Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1102 conjugacy classes of subgroups.
The subgroup lattice has 728 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20289488 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20287850 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20284379 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20276665 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20276664 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #20276663 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #20276662 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #20276661 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #360×D53 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #20276334 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C53×#2191 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #16811459 | — | 2 | 1 | no | — |
| 13 | #16811439 | — | 2 | 2 | no | — |
| 14 | #16811433 | — | 2 | 2 | no | — |
| 15 | #16811432 | — | 2 | 2 | no | — |
| 16 | #16811427 | — | 2 | 2 | no | — |
| 17 | #16811423 | C22 | 1 | 1 | yes | characteristic |
| 18 | #16811420 | — | 2 | 1 | no | — |
| 19 | #16811420 | C22 | 1 | 2 | yes | — |
| 20 | C2×#13133240 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×#13133237 | — | 2 | 1 | no | — |
| 22 | #135×D53 | — | 2 | 1 | no | — |
| 23 | #135×D53 | C22 | 1 | 2 | yes | — |
| 24 | C2×#13133225 | C22 | 1 | 1 | yes | characteristic |
| 25 | #16811203 | — | 2 | 1 | no | — |
| 26 | #16811065 | — | 2 | 2 | no | — |
| 27 | #16811064 | C22 | 1 | 2 | yes | complemented |
| 28 | #16811061 | C22 | 1 | 2 | yes | complemented |
| 29 | #16811060 | — | 2 | 2 | no | — |
| 30 | #16811058 | C22 | 1 | 2 | yes | complemented |
| 31 | #16811056 | — | 2 | 2 | no | — |
| 32 | #16811054 | — | 2 | 2 | no | — |
| 33 | M32×D53 | C22 | 1 | 2 | yes | complemented |
| 34 | #16810878 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #16810877 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #16810876 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #16810855 | — | 2 | 1 | no | — |
| 38 | #16810854 | — | 2 | 1 | no | — |
| 39 | #106×D53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #16810623 | — | 2 | 1 | no | — |
| 41 | #16810434 | C22 | 1 | 2 | yes | complemented |
| 42 | #16810433 | C22 | 1 | 2 | yes | complemented |
| 43 | #16810432 | C22 | 1 | 2 | yes | complemented |
| 44 | #16810405 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | #16810404 | C22 | 1 | 2 | yes | complemented |
| 46 | C53×#575 | C22 | 1 | 1 | yes | characteristic |
| 47 | C53×#510 | C22 | 1 | 2 | yes | complemented |
| 48 | C53×#470 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | C53×#360 | C22 | 1 | 2 | yes | complemented |
| 50 | C53×#349 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | #13133265 | — | 2 | 2 | no | — |
| 52 | #13133264 | — | 2 | 2 | no | — |
| 53 | #13133264 | — | 4 | 1 | no | — |
| 54 | #13133263 | — | 2 | 2 | no | — |
| 55 | #13133263 | — | 4 | 1 | no | — |
| 56 | #13133262 | — | 2 | 2 | no | — |
| 57 | #13133262 | — | 4 | 1 | no | — |
| 58 | #13133262 | — | 4 | 1 | no | — |
| 59 | C2×#11719949 | — | 2 | 1 | no | — |
| 60 | C2×#11719945 | — | 2 | 1 | no | — |
| 61 | C2×#11719945 | — | 4 | 2 | no | — |
| 62 | C2×#11719945 | D4 | 1 | 1 | yes | characteristic |
| 63 | #41×D53 | — | 2 | 2 | no | — |
| 64 | #41×D53 | — | 2 | 2 | no | — |
| 65 | #41×D53 | — | 4 | 2 | no | — |
| 66 | #13133250 | — | 2 | 2 | no | — |
| 67 | #13133249 | — | 2 | 2 | no | — |
| 68 | #13133249 | — | 2 | 2 | no | — |
| 69 | #13133246 | — | 2 | 2 | no | — |
| 70 | #13133246 | — | 2 | 2 | no | — |
| 71 | #13133245 | — | 2 | 2 | no | — |
| 72 | #13133244 | — | 2 | 2 | no | — |
| 73 | #13133244 | — | 2 | 2 | no | — |
| 74 | #13133241 | — | 2 | 2 | no | — |
| 75 | #13133241 | — | 2 | 2 | no | — |
| 76 | #13133240 | — | 2 | 1 | no | — |
| 77 | #13133240 | — | 2 | 2 | no | — |
| 78 | #13133240 | — | 2 | 2 | no | — |
| 79 | #13133240 | D4 | 1 | 2 | yes | complemented |
| 80 | #13133239 | — | 2 | 1 | no | — |
| 81 | #13133239 | C23 | 1 | 2 | yes | — |
| 82 | #13133238 | — | 2 | 2 | no | — |
| 83 | #13133238 | — | 2 | 2 | no | — |
| 84 | #13133237 | — | 2 | 2 | no | — |
| 85 | #13133237 | — | 2 | 2 | no | — |
| 86 | #13133237 | — | 2 | 2 | no | — |
| 87 | #13133237 | — | 2 | 2 | no | — |
| 88 | #13133236 | — | 2 | 1 | no | — |
| 89 | #13133236 | D4 | 1 | 2 | yes | complemented |
| 90 | C2×#11719925 | — | 2 | 1 | no | — |
| 91 | Q16×D53 | — | 2 | 1 | no | — |
| 92 | Q16×D53 | D4 | 1 | 2 | yes | complemented |
| 93 | C2×#11719923 | — | 2 | 1 | no | — |
| 94 | C2×#11719924 | — | 2 | 1 | no | — |
| 95 | C2×#11719924 | — | 2 | 1 | no | — |
| 96 | SD16×D53 | — | 2 | 2 | no | — |
| 97 | SD16×D53 | — | 2 | 2 | no | — |
| 98 | C2×D424 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×#11719922 | — | 2 | 1 | no | — |
| 100 | D8×D53 | — | 2 | 1 | no | — |
| 101 | D8×D53 | D4 | 1 | 2 | yes | complemented |
| 102 | #13133225 | — | 2 | 2 | no | — |
| 103 | #13133225 | — | 2 | 2 | no | — |
| 104 | C2×#11719912 | D4 | 1 | 1 | yes | characteristic |
| 105 | C2×#11719912 | C23 | 1 | 1 | yes | characteristic |
| 106 | C22×#88322 | D4 | 1 | 1 | yes | characteristic |
| 107 | C2×C8×D53 | D4 | 1 | 1 | yes | characteristic |
| 108 | C2×C8×D53 | C23 | 1 | 1 | yes | characteristic |
| 109 | #13133195 | — | 4 | 1 | no | — |
| 110 | #13133193 | — | 2 | 1 | no | — |
| 111 | #13133192 | — | 2 | 1 | no | — |
| 112 | #13133192 | — | 4 | 1 | no | — |
| 113 | #13133191 | — | 2 | 1 | no | — |
| 114 | #13133190 | — | 4 | 1 | no | — |
| 115 | #13133190 | — | 4 | 1 | no | — |
| 116 | C4⋊C4×D53 | — | 2 | 1 | no | — |
| 117 | #13133163 | — | 2 | 2 | no | — |
| 118 | #13133162 | — | 2 | 2 | no | — |
| 119 | #13133160 | — | 2 | 2 | no | — |
| 120 | #13133160 | — | 2 | 2 | no | — |
| 121 | D848 | — | 2 | 2 | no | — |
| 122 | #13133158 | — | 2 | 2 | no | — |
| 123 | #13133157 | C23 | 1 | 2 | yes | — |
| 124 | #13133156 | — | 2 | 2 | no | — |
| 125 | C16×D53 | — | 2 | 2 | no | — |
| 126 | #13133149 | C23 | 1 | 1 | yes | characteristic |
| 127 | #13133148 | — | 2 | 1 | no | — |
| 128 | #13133141 | — | 2 | 1 | no | — |
| 129 | #13133139 | — | 2 | 1 | no | — |
| 130 | #13133137 | — | 2 | 1 | no | — |
| 131 | C2×#41×C53 | — | 2 | 1 | no | — |
| 132 | #137×C53 | — | 2 | 2 | no | — |
| 133 | AGL(1,ℤ/8)×C53 | — | 2 | 2 | no | — |
| 134 | #135×C53 | — | 2 | 1 | no | — |
| 135 | #135×C53 | C23 | 1 | 2 | yes | — |
| 136 | C2×Q16×C53 | C23 | 1 | 1 | yes | characteristic |
| 137 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 138 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 139 | Q32×C53 | — | 2 | 2 | no | — |
| 140 | SD32×C53 | — | 2 | 2 | no | — |
| 141 | M32×C53 | C23 | 1 | 2 | yes | — |
| 142 | #106×C53 | C23 | 1 | 1 | yes | characteristic |
| 143 | #103×C53 | — | 2 | 1 | no | — |
| 144 | #41×C53 | — | 2 | 2 | no | — |
| 145 | #41×C53 | — | 2 | 2 | no | — |
| 146 | #41×C53 | — | 4 | 1 | no | — |
| 147 | #41×C53 | — | 4 | 1 | no | — |
| 148 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 149 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 150 | C2×D4×C53 | — | 2 | 1 | no | — |
| 151 | C2×D4×C53 | — | 4 | 1 | no | — |
| 152 | C22×C4×C53 | — | 4 | 1 | no | — |
| 153 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 154 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 155 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 156 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 157 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 158 | C2×C22⋊D53 | D8 | 1 | 1 | yes | characteristic |
| 159 | C2×C22⋊D53 | D8 | 1 | 1 | yes | characteristic |
| 160 | #11719949 | — | 2 | 2 | no | — |
| 161 | #11719949 | — | 2 | 2 | no | — |
| 162 | #11719949 | — | 4 | 2 | no | — |
| 163 | #11719949 | — | 4 | 2 | no | — |
| 164 | #11719949 | — | 4 | 2 | no | — |
| 165 | Q8×D53 | — | 2 | 2 | no | — |
| 166 | Q8×D53 | — | 2 | 2 | no | — |
| 167 | Q8×D53 | — | 4 | 2 | no | — |
| 168 | #11719947 | — | 2 | 2 | no | — |
| 169 | #11719947 | — | 2 | 2 | no | — |
| 170 | #11719947 | — | 4 | 2 | no | — |
| 171 | #11719947 | — | 4 | 2 | no | — |
| 172 | #11719947 | — | 4 | 2 | no | — |
| 173 | #11719947 | — | 4 | 2 | no | — |
| 174 | #11719947 | — | 4 | 2 | no | — |
| 175 | D4×D53 | — | 2 | 2 | no | — |
| 176 | D4×D53 | — | 2 | 2 | no | — |
| 177 | D4×D53 | — | 4 | 2 | no | — |
| 178 | D4×D53 | — | 4 | 2 | no | — |
| 179 | D4×D53 | — | 4 | 2 | no | — |
| 180 | D4×D53 | — | 4 | 2 | no | — |
| 181 | D4×D53 | — | 4 | 2 | no | — |
| 182 | #11719945 | — | 2 | 2 | no | — |
| 183 | #11719945 | — | 2 | 2 | no | — |
| 184 | #11719945 | — | 2 | 2 | no | — |
| 185 | #11719945 | — | 2 | 2 | no | — |
| 186 | #11719945 | — | 4 | 2 | no | — |
| 187 | #11719945 | — | 4 | 2 | no | — |
| 188 | #11719945 | — | 4 | 2 | no | — |
| 189 | #11719945 | — | 4 | 2 | no | — |
| 190 | #11719945 | — | 4 | 2 | no | — |
| 191 | #11719945 | — | 4 | 1 | no | — |
| 192 | #11719945 | — | 4 | 1 | no | — |
| 193 | #11719945 | — | 4 | 2 | no | — |
| 194 | C2×D212 | — | 2 | 1 | no | — |
| 195 | C2×D212 | — | 2 | 1 | no | — |
| 196 | C2×D212 | — | 4 | 2 | no | — |
| 197 | C2×D212 | — | 4 | 1 | no | — |
| 198 | C2×D212 | — | 4 | 1 | no | — |
| 199 | C2×D212 | D8 | 1 | 1 | yes | characteristic |
| 200 | C2×C4×D53 | — | 4 | 2 | no | — |
| 201 | C2×C4×D53 | — | 4 | 1 | no | — |
| 202 | C2×C4×D53 | — | 4 | 2 | no | — |
| 203 | C2×C4×D53 | — | 4 | 1 | no | — |
| 204 | C2×C4×D53 | — | 4 | 1 | no | — |
| 205 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 206 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 207 | C2×Dic106 | — | 2 | 1 | no | — |
| 208 | C2×Dic106 | — | 4 | 2 | no | — |
| 209 | C2×Dic106 | D8 | 1 | 1 | yes | characteristic |
| 210 | Q16×C53 | — | 2 | 1 | no | — |
| 211 | Q16×C53 | — | 2 | 2 | no | — |
| 212 | Q16×C53 | C2×D4 | 1 | 2 | yes | — |
| 213 | SD16×C53 | — | 2 | 2 | no | — |
| 214 | SD16×C53 | — | 2 | 2 | no | — |
| 215 | D8×C53 | — | 2 | 1 | no | — |
| 216 | D8×C53 | C2×D4 | 1 | 2 | yes | — |
| 217 | M16×C53 | — | 2 | 2 | no | — |
| 218 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 219 | C2×C8×C53 | C24 | 1 | 1 | yes | characteristic |
| 220 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 221 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 222 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 223 | #11719925 | — | 2 | 2 | no | — |
| 224 | #11719925 | — | 2 | 2 | no | — |
| 225 | #11719924 | — | 2 | 2 | no | — |
| 226 | #11719924 | — | 2 | 2 | no | — |
| 227 | #11719924 | — | 4 | 1 | no | — |
| 228 | #11719924 | — | 4 | 1 | no | — |
| 229 | #11719923 | — | 2 | 2 | no | — |
| 230 | #11719923 | — | 2 | 2 | no | — |
| 231 | #11719922 | — | 2 | 2 | no | — |
| 232 | #11719922 | — | 2 | 2 | no | — |
| 233 | #11719921 | — | 4 | 1 | no | — |
| 234 | #11719921 | — | 4 | 1 | no | — |
| 235 | #11719921 | — | 4 | 1 | no | — |
| 236 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 237 | #11719919 | — | 4 | 1 | no | — |
| 238 | #11719919 | — | 4 | 1 | no | — |
| 239 | C2×#88322 | — | 2 | 1 | no | — |
| 240 | C2×#88322 | — | 2 | 1 | no | — |
| 241 | C2×#88322 | C2×D4 | 1 | 1 | yes | characteristic |
| 242 | C2×#88322 | C2×D4 | 1 | 1 | yes | characteristic |
| 243 | Dic212 | — | 2 | 1 | no | — |
| 244 | Dic212 | C2×D4 | 1 | 2 | yes | — |
| 245 | D424 | — | 2 | 1 | no | — |
| 246 | D424 | — | 2 | 2 | no | — |
| 247 | D424 | C2×D4 | 1 | 2 | yes | — |
| 248 | #11719913 | — | 2 | 2 | no | — |
| 249 | #11719913 | — | 2 | 2 | no | — |
| 250 | #11719912 | — | 2 | 2 | no | — |
| 251 | #11719912 | — | 2 | 2 | no | — |
| 252 | C8×D53 | — | 2 | 1 | no | — |
| 253 | C8×D53 | — | 2 | 1 | no | — |
| 254 | C8×D53 | C2×D4 | 1 | 2 | yes | — |
| 255 | C8×D53 | C2×D4 | 1 | 2 | yes | — |
| 256 | C16×C53 | — | 2 | 2 | no | — |
| 257 | #11719908 | — | 2 | 2 | no | — |
| 258 | C23×C53 | — | 4 | 1 | no | — |
| 259 | C23×C53 | C2×D8 | 1 | 1 | yes | characteristic |
| 260 | C22×D53 | — | 4 | 2 | no | — |
| 261 | C22×D53 | — | 4 | 1 | no | — |
| 262 | C22×D53 | — | 4 | 2 | no | — |
| 263 | C22×D53 | — | 4 | 1 | no | — |
| 264 | C22×D53 | C2×D8 | 1 | 1 | yes | characteristic |
| 265 | C22×D53 | C2×D8 | 1 | 1 | yes | characteristic |
| 266 | Q8×C53 | — | 2 | 2 | no | — |
| 267 | Q8×C53 | — | 4 | 1 | no | — |
| 268 | Q8×C53 | — | 4 | 1 | no | — |
| 269 | Q8×C53 | — | 4 | 1 | no | — |
| 270 | D4×C53 | — | 2 | 2 | no | — |
| 271 | D4×C53 | — | 4 | 1 | no | — |
| 272 | D4×C53 | — | 4 | 2 | no | — |
| 273 | D4×C53 | — | 4 | 2 | no | — |
| 274 | C2×C4×C53 | — | 2 | 1 | no | — |
| 275 | C2×C4×C53 | — | 2 | 1 | no | — |
| 276 | C2×C4×C53 | — | 4 | 2 | no | — |
| 277 | C2×C4×C53 | — | 4 | 1 | no | — |
| 278 | C2×C4×C53 | — | 4 | 2 | no | — |
| 279 | C2×C4×C53 | — | 4 | 1 | no | — |
| 280 | C2×C4×C53 | — | 4 | 1 | no | — |
| 281 | C2×C4×C53 | C2×D8 | 1 | 1 | yes | characteristic |
| 282 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 283 | C22⋊D53 | — | 2 | 2 | no | — |
| 284 | C22⋊D53 | — | 2 | 2 | no | — |
| 285 | C22⋊D53 | — | 4 | 2 | no | — |
| 286 | C22⋊D53 | — | 4 | 2 | no | — |
| 287 | C22⋊D53 | — | 4 | 2 | no | — |
| 288 | C22⋊D53 | — | 4 | 2 | no | — |
| 289 | C22⋊D53 | — | 4 | 2 | no | — |
| 290 | C22⋊D53 | — | 4 | 2 | no | — |
| 291 | C22⋊D53 | — | 16 | 1 | no | — |
| 292 | C2×Dic53 | — | 4 | 2 | no | — |
| 293 | C2×Dic53 | — | 4 | 1 | no | — |
| 294 | C2×Dic53 | — | 4 | 2 | no | — |
| 295 | C2×Dic53 | — | 4 | 1 | no | — |
| 296 | C2×Dic53 | C2×D8 | 1 | 1 | yes | characteristic |
| 297 | C2×Dic53 | C2×D8 | 1 | 1 | yes | characteristic |
| 298 | D212 | — | 2 | 2 | no | — |
| 299 | D212 | — | 2 | 2 | no | — |
| 300 | D212 | — | 4 | 1 | no | — |
| 301 | D212 | — | 4 | 2 | no | — |
| 302 | D212 | — | 4 | 2 | no | — |
| 303 | D212 | — | 4 | 1 | no | — |
| 304 | D212 | — | 4 | 1 | no | — |
| 305 | D212 | — | 8 | 2 | no | — |
| 306 | D212 | — | 16 | 1 | no | — |
| 307 | C4×D53 | — | 2 | 1 | no | — |
| 308 | C4×D53 | — | 2 | 1 | no | — |
| 309 | C4×D53 | — | 4 | 2 | no | — |
| 310 | C4×D53 | — | 4 | 2 | no | — |
| 311 | C4×D53 | — | 4 | 2 | no | — |
| 312 | C4×D53 | — | 4 | 2 | no | — |
| 313 | C4×D53 | — | 4 | 2 | no | — |
| 314 | C4×D53 | — | 4 | 2 | no | — |
| 315 | C4×D53 | — | 8 | 2 | no | — |
| 316 | C4×D53 | — | 16 | 1 | no | — |
| 317 | C4×D53 | #120 | 1 | 2 | yes | — |
| 318 | C4×D53 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 319 | Dic106 | — | 2 | 2 | no | — |
| 320 | Dic106 | — | 2 | 2 | no | — |
| 321 | Dic106 | — | 4 | 2 | no | — |
| 322 | Dic106 | — | 4 | 1 | no | — |
| 323 | Dic106 | — | 4 | 2 | no | — |
| 324 | C8×C53 | — | 2 | 1 | no | — |
| 325 | C8×C53 | C22×D4 | 1 | 2 | yes | — |
| 326 | #88322 | — | 2 | 1 | no | — |
| 327 | #88322 | #120 | 1 | 1 | yes | characteristic |
| 328 | #88322 | #120 | 1 | 1 | yes | characteristic |
| 329 | #33533 | — | 53 | 1 | no | maximal, Sylow |
| 330 | C22×C53 | — | 2 | 1 | no | — |
| 331 | C22×C53 | — | 4 | 1 | no | — |
| 332 | C22×C53 | — | 4 | 2 | no | — |
| 333 | C22×C53 | — | 16 | 1 | no | — |
| 334 | C22×C53 | C22×D8 | 1 | 1 | yes | characteristic |
| 335 | C2×D53 | — | 2 | 1 | no | — |
| 336 | C2×D53 | — | 4 | 1 | no | — |
| 337 | C2×D53 | — | 4 | 1 | no | — |
| 338 | C2×D53 | — | 4 | 2 | no | — |
| 339 | C2×D53 | — | 8 | 1 | no | — |
| 340 | C2×D53 | — | 8 | 1 | no | — |
| 341 | C2×D53 | — | 8 | 1 | no | — |
| 342 | C2×D53 | — | 16 | 2 | no | — |
| 343 | C2×D53 | — | 16 | 2 | no | — |
| 344 | C2×D53 | — | 16 | 1 | no | — |
| 345 | C2×D53 | #447 | 1 | 2 | yes | — |
| 346 | C4×C53 | — | 2 | 1 | no | — |
| 347 | C4×C53 | — | 4 | 2 | no | — |
| 348 | C4×C53 | — | 8 | 1 | no | — |
| 349 | C4×C53 | — | 8 | 1 | no | — |
| 350 | C4×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 351 | C4×C53 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 352 | Dic53 | — | 2 | 1 | no | — |
| 353 | Dic53 | — | 4 | 2 | no | — |
| 354 | Dic53 | — | 8 | 1 | no | — |
| 355 | Dic53 | #447 | 1 | 2 | yes | — |
| 356 | #3584 | — | 53 | 1 | no | — |
| 357 | #3414 | — | 53 | 2 | no | — |
| 358 | #3060 | — | 53 | 1 | no | — |
| 359 | #2191 | — | 53 | 2 | no | — |
| 360 | #2191 | — | 53 | 1 | no | — |
| 361 | #2191 | D53 | 1 | 1 | yes | characteristic, complemented |
| 362 | #2190 | — | 53 | 2 | no | — |
| 363 | #2190 | — | 53 | 1 | no | — |
| 364 | #2190 | — | 53 | 1 | no | — |
| 365 | C2×#360 | — | 53 | 2 | no | — |
| 366 | #2115 | — | 53 | 1 | no | — |
| 367 | C2×C53 | — | 2 | 1 | no | — |
| 368 | C2×C53 | — | 4 | 1 | no | — |
| 369 | C2×C53 | — | 8 | 2 | no | — |
| 370 | C2×C53 | C2×#447 | 1 | 1 | yes | characteristic |
| 371 | D53 | — | 2 | 2 | no | — |
| 372 | D53 | — | 4 | 1 | no | — |
| 373 | D53 | — | 8 | 2 | no | — |
| 374 | D53 | — | 16 | 1 | no | — |
| 375 | #585 | — | 106 | 1 | no | — |
| 376 | #578 | — | 106 | 2 | no | — |
| 377 | #577 | — | 106 | 2 | no | — |
| 378 | #577 | — | 106 | 2 | no | — |
| 379 | #576 | — | 106 | 2 | no | — |
| 380 | #575 | — | 53 | 2 | no | — |
| 381 | #575 | — | 53 | 1 | no | — |
| 382 | #575 | — | 106 | 1 | no | — |
| 383 | #575 | C2×D53 | 1 | 1 | yes | characteristic |
| 384 | C2×#135 | — | 53 | 2 | no | — |
| 385 | C2×#135 | — | 53 | 1 | no | — |
| 386 | C2×#135 | — | 106 | 1 | no | — |
| 387 | C2×#135 | — | 106 | 1 | no | — |
| 388 | C2×#131 | — | 53 | 1 | no | — |
| 389 | #537 | — | 106 | 1 | no | — |
| 390 | #510 | — | 53 | 2 | no | — |
| 391 | #510 | — | 106 | 2 | no | — |
| 392 | #510 | C2×D53 | 1 | 2 | yes | complemented |
| 393 | #509 | — | 53 | 2 | no | — |
| 394 | #509 | — | 53 | 2 | no | — |
| 395 | #509 | — | 106 | 2 | no | — |
| 396 | #508 | — | 106 | 2 | no | — |
| 397 | #508 | — | 106 | 2 | no | — |
| 398 | C2×M32 | — | 53 | 2 | no | — |
| 399 | #470 | — | 53 | 1 | no | — |
| 400 | #470 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 401 | #469 | — | 53 | 1 | no | — |
| 402 | #469 | — | 53 | 1 | no | — |
| 403 | #465 | — | 106 | 1 | no | — |
| 404 | #465 | — | 106 | 1 | no | — |
| 405 | C2×#106 | — | 53 | 1 | no | — |
| 406 | #417 | — | 106 | 1 | no | — |
| 407 | #360 | — | 53 | 2 | no | — |
| 408 | #360 | — | 53 | 2 | no | — |
| 409 | #360 | — | 53 | 2 | no | — |
| 410 | #360 | C2×D53 | 1 | 2 | yes | complemented |
| 411 | #349 | — | 53 | 1 | no | — |
| 412 | #349 | — | 53 | 2 | no | — |
| 413 | #349 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 414 | C53 | #33533 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 415 | 2−1+4 | — | 106 | 2 | no | — |
| 416 | 2−1+4 | — | 106 | 2 | no | — |
| 417 | 2−1+4 | — | 212 | 1 | no | — |
| 418 | H(5,𝔽2) | — | 106 | 2 | no | — |
| 419 | H(5,𝔽2) | — | 106 | 2 | no | — |
| 420 | H(5,𝔽2) | — | 212 | 1 | no | — |
| 421 | H(5,𝔽2) | — | 212 | 1 | no | — |
| 422 | H(5,𝔽2) | — | 212 | 1 | no | — |
| 423 | C2×#41 | — | 2 | 1 | no | — |
| 424 | C2×#41 | — | 53 | 1 | no | — |
| 425 | C2×#41 | — | 106 | 1 | no | — |
| 426 | C2×#41 | — | 106 | 2 | no | — |
| 427 | C2×#41 | — | 106 | 2 | no | — |
| 428 | C2×#41 | — | 106 | 1 | no | — |
| 429 | C2×#41 | — | 212 | 2 | no | — |
| 430 | C2×#41 | — | 212 | 2 | no | — |
| 431 | #137 | — | 2 | 2 | no | — |
| 432 | #137 | — | 106 | 2 | no | — |
| 433 | #137 | — | 106 | 2 | no | — |
| 434 | #137 | — | 106 | 2 | no | — |
| 435 | #137 | — | 106 | 2 | no | — |
| 436 | #137 | — | 106 | 2 | no | — |
| 437 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 438 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 439 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 440 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 441 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 442 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 443 | #135 | — | 2 | 1 | no | — |
| 444 | #135 | — | 53 | 2 | no | — |
| 445 | #135 | — | 53 | 2 | no | — |
| 446 | #135 | — | 53 | 2 | no | — |
| 447 | #135 | — | 106 | 2 | no | — |
| 448 | #135 | — | 106 | 2 | no | — |
| 449 | #135 | — | 106 | 2 | no | — |
| 450 | #135 | — | 106 | 2 | no | — |
| 451 | #135 | — | 106 | 2 | no | — |
| 452 | #135 | — | 106 | 1 | no | — |
| 453 | #135 | — | 106 | 2 | no | — |
| 454 | #135 | — | 106 | 1 | no | — |
| 455 | #135 | — | 106 | 2 | no | — |
| 456 | #135 | — | 106 | 2 | no | — |
| 457 | #135 | — | 106 | 1 | no | — |
| 458 | #135 | C22×D53 | 1 | 2 | yes | — |
| 459 | C2×Q16 | — | 53 | 2 | no | — |
| 460 | C2×Q16 | — | 106 | 1 | no | — |
| 461 | C2×Q16 | — | 106 | 1 | no | — |
| 462 | C2×Q16 | C22×D53 | 1 | 1 | yes | characteristic |
| 463 | C2×SD16 | — | 106 | 2 | no | — |
| 464 | C2×SD16 | — | 106 | 1 | no | — |
| 465 | C2×SD16 | — | 106 | 2 | no | — |
| 466 | C2×SD16 | — | 106 | 1 | no | — |
| 467 | C2×SD16 | — | 106 | 1 | no | — |
| 468 | C2×D8 | — | 53 | 2 | no | — |
| 469 | C2×D8 | — | 53 | 1 | no | — |
| 470 | C2×D8 | — | 106 | 1 | no | — |
| 471 | C2×D8 | — | 106 | 1 | no | — |
| 472 | #131 | — | 106 | 2 | no | — |
| 473 | #131 | — | 106 | 2 | no | — |
| 474 | C2×M16 | — | 53 | 1 | no | — |
| 475 | C2×M16 | — | 53 | 1 | no | — |
| 476 | C2×M16 | C22×D53 | 1 | 1 | yes | characteristic |
| 477 | C22×C8 | — | 53 | 1 | no | — |
| 478 | C22×C8 | — | 53 | 1 | no | — |
| 479 | C22×C8 | — | 53 | 1 | no | — |
| 480 | C22⋊Q8 | — | 2 | 1 | no | — |
| 481 | C22⋊Q8 | — | 106 | 1 | no | — |
| 482 | C22⋊Q8 | — | 212 | 1 | no | — |
| 483 | #121 | — | 106 | 1 | no | — |
| 484 | #121 | — | 106 | 1 | no | — |
| 485 | #121 | — | 212 | 1 | no | — |
| 486 | #121 | — | 212 | 1 | no | — |
| 487 | #121 | — | 212 | 1 | no | — |
| 488 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 489 | Q32 | — | 2 | 2 | no | — |
| 490 | Q32 | — | 106 | 2 | no | — |
| 491 | SD32 | — | 2 | 2 | no | — |
| 492 | SD32 | — | 106 | 2 | no | — |
| 493 | SD32 | — | 106 | 2 | no | — |
| 494 | SD32 | — | 106 | 2 | no | — |
| 495 | D16 | — | 106 | 2 | no | — |
| 496 | D16 | — | 106 | 2 | no | — |
| 497 | M32 | — | 53 | 2 | no | — |
| 498 | M32 | — | 106 | 2 | no | — |
| 499 | M32 | C22×D53 | 1 | 2 | yes | — |
| 500 | C2×C16 | — | 106 | 2 | no | — |
| 501 | #106 | — | 53 | 1 | no | — |
| 502 | #106 | — | 106 | 1 | no | — |
| 503 | #106 | C22×D53 | 1 | 1 | yes | characteristic |
| 504 | #103 | — | 2 | 1 | no | — |
| 505 | #103 | — | 106 | 1 | no | — |
| 506 | #102 | — | 106 | 1 | no | — |
| 507 | #102 | — | 106 | 1 | no | — |
| 508 | #41 | — | 2 | 2 | no | — |
| 509 | #41 | — | 2 | 2 | no | — |
| 510 | #41 | — | 4 | 1 | no | — |
| 511 | #41 | — | 4 | 1 | no | — |
| 512 | #41 | — | 106 | 2 | no | — |
| 513 | #41 | — | 106 | 2 | no | — |
| 514 | #41 | — | 106 | 2 | no | — |
| 515 | #41 | — | 106 | 2 | no | — |
| 516 | #41 | — | 106 | 2 | no | — |
| 517 | #41 | — | 106 | 2 | no | — |
| 518 | #41 | — | 106 | 2 | no | — |
| 519 | #41 | — | 106 | 2 | no | — |
| 520 | #41 | — | 212 | 1 | no | — |
| 521 | #41 | — | 212 | 2 | no | — |
| 522 | #41 | — | 212 | 2 | no | — |
| 523 | #41 | — | 212 | 2 | no | — |
| 524 | #41 | — | 212 | 2 | no | — |
| 525 | #41 | — | 212 | 2 | no | — |
| 526 | #41 | — | 212 | 2 | no | — |
| 527 | #41 | — | 212 | 2 | no | — |
| 528 | #41 | — | 212 | 2 | no | — |
| 529 | #41 | — | 212 | 2 | no | — |
| 530 | #41 | — | 212 | 2 | no | — |
| 531 | #41 | — | 212 | 2 | no | — |
| 532 | #41 | — | 212 | 2 | no | — |
| 533 | #41 | — | 212 | 2 | no | — |
| 534 | #41 | — | 212 | 2 | no | — |
| 535 | #41 | — | 212 | 1 | no | — |
| 536 | C2×Q8 | — | 2 | 1 | no | — |
| 537 | C2×Q8 | — | 2 | 1 | no | — |
| 538 | C2×Q8 | — | 53 | 1 | no | — |
| 539 | C2×Q8 | — | 106 | 1 | no | — |
| 540 | C2×Q8 | — | 106 | 2 | no | — |
| 541 | C2×Q8 | — | 106 | 2 | no | — |
| 542 | C2×Q8 | — | 212 | 2 | no | — |
| 543 | C2×Q8 | — | 212 | 2 | no | — |
| 544 | C2×D4 | — | 2 | 1 | no | — |
| 545 | C2×D4 | — | 4 | 1 | no | — |
| 546 | C2×D4 | — | 53 | 1 | no | — |
| 547 | C2×D4 | — | 53 | 1 | no | — |
| 548 | C2×D4 | — | 53 | 1 | no | — |
| 549 | C2×D4 | — | 106 | 1 | no | — |
| 550 | C2×D4 | — | 106 | 2 | no | — |
| 551 | C2×D4 | — | 106 | 2 | no | — |
| 552 | C2×D4 | — | 106 | 1 | no | — |
| 553 | C2×D4 | — | 212 | 1 | no | — |
| 554 | C2×D4 | — | 212 | 2 | no | — |
| 555 | C2×D4 | — | 212 | 1 | no | — |
| 556 | C2×D4 | — | 212 | 2 | no | — |
| 557 | C2×D4 | — | 212 | 2 | no | — |
| 558 | C2×D4 | — | 212 | 2 | no | — |
| 559 | C2×D4 | — | 212 | 2 | no | — |
| 560 | C2×D4 | — | 212 | 2 | no | — |
| 561 | C2×D4 | — | 212 | 1 | no | — |
| 562 | C2×D4 | — | 212 | 2 | no | — |
| 563 | C2×D4 | — | 212 | 2 | no | — |
| 564 | C2×D4 | — | 212 | 1 | no | — |
| 565 | C22×C4 | — | 4 | 1 | no | — |
| 566 | C22×C4 | — | 53 | 1 | no | — |
| 567 | C22×C4 | — | 53 | 1 | no | — |
| 568 | C22×C4 | — | 212 | 1 | no | — |
| 569 | C22×C4 | — | 212 | 1 | no | — |
| 570 | C22×C4 | — | 212 | 2 | no | — |
| 571 | C22×C4 | — | 212 | 1 | no | — |
| 572 | C22×C4 | — | 212 | 2 | no | — |
| 573 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 574 | Q16 | — | 2 | 1 | no | — |
| 575 | Q16 | — | 2 | 2 | no | — |
| 576 | Q16 | — | 53 | 2 | no | — |
| 577 | Q16 | — | 106 | 1 | no | — |
| 578 | Q16 | — | 106 | 2 | no | — |
| 579 | Q16 | — | 106 | 2 | no | — |
| 580 | Q16 | D4×D53 | 1 | 2 | yes | — |
| 581 | SD16 | — | 2 | 2 | no | — |
| 582 | SD16 | — | 2 | 2 | no | — |
| 583 | SD16 | — | 106 | 2 | no | — |
| 584 | SD16 | — | 106 | 2 | no | — |
| 585 | SD16 | — | 106 | 2 | no | — |
| 586 | SD16 | — | 106 | 2 | no | — |
| 587 | SD16 | — | 106 | 2 | no | — |
| 588 | SD16 | — | 106 | 2 | no | — |
| 589 | SD16 | — | 212 | 1 | no | — |
| 590 | SD16 | — | 212 | 1 | no | — |
| 591 | D8 | — | 2 | 1 | no | — |
| 592 | D8 | — | 53 | 2 | no | — |
| 593 | D8 | — | 106 | 1 | no | — |
| 594 | D8 | — | 106 | 2 | no | — |
| 595 | D8 | — | 106 | 2 | no | — |
| 596 | D8 | — | 106 | 2 | no | — |
| 597 | D8 | D4×D53 | 1 | 2 | yes | — |
| 598 | M16 | — | 2 | 2 | no | — |
| 599 | M16 | — | 106 | 2 | no | — |
| 600 | M16 | — | 106 | 2 | no | — |
| 601 | C2×C8 | — | 53 | 1 | no | — |
| 602 | C2×C8 | — | 53 | 2 | no | — |
| 603 | C2×C8 | — | 53 | 2 | no | — |
| 604 | C2×C8 | — | 53 | 1 | no | — |
| 605 | C2×C8 | — | 106 | 1 | no | — |
| 606 | C2×C8 | — | 106 | 1 | no | — |
| 607 | C2×C8 | — | 106 | 1 | no | — |
| 608 | C2×C8 | — | 106 | 1 | no | — |
| 609 | C2×C8 | D4×D53 | 1 | 1 | yes | characteristic |
| 610 | C2×C8 | C23×D53 | 1 | 1 | yes | characteristic |
| 611 | C4⋊C4 | — | 2 | 1 | no | — |
| 612 | C4⋊C4 | — | 4 | 1 | no | — |
| 613 | C4⋊C4 | — | 106 | 1 | no | — |
| 614 | C4⋊C4 | — | 212 | 1 | no | — |
| 615 | C4⋊C4 | — | 212 | 1 | no | — |
| 616 | C22⋊C4 | — | 4 | 1 | no | — |
| 617 | C22⋊C4 | — | 212 | 1 | no | — |
| 618 | C22⋊C4 | — | 212 | 1 | no | — |
| 619 | C22⋊C4 | — | 212 | 1 | no | — |
| 620 | C16 | — | 2 | 2 | no | — |
| 621 | C16 | — | 106 | 2 | no | — |
| 622 | C23 | — | 4 | 1 | no | — |
| 623 | C23 | — | 53 | 1 | no | — |
| 624 | C23 | — | 53 | 1 | no | — |
| 625 | C23 | — | 212 | 1 | no | — |
| 626 | C23 | — | 212 | 2 | no | — |
| 627 | C23 | — | 212 | 2 | no | — |
| 628 | C23 | — | 212 | 1 | no | — |
| 629 | C23 | D8×D53 | 1 | 1 | yes | characteristic |
| 630 | Q8 | — | 2 | 2 | no | — |
| 631 | Q8 | — | 4 | 1 | no | — |
| 632 | Q8 | — | 4 | 1 | no | — |
| 633 | Q8 | — | 4 | 1 | no | — |
| 634 | Q8 | — | 106 | 2 | no | — |
| 635 | Q8 | — | 106 | 2 | no | — |
| 636 | Q8 | — | 212 | 1 | no | — |
| 637 | Q8 | — | 212 | 2 | no | — |
| 638 | Q8 | — | 212 | 2 | no | — |
| 639 | D4 | — | 2 | 2 | no | — |
| 640 | D4 | — | 4 | 1 | no | — |
| 641 | D4 | — | 4 | 2 | no | — |
| 642 | D4 | — | 4 | 2 | no | — |
| 643 | D4 | — | 848 | 1 | no | — |
| 644 | D4 | — | 848 | 1 | no | — |
| 645 | D4 | — | 106 | 2 | no | — |
| 646 | D4 | — | 106 | 2 | no | — |
| 647 | D4 | — | 106 | 2 | no | — |
| 648 | D4 | — | 106 | 2 | no | — |
| 649 | D4 | — | 424 | 2 | no | — |
| 650 | D4 | — | 212 | 1 | no | — |
| 651 | D4 | — | 212 | 2 | no | — |
| 652 | D4 | — | 212 | 2 | no | — |
| 653 | D4 | — | 212 | 2 | no | — |
| 654 | D4 | — | 212 | 2 | no | — |
| 655 | D4 | — | 212 | 2 | no | — |
| 656 | D4 | — | 212 | 2 | no | — |
| 657 | D4 | — | 212 | 2 | no | — |
| 658 | D4 | — | 212 | 2 | no | — |
| 659 | D4 | — | 212 | 1 | no | — |
| 660 | D4 | — | 212 | 1 | no | — |
| 661 | C2×C4 | — | 2 | 1 | no | — |
| 662 | C2×C4 | — | 2 | 1 | no | — |
| 663 | C2×C4 | — | 4 | 2 | no | — |
| 664 | C2×C4 | — | 4 | 1 | no | — |
| 665 | C2×C4 | — | 4 | 2 | no | — |
| 666 | C2×C4 | — | 4 | 1 | no | — |
| 667 | C2×C4 | — | 4 | 1 | no | — |
| 668 | C2×C4 | — | 53 | 1 | no | — |
| 669 | C2×C4 | — | 53 | 2 | no | — |
| 670 | C2×C4 | — | 53 | 2 | no | — |
| 671 | C2×C4 | — | 53 | 1 | no | — |
| 672 | C2×C4 | — | 848 | 1 | no | — |
| 673 | C2×C4 | — | 106 | 1 | no | — |
| 674 | C2×C4 | — | 106 | 1 | no | — |
| 675 | C2×C4 | — | 424 | 2 | no | — |
| 676 | C2×C4 | — | 212 | 2 | no | — |
| 677 | C2×C4 | — | 212 | 2 | no | — |
| 678 | C2×C4 | — | 212 | 2 | no | — |
| 679 | C2×C4 | — | 212 | 2 | no | — |
| 680 | C2×C4 | — | 212 | 2 | no | — |
| 681 | C2×C4 | — | 212 | 2 | no | — |
| 682 | C2×C4 | — | 212 | 2 | no | — |
| 683 | C2×C4 | — | 212 | 1 | no | — |
| 684 | C2×C4 | — | 212 | 1 | no | — |
| 685 | C2×C4 | — | 212 | 2 | no | — |
| 686 | C2×C4 | D8×D53 | 1 | 1 | yes | characteristic |
| 687 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 688 | C8 | — | 2 | 1 | no | — |
| 689 | C8 | — | 53 | 1 | no | — |
| 690 | C8 | — | 53 | 1 | no | — |
| 691 | C8 | — | 106 | 1 | no | — |
| 692 | C8 | C2×D4×D53 | 1 | 2 | yes | — |
| 693 | C22 | — | 2 | 1 | no | — |
| 694 | C22 | — | 4 | 1 | no | — |
| 695 | C22 | — | 4 | 2 | no | — |
| 696 | C22 | — | 16 | 1 | no | — |
| 697 | C22 | — | 53 | 2 | no | — |
| 698 | C22 | — | 848 | 1 | no | — |
| 699 | C22 | — | 848 | 2 | no | — |
| 700 | C22 | — | 848 | 2 | no | — |
| 701 | C22 | — | 106 | 1 | no | — |
| 702 | C22 | — | 424 | 1 | no | — |
| 703 | C22 | — | 424 | 1 | no | — |
| 704 | C22 | — | 424 | 1 | no | — |
| 705 | C22 | — | 212 | 1 | no | — |
| 706 | C22 | — | 212 | 1 | no | — |
| 707 | C22 | — | 212 | 2 | no | — |
| 708 | C22 | C2×D8×D53 | 1 | 1 | yes | characteristic |
| 709 | C4 | — | 2 | 1 | no | — |
| 710 | C4 | — | 4 | 2 | no | — |
| 711 | C4 | — | 8 | 1 | no | — |
| 712 | C4 | — | 8 | 1 | no | — |
| 713 | C4 | — | 53 | 2 | no | — |
| 714 | C4 | — | 106 | 1 | no | — |
| 715 | C4 | — | 424 | 1 | no | — |
| 716 | C4 | — | 212 | 2 | no | — |
| 717 | C4 | #120×D53 | 1 | 1 | yes | characteristic |
| 718 | C4 | AGL(1,ℤ/8)×D53 | 1 | 1 | yes | characteristic |
| 719 | C2 | — | 2 | 1 | no | — |
| 720 | C2 | — | 4 | 1 | no | — |
| 721 | C2 | — | 8 | 2 | no | — |
| 722 | C2 | — | 848 | 1 | no | — |
| 723 | C2 | — | 106 | 2 | no | — |
| 724 | C2 | — | 424 | 2 | no | — |
| 725 | C2 | — | 212 | 1 | no | — |
| 726 | C2 | #447×D53 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20289488 | C2 | semidirect |
| 2. #20287850 | C2 | semidirect |
| 3. #20284379 | C2 | semidirect |
| 4. #20276665 | C2 | semidirect |
| 5. #20276664 | C2 | semidirect |
| 6. #20276663 | C2 | semidirect |
| 7. #20276662 | C2 | semidirect |
| 8. #20276661 | C2 | semidirect |
| 9. #360×D53 | C2 | semidirect |
| 10. #20276334 | C2 | semidirect |
| 11. C53×#2191 | C2 | semidirect |
| 20. C2×#13133240 | C22 | semidirect |
| 27. #16811064 | C22 | semidirect |
| 28. #16811061 | C22 | semidirect |
| 30. #16811058 | C22 | semidirect |
| 33. M32×D53 | C22 | semidirect |
| 34. #16810878 | C22 | semidirect |
| 35. #16810877 | C22 | semidirect |
| 36. #16810876 | C22 | semidirect |
| 39. #106×D53 | C22 | semidirect |
| 41. #16810434 | C22 | semidirect |
| 42. #16810433 | C22 | semidirect |
| 43. #16810432 | C22 | semidirect |
| 44. #16810405 | C22 | semidirect |
| 45. #16810404 | C22 | semidirect |
| 47. C53×#510 | C22 | semidirect |
| 48. C53×#470 | C22 | semidirect |
| 49. C53×#360 | C22 | semidirect |
| 50. C53×#349 | C22 | semidirect |
| 79. #13133240 | D4 | semidirect |
| 89. #13133236 | D4 | semidirect |
| 92. Q16×D53 | D4 | semidirect |
| 101. D8×D53 | D4 | semidirect |
| 361. #2191 | D53 | semidirect |
| 392. #510 | C2×D53 | semidirect |
| 400. #470 | C2×D53 | semidirect |
| 410. #360 | C2×D53 | semidirect |
| 413. #349 | C2×D53 | semidirect |
| 414. C53 | #33533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289488 | 2 |
| #20287850 | 2 |
| #20284379 | 2 |
| #20276665 | 2 |
| #20276664 | 2 |
| #20276663 | 2 |
| #20276662 | 2 |
| #20276661 | 2 |
| #360×D53 | 2 |
| #20276334 | 2 |
| C53×#2191 | 2 |
| #33533 | 53 |