1 | no | — |
| 763 | C42 | — | 106 | 1 | no | — |
| 764 | C42 | — | 106 | 1 | no | — |
| 765 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 766 | C23 | — | 2 | 1 | no | — |
| 767 | C23 | — | 2 | 2 | no | — |
| 768 | C23 | — | 4 | 1 | no | — |
| 769 | C23 | — | 53 | 1 | no | — |
| 770 | C23 | — | 106 | 1 | no | — |
| 771 | C23 | — | 106 | 1 | no | — |
| 772 | C23 | — | 106 | 2 | no | — |
| 773 | C23 | — | 424 | 2 | no | — |
| 774 | C23 | — | 424 | 2 | no | — |
| 775 | C23 | — | 424 | 2 | no | — |
| 776 | C23 | — | 424 | 2 | no | — |
| 777 | C23 | — | 424 | 2 | no | — |
| 778 | C23 | — | 424 | 2 | no | — |
| 779 | C23 | — | 424 | 2 | no | — |
| 780 | C23 | — | 424 | 2 | no | — |
| 781 | C23 | — | 424 | 2 | no | — |
| 782 | C23 | — | 212 | 4 | no | — |
| 783 | C23 | — | 212 | 4 | no | — |
| 784 | C23 | — | 212 | 4 | no | — |
| 785 | C23 | — | 212 | 1 | no | — |
| 786 | Q8 | — | 2 | 1 | no | — |
| 787 | Q8 | — | 212 | 2 | no | — |
| 788 | Q8 | D8×D53 | 1 | 2 | yes | complemented |
| 789 | D4 | — | 2 | 1 | no | — |
| 790 | D4 | — | 2 | 1 | no | — |
| 791 | D4 | — | 4 | 2 | no | — |
| 792 | D4 | — | 4 | 4 | no | — |
| 793 | D4 | — | 4 | 2 | no | — |
| 794 | D4 | — | 4 | 1 | no | — |
| 795 | D4 | — | 4 | 1 | no | — |
| 796 | D4 | — | 4 | 1 | no | — |
| 797 | D4 | — | 4 | 1 | no | — |
| 798 | D4 | — | 4 | 1 | no | — |
| 799 | D4 | — | 4 | 1 | no | — |
| 800 | D4 | — | 4 | 1 | no | — |
| 801 | D4 | — | 4 | 1 | no | — |
| 802 | D4 | — | 8 | 2 | no | — |
| 803 | D4 | — | 53 | 2 | no | — |
| 804 | D4 | — | 106 | 4 | no | — |
| 805 | D4 | — | 106 | 1 | no | — |
| 806 | D4 | — | 106 | 1 | no | — |
| 807 | D4 | — | 106 | 1 | no | — |
| 808 | D4 | — | 424 | 2 | no | — |
| 809 | D4 | — | 424 | 2 | no | — |
| 810 | D4 | — | 424 | 2 | no | — |
| 811 | D4 | — | 424 | 2 | no | — |
| 812 | D4 | — | 424 | 2 | no | — |
| 813 | D4 | — | 424 | 2 | no | — |
| 814 | D4 | — | 424 | 2 | no | — |
| 815 | D4 | — | 212 | 2 | no | — |
| 816 | D4 | — | 212 | 2 | no | — |
| 817 | D4 | — | 212 | 4 | no | — |
| 818 | D4 | — | 212 | 2 | no | — |
| 819 | D4 | — | 212 | 4 | no | — |
| 820 | D4 | — | 212 | 2 | no | — |
| 821 | D4 | — | 212 | 4 | no | — |
| 822 | D4 | — | 212 | 4 | no | — |
| 823 | D4 | — | 212 | 2 | no | — |
| 824 | D4 | — | 212 | 2 | no | — |
| 825 | D4 | — | 212 | 4 | no | — |
| 826 | D4 | — | 212 | 1 | no | — |
| 827 | D4 | — | 212 | 1 | no | — |
| 828 | D4 | — | 212 | 1 | no | — |
| 829 | D4 | — | 212 | 1 | no | — |
| 830 | D4 | — | 212 | 1 | no | — |
| 831 | D4 | — | 212 | 1 | no | — |
| 832 | D4 | — | 212 | 1 | no | — |
| 833 | D4 | — | 212 | 1 | no | — |
| 834 | C2×C4 | — | 2 | 1 | no | — |
| 835 | C2×C4 | — | 2 | 1 | no | — |
| 836 | C2×C4 | — | 2 | 1 | no | — |
| 837 | C2×C4 | — | 4 | 4 | no | — |
| 838 | C2×C4 | — | 4 | 1 | no | — |
| 839 | C2×C4 | — | 4 | 1 | no | — |
| 840 | C2×C4 | — | 53 | 1 | no | — |
| 841 | C2×C4 | — | 53 | 1 | no | — |
| 842 | C2×C4 | — | 53 | 2 | no | — |
| 843 | C2×C4 | — | 53 | 2 | no | — |
| 844 | C2×C4 | — | 53 | 1 | no | — |
| 845 | C2×C4 | — | 106 | 2 | no | — |
| 846 | C2×C4 | — | 106 | 4 | no | — |
| 847 | C2×C4 | — | 106 | 1 | no | — |
| 848 | C2×C4 | — | 106 | 1 | no | — |
| 849 | C2×C4 | — | 106 | 1 | no | — |
| 850 | C2×C4 | — | 106 | 1 | no | — |
| 851 | C2×C4 | — | 212 | 4 | no | — |
| 852 | C2×C4 | — | 212 | 2 | no | — |
| 853 | C2×C4 | — | 212 | 1 | no | — |
| 854 | C2×C4 | — | 212 | 1 | no | — |
| 855 | C2×C4 | — | 212 | 1 | no | — |
| 856 | C2×C4 | — | 212 | 1 | no | — |
| 857 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 858 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 859 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 860 | C8 | — | 2 | 2 | no | — |
| 861 | C8 | — | 4 | 1 | no | — |
| 862 | C8 | — | 4 | 1 | no | — |
| 863 | C8 | — | 106 | 2 | no | — |
| 864 | C8 | — | 212 | 1 | no | — |
| 865 | C8 | — | 212 | 1 | no | — |
| 866 | C22 | — | 4 | 1 | no | — |
| 867 | C22 | — | 4 | 2 | no | — |
| 868 | C22 | — | 4 | 2 | no | — |
| 869 | C22 | — | 4 | 1 | no | — |
| 870 | C22 | — | 4 | 2 | no | — |
| 871 | C22 | — | 4 | 1 | no | — |
| 872 | C22 | — | 8 | 1 | no | — |
| 873 | C22 | — | 8 | 1 | no | — |
| 874 | C22 | — | 8 | 1 | no | — |
| 875 | C22 | — | 53 | 2 | no | — |
| 876 | C22 | — | 848 | 4 | no | — |
| 877 | C22 | — | 848 | 4 | no | — |
| 878 | C22 | — | 848 | 4 | no | — |
| 879 | C22 | — | 848 | 4 | no | — |
| 880 | C22 | — | 106 | 1 | no | — |
| 881 | C22 | — | 106 | 1 | no | — |
| 882 | C22 | — | 106 | 2 | no | — |
| 883 | C22 | — | 424 | 1 | no | — |
| 884 | C22 | — | 424 | 1 | no | — |
| 885 | C22 | — | 424 | 1 | no | — |
| 886 | C22 | — | 212 | 1 | no | — |
| 887 | C22 | — | 212 | 2 | no | — |
| 888 | C22 | — | 212 | 1 | no | — |
| 889 | C22 | — | 212 | 2 | no | — |
| 890 | C22 | — | 212 | 2 | no | — |
| 891 | C22 | — | 212 | 1 | no | — |
| 892 | C22 | — | 212 | 1 | no | — |
| 893 | C22 | — | 212 | 1 | no | — |
| 894 | C22 | #120×D53 | 1 | 1 | yes | characteristic |
| 895 | C4 | — | 2 | 1 | no | — |
| 896 | C4 | — | 2 | 2 | no | — |
| 897 | C4 | — | 4 | 1 | no | — |
| 898 | C4 | — | 4 | 1 | no | — |
| 899 | C4 | — | 53 | 2 | no | — |
| 900 | C4 | — | 53 | 2 | no | — |
| 901 | C4 | — | 106 | 1 | no | — |
| 902 | C4 | — | 212 | 1 | no | — |
| 903 | C4 | — | 212 | 1 | no | — |
| 904 | C4 | C2×D8×D53 | 1 | 1 | yes | characteristic |
| 905 | C4 | AGL(1,ℤ/8)×D53 | 1 | 1 | yes | characteristic |
| 906 | C4 | #16811425 | 1 | 1 | yes | characteristic |
| 907 | C4 | #16811427 | 1 | 1 | yes | characteristic |
| 908 | C2 | — | 8 | 1 | no | — |
| 909 | C2 | — | 8 | 2 | no | — |
| 910 | C2 | — | 16 | 1 | no | — |
| 911 | C2 | — | 848 | 1 | no | — |
| 912 | C2 | — | 106 | 2 | no | — |
| 913 | C2 | — | 424 | 2 | no | — |
| 914 | C2 | — | 424 | 1 | no | — |
| 915 | C2 | — | 212 | 2 | no | — |
| 916 | C2 | #447×D53 | 1 | 1 | yes | characteristic |
| 917 | C2 | #20283980 | 1 | 1 | yes | characteristic |
| 918 | C2 | #453×D53 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20288492 | C2 | semidirect |
| 2. #20285632 | C2 | semidirect |
| 3. #493×D53 | C2 | semidirect |
| 4. #20284192 | C2 | semidirect |
| 5. #20273782 | C2 | semidirect |
| 6. #20273780 | C2 | semidirect |
| 7. #20273778 | C2 | semidirect |
| 8. #20273771 | C2 | semidirect |
| 9. #20273770 | C2 | semidirect |
| 10. #20273768 | C2 | semidirect |
| 11. #20273767 | C2 | semidirect |
| 12. #20273381 | C2 | semidirect |
| 13. #20273164 | C2 | semidirect |
| 14. #20273096 | C2 | semidirect |
| 15. C53×#1621 | C2 | semidirect |
| 19. #16811295 | C22 | semidirect |
| 22. D4×D212 | C22 | semidirect |
| 24. #16811258 | C22 | semidirect |
| 33. #127×D53 | C22 | semidirect |
| 35. #16811000 | C22 | semidirect |
| 36. #16810999 | C22 | semidirect |
| 37. #16810999 | C22 | semidirect |
| 41. #16810823 | C22 | semidirect |
| 43. #16810819 | C22 | semidirect |
| 44. #16810819 | C22 | semidirect |
| 45. #16810818 | C22 | semidirect |
| 47. #16810815 | C22 | semidirect |
| 48. #16810815 | C22 | semidirect |
| 51. #16810675 | C22 | semidirect |
| 52. #16810645 | C22 | semidirect |
| 54. C4×C8×D53 | C22 | semidirect |
| 55. #16810367 | C22 | semidirect |
| 56. #16810366 | C22 | semidirect |
| 57. #16810366 | C22 | semidirect |
| 58. Q8⋊#88322 | C22 | semidirect |
| 59. #16810352 | C22 | semidirect |
| 60. #16810352 | C22 | semidirect |
| 61. D4⋊#88322 | C22 | semidirect |
| 62. #16810350 | C22 | semidirect |
| 63. #16810350 | C22 | semidirect |
| 64. C53×#550 | C22 | semidirect |
| 65. C53×#493 | C22 | semidirect |
| 66. C53×#460 | C22 | semidirect |
| 67. C53×#459 | C22 | semidirect |
| 68. C53×#331 | C22 | semidirect |
| 69. C53×Q8⋊C8 | C22 | semidirect |
| 70. C53×D4⋊C8 | C22 | semidirect |
| 213. #11719949 | D8 | semidirect |
| 327. Q8×C53 | C2×D8 | semidirect |
| 386. D212 | C2×D8 | semidirect |
| 456. #1621 | D53 | semidirect |
| 480. #550 | C2×D53 | semidirect |
| 500. #493 | C2×D53 | semidirect |
| 504. #460 | C2×D53 | semidirect |
| 511. #459 | C2×D53 | semidirect |
| 521. #331 | C2×D53 | semidirect |
| 523. Q8⋊C8 | C2×D53 | semidirect |
| 529. D4⋊C8 | C2×D53 | semidirect |
| 530. C53 | #18620 | semidirect |
| 788. Q8 | D8×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288492 | 2 |
| #20285632 | 2 |
| #493×D53 | 2 |
| #20284192 | 2 |
| #20273782 | 2 |
| #20273780 | 2 |
| #20273778 | 2 |
| #20273771 | 2 |
| #20273770 | 2 |
| #20273768 | 2 |
| #20273767 | 2 |
| #20273381 | 2 |
| #20273164 | 2 |
| #20273096 | 2 |
| C53×#1621 | 2 |
| #18620 | 53 |