| 1 | C53×#3380 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C53×#3360 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C53×#3356 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C53×#3338 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C53×#1723 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C53×#1695 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C53×#1684 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C53×#1676 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C53×#1671 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C53×#1643 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C53×#1638 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C53×#1632 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C53×#1632 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C53×#1581 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | C53×#1579 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C53×#556 | C22 | 1 | 1 | yes | characteristic |
| 17 | C53×#554 | C22 | 1 | 1 | yes | characteristic |
| 18 | C53×#554 | C22 | 1 | 1 | yes | characteristic |
| 19 | C53×#554 | C22 | 1 | 1 | yes | characteristic |
| 20 | C53×#500 | C22 | 1 | 1 | yes | characteristic |
| 21 | C53×#500 | C22 | 1 | 1 | yes | characteristic |
| 22 | C53×#499 | — | 2 | 1 | no | — |
| 23 | C53×#498 | C22 | 1 | 1 | yes | characteristic |
| 24 | C53×#494 | C22 | 1 | 1 | yes | characteristic |
| 25 | C53×#488 | — | 2 | 1 | no | — |
| 26 | C53×#487 | C22 | 1 | 1 | yes | characteristic |
| 27 | C53×#487 | C22 | 1 | 1 | yes | characteristic |
| 28 | C53×#485 | — | 2 | 1 | no | — |
| 29 | C53×#484 | — | 2 | 1 | no | — |
| 30 | C53×#484 | — | 2 | 1 | no | — |
| 31 | C53×#483 | — | 2 | 1 | no | — |
| 32 | C53×#479 | — | 2 | 1 | no | — |
| 33 | C53×#478 | — | 2 | 1 | no | — |
| 34 | C53×#478 | — | 2 | 1 | no | — |
| 35 | C53×#477 | C22 | 1 | 1 | yes | characteristic |
| 36 | C53×#477 | C22 | 1 | 1 | yes | characteristic |
| 37 | C53×#477 | C22 | 1 | 1 | yes | characteristic |
| 38 | C53×#476 | C22 | 1 | 1 | yes | characteristic |
| 39 | C53×#476 | C22 | 1 | 1 | yes | characteristic |
| 40 | C53×#476 | C22 | 1 | 1 | yes | characteristic |
| 41 | C53×#475 | C22 | 1 | 1 | yes | characteristic |
| 42 | C53×#470 | — | 2 | 1 | no | — |
| 43 | C53×#467 | — | 2 | 1 | no | — |
| 44 | C53×#463 | — | 2 | 1 | no | — |
| 45 | C53×#461 | C22 | 1 | 1 | yes | characteristic |
| 46 | C8×Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 47 | C8×Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 48 | C4×Q16×C53 | C22 | 1 | 1 | yes | characteristic |
| 49 | C4×SD16×C53 | — | 2 | 1 | no | — |
| 50 | C4×D8×C53 | — | 2 | 1 | no | — |
| 51 | C4×D8×C53 | C22 | 1 | 1 | yes | characteristic |
| 52 | C53×#436 | C22 | 1 | 1 | yes | characteristic |
| 53 | C8×D4×C53 | C22 | 1 | 1 | yes | characteristic |
| 54 | C53×#428 | — | 2 | 1 | no | — |
| 55 | C2×#107×C53 | — | 2 | 1 | no | — |
| 56 | C53×#335 | C22 | 1 | 1 | yes | characteristic |
| 57 | C53×#334 | C22 | 1 | 1 | yes | characteristic |
| 58 | C53×#333 | C22 | 1 | 1 | yes | characteristic |
| 59 | C53×#333 | C22 | 1 | 1 | yes | characteristic |
| 60 | C53×#333 | C22 | 1 | 1 | yes | characteristic |
| 61 | C53×#332 | C22 | 1 | 1 | yes | characteristic |
| 62 | C53×Q8⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 63 | C53×Q8⋊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×Q16×C53 | — | 4 | 1 | no | — |
| 68 | C2×Q16×C53 | D4 | 1 | 1 | yes | characteristic |
| 69 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 70 | C2×D8×C53 | D4 | 1 | 1 | yes | characteristic |
| 71 | C2×M16×C53 | — | 2 | 1 | no | — |
| 72 | C22×C8×C53 | — | 2 | 1 | no | — |
| 73 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 74 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 75 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 76 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 77 | #126×C53 | — | 4 | 1 | no | — |
| 78 | #125×C53 | — | 2 | 1 | no | — |
| 79 | #125×C53 | — | 2 | 1 | no | — |
| 80 | #125×C53 | — | 2 | 1 | no | — |
| 81 | #124×C53 | — | 2 | 1 | no | — |
| 82 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 83 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 84 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 85 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 86 | C22⋊Q8×C53 | — | 4 | 1 | no | — |
| 87 | C22⋊Q8×C53 | — | 4 | 1 | no | — |
| 88 | C22⋊Q8×C53 | — | 4 | 1 | no | — |
| 89 | C4×Q8×C53 | — | 2 | 1 | no | — |
| 90 | C4×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 91 | C4×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 92 | C4×D4×C53 | — | 2 | 1 | no | — |
| 93 | C4×D4×C53 | — | 2 | 1 | no | — |
| 94 | C4×D4×C53 | — | 2 | 1 | no | — |
| 95 | C4×D4×C53 | C23 | 1 | 1 | yes | characteristic |
| 96 | C4×D4×C53 | C23 | 1 | 1 | yes | characteristic |
| 97 | #117×C53 | — | 2 | 1 | no | — |
| 98 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 99 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 100 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 101 | #107×C53 | — | 2 | 1 | no | — |
| 102 | #107×C53 | — | 2 | 1 | no | — |
| 103 | #107×C53 | — | 2 | 1 | no | — |
| 104 | #107×C53 | — | 2 | 1 | no | — |
| 105 | #107×C53 | — | 2 | 1 | no | — |
| 106 | #107×C53 | — | 2 | 1 | no | — |
| 107 | #107×C53 | — | 2 | 1 | no | — |
| 108 | #107×C53 | D4 | 1 | 1 | yes | characteristic |
| 109 | #107×C53 | D4 | 1 | 1 | yes | characteristic |
| 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 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 117 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 118 | C4⋊C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 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 | #103×C53 | — | 2 | 1 | no | — |
| 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 | — | 4 | 1 | no | — |
| 130 | #103×C53 | D4 | 1 | 1 | yes | characteristic |
| 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 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 138 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 139 | C4×C8×C53 | — | 2 | 1 | no | — |
| 140 | C4×C8×C53 | — | 2 | 1 | no | — |
| 141 | C4×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 142 | C4×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 143 | C4×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 144 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 145 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 146 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 147 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 148 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 150 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 151 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 152 | C22×C4×C53 | — | 2 | 1 | no | — |
| 153 | C22×C4×C53 | — | 2 | 1 | no | — |
| 154 | C22×C4×C53 | — | 4 | 1 | no | — |
| 155 | C22×C4×C53 | — | 4 | 1 | no | — |
| 156 | C22×C4×C53 | — | 4 | 1 | no | — |
| 157 | Q16×C53 | — | 2 | 2 | no | — |
| 158 | Q16×C53 | — | 8 | 2 | no | — |
| 159 | SD16×C53 | — | 4 | 2 | no | — |
| 160 | D8×C53 | — | 2 | 2 | no | — |
| 161 | M16×C53 | — | 4 | 2 | no | — |
| 162 | C2×C8×C53 | — | 2 | 1 | no | — |
| 163 | C2×C8×C53 | — | 2 | 1 | no | — |
| 164 | C2×C8×C53 | — | 2 | 1 | no | — |
| 165 | C2×C8×C53 | — | 2 | 1 | no | — |
| 166 | C2×C8×C53 | — | 2 | 1 | no | — |
| 167 | C2×C8×C53 | — | 4 | 2 | no | — |
| 168 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 169 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 173 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 174 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 175 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 176 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 177 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 178 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 179 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 180 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 181 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 182 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 183 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 184 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 185 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 186 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 187 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 188 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 189 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 191 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 192 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 193 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 194 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 195 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 196 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 197 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 198 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 199 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 200 | C42×C53 | — | 2 | 1 | no | — |
| 201 | C42×C53 | — | 2 | 1 | no | — |
| 202 | C42×C53 | — | 4 | 1 | no | — |
| 203 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 204 | C23×C53 | — | 2 | 1 | no | — |
| 205 | C23×C53 | — | 2 | 1 | no | — |
| 206 | Q8×C53 | — | 2 | 1 | no | — |
| 207 | Q8×C53 | — | 2 | 1 | no | — |
| 208 | Q8×C53 | — | 2 | 1 | no | — |
| 209 | Q8×C53 | — | 2 | 1 | no | — |
| 210 | Q8×C53 | — | 4 | 1 | no | — |
| 211 | Q8×C53 | — | 4 | 1 | no | — |
| 212 | Q8×C53 | — | 8 | 1 | no | — |
| 213 | Q8×C53 | — | 8 | 1 | no | — |
| 214 | Q8×C53 | — | 8 | 1 | no | — |
| 215 | D4×C53 | — | 2 | 1 | no | — |
| 216 | D4×C53 | — | 2 | 1 | no | — |
| 217 | D4×C53 | — | 2 | 1 | no | — |
| 218 | D4×C53 | #137 | 1 | 2 | yes | — |
| 219 | C2×C4×C53 | — | 2 | 1 | no | — |
| 220 | C2×C4×C53 | — | 2 | 1 | no | — |
| 221 | C2×C4×C53 | — | 2 | 1 | no | — |
| 222 | C2×C4×C53 | — | 2 | 1 | no | — |
| 223 | C2×C4×C53 | — | 2 | 1 | no | — |
| 224 | C2×C4×C53 | — | 2 | 1 | no | — |
| 225 | C2×C4×C53 | — | 4 | 1 | no | — |
| 226 | C2×C4×C53 | — | 4 | 1 | no | — |
| 227 | C2×C4×C53 | — | 4 | 1 | no | — |
| 228 | C2×C4×C53 | — | 4 | 1 | no | — |
| 229 | C2×C4×C53 | — | 4 | 1 | no | — |
| 230 | C2×C4×C53 | — | 4 | 1 | no | — |
| 231 | C2×C4×C53 | — | 4 | 1 | no | — |
| 232 | C2×C4×C53 | — | 4 | 1 | no | — |
| 233 | C2×C4×C53 | — | 16 | 1 | no | — |
| 234 | C2×C4×C53 | — | 16 | 1 | no | — |
| 235 | C2×C4×C53 | — | 16 | 1 | no | — |
| 236 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 237 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 238 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 239 | C8×C53 | — | 2 | 1 | no | — |
| 240 | C8×C53 | — | 2 | 1 | no | — |
| 241 | C8×C53 | — | 2 | 1 | no | — |
| 242 | C8×C53 | — | 4 | 1 | no | — |
| 243 | C8×C53 | — | 4 | 1 | no | — |
| 244 | C8×C53 | — | 4 | 1 | no | — |
| 245 | C8×C53 | — | 4 | 1 | no | — |
| 246 | C8×C53 | — | 4 | 1 | no | — |
| 247 | C8×C53 | #135 | 1 | 2 | yes | — |
| 248 | #19865 | C53 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 249 | C22×C53 | — | 2 | 2 | no | — |
| 250 | C22×C53 | — | 4 | 1 | no | — |
| 251 | C22×C53 | — | 4 | 1 | no | — |
| 252 | C22×C53 | — | 4 | 1 | no | — |
| 253 | C22×C53 | — | 4 | 1 | no | — |
| 254 | C22×C53 | — | 4 | 1 | no | — |
| 255 | C22×C53 | D42 | 1 | 1 | yes | characteristic |
| 256 | C4×C53 | — | 2 | 1 | no | — |
| 257 | C4×C53 | — | 4 | 1 | no | — |
| 258 | C4×C53 | — | 4 | 1 | no | — |
| 259 | C4×C53 | — | 4 | 1 | no | — |
| 260 | C4×C53 | — | 4 | 1 | no | — |
| 261 | C4×C53 | — | 4 | 1 | no | — |
| 262 | C4×C53 | — | 4 | 1 | no | — |
| 263 | C4×C53 | — | 8 | 1 | no | — |
| 264 | C4×C53 | — | 8 | 1 | no | — |
| 265 | C4×C53 | — | 8 | 1 | no | — |
| 266 | C4×C53 | — | 8 | 1 | no | — |
| 267 | C4×C53 | C2×#135 | 1 | 1 | yes | characteristic |
| 268 | C4×C53 | C2×#137 | 1 | 1 | yes | characteristic |
| 269 | C4×C53 | #578 | 1 | 1 | yes | characteristic |
| 270 | C4×C53 | #578 | 1 | 1 | yes | characteristic |
| 271 | #3380 | C2×C53 | 1 | 1 | yes | characteristic |
| 272 | #3360 | C2×C53 | 1 | 1 | yes | characteristic |
| 273 | #3356 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 274 | #3338 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 275 | #1723 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 276 | #1695 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 277 | #1684 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 278 | #1676 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 279 | #1671 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 280 | #1643 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 281 | #1638 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 282 | #1632 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 283 | #1632 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 284 | #1581 | C2×C53 | 1 | 1 | yes | characteristic |
| 285 | #1579 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 286 | C2×C53 | — | 4 | 2 | no | — |
| 287 | C2×C53 | — | 8 | 1 | no | — |
| 288 | C2×C53 | #3270 | 1 | 1 | yes | characteristic |
| 289 | C2×C53 | #3283 | 1 | 1 | yes | characteristic |
| 290 | C2×C53 | #3288 | 1 | 1 | yes | characteristic |
| 291 | #556 | C22×C53 | 1 | 1 | yes | characteristic |
| 292 | #554 | C22×C53 | 1 | 1 | yes | characteristic |
| 293 | #554 | C22×C53 | 1 | 1 | yes | characteristic |
| 294 | #554 | C22×C53 | 1 | 1 | yes | characteristic |
| 295 | #500 | C22×C53 | 1 | 1 | yes | characteristic |
| 296 | #500 | C22×C53 | 1 | 1 | yes | characteristic |
| 297 | #499 | — | 2 | 1 | no | — |
| 298 | #498 | C22×C53 | 1 | 1 | yes | characteristic |
| 299 | #494 | C22×C53 | 1 | 1 | yes | characteristic |
| 300 | #488 | — | 2 | 1 | no | — |
| 301 | #487 | C22×C53 | 1 | 1 | yes | characteristic |
| 302 | #487 | C22×C53 | 1 | 1 | yes | characteristic |
| 303 | #485 | — | 2 | 1 | no | — |
| 304 | #484 | — | 2 | 1 | no | — |
| 305 | #484 | — | 2 | 1 | no | — |
| 306 | #483 | — | 2 | 1 | no | — |
| 307 | #479 | — | 2 | 1 | no | — |
| 308 | #478 | — | 2 | 1 | no | — |
| 309 | #478 | — | 2 | 1 | no | — |
| 310 | #477 | C22×C53 | 1 | 1 | yes | characteristic |
| 311 | #477 | C22×C53 | 1 | 1 | yes | characteristic |
| 312 | #477 | C22×C53 | 1 | 1 | yes | characteristic |
| 313 | #476 | C22×C53 | 1 | 1 | yes | characteristic |
| 314 | #476 | C22×C53 | 1 | 1 | yes | characteristic |
| 315 | #476 | C22×C53 | 1 | 1 | yes | characteristic |
| 316 | #475 | C22×C53 | 1 | 1 | yes | characteristic |
| 317 | #470 | — | 2 | 1 | no | — |
| 318 | #467 | — | 2 | 1 | no | — |
| 319 | #463 | — | 2 | 1 | no | — |
| 320 | #461 | C22×C53 | 1 | 1 | yes | characteristic |
| 321 | C8×Q8 | C22×C53 | 1 | 1 | yes | characteristic |
| 322 | C8×Q8 | C22×C53 | 1 | 1 | yes | characteristic |
| 323 | C4×Q16 | C22×C53 | 1 | 1 | yes | characteristic |
| 324 | C4×SD16 | — | 2 | 1 | no | — |
| 325 | C4×D8 | — | 2 | 1 | no | — |
| 326 | C4×D8 | C22×C53 | 1 | 1 | yes | characteristic |
| 327 | #436 | C22×C53 | 1 | 1 | yes | characteristic |
| 328 | C8×D4 | C22×C53 | 1 | 1 | yes | characteristic |
| 329 | #428 | — | 2 | 1 | no | — |
| 330 | C2×#107 | — | 2 | 1 | no | — |
| 331 | #335 | C22×C53 | 1 | 1 | yes | characteristic |
| 332 | #334 | C22×C53 | 1 | 1 | yes | characteristic |
| 333 | #333 | C22×C53 | 1 | 1 | yes | characteristic |
| 334 | #333 | C22×C53 | 1 | 1 | yes | characteristic |
| 335 | #333 | C22×C53 | 1 | 1 | yes | characteristic |
| 336 | #332 | C22×C53 | 1 | 1 | yes | characteristic |
| 337 | Q8⋊C8 | C22×C53 | 1 | 1 | yes | characteristic |
| 338 | Q8⋊C8 | C22×C53 | 1 | 1 | yes | characteristic |
| 339 | D4⋊C8 | C22×C53 | 1 | 1 | yes | characteristic |
| 340 | D4⋊C8 | C22×C53 | 1 | 1 | yes | characteristic |
| 341 | #322 | C22×C53 | 1 | 1 | yes | characteristic |
| 342 | C53 | #19865 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 343 | C2×Q16 | — | 4 | 1 | no | — |
| 344 | C2×Q16 | D4×C53 | 1 | 1 | yes | characteristic |
| 345 | C2×SD16 | — | 2 | 1 | no | — |
| 346 | C2×D8 | D4×C53 | 1 | 1 | yes | characteristic |
| 347 | C2×M16 | — | 2 | 1 | no | — |
| 348 | C22×C8 | — | 2 | 1 | no | — |
| 349 | C4⋊Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 350 | C4⋊Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 351 | C4⋊Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 352 | C4⋊Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 353 | #126 | — | 4 | 1 | no | — |
| 354 | #125 | — | 2 | 1 | no | — |
| 355 | #125 | — | 2 | 1 | no | — |
| 356 | #125 | — | 2 | 1 | no | — |
| 357 | #124 | — | 2 | 1 | no | — |
| 358 | C22⋊Q8 | — | 2 | 1 | no | — |
| 359 | C22⋊Q8 | — | 2 | 1 | no | — |
| 360 | C22⋊Q8 | — | 2 | 1 | no | — |
| 361 | C22⋊Q8 | — | 2 | 1 | no | — |
| 362 | C22⋊Q8 | — | 4 | 1 | no | — |
| 363 | C22⋊Q8 | — | 4 | 1 | no | — |
| 364 | C22⋊Q8 | — | 4 | 1 | no | — |
| 365 | C4×Q8 | — | 2 | 1 | no | — |
| 366 | C4×Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 367 | C4×Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 368 | C4×D4 | — | 2 | 1 | no | — |
| 369 | C4×D4 | — | 2 | 1 | no | — |
| 370 | C4×D4 | — | 2 | 1 | no | — |
| 371 | C4×D4 | C23×C53 | 1 | 1 | yes | characteristic |
| 372 | C4×D4 | C23×C53 | 1 | 1 | yes | characteristic |
| 373 | #117 | — | 2 | 1 | no | — |
| 374 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 375 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 376 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 377 | #107 | — | 2 | 1 | no | — |
| 378 | #107 | — | 2 | 1 | no | — |
| 379 | #107 | — | 2 | 1 | no | — |
| 380 | #107 | — | 2 | 1 | no | — |
| 381 | #107 | — | 2 | 1 | no | — |
| 382 | #107 | — | 2 | 1 | no | — |
| 383 | #107 | — | 2 | 1 | no | — |
| 384 | #107 | D4×C53 | 1 | 1 | yes | characteristic |
| 385 | #107 | D4×C53 | 1 | 1 | yes | characteristic |
| 386 | #106 | — | 2 | 1 | no | — |
| 387 | #106 | — | 2 | 1 | no | — |
| 388 | #106 | — | 2 | 1 | no | — |
| 389 | #106 | — | 2 | 1 | no | — |
| 390 | #106 | — | 2 | 1 | no | — |
| 391 | #106 | — | 2 | 1 | no | — |
| 392 | C4⋊C8 | — | 2 | 1 | no | — |
| 393 | C4⋊C8 | — | 2 | 1 | no | — |
| 394 | C4⋊C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 395 | C4⋊C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 396 | C4⋊C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 397 | C4⋊C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 398 | #103 | — | 2 | 1 | no | — |
| 399 | #103 | — | 2 | 1 | no | — |
| 400 | #103 | — | 2 | 1 | no | — |
| 401 | #103 | — | 2 | 1 | no | — |
| 402 | #103 | — | 2 | 1 | no | — |
| 403 | #103 | — | 2 | 1 | no | — |
| 404 | #103 | — | 2 | 1 | no | — |
| 405 | #103 | — | 4 | 1 | no | — |
| 406 | #103 | D4×C53 | 1 | 1 | yes | characteristic |
| 407 | #103 | D4×C53 | 1 | 1 | yes | characteristic |
| 408 | #102 | — | 2 | 1 | no | — |
| 409 | #102 | — | 2 | 1 | no | — |
| 410 | #102 | — | 2 | 1 | no | — |
| 411 | #102 | D4×C53 | 1 | 1 | yes | characteristic |
| 412 | #102 | D4×C53 | 1 | 1 | yes | characteristic |
| 413 | C22⋊C8 | — | 2 | 1 | no | — |
| 414 | C22⋊C8 | — | 2 | 1 | no | — |
| 415 | C4×C8 | — | 2 | 1 | no | — |
| 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 | C2×Q8 | — | 2 | 1 | no | — |
| 421 | C2×Q8 | — | 2 | 1 | no | — |
| 422 | C2×Q8 | — | 2 | 1 | no | — |
| 423 | C2×Q8 | — | 2 | 1 | no | — |
| 424 | C2×Q8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 425 | C2×Q8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 426 | C2×D4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 427 | C2×D4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 428 | C22×C4 | — | 2 | 1 | no | — |
| 429 | C22×C4 | — | 2 | 1 | no | — |
| 430 | C22×C4 | — | 4 | 1 | no | — |
| 431 | C22×C4 | — | 4 | 1 | no | — |
| 432 | C22×C4 | — | 4 | 1 | no | — |
| 433 | Q16 | — | 2 | 2 | no | — |
| 434 | Q16 | — | 8 | 2 | no | — |
| 435 | SD16 | — | 4 | 2 | no | — |
| 436 | D8 | — | 2 | 2 | no | — |
| 437 | M16 | — | 4 | 2 | no | — |
| 438 | C2×C8 | — | 2 | 1 | no | — |
| 439 | C2×C8 | — | 2 | 1 | no | — |
| 440 | C2×C8 | — | 2 | 1 | no | — |
| 441 | C2×C8 | — | 2 | 1 | no | — |
| 442 | C2×C8 | — | 2 | 1 | no | — |
| 443 | C2×C8 | — | 4 | 2 | no | — |
| 444 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 445 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 446 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 447 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 448 | C4⋊C4 | — | 2 | 1 | no | — |
| 449 | C4⋊C4 | — | 2 | 1 | no | — |
| 450 | C4⋊C4 | — | 2 | 1 | no | — |
| 451 | C4⋊C4 | — | 2 | 1 | no | — |
| 452 | C4⋊C4 | — | 2 | 1 | no | — |
| 453 | C4⋊C4 | — | 2 | 1 | no | — |
| 454 | C4⋊C4 | — | 2 | 1 | no | — |
| 455 | C4⋊C4 | — | 2 | 1 | no | — |
| 456 | C4⋊C4 | — | 2 | 1 | no | — |
| 457 | C4⋊C4 | — | 2 | 1 | no | — |
| 458 | C4⋊C4 | — | 4 | 1 | no | — |
| 459 | C4⋊C4 | — | 4 | 1 | no | — |
| 460 | C4⋊C4 | — | 4 | 1 | no | — |
| 461 | C4⋊C4 | — | 4 | 1 | no | — |
| 462 | C4⋊C4 | — | 4 | 1 | no | — |
| 463 | C4⋊C4 | — | 4 | 1 | no | — |
| 464 | C4⋊C4 | — | 4 | 1 | no | — |
| 465 | C4⋊C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 466 | C4⋊C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 467 | C4⋊C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 468 | C4⋊C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 469 | C22⋊C4 | — | 2 | 1 | no | — |
| 470 | C22⋊C4 | — | 2 | 1 | no | — |
| 471 | C22⋊C4 | — | 4 | 1 | no | — |
| 472 | C22⋊C4 | — | 4 | 1 | no | — |
| 473 | C22⋊C4 | — | 4 | 1 | no | — |
| 474 | C22⋊C4 | — | 4 | 1 | no | — |
| 475 | C22⋊C4 | — | 4 | 1 | no | — |
| 476 | C42 | — | 2 | 1 | no | — |
| 477 | C42 | — | 2 | 1 | no | — |
| 478 | C42 | — | 4 | 1 | no | — |
| 479 | C42 | C24×C53 | 1 | 1 | yes | characteristic |
| 480 | C23 | — | 2 | 1 | no | — |
| 481 | C23 | — | 2 | 1 | no | — |
| 482 | Q8 | — | 2 | 1 | no | — |
| 483 | Q8 | — | 2 | 1 | no | — |
| 484 | Q8 | — | 2 | 1 | no | — |
| 485 | Q8 | — | 2 | 1 | no | — |
| 486 | Q8 | — | 4 | 1 | no | — |
| 487 | Q8 | — | 4 | 1 | no | — |
| 488 | Q8 | — | 8 | 1 | no | — |
| 489 | Q8 | — | 8 | 1 | no | — |
| 490 | Q8 | — | 8 | 1 | no | — |
| 491 | D4 | — | 2 | 1 | no | — |
| 492 | D4 | — | 2 | 1 | no | — |
| 493 | D4 | — | 2 | 1 | no | — |
| 494 | D4 | #137×C53 | 1 | 2 | yes | — |
| 495 | C2×C4 | — | 2 | 1 | no | — |
| 496 | C2×C4 | — | 2 | 1 | no | — |
| 497 | C2×C4 | — | 2 | 1 | no | — |
| 498 | C2×C4 | — | 2 | 1 | no | — |
| 499 | C2×C4 | — | 2 | 1 | no | — |
| 500 | C2×C4 | — | 2 | 1 | no | — |
| 501 | C2×C4 | — | 4 | 1 | no | — |
| 502 | C2×C4 | — | 4 | 1 | no | — |
| 503 | C2×C4 | — | 4 | 1 | no | — |
| 504 | C2×C4 | — | 4 | 1 | no | — |
| 505 | C2×C4 | — | 4 | 1 | no | — |
| 506 | C2×C4 | — | 4 | 1 | no | — |
| 507 | C2×C4 | — | 4 | 1 | no | — |
| 508 | C2×C4 | — | 4 | 1 | no | — |
| 509 | C2×C4 | — | 16 | 1 | no | — |
| 510 | C2×C4 | — | 16 | 1 | no | — |
| 511 | C2×C4 | — | 16 | 1 | no | — |
| 512 | C2×C4 | C22×D4×C53 | 1 | 1 | yes | characteristic |
| 513 | C2×C4 | C22×D4×C53 | 1 | 1 | yes | characteristic |
| 514 | C2×C4 | H(5,𝔽2)×C53 | 1 | 1 | yes | characteristic |
| 515 | C8 | — | 2 | 1 | no | — |
| 516 | C8 | — | 2 | 1 | no | — |
| 517 | C8 | — | 2 | 1 | no | — |
| 518 | C8 | — | 4 | 1 | no | — |
| 519 | C8 | — | 4 | 1 | no | — |
| 520 | C8 | — | 4 | 1 | no | — |
| 521 | C8 | — | 4 | 1 | no | — |
| 522 | C8 | — | 4 | 1 | no | — |
| 523 | C8 | #135×C53 | 1 | 2 | yes | — |
| 524 | C22 | — | 2 | 2 | no | — |
| 525 | C22 | — | 4 | 1 | no | — |
| 526 | C22 | — | 4 | 1 | no | — |
| 527 | C22 | — | 4 | 1 | no | — |
| 528 | C22 | — | 4 | 1 | no | — |
| 529 | C22 | — | 4 | 1 | no | — |
| 530 | C22 | D42×C53 | 1 | 1 | yes | characteristic |
| 531 | C4 | — | 2 | 1 | no | — |
| 532 | C4 | — | 4 | 1 | no | — |
| 533 | C4 | — | 4 | 1 | no | — |
| 534 | C4 | — | 4 | 1 | no | — |
| 535 | C4 | — | 4 | 1 | no | — |
| 536 | C4 | — | 4 | 1 | no | — |
| 537 | C4 | — | 4 | 1 | no | — |
| 538 | C4 | — | 8 | 1 | no | — |
| 539 | C4 | — | 8 | 1 | no | — |
| 540 | C4 | — | 8 | 1 | no | — |
| 541 | C4 | — | 8 | 1 | no | — |
| 542 | C4 | C2×#135×C53 | 1 | 1 | yes | characteristic |
| 543 | C4 | C2×#137×C53 | 1 | 1 | yes | characteristic |
| 544 | C4 | C53×#578 | 1 | 1 | yes | characteristic |
| 545 | C4 | C53×#578 | 1 | 1 | yes | characteristic |
| 546 | C2 | — | 4 | 2 | no | — |
| 547 | C2 | — | 8 | 1 | no | — |
| 548 | C2 | C53×#3270 | 1 | 1 | yes | characteristic |
| 549 | C2 | C53×#3283 | 1 | 1 | yes | characteristic |
| 550 | C2 | C53×#3288 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta