| 1 | C53×#3384 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C53×#3335 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C53×#3298 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C53×#3283 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C53×#1716 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C53×#1690 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C53×#1679 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C53×#1671 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C53×#1671 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C53×#1654 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C53×#1651 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C53×#1643 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C53×#1635 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C53×#1582 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C53×#1580 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#135×C53 | — | 2 | 1 | no | — |
| 17 | C53×#554 | C22 | 1 | 1 | yes | characteristic |
| 18 | D4×Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 19 | C53×#547 | C22 | 1 | 1 | yes | characteristic |
| 20 | C53×#547 | C22 | 1 | 1 | yes | characteristic |
| 21 | C53×#501 | — | 2 | 1 | no | — |
| 22 | C53×#498 | C22 | 1 | 1 | yes | characteristic |
| 23 | C53×#498 | C22 | 1 | 1 | yes | characteristic |
| 24 | C53×#498 | C22 | 1 | 1 | yes | characteristic |
| 25 | C53×#494 | C22 | 1 | 1 | yes | characteristic |
| 26 | C53×#487 | C22 | 1 | 1 | yes | characteristic |
| 27 | C53×#487 | C22 | 1 | 1 | yes | characteristic |
| 28 | C53×#483 | — | 2 | 1 | no | — |
| 29 | C53×#483 | — | 2 | 1 | no | — |
| 30 | C53×#481 | — | 2 | 1 | no | — |
| 31 | C53×#478 | — | 2 | 1 | no | — |
| 32 | C53×#476 | — | 2 | 1 | no | — |
| 33 | C53×#476 | C22 | 1 | 1 | yes | characteristic |
| 34 | C53×#476 | C22 | 1 | 1 | yes | characteristic |
| 35 | C53×#475 | C22 | 1 | 1 | yes | characteristic |
| 36 | C53×#475 | C22 | 1 | 1 | yes | characteristic |
| 37 | C53×#474 | C22 | 1 | 1 | yes | characteristic |
| 38 | C53×#467 | — | 2 | 1 | no | — |
| 39 | C53×#465 | — | 2 | 1 | no | — |
| 40 | C53×#465 | — | 2 | 1 | no | — |
| 41 | C53×#461 | C22 | 1 | 1 | yes | characteristic |
| 42 | C53×#461 | C22 | 1 | 1 | yes | characteristic |
| 43 | C53×#461 | C22 | 1 | 1 | yes | characteristic |
| 44 | C53×#452 | — | 2 | 1 | no | — |
| 45 | C53×#452 | — | 2 | 1 | no | — |
| 46 | C53×#448 | — | 2 | 1 | no | — |
| 47 | C53×#446 | C22 | 1 | 1 | yes | characteristic |
| 48 | C53×#442 | — | 2 | 1 | no | — |
| 49 | C4×SD16×C53 | C22 | 1 | 1 | yes | characteristic |
| 50 | C4×D8×C53 | C22 | 1 | 1 | yes | characteristic |
| 51 | C8×D4×C53 | C22 | 1 | 1 | yes | characteristic |
| 52 | C8×D4×C53 | C22 | 1 | 1 | yes | characteristic |
| 53 | C8×D4×C53 | C22 | 1 | 1 | yes | characteristic |
| 54 | C2×#106×C53 | — | 2 | 1 | no | — |
| 55 | C2×#103×C53 | — | 2 | 1 | no | — |
| 56 | C53×#334 | C22 | 1 | 1 | yes | characteristic |
| 57 | C53×#334 | C22 | 1 | 1 | yes | characteristic |
| 58 | C53×#333 | C22 | 1 | 1 | yes | characteristic |
| 59 | C53×#332 | C22 | 1 | 1 | yes | characteristic |
| 60 | C53×#332 | C22 | 1 | 1 | yes | characteristic |
| 61 | C53×#332 | C22 | 1 | 1 | yes | characteristic |
| 62 | C53×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 63 | C53×D4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 64 | C53×D4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 65 | C53×D4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 66 | C53×#322 | C22 | 1 | 1 | yes | characteristic |
| 67 | C2×#41×C53 | — | 2 | 1 | no | — |
| 68 | C2×#41×C53 | — | 2 | 1 | no | — |
| 69 | C22×Q8×C53 | — | 2 | 1 | no | — |
| 70 | #135×C53 | — | 4 | 4 | no | — |
| 71 | C2×Q16×C53 | — | 2 | 1 | no | — |
| 72 | C2×Q16×C53 | — | 2 | 1 | no | — |
| 73 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 74 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 75 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 76 | C2×SD16×C53 | D4 | 1 | 1 | yes | characteristic |
| 77 | C2×D8×C53 | D4 | 1 | 1 | yes | characteristic |
| 78 | C22×C8×C53 | — | 2 | 1 | no | — |
| 79 | C22×C8×C53 | — | 2 | 1 | no | — |
| 80 | C22×C8×C53 | — | 2 | 1 | no | — |
| 81 | C4⋊Q8×C53 | — | 2 | 1 | no | — |
| 82 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 83 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 84 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 85 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 86 | #125×C53 | — | 2 | 1 | no | — |
| 87 | #123×C53 | — | 4 | 1 | no | — |
| 88 | #123×C53 | — | 4 | 1 | no | — |
| 89 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 90 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 91 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 92 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 93 | C22⋊Q8×C53 | — | 4 | 1 | no | — |
| 94 | C22⋊Q8×C53 | — | 4 | 1 | no | — |
| 95 | #121×C53 | — | 2 | 1 | no | — |
| 96 | #121×C53 | — | 2 | 1 | no | — |
| 97 | C4×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 98 | C4×D4×C53 | — | 2 | 1 | no | — |
| 99 | C4×D4×C53 | — | 2 | 1 | no | — |
| 100 | C4×D4×C53 | C23 | 1 | 1 | yes | characteristic |
| 101 | C4×D4×C53 | C23 | 1 | 1 | yes | characteristic |
| 102 | C4×D4×C53 | C23 | 1 | 1 | yes | characteristic |
| 103 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 104 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 105 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 106 | #107×C53 | — | 2 | 1 | no | — |
| 107 | #107×C53 | D4 | 1 | 1 | yes | characteristic |
| 108 | #106×C53 | — | 2 | 1 | no | — |
| 109 | #106×C53 | — | 2 | 1 | no | — |
| 110 | #106×C53 | — | 2 | 1 | no | — |
| 111 | #106×C53 | — | 2 | 1 | no | — |
| 112 | #106×C53 | — | 2 | 1 | no | — |
| 113 | #106×C53 | — | 2 | 1 | no | — |
| 114 | #106×C53 | — | 2 | 1 | no | — |
| 115 | #106×C53 | — | 2 | 1 | no | — |
| 116 | #106×C53 | — | 4 | 1 | no | — |
| 117 | #106×C53 | D4 | 1 | 1 | yes | characteristic |
| 118 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 119 | C4⋊C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 120 | C4⋊C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 121 | C4⋊C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 122 | C4⋊C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 123 | #103×C53 | — | 2 | 1 | no | — |
| 124 | #103×C53 | — | 2 | 1 | no | — |
| 125 | #103×C53 | — | 2 | 1 | no | — |
| 126 | #103×C53 | — | 2 | 1 | no | — |
| 127 | #103×C53 | — | 2 | 1 | no | — |
| 128 | #103×C53 | — | 2 | 1 | no | — |
| 129 | #103×C53 | — | 2 | 1 | no | — |
| 130 | #103×C53 | — | 4 | 1 | no | — |
| 131 | #103×C53 | D4 | 1 | 1 | yes | characteristic |
| 132 | #102×C53 | — | 2 | 1 | no | — |
| 133 | #102×C53 | — | 2 | 1 | no | — |
| 134 | #102×C53 | — | 2 | 1 | no | — |
| 135 | #102×C53 | D4 | 1 | 1 | yes | characteristic |
| 136 | #102×C53 | D4 | 1 | 1 | yes | characteristic |
| 137 | #102×C53 | D4 | 1 | 1 | yes | characteristic |
| 138 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 139 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 140 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 141 | #97×C53 | — | 2 | 1 | no | — |
| 142 | C4×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 143 | C4×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 144 | C4×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 145 | #41×C53 | — | 4 | 2 | no | — |
| 146 | #41×C53 | — | 4 | 2 | no | — |
| 147 | #41×C53 | — | 8 | 1 | no | — |
| 148 | #41×C53 | — | 8 | 1 | no | — |
| 149 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 150 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 151 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 152 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 153 | C2×Q8×C53 | — | 4 | 1 | no | — |
| 154 | C2×Q8×C53 | — | 4 | 2 | no | — |
| 155 | C2×Q8×C53 | — | 8 | 1 | no | — |
| 156 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C2×D4×C53 | — | 4 | 1 | no | — |
| 158 | C2×D4×C53 | — | 4 | 1 | no | — |
| 159 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 160 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 161 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 162 | C22×C4×C53 | — | 2 | 1 | no | — |
| 163 | C22×C4×C53 | — | 2 | 1 | no | — |
| 164 | C22×C4×C53 | — | 2 | 1 | no | — |
| 165 | C22×C4×C53 | — | 4 | 1 | no | — |
| 166 | C22×C4×C53 | — | 4 | 1 | no | — |
| 167 | C22×C4×C53 | — | 4 | 1 | no | — |
| 168 | C22×C4×C53 | — | 4 | 1 | no | — |
| 169 | Q16×C53 | — | 4 | 2 | no | — |
| 170 | Q16×C53 | — | 8 | 1 | no | — |
| 171 | SD16×C53 | — | 4 | 1 | no | — |
| 172 | SD16×C53 | — | 4 | 2 | no | — |
| 173 | SD16×C53 | — | 4 | 2 | no | — |
| 174 | SD16×C53 | — | 8 | 1 | no | — |
| 175 | D8×C53 | SD16 | 1 | 4 | yes | complemented |
| 176 | C2×C8×C53 | — | 2 | 1 | no | — |
| 177 | C2×C8×C53 | — | 2 | 1 | no | — |
| 178 | C2×C8×C53 | — | 2 | 1 | no | — |
| 179 | C2×C8×C53 | — | 2 | 1 | no | — |
| 180 | C2×C8×C53 | — | 2 | 1 | no | — |
| 181 | C2×C8×C53 | — | 4 | 2 | no | — |
| 182 | C2×C8×C53 | — | 4 | 2 | no | — |
| 183 | C2×C8×C53 | — | 8 | 1 | no | — |
| 184 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 185 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 186 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 189 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 190 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 191 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 192 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 193 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 194 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 195 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 196 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 197 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 198 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 199 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 200 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 201 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 202 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 203 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 204 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 205 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 206 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 207 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 208 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 209 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 210 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 211 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 212 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 213 | C42×C53 | — | 2 | 1 | no | — |
| 214 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 215 | C23×C53 | — | 2 | 1 | no | — |
| 216 | C23×C53 | — | 2 | 1 | no | — |
| 217 | C23×C53 | — | 2 | 1 | no | — |
| 218 | Q8×C53 | — | 2 | 1 | no | — |
| 219 | Q8×C53 | — | 2 | 1 | no | — |
| 220 | Q8×C53 | — | 4 | 1 | no | — |
| 221 | Q8×C53 | — | 4 | 1 | no | — |
| 222 | Q8×C53 | — | 4 | 1 | no | — |
| 223 | Q8×C53 | — | 4 | 1 | no | — |
| 224 | Q8×C53 | — | 4 | 1 | no | — |
| 225 | Q8×C53 | — | 4 | 1 | no | — |
| 226 | Q8×C53 | — | 8 | 1 | no | — |
| 227 | Q8×C53 | — | 8 | 2 | no | — |
| 228 | D4×C53 | — | 2 | 1 | no | — |
| 229 | D4×C53 | — | 2 | 1 | no | — |
| 230 | D4×C53 | — | 2 | 1 | no | — |
| 231 | D4×C53 | — | 2 | 1 | no | — |
| 232 | D4×C53 | — | 8 | 2 | no | — |
| 233 | D4×C53 | — | 8 | 2 | no | — |
| 234 | D4×C53 | C2×SD16 | 1 | 2 | yes | — |
| 235 | D4×C53 | C2×SD16 | 1 | 2 | yes | — |
| 236 | C2×C4×C53 | — | 2 | 1 | no | — |
| 237 | C2×C4×C53 | — | 2 | 1 | no | — |
| 238 | C2×C4×C53 | — | 2 | 1 | no | — |
| 239 | C2×C4×C53 | — | 2 | 1 | no | — |
| 240 | C2×C4×C53 | — | 2 | 1 | no | — |
| 241 | C2×C4×C53 | — | 4 | 1 | no | — |
| 242 | C2×C4×C53 | — | 4 | 1 | no | — |
| 243 | C2×C4×C53 | — | 4 | 1 | no | — |
| 244 | C2×C4×C53 | — | 4 | 1 | no | — |
| 245 | C2×C4×C53 | — | 4 | 1 | no | — |
| 246 | C2×C4×C53 | — | 4 | 1 | no | — |
| 247 | C2×C4×C53 | — | 4 | 1 | no | — |
| 248 | C2×C4×C53 | — | 4 | 1 | no | — |
| 249 | C2×C4×C53 | — | 4 | 1 | no | — |
| 250 | C2×C4×C53 | — | 4 | 1 | no | — |
| 251 | C2×C4×C53 | — | 8 | 2 | no | — |
| 252 | C2×C4×C53 | — | 8 | 2 | no | — |
| 253 | C2×C4×C53 | — | 8 | 2 | no | — |
| 254 | C2×C4×C53 | — | 16 | 1 | no | — |
| 255 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 256 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 257 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 258 | C8×C53 | — | 2 | 1 | no | — |
| 259 | C8×C53 | — | 2 | 1 | no | — |
| 260 | C8×C53 | — | 2 | 1 | no | — |
| 261 | C8×C53 | — | 4 | 1 | no | — |
| 262 | C8×C53 | — | 4 | 1 | no | — |
| 263 | C8×C53 | — | 4 | 1 | no | — |
| 264 | C8×C53 | — | 4 | 1 | no | — |
| 265 | C8×C53 | — | 4 | 1 | no | — |
| 266 | C8×C53 | C2×SD16 | 1 | 2 | yes | — |
| 267 | #19766 | C53 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 268 | C22×C53 | — | 2 | 2 | no | — |
| 269 | C22×C53 | — | 2 | 2 | no | — |
| 270 | C22×C53 | — | 4 | 1 | no | — |
| 271 | C22×C53 | — | 4 | 1 | no | — |
| 272 | C22×C53 | — | 4 | 1 | no | — |
| 273 | C22×C53 | — | 4 | 1 | no | — |
| 274 | C22×C53 | — | 4 | 1 | no | — |
| 275 | C22×C53 | — | 4 | 1 | no | — |
| 276 | C22×C53 | — | 4 | 1 | no | — |
| 277 | C22×C53 | D42 | 1 | 1 | yes | characteristic |
| 278 | C4×C53 | — | 2 | 1 | no | — |
| 279 | C4×C53 | — | 4 | 1 | no | — |
| 280 | C4×C53 | — | 4 | 1 | no | — |
| 281 | C4×C53 | — | 4 | 1 | no | — |
| 282 | C4×C53 | — | 4 | 1 | no | — |
| 283 | C4×C53 | — | 4 | 1 | no | — |
| 284 | C4×C53 | — | 8 | 1 | no | — |
| 285 | C4×C53 | — | 8 | 1 | no | — |
| 286 | C4×C53 | — | 8 | 1 | no | — |
| 287 | C4×C53 | — | 8 | 1 | no | — |
| 288 | C4×C53 | C22×SD16 | 1 | 1 | yes | characteristic |
| 289 | C4×C53 | #575 | 1 | 1 | yes | characteristic |
| 290 | C4×C53 | #577 | 1 | 1 | yes | characteristic |
| 291 | C4×C53 | #577 | 1 | 1 | yes | characteristic |
| 292 | #3384 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 293 | #3335 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 294 | #3298 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 295 | #3283 | C2×C53 | 1 | 1 | yes | characteristic |
| 296 | #1716 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 297 | #1690 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 298 | #1679 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 299 | #1671 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 300 | #1671 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 301 | #1654 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 302 | #1651 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 303 | #1643 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 304 | #1635 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 305 | #1582 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 306 | #1580 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 307 | C2×C53 | — | 4 | 2 | no | — |
| 308 | C2×C53 | — | 4 | 2 | no | — |
| 309 | C2×C53 | — | 8 | 1 | no | — |
| 310 | C2×C53 | #3267 | 1 | 1 | yes | characteristic |
| 311 | C2×C53 | D4×SD16 | 1 | 1 | yes | characteristic |
| 312 | C2×C53 | #3289 | 1 | 1 | yes | characteristic |
| 313 | C2×#135 | — | 2 | 1 | no | — |
| 314 | #554 | C22×C53 | 1 | 1 | yes | characteristic |
| 315 | D4×Q8 | C22×C53 | 1 | 1 | yes | characteristic |
| 316 | #547 | C22×C53 | 1 | 1 | yes | characteristic |
| 317 | #547 | C22×C53 | 1 | 1 | yes | characteristic |
| 318 | #501 | — | 2 | 1 | no | — |
| 319 | #498 | C22×C53 | 1 | 1 | yes | characteristic |
| 320 | #498 | C22×C53 | 1 | 1 | yes | characteristic |
| 321 | #498 | C22×C53 | 1 | 1 | yes | characteristic |
| 322 | #494 | C22×C53 | 1 | 1 | yes | characteristic |
| 323 | #487 | C22×C53 | 1 | 1 | yes | characteristic |
| 324 | #487 | C22×C53 | 1 | 1 | yes | characteristic |
| 325 | #483 | — | 2 | 1 | no | — |
| 326 | #483 | — | 2 | 1 | no | — |
| 327 | #481 | — | 2 | 1 | no | — |
| 328 | #478 | — | 2 | 1 | no | — |
| 329 | #476 | — | 2 | 1 | no | — |
| 330 | #476 | C22×C53 | 1 | 1 | yes | characteristic |
| 331 | #476 | C22×C53 | 1 | 1 | yes | characteristic |
| 332 | #475 | C22×C53 | 1 | 1 | yes | characteristic |
| 333 | #475 | C22×C53 | 1 | 1 | yes | characteristic |
| 334 | #474 | C22×C53 | 1 | 1 | yes | characteristic |
| 335 | #467 | — | 2 | 1 | no | — |
| 336 | #465 | — | 2 | 1 | no | — |
| 337 | #465 | — | 2 | 1 | no | — |
| 338 | #461 | C22×C53 | 1 | 1 | yes | characteristic |
| 339 | #461 | C22×C53 | 1 | 1 | yes | characteristic |
| 340 | #461 | C22×C53 | 1 | 1 | yes | characteristic |
| 341 | #452 | — | 2 | 1 | no | — |
| 342 | #452 | — | 2 | 1 | no | — |
| 343 | #448 | — | 2 | 1 | no | — |
| 344 | #446 | C22×C53 | 1 | 1 | yes | characteristic |
| 345 | #442 | — | 2 | 1 | no | — |
| 346 | C4×SD16 | C22×C53 | 1 | 1 | yes | characteristic |
| 347 | C4×D8 | C22×C53 | 1 | 1 | yes | characteristic |
| 348 | C8×D4 | C22×C53 | 1 | 1 | yes | characteristic |
| 349 | C8×D4 | C22×C53 | 1 | 1 | yes | characteristic |
| 350 | C8×D4 | C22×C53 | 1 | 1 | yes | characteristic |
| 351 | C2×#106 | — | 2 | 1 | no | — |
| 352 | C2×#103 | — | 2 | 1 | no | — |
| 353 | #334 | C22×C53 | 1 | 1 | yes | characteristic |
| 354 | #334 | C22×C53 | 1 | 1 | yes | characteristic |
| 355 | #333 | C22×C53 | 1 | 1 | yes | characteristic |
| 356 | #332 | C22×C53 | 1 | 1 | yes | characteristic |
| 357 | #332 | C22×C53 | 1 | 1 | yes | characteristic |
| 358 | #332 | C22×C53 | 1 | 1 | yes | characteristic |
| 359 | Q8⋊C8 | C22×C53 | 1 | 1 | yes | characteristic |
| 360 | D4⋊C8 | C22×C53 | 1 | 1 | yes | characteristic |
| 361 | D4⋊C8 | C22×C53 | 1 | 1 | yes | characteristic |
| 362 | D4⋊C8 | C22×C53 | 1 | 1 | yes | characteristic |
| 363 | #322 | C22×C53 | 1 | 1 | yes | characteristic |
| 364 | C53 | #19766 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 365 | C2×#41 | — | 2 | 1 | no | — |
| 366 | C2×#41 | — | 2 | 1 | no | — |
| 367 | C22×Q8 | — | 2 | 1 | no | — |
| 368 | #135 | — | 4 | 4 | no | — |
| 369 | C2×Q16 | — | 2 | 1 | no | — |
| 370 | C2×Q16 | — | 2 | 1 | no | — |
| 371 | C2×SD16 | — | 2 | 1 | no | — |
| 372 | C2×SD16 | — | 2 | 1 | no | — |
| 373 | C2×SD16 | — | 2 | 1 | no | — |
| 374 | C2×SD16 | D4×C53 | 1 | 1 | yes | characteristic |
| 375 | C2×D8 | D4×C53 | 1 | 1 | yes | characteristic |
| 376 | C22×C8 | — | 2 | 1 | no | — |
| 377 | C22×C8 | — | 2 | 1 | no | — |
| 378 | C22×C8 | — | 2 | 1 | no | — |
| 379 | C4⋊Q8 | — | 2 | 1 | no | — |
| 380 | C4⋊Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 381 | C4⋊Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 382 | C4⋊Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 383 | C4⋊Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 384 | #125 | — | 2 | 1 | no | — |
| 385 | #123 | — | 4 | 1 | no | — |
| 386 | #123 | — | 4 | 1 | no | — |
| 387 | C22⋊Q8 | — | 2 | 1 | no | — |
| 388 | C22⋊Q8 | — | 2 | 1 | no | — |
| 389 | C22⋊Q8 | — | 2 | 1 | no | — |
| 390 | C22⋊Q8 | — | 2 | 1 | no | — |
| 391 | C22⋊Q8 | — | 4 | 1 | no | — |
| 392 | C22⋊Q8 | — | 4 | 1 | no | — |
| 393 | #121 | — | 2 | 1 | no | — |
| 394 | #121 | — | 2 | 1 | no | — |
| 395 | C4×Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 396 | C4×D4 | — | 2 | 1 | no | — |
| 397 | C4×D4 | — | 2 | 1 | no | — |
| 398 | C4×D4 | C23×C53 | 1 | 1 | yes | characteristic |
| 399 | C4×D4 | C23×C53 | 1 | 1 | yes | characteristic |
| 400 | C4×D4 | C23×C53 | 1 | 1 | yes | characteristic |
| 401 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 402 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 403 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 404 | #107 | — | 2 | 1 | no | — |
| 405 | #107 | D4×C53 | 1 | 1 | yes | characteristic |
| 406 | #106 | — | 2 | 1 | no | — |
| 407 | #106 | — | 2 | 1 | no | — |
| 408 | #106 | — | 2 | 1 | no | — |
| 409 | #106 | — | 2 | 1 | no | — |
| 410 | #106 | — | 2 | 1 | no | — |
| 411 | #106 | — | 2 | 1 | no | — |
| 412 | #106 | — | 2 | 1 | no | — |
| 413 | #106 | — | 2 | 1 | no | — |
| 414 | #106 | — | 4 | 1 | no | — |
| 415 | #106 | D4×C53 | 1 | 1 | yes | characteristic |
| 416 | C4⋊C8 | — | 2 | 1 | no | — |
| 417 | C4⋊C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 418 | C4⋊C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 419 | C4⋊C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 420 | C4⋊C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 421 | #103 | — | 2 | 1 | no | — |
| 422 | #103 | — | 2 | 1 | no | — |
| 423 | #103 | — | 2 | 1 | no | — |
| 424 | #103 | — | 2 | 1 | no | — |
| 425 | #103 | — | 2 | 1 | no | — |
| 426 | #103 | — | 2 | 1 | no | — |
| 427 | #103 | — | 2 | 1 | no | — |
| 428 | #103 | — | 4 | 1 | no | — |
| 429 | #103 | D4×C53 | 1 | 1 | yes | characteristic |
| 430 | #102 | — | 2 | 1 | no | — |
| 431 | #102 | — | 2 | 1 | no | — |
| 432 | #102 | — | 2 | 1 | no | — |
| 433 | #102 | D4×C53 | 1 | 1 | yes | characteristic |
| 434 | #102 | D4×C53 | 1 | 1 | yes | characteristic |
| 435 | #102 | D4×C53 | 1 | 1 | yes | characteristic |
| 436 | C22⋊C8 | — | 2 | 1 | no | — |
| 437 | C22⋊C8 | — | 2 | 1 | no | — |
| 438 | C22⋊C8 | — | 2 | 1 | no | — |
| 439 | #97 | — | 2 | 1 | no | — |
| 440 | C4×C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 441 | C4×C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 442 | C4×C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 443 | #41 | — | 4 | 2 | no | — |
| 444 | #41 | — | 4 | 2 | no | — |
| 445 | #41 | — | 8 | 1 | no | — |
| 446 | #41 | — | 8 | 1 | no | — |
| 447 | C2×Q8 | — | 2 | 1 | no | — |
| 448 | C2×Q8 | — | 2 | 1 | no | — |
| 449 | C2×Q8 | — | 2 | 1 | no | — |
| 450 | C2×Q8 | — | 2 | 1 | no | — |
| 451 | C2×Q8 | — | 4 | 1 | no | — |
| 452 | C2×Q8 | — | 4 | 2 | no | — |
| 453 | C2×Q8 | — | 8 | 1 | no | — |
| 454 | C2×Q8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 455 | C2×D4 | — | 4 | 1 | no | — |
| 456 | C2×D4 | — | 4 | 1 | no | — |
| 457 | C2×D4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 458 | C2×D4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 459 | C2×D4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 460 | C22×C4 | — | 2 | 1 | no | — |
| 461 | C22×C4 | — | 2 | 1 | no | — |
| 462 | C22×C4 | — | 2 | 1 | no | — |
| 463 | C22×C4 | — | 4 | 1 | no | — |
| 464 | C22×C4 | — | 4 | 1 | no | — |
| 465 | C22×C4 | — | 4 | 1 | no | — |
| 466 | C22×C4 | — | 4 | 1 | no | — |
| 467 | Q16 | — | 4 | 2 | no | — |
| 468 | Q16 | — | 8 | 1 | no | — |
| 469 | SD16 | — | 4 | 1 | no | — |
| 470 | SD16 | — | 4 | 2 | no | — |
| 471 | SD16 | — | 4 | 2 | no | — |
| 472 | SD16 | — | 8 | 1 | no | — |
| 473 | D8 | SD16×C53 | 1 | 4 | yes | complemented |
| 474 | C2×C8 | — | 2 | 1 | no | — |
| 475 | C2×C8 | — | 2 | 1 | no | — |
| 476 | C2×C8 | — | 2 | 1 | no | — |
| 477 | C2×C8 | — | 2 | 1 | no | — |
| 478 | C2×C8 | — | 2 | 1 | no | — |
| 479 | C2×C8 | — | 4 | 2 | no | — |
| 480 | C2×C8 | — | 4 | 2 | no | — |
| 481 | C2×C8 | — | 8 | 1 | no | — |
| 482 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 483 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 484 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 485 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 486 | C4⋊C4 | — | 2 | 1 | no | — |
| 487 | C4⋊C4 | — | 2 | 1 | no | — |
| 488 | C4⋊C4 | — | 2 | 1 | no | — |
| 489 | C4⋊C4 | — | 2 | 1 | no | — |
| 490 | C4⋊C4 | — | 2 | 1 | no | — |
| 491 | C4⋊C4 | — | 2 | 1 | no | — |
| 492 | C4⋊C4 | — | 2 | 1 | no | — |
| 493 | C4⋊C4 | — | 2 | 1 | no | — |
| 494 | C4⋊C4 | — | 2 | 1 | no | — |
| 495 | C4⋊C4 | — | 4 | 1 | no | — |
| 496 | C4⋊C4 | — | 4 | 1 | no | — |
| 497 | C4⋊C4 | — | 4 | 1 | no | — |
| 498 | C4⋊C4 | — | 4 | 1 | no | — |
| 499 | C4⋊C4 | — | 4 | 1 | no | — |
| 500 | C4⋊C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 501 | C4⋊C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 502 | C4⋊C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 503 | C4⋊C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 504 | C22⋊C4 | — | 2 | 1 | no | — |
| 505 | C22⋊C4 | — | 2 | 1 | no | — |
| 506 | C22⋊C4 | — | 2 | 1 | no | — |
| 507 | C22⋊C4 | — | 4 | 1 | no | — |
| 508 | C22⋊C4 | — | 4 | 1 | no | — |
| 509 | C22⋊C4 | — | 4 | 1 | no | — |
| 510 | C22⋊C4 | — | 4 | 1 | no | — |
| 511 | C42 | — | 2 | 1 | no | — |
| 512 | C42 | C24×C53 | 1 | 1 | yes | characteristic |
| 513 | C23 | — | 2 | 1 | no | — |
| 514 | C23 | — | 2 | 1 | no | — |
| 515 | C23 | — | 2 | 1 | no | — |
| 516 | Q8 | — | 2 | 1 | no | — |
| 517 | Q8 | — | 2 | 1 | no | — |
| 518 | Q8 | — | 4 | 1 | no | — |
| 519 | Q8 | — | 4 | 1 | no | — |
| 520 | Q8 | — | 4 | 1 | no | — |
| 521 | Q8 | — | 4 | 1 | no | — |
| 522 | Q8 | — | 4 | 1 | no | — |
| 523 | Q8 | — | 4 | 1 | no | — |
| 524 | Q8 | — | 8 | 1 | no | — |
| 525 | Q8 | — | 8 | 2 | no | — |
| 526 | D4 | — | 2 | 1 | no | — |
| 527 | D4 | — | 2 | 1 | no | — |
| 528 | D4 | — | 2 | 1 | no | — |
| 529 | D4 | — | 2 | 1 | no | — |
| 530 | D4 | — | 8 | 2 | no | — |
| 531 | D4 | — | 8 | 2 | no | — |
| 532 | D4 | C2×SD16×C53 | 1 | 2 | yes | — |
| 533 | D4 | C2×SD16×C53 | 1 | 2 | yes | — |
| 534 | C2×C4 | — | 2 | 1 | no | — |
| 535 | C2×C4 | — | 2 | 1 | no | — |
| 536 | C2×C4 | — | 2 | 1 | no | — |
| 537 | C2×C4 | — | 2 | 1 | no | — |
| 538 | C2×C4 | — | 2 | 1 | no | — |
| 539 | C2×C4 | — | 4 | 1 | no | — |
| 540 | C2×C4 | — | 4 | 1 | no | — |
| 541 | C2×C4 | — | 4 | 1 | no | — |
| 542 | C2×C4 | — | 4 | 1 | no | — |
| 543 | C2×C4 | — | 4 | 1 | no | — |
| 544 | C2×C4 | — | 4 | 1 | no | — |
| 545 | C2×C4 | — | 4 | 1 | no | — |
| 546 | C2×C4 | — | 4 | 1 | no | — |
| 547 | C2×C4 | — | 4 | 1 | no | — |
| 548 | C2×C4 | — | 4 | 1 | no | — |
| 549 | C2×C4 | — | 8 | 2 | no | — |
| 550 | C2×C4 | — | 8 | 2 | no | — |
| 551 | C2×C4 | — | 8 | 2 | no | — |
| 552 | C2×C4 | — | 16 | 1 | no | — |
| 553 | C2×C4 | C22×D4×C53 | 1 | 1 | yes | characteristic |
| 554 | C2×C4 | C22×D4×C53 | 1 | 1 | yes | characteristic |
| 555 | C2×C4 | H(5,𝔽2)×C53 | 1 | 1 | yes | characteristic |
| 556 | C8 | — | 2 | 1 | no | — |
| 557 | C8 | — | 2 | 1 | no | — |
| 558 | C8 | — | 2 | 1 | no | — |
| 559 | C8 | — | 4 | 1 | no | — |
| 560 | C8 | — | 4 | 1 | no | — |
| 561 | C8 | — | 4 | 1 | no | — |
| 562 | C8 | — | 4 | 1 | no | — |
| 563 | C8 | — | 4 | 1 | no | — |
| 564 | C8 | C2×SD16×C53 | 1 | 2 | yes | — |
| 565 | C22 | — | 2 | 2 | no | — |
| 566 | C22 | — | 2 | 2 | no | — |
| 567 | C22 | — | 4 | 1 | no | — |
| 568 | C22 | — | 4 | 1 | no | — |
| 569 | C22 | — | 4 | 1 | no | — |
| 570 | C22 | — | 4 | 1 | no | — |
| 571 | C22 | — | 4 | 1 | no | — |
| 572 | C22 | — | 4 | 1 | no | — |
| 573 | C22 | — | 4 | 1 | no | — |
| 574 | C22 | D42×C53 | 1 | 1 | yes | characteristic |
| 575 | C4 | — | 2 | 1 | no | — |
| 576 | C4 | — | 4 | 1 | no | — |
| 577 | C4 | — | 4 | 1 | no | — |
| 578 | C4 | — | 4 | 1 | no | — |
| 579 | C4 | — | 4 | 1 | no | — |
| 580 | C4 | — | 4 | 1 | no | — |
| 581 | C4 | — | 8 | 1 | no | — |
| 582 | C4 | — | 8 | 1 | no | — |
| 583 | C4 | — | 8 | 1 | no | — |
| 584 | C4 | — | 8 | 1 | no | — |
| 585 | C4 | C22×SD16×C53 | 1 | 1 | yes | characteristic |
| 586 | C4 | C53×#575 | 1 | 1 | yes | characteristic |
| 587 | C4 | C53×#577 | 1 | 1 | yes | characteristic |
| 588 | C4 | C53×#577 | 1 | 1 | yes | characteristic |
| 589 | C2 | — | 4 | 2 | no | — |
| 590 | C2 | — | 4 | 2 | no | — |
| 591 | C2 | — | 8 | 1 | no | — |
| 592 | C2 | C53×#3267 | 1 | 1 | yes | characteristic |
| 593 | C2 | D4×SD16×C53 | 1 | 1 | yes | characteristic |
| 594 | C2 | C53×#3289 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta