Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1132 conjugacy classes of subgroups.
The subgroup lattice has 778 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #575×D53 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20287847 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20284322 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20276668 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20276667 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #20276666 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #20276660 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #20276659 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #20276449 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #349×D53 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C53×#2190 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#41×D53 | — | 2 | 1 | no | — |
| 13 | #16811423 | C22 | 1 | 1 | yes | characteristic |
| 14 | #16811422 | — | 2 | 2 | no | — |
| 15 | #16811421 | — | 2 | 1 | no | — |
| 16 | #16811420 | — | 2 | 1 | no | — |
| 17 | #16811420 | C22 | 1 | 2 | yes | — |
| 18 | #16811419 | — | 2 | 2 | no | — |
| 19 | #137×D53 | — | 2 | 2 | no | — |
| 20 | AGL(1,ℤ/8)×D53 | — | 2 | 2 | no | — |
| 21 | C2×#13133236 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #135×D53 | — | 2 | 1 | no | — |
| 23 | #135×D53 | C22 | 1 | 2 | yes | — |
| 24 | C2×M16×D53 | C22 | 1 | 1 | yes | characteristic |
| 25 | #16811133 | — | 2 | 1 | no | — |
| 26 | #16811066 | C22 | 1 | 2 | yes | complemented |
| 27 | #16811063 | C22 | 1 | 2 | yes | complemented |
| 28 | #16811062 | — | 2 | 2 | no | — |
| 29 | #16811059 | C22 | 1 | 2 | yes | complemented |
| 30 | #16811057 | — | 2 | 2 | no | — |
| 31 | #16811054 | — | 2 | 2 | no | — |
| 32 | #16811052 | — | 2 | 2 | no | — |
| 33 | M32×D53 | C22 | 1 | 2 | yes | complemented |
| 34 | #16810882 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #16810881 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #16810873 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #16810868 | — | 2 | 1 | no | — |
| 38 | #16810867 | — | 2 | 1 | no | — |
| 39 | #16810658 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #16810616 | — | 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×#509 | C22 | 1 | 2 | yes | complemented |
| 48 | C53×#469 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | C53×#360 | C22 | 1 | 2 | yes | complemented |
| 50 | C53×#349 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | C2×#11719949 | — | 2 | 1 | no | — |
| 52 | C2×#11719945 | — | 2 | 1 | no | — |
| 53 | C2×#11719945 | — | 4 | 1 | no | — |
| 54 | C2×#11719947 | — | 2 | 1 | no | — |
| 55 | C2×#11719947 | — | 2 | 1 | no | — |
| 56 | C2×#11719947 | — | 4 | 1 | no | — |
| 57 | #41×D53 | — | 2 | 2 | no | — |
| 58 | #41×D53 | — | 2 | 2 | no | — |
| 59 | #41×D53 | — | 2 | 2 | no | — |
| 60 | #41×D53 | — | 2 | 2 | no | — |
| 61 | #41×D53 | — | 4 | 1 | no | — |
| 62 | #41×D53 | — | 4 | 1 | no | — |
| 63 | #41×D53 | — | 4 | 1 | no | — |
| 64 | #41×D53 | — | 4 | 1 | no | — |
| 65 | C2×Q8×D53 | — | 2 | 1 | no | — |
| 66 | C2×D4×D53 | — | 2 | 1 | no | — |
| 67 | C2×D4×D53 | — | 4 | 1 | no | — |
| 68 | C22×C4×D53 | — | 4 | 1 | no | — |
| 69 | C22×C4×D53 | D4 | 1 | 1 | yes | characteristic |
| 70 | #13133250 | — | 2 | 2 | no | — |
| 71 | #13133249 | — | 2 | 2 | no | — |
| 72 | #13133249 | — | 2 | 2 | no | — |
| 73 | #13133248 | — | 2 | 2 | no | — |
| 74 | #13133247 | — | 2 | 2 | no | — |
| 75 | #13133246 | — | 2 | 2 | no | — |
| 76 | #13133246 | — | 2 | 2 | no | — |
| 77 | #13133245 | — | 2 | 2 | no | — |
| 78 | #13133244 | — | 2 | 2 | no | — |
| 79 | #13133244 | — | 2 | 2 | no | — |
| 80 | #13133243 | — | 2 | 2 | no | — |
| 81 | #13133242 | — | 2 | 2 | no | — |
| 82 | #13133241 | — | 2 | 2 | no | — |
| 83 | #13133241 | — | 2 | 2 | no | — |
| 84 | #13133240 | — | 2 | 1 | no | — |
| 85 | #13133240 | D4 | 1 | 2 | yes | complemented |
| 86 | #13133239 | — | 2 | 1 | no | — |
| 87 | #13133239 | C23 | 1 | 2 | yes | — |
| 88 | #13133238 | — | 2 | 2 | no | — |
| 89 | #13133238 | — | 2 | 2 | no | — |
| 90 | #13133237 | — | 2 | 2 | no | — |
| 91 | #13133237 | — | 2 | 2 | no | — |
| 92 | #13133236 | — | 2 | 1 | no | — |
| 93 | #13133236 | — | 2 | 2 | no | — |
| 94 | #13133236 | — | 2 | 2 | no | — |
| 95 | #13133236 | D4 | 1 | 2 | yes | complemented |
| 96 | C2×Dic212 | C23 | 1 | 1 | yes | characteristic, complemented |
| 97 | Q16×D53 | — | 2 | 1 | no | — |
| 98 | Q16×D53 | D4 | 1 | 2 | yes | complemented |
| 99 | C2×#11719923 | — | 2 | 1 | no | — |
| 100 | SD16×D53 | — | 2 | 2 | no | — |
| 101 | SD16×D53 | — | 2 | 2 | no | — |
| 102 | D8×D53 | — | 2 | 1 | no | — |
| 103 | D8×D53 | D4 | 1 | 2 | yes | complemented |
| 104 | C2×#11719917 | D4 | 1 | 1 | yes | characteristic |
| 105 | C2×#11719912 | D4 | 1 | 1 | yes | characteristic |
| 106 | C2×#11719912 | C23 | 1 | 1 | yes | characteristic |
| 107 | M16×D53 | — | 2 | 2 | no | — |
| 108 | M16×D53 | — | 2 | 2 | no | — |
| 109 | C2×C8×D53 | D4 | 1 | 1 | yes | characteristic |
| 110 | C2×C8×D53 | C23 | 1 | 1 | yes | characteristic |
| 111 | #13133199 | — | 4 | 1 | no | — |
| 112 | #13133197 | — | 2 | 1 | no | — |
| 113 | #13133196 | — | 2 | 1 | no | — |
| 114 | #13133188 | — | 2 | 1 | no | — |
| 115 | #13133185 | — | 4 | 1 | no | — |
| 116 | D4×Dic53 | — | 4 | 1 | no | — |
| 117 | #13133177 | — | 4 | 1 | no | — |
| 118 | #13133175 | — | 2 | 1 | no | — |
| 119 | Dic424 | — | 2 | 2 | no | — |
| 120 | #13133163 | — | 2 | 2 | no | — |
| 121 | #13133162 | — | 2 | 2 | no | — |
| 122 | #13133161 | — | 2 | 2 | no | — |
| 123 | #13133161 | — | 2 | 2 | no | — |
| 124 | #13133158 | — | 2 | 2 | no | — |
| 125 | #13133157 | C23 | 1 | 2 | yes | complemented |
| 126 | #13133156 | — | 2 | 2 | no | — |
| 127 | C16×D53 | — | 2 | 2 | no | — |
| 128 | #13133150 | — | 2 | 1 | no | — |
| 129 | #13133149 | C23 | 1 | 1 | yes | characteristic, complemented |
| 130 | #13133142 | — | 2 | 1 | no | — |
| 131 | #13133140 | — | 2 | 1 | no | — |
| 132 | #13133138 | — | 2 | 1 | no | — |
| 133 | C2×#41×C53 | — | 2 | 1 | no | — |
| 134 | #137×C53 | — | 2 | 2 | no | — |
| 135 | AGL(1,ℤ/8)×C53 | — | 2 | 2 | no | — |
| 136 | #135×C53 | — | 2 | 1 | no | — |
| 137 | #135×C53 | C23 | 1 | 2 | yes | — |
| 138 | C2×D8×C53 | C23 | 1 | 1 | yes | characteristic, complemented |
| 139 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 140 | #121×C53 | — | 2 | 1 | no | — |
| 141 | SD32×C53 | — | 2 | 2 | no | — |
| 142 | D16×C53 | — | 2 | 2 | no | — |
| 143 | M32×C53 | C23 | 1 | 2 | yes | complemented |
| 144 | #106×C53 | C23 | 1 | 1 | yes | characteristic, complemented |
| 145 | #102×C53 | — | 2 | 1 | no | — |
| 146 | C23×D53 | — | 4 | 1 | no | — |
| 147 | C23×D53 | D8 | 1 | 1 | yes | characteristic |
| 148 | #41×C53 | — | 2 | 2 | no | — |
| 149 | #41×C53 | — | 2 | 2 | no | — |
| 150 | #41×C53 | — | 4 | 1 | no | — |
| 151 | #41×C53 | — | 4 | 1 | no | — |
| 152 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 153 | C2×D4×C53 | — | 2 | 1 | no | — |
| 154 | C2×D4×C53 | — | 2 | 1 | no | — |
| 155 | C2×D4×C53 | — | 4 | 1 | no | — |
| 156 | C2×D4×C53 | — | 4 | 1 | no | — |
| 157 | C22×C4×C53 | — | 4 | 1 | no | — |
| 158 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 160 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 161 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 162 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 163 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 164 | C22×Dic53 | — | 4 | 1 | no | — |
| 165 | C22×Dic53 | — | 4 | 1 | no | — |
| 166 | C22×Dic53 | D8 | 1 | 1 | yes | characteristic |
| 167 | #11719949 | — | 2 | 2 | no | — |
| 168 | #11719949 | — | 2 | 2 | no | — |
| 169 | #11719949 | — | 4 | 1 | no | — |
| 170 | #11719949 | — | 4 | 1 | no | — |
| 171 | Q8×D53 | — | 2 | 2 | no | — |
| 172 | Q8×D53 | — | 2 | 2 | no | — |
| 173 | Q8×D53 | — | 4 | 1 | no | — |
| 174 | Q8×D53 | — | 4 | 1 | no | — |
| 175 | #11719947 | — | 2 | 2 | no | — |
| 176 | #11719947 | — | 2 | 2 | no | — |
| 177 | #11719947 | — | 4 | 1 | no | — |
| 178 | #11719947 | — | 4 | 1 | no | — |
| 179 | #11719947 | — | 4 | 2 | no | — |
| 180 | #11719947 | — | 4 | 2 | no | — |
| 181 | #11719947 | — | 4 | 2 | no | — |
| 182 | #11719947 | — | 4 | 2 | no | — |
| 183 | #11719947 | — | 4 | 1 | no | — |
| 184 | #11719947 | — | 4 | 1 | no | — |
| 185 | #11719947 | — | 4 | 1 | no | — |
| 186 | #11719947 | — | 4 | 1 | no | — |
| 187 | D4×D53 | — | 2 | 2 | no | — |
| 188 | D4×D53 | — | 2 | 2 | no | — |
| 189 | D4×D53 | — | 4 | 1 | no | — |
| 190 | D4×D53 | — | 4 | 1 | no | — |
| 191 | D4×D53 | — | 4 | 2 | no | — |
| 192 | D4×D53 | — | 4 | 2 | no | — |
| 193 | D4×D53 | — | 4 | 2 | no | — |
| 194 | D4×D53 | — | 4 | 2 | no | — |
| 195 | #11719945 | — | 2 | 2 | no | — |
| 196 | #11719945 | — | 2 | 2 | no | — |
| 197 | #11719945 | — | 4 | 2 | no | — |
| 198 | #11719945 | — | 4 | 2 | no | — |
| 199 | #11719945 | — | 4 | 2 | no | — |
| 200 | #11719945 | — | 4 | 1 | no | — |
| 201 | #11719945 | — | 4 | 1 | no | — |
| 202 | #11719945 | — | 4 | 2 | no | — |
| 203 | C2×D212 | — | 2 | 1 | no | — |
| 204 | C2×D212 | — | 4 | 1 | no | — |
| 205 | C2×C4×D53 | — | 2 | 1 | no | — |
| 206 | C2×C4×D53 | — | 2 | 1 | no | — |
| 207 | C2×C4×D53 | — | 2 | 1 | no | — |
| 208 | C2×C4×D53 | — | 2 | 1 | no | — |
| 209 | C2×C4×D53 | — | 4 | 2 | no | — |
| 210 | C2×C4×D53 | — | 4 | 2 | no | — |
| 211 | C2×C4×D53 | — | 4 | 2 | no | — |
| 212 | C2×C4×D53 | — | 4 | 1 | no | — |
| 213 | C2×C4×D53 | — | 4 | 1 | no | — |
| 214 | C2×C4×D53 | — | 4 | 1 | no | — |
| 215 | C2×C4×D53 | — | 4 | 2 | no | — |
| 216 | C2×C4×D53 | D8 | 1 | 1 | yes | characteristic |
| 217 | C2×C4×D53 | D8 | 1 | 1 | yes | characteristic |
| 218 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 219 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 220 | C2×Dic106 | — | 2 | 1 | no | — |
| 221 | C2×Dic106 | — | 2 | 1 | no | — |
| 222 | C2×Dic106 | — | 4 | 1 | no | — |
| 223 | Q16×C53 | — | 2 | 1 | no | — |
| 224 | Q16×C53 | C2×D4 | 1 | 2 | yes | — |
| 225 | SD16×C53 | — | 2 | 2 | no | — |
| 226 | SD16×C53 | — | 2 | 2 | no | — |
| 227 | D8×C53 | — | 2 | 1 | no | — |
| 228 | D8×C53 | — | 2 | 2 | no | — |
| 229 | D8×C53 | C2×D4 | 1 | 2 | yes | — |
| 230 | M16×C53 | — | 2 | 2 | no | — |
| 231 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 232 | C2×C8×C53 | C24 | 1 | 1 | yes | characteristic |
| 233 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 234 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 235 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 236 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 237 | #11719925 | — | 2 | 2 | no | — |
| 238 | #11719925 | — | 2 | 2 | no | — |
| 239 | #11719924 | — | 2 | 2 | no | — |
| 240 | #11719924 | — | 2 | 2 | no | — |
| 241 | #11719923 | — | 2 | 2 | no | — |
| 242 | #11719923 | — | 2 | 2 | no | — |
| 243 | #11719923 | — | 4 | 2 | no | — |
| 244 | #11719922 | — | 2 | 2 | no | — |
| 245 | #11719922 | — | 2 | 2 | no | — |
| 246 | #11719921 | — | 4 | 1 | no | — |
| 247 | #11719921 | — | 4 | 1 | no | — |
| 248 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 249 | C4⋊Dic53 | — | 4 | 1 | no | — |
| 250 | #11719919 | — | 4 | 1 | no | — |
| 251 | C4×Dic53 | — | 4 | 1 | no | — |
| 252 | #11719917 | — | 2 | 2 | no | — |
| 253 | C2×#88322 | C2×D4 | 1 | 1 | yes | characteristic |
| 254 | C2×#88322 | C2×D4 | 1 | 1 | yes | characteristic |
| 255 | Dic212 | — | 2 | 1 | no | — |
| 256 | Dic212 | — | 2 | 2 | no | — |
| 257 | Dic212 | C2×D4 | 1 | 2 | yes | — |
| 258 | D424 | — | 2 | 1 | no | — |
| 259 | D424 | C2×D4 | 1 | 2 | yes | — |
| 260 | #11719913 | — | 2 | 2 | no | — |
| 261 | #11719913 | — | 2 | 2 | no | — |
| 262 | #11719912 | — | 2 | 2 | no | — |
| 263 | #11719912 | — | 2 | 2 | no | — |
| 264 | C8×D53 | — | 2 | 1 | no | — |
| 265 | C8×D53 | — | 2 | 1 | no | — |
| 266 | C8×D53 | C2×D4 | 1 | 2 | yes | — |
| 267 | C8×D53 | C2×D4 | 1 | 2 | yes | — |
| 268 | C16×C53 | — | 2 | 2 | no | — |
| 269 | #11719908 | — | 2 | 2 | no | — |
| 270 | C23×C53 | — | 4 | 1 | no | — |
| 271 | C23×C53 | — | 4 | 1 | no | — |
| 272 | C23×C53 | C2×D8 | 1 | 1 | yes | characteristic |
| 273 | C22×D53 | — | 2 | 1 | no | — |
| 274 | C22×D53 | — | 2 | 1 | no | — |
| 275 | C22×D53 | — | 4 | 2 | no | — |
| 276 | C22×D53 | — | 4 | 1 | no | — |
| 277 | C22×D53 | — | 4 | 2 | no | — |
| 278 | C22×D53 | — | 8 | 1 | no | — |
| 279 | C22×D53 | — | 8 | 4 | no | — |
| 280 | C22×D53 | C2×D8 | 1 | 1 | yes | characteristic |
| 281 | C22×D53 | C2×D8 | 1 | 1 | yes | characteristic |
| 282 | Q8×C53 | — | 2 | 2 | no | — |
| 283 | Q8×C53 | — | 4 | 1 | no | — |
| 284 | D4×C53 | — | 2 | 2 | no | — |
| 285 | D4×C53 | — | 4 | 1 | no | — |
| 286 | D4×C53 | — | 4 | 2 | no | — |
| 287 | D4×C53 | — | 4 | 2 | no | — |
| 288 | D4×C53 | — | 4 | 1 | no | — |
| 289 | D4×C53 | — | 4 | 1 | no | — |
| 290 | D4×C53 | — | 8 | 2 | no | — |
| 291 | C2×C4×C53 | — | 2 | 1 | no | — |
| 292 | C2×C4×C53 | — | 2 | 1 | no | — |
| 293 | C2×C4×C53 | — | 4 | 2 | no | — |
| 294 | C2×C4×C53 | — | 4 | 1 | no | — |
| 295 | C2×C4×C53 | — | 4 | 2 | no | — |
| 296 | C2×C4×C53 | — | 4 | 1 | no | — |
| 297 | C2×C4×C53 | C2×D8 | 1 | 1 | yes | characteristic |
| 298 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 299 | C22⋊D53 | — | 4 | 2 | no | — |
| 300 | C22⋊D53 | — | 4 | 2 | no | — |
| 301 | C22⋊D53 | — | 4 | 2 | no | — |
| 302 | C22⋊D53 | — | 4 | 2 | no | — |
| 303 | C22⋊D53 | — | 4 | 2 | no | — |
| 304 | C22⋊D53 | — | 4 | 2 | no | — |
| 305 | C22⋊D53 | — | 8 | 2 | no | — |
| 306 | C22⋊D53 | — | 8 | 1 | no | — |
| 307 | C22⋊D53 | — | 8 | 1 | no | — |
| 308 | C2×Dic53 | — | 2 | 1 | no | — |
| 309 | C2×Dic53 | — | 2 | 1 | no | — |
| 310 | C2×Dic53 | — | 4 | 2 | no | — |
| 311 | C2×Dic53 | — | 4 | 1 | no | — |
| 312 | C2×Dic53 | — | 4 | 2 | no | — |
| 313 | C2×Dic53 | — | 4 | 1 | no | — |
| 314 | C2×Dic53 | — | 4 | 1 | no | — |
| 315 | C2×Dic53 | — | 8 | 1 | no | — |
| 316 | C2×Dic53 | — | 8 | 1 | no | — |
| 317 | C2×Dic53 | C2×D8 | 1 | 1 | yes | characteristic |
| 318 | C2×Dic53 | C2×D8 | 1 | 1 | yes | characteristic |
| 319 | D212 | — | 2 | 2 | no | — |
| 320 | D212 | — | 4 | 1 | no | — |
| 321 | D212 | — | 4 | 2 | no | — |
| 322 | D212 | — | 4 | 2 | no | — |
| 323 | C4×D53 | — | 2 | 1 | no | — |
| 324 | C4×D53 | — | 2 | 1 | no | — |
| 325 | C4×D53 | — | 2 | 1 | no | — |
| 326 | C4×D53 | — | 2 | 1 | no | — |
| 327 | C4×D53 | — | 2 | 1 | no | — |
| 328 | C4×D53 | — | 2 | 1 | no | — |
| 329 | C4×D53 | — | 4 | 2 | no | — |
| 330 | C4×D53 | — | 4 | 2 | no | — |
| 331 | C4×D53 | — | 4 | 2 | no | — |
| 332 | C4×D53 | — | 4 | 2 | no | — |
| 333 | C4×D53 | — | 4 | 2 | no | — |
| 334 | C4×D53 | — | 4 | 2 | no | — |
| 335 | C4×D53 | #120 | 1 | 1 | yes | characteristic |
| 336 | C4×D53 | #120 | 1 | 1 | yes | characteristic |
| 337 | C4×D53 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 338 | C4×D53 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 339 | Dic106 | — | 2 | 2 | no | — |
| 340 | Dic106 | — | 4 | 2 | no | — |
| 341 | Dic106 | — | 4 | 1 | no | — |
| 342 | Dic106 | — | 4 | 2 | no | — |
| 343 | Dic106 | — | 4 | 1 | no | — |
| 344 | Dic106 | — | 4 | 1 | no | — |
| 345 | C8×C53 | — | 2 | 1 | no | — |
| 346 | C8×C53 | C22×D4 | 1 | 2 | yes | — |
| 347 | #88322 | — | 2 | 1 | no | — |
| 348 | #88322 | #120 | 1 | 2 | yes | — |
| 349 | #33530 | — | 53 | 1 | no | maximal, Sylow |
| 350 | C22×C53 | — | 2 | 1 | no | — |
| 351 | C22×C53 | — | 4 | 1 | no | — |
| 352 | C22×C53 | — | 4 | 2 | no | — |
| 353 | C22×C53 | — | 8 | 1 | no | — |
| 354 | C22×C53 | — | 8 | 1 | no | — |
| 355 | C22×C53 | — | 8 | 2 | no | — |
| 356 | C22×C53 | — | 8 | 1 | no | — |
| 357 | C22×C53 | C22×D8 | 1 | 1 | yes | characteristic |
| 358 | C2×D53 | — | 2 | 1 | no | — |
| 359 | C2×D53 | — | 4 | 1 | no | — |
| 360 | C2×D53 | — | 4 | 2 | no | — |
| 361 | C2×D53 | — | 4 | 1 | no | — |
| 362 | C2×D53 | — | 4 | 2 | no | — |
| 363 | C2×D53 | — | 8 | 1 | no | — |
| 364 | C2×D53 | — | 8 | 4 | no | — |
| 365 | C2×D53 | — | 8 | 4 | no | — |
| 366 | C2×D53 | — | 8 | 2 | no | — |
| 367 | C2×D53 | #447 | 1 | 1 | yes | characteristic |
| 368 | C2×D53 | #447 | 1 | 1 | yes | characteristic |
| 369 | C4×C53 | — | 2 | 1 | no | — |
| 370 | C4×C53 | — | 4 | 2 | no | — |
| 371 | C4×C53 | — | 8 | 1 | no | — |
| 372 | C4×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 373 | C4×C53 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 374 | Dic53 | — | 2 | 1 | no | — |
| 375 | Dic53 | — | 4 | 2 | no | — |
| 376 | Dic53 | — | 8 | 1 | no | — |
| 377 | Dic53 | — | 8 | 1 | no | — |
| 378 | Dic53 | #447 | 1 | 1 | yes | characteristic |
| 379 | Dic53 | #447 | 1 | 1 | yes | characteristic |
| 380 | C2×#575 | — | 53 | 1 | no | — |
| 381 | #3414 | — | 53 | 2 | no | — |
| 382 | #3054 | — | 53 | 1 | no | — |
| 383 | #2191 | — | 53 | 2 | no | — |
| 384 | #2191 | — | 53 | 1 | no | — |
| 385 | #2191 | — | 53 | 1 | no | — |
| 386 | #2190 | — | 53 | 2 | no | — |
| 387 | #2190 | — | 53 | 1 | no | — |
| 388 | #2190 | D53 | 1 | 1 | yes | characteristic, complemented |
| 389 | #2145 | — | 53 | 2 | no | — |
| 390 | C2×#349 | — | 53 | 1 | no | — |
| 391 | C2×C53 | — | 2 | 1 | no | — |
| 392 | C2×C53 | — | 4 | 1 | no | — |
| 393 | C2×C53 | — | 8 | 2 | no | — |
| 394 | C2×C53 | — | 16 | 1 | no | — |
| 395 | C2×C53 | C2×#447 | 1 | 1 | yes | characteristic |
| 396 | D53 | — | 2 | 1 | no | — |
| 397 | D53 | — | 2 | 1 | no | — |
| 398 | D53 | — | 4 | 1 | no | — |
| 399 | D53 | — | 8 | 2 | no | — |
| 400 | C22×#41 | — | 106 | 1 | no | — |
| 401 | #575 | — | 53 | 2 | no | — |
| 402 | #575 | — | 53 | 1 | no | — |
| 403 | #575 | — | 106 | 1 | no | — |
| 404 | #575 | — | 106 | 1 | no | — |
| 405 | #575 | — | 106 | 2 | no | — |
| 406 | #575 | — | 106 | 2 | no | — |
| 407 | #575 | C2×D53 | 1 | 1 | yes | characteristic |
| 408 | C2×#137 | — | 106 | 2 | no | — |
| 409 | C2×AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 410 | C2×#135 | — | 53 | 2 | no | — |
| 411 | C2×#135 | — | 53 | 1 | no | — |
| 412 | C2×#135 | — | 106 | 1 | no | — |
| 413 | C22×M16 | — | 53 | 1 | no | — |
| 414 | #525 | — | 106 | 1 | no | — |
| 415 | #510 | — | 53 | 2 | no | — |
| 416 | #510 | — | 53 | 2 | no | — |
| 417 | #510 | — | 106 | 2 | no | — |
| 418 | #509 | — | 53 | 2 | no | — |
| 419 | #509 | — | 106 | 2 | no | — |
| 420 | #509 | C2×D53 | 1 | 2 | yes | complemented |
| 421 | #508 | — | 106 | 2 | no | — |
| 422 | #508 | — | 106 | 2 | no | — |
| 423 | C2×M32 | — | 53 | 2 | no | — |
| 424 | #470 | — | 53 | 1 | no | — |
| 425 | #470 | — | 53 | 1 | no | — |
| 426 | #469 | — | 53 | 1 | no | — |
| 427 | #469 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 428 | #468 | — | 106 | 1 | no | — |
| 429 | #468 | — | 106 | 1 | no | — |
| 430 | #427 | — | 53 | 1 | no | — |
| 431 | #416 | — | 106 | 1 | no | — |
| 432 | #360 | — | 53 | 2 | no | — |
| 433 | #360 | — | 53 | 2 | no | — |
| 434 | #360 | — | 53 | 2 | no | — |
| 435 | #360 | C2×D53 | 1 | 2 | yes | complemented |
| 436 | #349 | — | 53 | 1 | no | — |
| 437 | #349 | — | 53 | 2 | no | — |
| 438 | #349 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 439 | C53 | #33530 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 440 | C2×#41 | — | 2 | 1 | no | — |
| 441 | C2×#41 | — | 106 | 1 | no | — |
| 442 | C2×#41 | — | 106 | 2 | no | — |
| 443 | C2×#41 | — | 106 | 2 | no | — |
| 444 | C2×#41 | — | 106 | 1 | no | — |
| 445 | C2×#41 | — | 106 | 1 | no | — |
| 446 | C2×#41 | — | 106 | 2 | no | — |
| 447 | C2×#41 | — | 106 | 2 | no | — |
| 448 | C2×#41 | — | 106 | 1 | no | — |
| 449 | C2×#41 | — | 212 | 1 | no | — |
| 450 | C2×#41 | — | 212 | 1 | no | — |
| 451 | C2×#41 | — | 212 | 1 | no | — |
| 452 | C2×#41 | — | 212 | 1 | no | — |
| 453 | C2×#41 | — | 212 | 1 | no | — |
| 454 | C2×#41 | — | 212 | 1 | no | — |
| 455 | C22×Q8 | — | 106 | 1 | no | — |
| 456 | C22×D4 | — | 106 | 1 | no | — |
| 457 | C22×D4 | — | 212 | 1 | no | — |
| 458 | C23×C4 | — | 53 | 1 | no | — |
| 459 | C23×C4 | — | 212 | 1 | no | — |
| 460 | #137 | — | 2 | 2 | no | — |
| 461 | #137 | — | 106 | 2 | no | — |
| 462 | #137 | — | 106 | 2 | no | — |
| 463 | #137 | — | 106 | 2 | no | — |
| 464 | #137 | — | 106 | 2 | no | — |
| 465 | #137 | — | 106 | 2 | no | — |
| 466 | #137 | — | 106 | 2 | no | — |
| 467 | #137 | — | 106 | 2 | no | — |
| 468 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 469 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 470 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 471 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 472 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 473 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 474 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 475 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 476 | #135 | — | 2 | 1 | no | — |
| 477 | #135 | — | 53 | 2 | no | — |
| 478 | #135 | — | 53 | 2 | no | — |
| 479 | #135 | — | 53 | 2 | no | — |
| 480 | #135 | — | 106 | 2 | no | — |
| 481 | #135 | — | 106 | 2 | no | — |
| 482 | #135 | — | 106 | 2 | no | — |
| 483 | #135 | — | 106 | 2 | no | — |
| 484 | #135 | — | 106 | 2 | no | — |
| 485 | #135 | — | 106 | 1 | no | — |
| 486 | #135 | — | 106 | 2 | no | — |
| 487 | #135 | — | 106 | 1 | no | — |
| 488 | #135 | — | 106 | 1 | no | — |
| 489 | #135 | C22×D53 | 1 | 2 | yes | — |
| 490 | C2×Q16 | — | 53 | 2 | no | — |
| 491 | C2×Q16 | — | 53 | 1 | no | — |
| 492 | C2×Q16 | — | 106 | 1 | no | — |
| 493 | C2×SD16 | — | 106 | 2 | no | — |
| 494 | C2×SD16 | — | 106 | 1 | no | — |
| 495 | C2×SD16 | — | 106 | 2 | no | — |
| 496 | C2×D8 | — | 53 | 2 | no | — |
| 497 | C2×D8 | — | 106 | 1 | no | — |
| 498 | C2×D8 | C22×D53 | 1 | 1 | yes | characteristic, complemented |
| 499 | C2×M16 | — | 53 | 1 | no | — |
| 500 | C2×M16 | — | 53 | 1 | no | — |
| 501 | C2×M16 | — | 53 | 1 | no | — |
| 502 | C2×M16 | — | 106 | 2 | no | — |
| 503 | C2×M16 | — | 106 | 2 | no | — |
| 504 | C2×M16 | C22×D53 | 1 | 1 | yes | characteristic |
| 505 | C22×C8 | — | 53 | 1 | no | — |
| 506 | C22×C8 | — | 53 | 1 | no | — |
| 507 | #123 | — | 212 | 1 | no | — |
| 508 | C22⋊Q8 | — | 106 | 1 | no | — |
| 509 | C22⋊Q8 | — | 106 | 1 | no | — |
| 510 | #121 | — | 2 | 1 | no | — |
| 511 | #121 | — | 106 | 1 | no | — |
| 512 | #120 | — | 212 | 1 | no | — |
| 513 | C4×D4 | — | 212 | 1 | no | — |
| 514 | C4×D4 | — | 212 | 1 | no | — |
| 515 | #117 | — | 106 | 1 | no | — |
| 516 | Q32 | — | 106 | 2 | no | — |
| 517 | Q32 | — | 106 | 2 | no | — |
| 518 | SD32 | — | 2 | 2 | no | — |
| 519 | SD32 | — | 106 | 2 | no | — |
| 520 | SD32 | — | 106 | 2 | no | — |
| 521 | SD32 | — | 106 | 2 | no | — |
| 522 | D16 | — | 2 | 2 | no | — |
| 523 | D16 | — | 106 | 2 | no | — |
| 524 | M32 | — | 53 | 2 | no | — |
| 525 | M32 | — | 106 | 2 | no | — |
| 526 | M32 | C22×D53 | 1 | 2 | yes | complemented |
| 527 | C2×C16 | — | 106 | 2 | no | — |
| 528 | #107 | — | 106 | 1 | no | — |
| 529 | #106 | — | 53 | 1 | no | — |
| 530 | #106 | C22×D53 | 1 | 1 | yes | characteristic, complemented |
| 531 | #103 | — | 106 | 1 | no | — |
| 532 | #103 | — | 106 | 1 | no | — |
| 533 | #102 | — | 2 | 1 | no | — |
| 534 | #102 | — | 106 | 1 | no | — |
| 535 | C24 | — | 53 | 1 | no | — |
| 536 | C24 | — | 212 | 1 | no | — |
| 537 | #41 | — | 2 | 2 | no | — |
| 538 | #41 | — | 2 | 2 | no | — |
| 539 | #41 | — | 4 | 1 | no | — |
| 540 | #41 | — | 4 | 1 | no | — |
| 541 | #41 | — | 106 | 2 | no | — |
| 542 | #41 | — | 106 | 2 | no | — |
| 543 | #41 | — | 106 | 2 | no | — |
| 544 | #41 | — | 106 | 2 | no | — |
| 545 | #41 | — | 106 | 2 | no | — |
| 546 | #41 | — | 106 | 2 | no | — |
| 547 | #41 | — | 212 | 1 | no | — |
| 548 | #41 | — | 212 | 2 | no | — |
| 549 | #41 | — | 212 | 2 | no | — |
| 550 | #41 | — | 212 | 2 | no | — |
| 551 | #41 | — | 212 | 2 | no | — |
| 552 | #41 | — | 212 | 1 | no | — |
| 553 | #41 | — | 212 | 1 | no | — |
| 554 | #41 | — | 212 | 1 | no | — |
| 555 | #41 | — | 212 | 1 | no | — |
| 556 | #41 | — | 212 | 2 | no | — |
| 557 | #41 | — | 212 | 2 | no | — |
| 558 | #41 | — | 212 | 1 | no | — |
| 559 | #41 | — | 212 | 1 | no | — |
| 560 | #41 | — | 212 | 2 | no | — |
| 561 | #41 | — | 212 | 2 | no | — |
| 562 | #41 | — | 212 | 1 | no | — |
| 563 | #41 | — | 212 | 1 | no | — |
| 564 | #41 | — | 212 | 1 | no | — |
| 565 | C2×Q8 | — | 2 | 1 | no | — |
| 566 | C2×Q8 | — | 106 | 1 | no | — |
| 567 | C2×Q8 | — | 106 | 2 | no | — |
| 568 | C2×Q8 | — | 106 | 2 | no | — |
| 569 | C2×Q8 | — | 106 | 1 | no | — |
| 570 | C2×Q8 | — | 212 | 1 | no | — |
| 571 | C2×Q8 | — | 212 | 1 | no | — |
| 572 | C2×Q8 | — | 212 | 1 | no | — |
| 573 | C2×D4 | — | 2 | 1 | no | — |
| 574 | C2×D4 | — | 2 | 1 | no | — |
| 575 | C2×D4 | — | 4 | 1 | no | — |
| 576 | C2×D4 | — | 4 | 1 | no | — |
| 577 | C2×D4 | — | 106 | 1 | no | — |
| 578 | C2×D4 | — | 106 | 2 | no | — |
| 579 | C2×D4 | — | 106 | 2 | no | — |
| 580 | C2×D4 | — | 212 | 1 | no | — |
| 581 | C2×D4 | — | 212 | 1 | no | — |
| 582 | C2×D4 | — | 212 | 1 | no | — |
| 583 | C2×D4 | — | 212 | 1 | no | — |
| 584 | C2×D4 | — | 212 | 2 | no | — |
| 585 | C2×D4 | — | 212 | 2 | no | — |
| 586 | C2×D4 | — | 212 | 2 | no | — |
| 587 | C2×D4 | — | 212 | 2 | no | — |
| 588 | C2×D4 | — | 212 | 1 | no | — |
| 589 | C2×D4 | — | 212 | 1 | no | — |
| 590 | C2×D4 | — | 212 | 1 | no | — |
| 591 | C2×D4 | — | 212 | 1 | no | — |
| 592 | C22×C4 | — | 4 | 1 | no | — |
| 593 | C22×C4 | — | 53 | 1 | no | — |
| 594 | C22×C4 | — | 53 | 1 | no | — |
| 595 | C22×C4 | — | 53 | 1 | no | — |
| 596 | C22×C4 | — | 53 | 1 | no | — |
| 597 | C22×C4 | — | 53 | 1 | no | — |
| 598 | C22×C4 | — | 106 | 1 | no | — |
| 599 | C22×C4 | — | 106 | 1 | no | — |
| 600 | C22×C4 | — | 106 | 1 | no | — |
| 601 | C22×C4 | — | 106 | 1 | no | — |
| 602 | C22×C4 | — | 212 | 1 | no | — |
| 603 | C22×C4 | — | 212 | 2 | no | — |
| 604 | C22×C4 | — | 212 | 2 | no | — |
| 605 | C22×C4 | — | 212 | 2 | no | — |
| 606 | C22×C4 | — | 212 | 1 | no | — |
| 607 | C22×C4 | — | 212 | 2 | no | — |
| 608 | C22×C4 | — | 212 | 1 | no | — |
| 609 | C22×C4 | — | 212 | 1 | no | — |
| 610 | C22×C4 | — | 212 | 1 | no | — |
| 611 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 612 | Q16 | — | 2 | 1 | no | — |
| 613 | Q16 | — | 53 | 2 | no | — |
| 614 | Q16 | — | 106 | 1 | no | — |
| 615 | Q16 | — | 106 | 2 | no | — |
| 616 | Q16 | — | 106 | 2 | no | — |
| 617 | Q16 | — | 106 | 2 | no | — |
| 618 | Q16 | D4×D53 | 1 | 2 | yes | — |
| 619 | SD16 | — | 2 | 2 | no | — |
| 620 | SD16 | — | 2 | 2 | no | — |
| 621 | SD16 | — | 106 | 2 | no | — |
| 622 | SD16 | — | 106 | 2 | no | — |
| 623 | SD16 | — | 106 | 2 | no | — |
| 624 | SD16 | — | 106 | 2 | no | — |
| 625 | SD16 | — | 106 | 2 | no | — |
| 626 | SD16 | — | 106 | 2 | no | — |
| 627 | SD16 | — | 212 | 2 | no | — |
| 628 | D8 | — | 2 | 1 | no | — |
| 629 | D8 | — | 2 | 2 | no | — |
| 630 | D8 | — | 53 | 2 | no | — |
| 631 | D8 | — | 106 | 1 | no | — |
| 632 | D8 | — | 106 | 2 | no | — |
| 633 | D8 | — | 106 | 2 | no | — |
| 634 | D8 | D4×D53 | 1 | 2 | yes | — |
| 635 | M16 | — | 2 | 2 | no | — |
| 636 | M16 | — | 106 | 2 | no | — |
| 637 | M16 | — | 106 | 2 | no | — |
| 638 | M16 | — | 106 | 2 | no | — |
| 639 | C2×C8 | — | 53 | 1 | no | — |
| 640 | C2×C8 | — | 53 | 2 | no | — |
| 641 | C2×C8 | — | 53 | 2 | no | — |
| 642 | C2×C8 | — | 53 | 1 | no | — |
| 643 | C2×C8 | — | 106 | 1 | no | — |
| 644 | C2×C8 | — | 106 | 1 | no | — |
| 645 | C2×C8 | D4×D53 | 1 | 1 | yes | characteristic |
| 646 | C2×C8 | C23×D53 | 1 | 1 | yes | characteristic |
| 647 | C4⋊C4 | — | 2 | 1 | no | — |
| 648 | C4⋊C4 | — | 106 | 1 | no | — |
| 649 | C4⋊C4 | — | 212 | 1 | no | — |
| 650 | C4⋊C4 | — | 212 | 1 | no | — |
| 651 | C22⋊C4 | — | 4 | 1 | no | — |
| 652 | C22⋊C4 | — | 212 | 1 | no | — |
| 653 | C22⋊C4 | — | 212 | 1 | no | — |
| 654 | C22⋊C4 | — | 212 | 1 | no | — |
| 655 | C22⋊C4 | — | 212 | 1 | no | — |
| 656 | C42 | — | 212 | 1 | no | — |
| 657 | C16 | — | 2 | 2 | no | — |
| 658 | C16 | — | 106 | 2 | no | — |
| 659 | C23 | — | 4 | 1 | no | — |
| 660 | C23 | — | 4 | 1 | no | — |
| 661 | C23 | — | 53 | 1 | no | — |
| 662 | C23 | — | 53 | 1 | no | — |
| 663 | C23 | — | 106 | 1 | no | — |
| 664 | C23 | — | 106 | 1 | no | — |
| 665 | C23 | — | 424 | 1 | no | — |
| 666 | C23 | — | 424 | 4 | no | — |
| 667 | C23 | — | 212 | 1 | no | — |
| 668 | C23 | — | 212 | 2 | no | — |
| 669 | C23 | — | 212 | 2 | no | — |
| 670 | C23 | D8×D53 | 1 | 1 | yes | characteristic |
| 671 | Q8 | — | 2 | 2 | no | — |
| 672 | Q8 | — | 4 | 1 | no | — |
| 673 | Q8 | — | 106 | 2 | no | — |
| 674 | Q8 | — | 212 | 1 | no | — |
| 675 | Q8 | — | 212 | 2 | no | — |
| 676 | Q8 | — | 212 | 2 | no | — |
| 677 | Q8 | — | 212 | 1 | no | — |
| 678 | Q8 | — | 212 | 1 | no | — |
| 679 | D4 | — | 2 | 2 | no | — |
| 680 | D4 | — | 4 | 1 | no | — |
| 681 | D4 | — | 4 | 2 | no | — |
| 682 | D4 | — | 4 | 2 | no | — |
| 683 | D4 | — | 4 | 1 | no | — |
| 684 | D4 | — | 4 | 1 | no | — |
| 685 | D4 | — | 8 | 2 | no | — |
| 686 | D4 | — | 106 | 2 | no | — |
| 687 | D4 | — | 424 | 1 | no | — |
| 688 | D4 | — | 424 | 1 | no | — |
| 689 | D4 | — | 424 | 2 | no | — |
| 690 | D4 | — | 212 | 1 | no | — |
| 691 | D4 | — | 212 | 2 | no | — |
| 692 | D4 | — | 212 | 2 | no | — |
| 693 | D4 | — | 212 | 2 | no | — |
| 694 | D4 | — | 212 | 2 | no | — |
| 695 | D4 | — | 212 | 2 | no | — |
| 696 | D4 | — | 212 | 2 | no | — |
| 697 | D4 | — | 212 | 2 | no | — |
| 698 | D4 | — | 212 | 2 | no | — |
| 699 | C2×C4 | — | 2 | 1 | no | — |
| 700 | C2×C4 | — | 2 | 1 | no | — |
| 701 | C2×C4 | — | 4 | 2 | no | — |
| 702 | C2×C4 | — | 4 | 1 | no | — |
| 703 | C2×C4 | — | 4 | 2 | no | — |
| 704 | C2×C4 | — | 4 | 1 | no | — |
| 705 | C2×C4 | — | 53 | 1 | no | — |
| 706 | C2×C4 | — | 53 | 1 | no | — |
| 707 | C2×C4 | — | 53 | 1 | no | — |
| 708 | C2×C4 | — | 53 | 1 | no | — |
| 709 | C2×C4 | — | 53 | 1 | no | — |
| 710 | C2×C4 | — | 53 | 1 | no | — |
| 711 | C2×C4 | — | 106 | 1 | no | — |
| 712 | C2×C4 | — | 106 | 1 | no | — |
| 713 | C2×C4 | — | 106 | 1 | no | — |
| 714 | C2×C4 | — | 106 | 1 | no | — |
| 715 | C2×C4 | — | 106 | 1 | no | — |
| 716 | C2×C4 | — | 106 | 1 | no | — |
| 717 | C2×C4 | — | 106 | 1 | no | — |
| 718 | C2×C4 | — | 106 | 1 | no | — |
| 719 | C2×C4 | — | 424 | 1 | no | — |
| 720 | C2×C4 | — | 424 | 1 | no | — |
| 721 | C2×C4 | — | 212 | 2 | no | — |
| 722 | C2×C4 | — | 212 | 2 | no | — |
| 723 | C2×C4 | — | 212 | 2 | no | — |
| 724 | C2×C4 | — | 212 | 2 | no | — |
| 725 | C2×C4 | — | 212 | 2 | no | — |
| 726 | C2×C4 | — | 212 | 2 | no | — |
| 727 | C2×C4 | — | 212 | 2 | no | — |
| 728 | C2×C4 | — | 212 | 1 | no | — |
| 729 | C2×C4 | — | 212 | 1 | no | — |
| 730 | C2×C4 | — | 212 | 1 | no | — |
| 731 | C2×C4 | — | 212 | 2 | no | — |
| 732 | C2×C4 | D8×D53 | 1 | 1 | yes | characteristic |
| 733 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 734 | C8 | — | 2 | 1 | no | — |
| 735 | C8 | — | 53 | 2 | no | — |
| 736 | C8 | — | 106 | 1 | no | — |
| 737 | C8 | C2×D4×D53 | 1 | 2 | yes | — |
| 738 | C22 | — | 2 | 1 | no | — |
| 739 | C22 | — | 4 | 1 | no | — |
| 740 | C22 | — | 4 | 2 | no | — |
| 741 | C22 | — | 8 | 1 | no | — |
| 742 | C22 | — | 8 | 1 | no | — |
| 743 | C22 | — | 8 | 2 | no | — |
| 744 | C22 | — | 8 | 1 | no | — |
| 745 | C22 | — | 53 | 1 | no | — |
| 746 | C22 | — | 53 | 1 | no | — |
| 747 | C22 | — | 106 | 1 | no | — |
| 748 | C22 | — | 424 | 1 | no | — |
| 749 | C22 | — | 424 | 2 | no | — |
| 750 | C22 | — | 424 | 4 | no | — |
| 751 | C22 | — | 424 | 4 | no | — |
| 752 | C22 | — | 212 | 1 | no | — |
| 753 | C22 | — | 212 | 1 | no | — |
| 754 | C22 | — | 212 | 2 | no | — |
| 755 | C22 | — | 212 | 2 | no | — |
| 756 | C22 | C2×D8×D53 | 1 | 1 | yes | characteristic |
| 757 | C4 | — | 2 | 1 | no | — |
| 758 | C4 | — | 4 | 2 | no | — |
| 759 | C4 | — | 8 | 1 | no | — |
| 760 | C4 | — | 53 | 1 | no | — |
| 761 | C4 | — | 53 | 1 | no | — |
| 762 | C4 | — | 106 | 1 | no | — |
| 763 | C4 | — | 424 | 1 | no | — |
| 764 | C4 | — | 424 | 1 | no | — |
| 765 | C4 | — | 212 | 2 | no | — |
| 766 | C4 | #120×D53 | 1 | 1 | yes | characteristic |
| 767 | C4 | AGL(1,ℤ/8)×D53 | 1 | 1 | yes | characteristic |
| 768 | C2 | — | 2 | 1 | no | — |
| 769 | C2 | — | 4 | 1 | no | — |
| 770 | C2 | — | 8 | 2 | no | — |
| 771 | C2 | — | 16 | 1 | no | — |
| 772 | C2 | — | 106 | 1 | no | — |
| 773 | C2 | — | 106 | 1 | no | — |
| 774 | C2 | — | 424 | 2 | no | — |
| 775 | C2 | — | 212 | 1 | no | — |
| 776 | C2 | #447×D53 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #575×D53 | C2 | semidirect |
| 2. #20287847 | C2 | semidirect |
| 3. #20284322 | C2 | semidirect |
| 4. #20276668 | C2 | semidirect |
| 5. #20276667 | C2 | semidirect |
| 6. #20276666 | C2 | semidirect |
| 7. #20276660 | C2 | semidirect |
| 8. #20276659 | C2 | semidirect |
| 9. #20276449 | C2 | semidirect |
| 10. #349×D53 | C2 | semidirect |
| 11. C53×#2190 | C2 | semidirect |
| 21. C2×#13133236 | C22 | semidirect |
| 26. #16811066 | C22 | semidirect |
| 27. #16811063 | C22 | semidirect |
| 29. #16811059 | C22 | semidirect |
| 33. M32×D53 | C22 | semidirect |
| 34. #16810882 | C22 | semidirect |
| 35. #16810881 | C22 | semidirect |
| 36. #16810873 | C22 | semidirect |
| 39. #16810658 | C22 | semidirect |
| 41. #16810434 | C22 | semidirect |
| 42. #16810433 | C22 | semidirect |
| 43. #16810432 | C22 | semidirect |
| 44. #16810405 | C22 | semidirect |
| 45. #16810404 | C22 | semidirect |
| 47. C53×#509 | C22 | semidirect |
| 48. C53×#469 | C22 | semidirect |
| 49. C53×#360 | C22 | semidirect |
| 50. C53×#349 | C22 | semidirect |
| 85. #13133240 | D4 | semidirect |
| 95. #13133236 | D4 | semidirect |
| 96. C2×Dic212 | C23 | semidirect |
| 98. Q16×D53 | D4 | semidirect |
| 103. D8×D53 | D4 | semidirect |
| 125. #13133157 | C23 | semidirect |
| 129. #13133149 | C23 | semidirect |
| 138. C2×D8×C53 | C23 | semidirect |
| 143. M32×C53 | C23 | semidirect |
| 144. #106×C53 | C23 | semidirect |
| 388. #2190 | D53 | semidirect |
| 420. #509 | C2×D53 | semidirect |
| 427. #469 | C2×D53 | semidirect |
| 435. #360 | C2×D53 | semidirect |
| 438. #349 | C2×D53 | semidirect |
| 439. C53 | #33530 | semidirect |
| 498. C2×D8 | C22×D53 | semidirect |
| 526. M32 | C22×D53 | semidirect |
| 530. #106 | C22×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #575×D53 | 2 |
| #20287847 | 2 |
| #20284322 | 2 |
| #20276668 | 2 |
| #20276667 | 2 |
| #20276666 | 2 |
| #20276660 | 2 |
| #20276659 | 2 |
| #20276449 | 2 |
| #349×D53 | 2 |
| C53×#2190 | 2 |
| #33530 | 53 |