| 1 | C53×#3529 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C53×#3219 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C53×#3214 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C53×#3180 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C53×#1664 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C53×#1662 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C53×#1661 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C53×#1659 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C53×#1657 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C53×#1656 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C53×#1656 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C53×#1655 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C53×#1535 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C53×#1532 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C53×#1530 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C53×#563 | — | 2 | 1 | no | — |
| 17 | C53×#563 | C22 | 1 | 1 | yes | characteristic |
| 18 | C53×#562 | — | 2 | 1 | no | — |
| 19 | C53×#562 | — | 2 | 1 | no | — |
| 20 | C53×#562 | C22 | 1 | 1 | yes | characteristic |
| 21 | C53×#562 | C22 | 1 | 1 | yes | characteristic |
| 22 | C53×H(3,𝔽4) | C22 | 1 | 1 | yes | characteristic |
| 23 | C53×#560 | — | 2 | 1 | no | — |
| 24 | C53×#560 | — | 2 | 1 | no | — |
| 25 | C53×#560 | — | 2 | 1 | no | — |
| 26 | C53×#532 | — | 2 | 1 | no | — |
| 27 | C53×#532 | C22 | 1 | 1 | yes | characteristic |
| 28 | C53×#532 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C53×#529 | — | 2 | 1 | no | — |
| 30 | C53×#529 | — | 2 | 1 | no | — |
| 31 | C53×#529 | C22 | 1 | 1 | yes | characteristic |
| 32 | C53×#529 | C22 | 1 | 1 | yes | characteristic |
| 33 | C53×#525 | — | 2 | 1 | no | — |
| 34 | C53×#525 | — | 2 | 1 | no | — |
| 35 | C53×#525 | — | 2 | 1 | no | — |
| 36 | C53×#501 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | C53×#497 | C22 | 1 | 1 | yes | characteristic |
| 38 | C53×#496 | C22 | 1 | 1 | yes | characteristic |
| 39 | C53×#496 | C22 | 1 | 1 | yes | characteristic |
| 40 | C53×#496 | C22 | 1 | 1 | yes | characteristic |
| 41 | C53×#496 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | C53×#491 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | C53×#490 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | C53×#490 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | C53×#489 | C22 | 1 | 1 | yes | characteristic |
| 46 | C53×#489 | C22 | 1 | 1 | yes | characteristic |
| 47 | C53×#489 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | C53×#466 | — | 2 | 1 | no | — |
| 49 | C53×#465 | — | 2 | 1 | no | — |
| 50 | C53×#464 | — | 2 | 1 | no | — |
| 51 | C53×#463 | — | 2 | 1 | no | — |
| 52 | C53×#461 | — | 2 | 1 | no | — |
| 53 | C53×#459 | — | 2 | 1 | no | — |
| 54 | C53×#452 | — | 2 | 1 | no | — |
| 55 | C53×#449 | — | 2 | 1 | no | — |
| 56 | C53×#449 | — | 2 | 1 | no | — |
| 57 | C53×#449 | — | 2 | 1 | no | — |
| 58 | C53×#442 | — | 2 | 1 | no | — |
| 59 | C53×#440 | — | 2 | 1 | no | — |
| 60 | C53×#432 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | C53×#432 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | C2×#97×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | C53×#330 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | C53×#330 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | C53×#330 | C22 | 1 | 1 | yes | characteristic, complemented |
| 66 | C53×#330 | C22 | 1 | 1 | yes | characteristic, complemented |
| 67 | C53×#329 | C22 | 1 | 1 | yes | characteristic |
| 68 | C53×#329 | C22 | 1 | 1 | yes | characteristic |
| 69 | C53×#329 | C22 | 1 | 1 | yes | characteristic |
| 70 | C53×#329 | C22 | 1 | 1 | yes | characteristic |
| 71 | C53×#329 | C22 | 1 | 1 | yes | characteristic |
| 72 | C53×#329 | C22 | 1 | 1 | yes | characteristic |
| 73 | C53×#329 | C22 | 1 | 1 | yes | characteristic, complemented |
| 74 | C53×#329 | C22 | 1 | 1 | yes | characteristic, complemented |
| 75 | C2×#41×C53 | — | 2 | 1 | no | — |
| 76 | C2×#41×C53 | — | 2 | 1 | no | — |
| 77 | C2×#41×C53 | D4 | 1 | 1 | yes | characteristic |
| 78 | C2×#41×C53 | D4 | 1 | 1 | yes | characteristic |
| 79 | C23×C4×C53 | — | 2 | 1 | no | — |
| 80 | C2×Q16×C53 | — | 2 | 1 | no | — |
| 81 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 82 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 83 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 84 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 85 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 86 | C2×D8×C53 | — | 2 | 1 | no | — |
| 87 | C2×D8×C53 | — | 2 | 1 | no | — |
| 88 | C2×D8×C53 | — | 2 | 1 | no | — |
| 89 | C2×D8×C53 | — | 2 | 1 | no | — |
| 90 | C22×C8×C53 | — | 2 | 1 | no | — |
| 91 | C4⋊Q8×C53 | — | 2 | 1 | no | — |
| 92 | C4⋊Q8×C53 | D4 | 1 | 1 | yes | characteristic |
| 93 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 94 | #127×C53 | — | 2 | 1 | no | — |
| 95 | #127×C53 | D4 | 1 | 1 | yes | characteristic |
| 96 | #127×C53 | C23 | 1 | 1 | yes | characteristic |
| 97 | #126×C53 | — | 2 | 1 | no | — |
| 98 | #126×C53 | — | 2 | 1 | no | — |
| 99 | #126×C53 | — | 2 | 1 | no | — |
| 100 | #126×C53 | — | 2 | 1 | no | — |
| 101 | #126×C53 | — | 2 | 1 | no | — |
| 102 | #126×C53 | — | 2 | 1 | no | — |
| 103 | #125×C53 | — | 2 | 1 | no | — |
| 104 | #125×C53 | — | 2 | 1 | no | — |
| 105 | #125×C53 | C23 | 1 | 1 | yes | characteristic |
| 106 | #125×C53 | C23 | 1 | 1 | yes | characteristic |
| 107 | #124×C53 | — | 2 | 1 | no | — |
| 108 | #124×C53 | — | 2 | 1 | no | — |
| 109 | #124×C53 | — | 2 | 1 | no | — |
| 110 | #124×C53 | — | 2 | 1 | no | — |
| 111 | #124×C53 | — | 2 | 1 | no | — |
| 112 | #124×C53 | C23 | 1 | 1 | yes | characteristic |
| 113 | #124×C53 | C23 | 1 | 1 | yes | characteristic |
| 114 | #124×C53 | C23 | 1 | 1 | yes | characteristic |
| 115 | #124×C53 | C23 | 1 | 1 | yes | characteristic |
| 116 | #123×C53 | — | 2 | 1 | no | — |
| 117 | #123×C53 | — | 2 | 1 | no | — |
| 118 | #123×C53 | — | 2 | 1 | no | — |
| 119 | #123×C53 | — | 2 | 1 | no | — |
| 120 | #123×C53 | — | 2 | 1 | no | — |
| 121 | #123×C53 | — | 2 | 1 | no | — |
| 122 | #123×C53 | — | 2 | 1 | no | — |
| 123 | #123×C53 | — | 2 | 1 | no | — |
| 124 | #123×C53 | — | 2 | 1 | no | — |
| 125 | #123×C53 | — | 2 | 1 | no | — |
| 126 | #123×C53 | — | 2 | 1 | no | — |
| 127 | #123×C53 | — | 2 | 1 | no | — |
| 128 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 129 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 130 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 131 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 132 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 133 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 134 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 135 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 136 | C22⋊Q8×C53 | D4 | 1 | 1 | yes | characteristic |
| 137 | C22⋊Q8×C53 | D4 | 1 | 1 | yes | characteristic |
| 138 | #121×C53 | — | 2 | 1 | no | — |
| 139 | #121×C53 | — | 2 | 1 | no | — |
| 140 | #121×C53 | — | 2 | 1 | no | — |
| 141 | #121×C53 | — | 2 | 1 | no | — |
| 142 | #121×C53 | — | 2 | 1 | no | — |
| 143 | #121×C53 | — | 2 | 1 | no | — |
| 144 | #121×C53 | — | 2 | 1 | no | — |
| 145 | #121×C53 | — | 2 | 1 | no | — |
| 146 | #121×C53 | — | 2 | 1 | no | — |
| 147 | #121×C53 | — | 2 | 1 | no | — |
| 148 | #121×C53 | — | 2 | 1 | no | — |
| 149 | #121×C53 | — | 2 | 1 | no | — |
| 150 | #121×C53 | — | 2 | 1 | no | — |
| 151 | #121×C53 | — | 2 | 1 | no | — |
| 152 | #121×C53 | — | 2 | 1 | no | — |
| 153 | #121×C53 | — | 2 | 1 | no | — |
| 154 | #121×C53 | D4 | 1 | 1 | yes | characteristic |
| 155 | #121×C53 | D4 | 1 | 1 | yes | characteristic |
| 156 | #120×C53 | — | 2 | 1 | no | — |
| 157 | #120×C53 | — | 2 | 1 | no | — |
| 158 | #120×C53 | — | 2 | 1 | no | — |
| 159 | #120×C53 | — | 2 | 1 | no | — |
| 160 | #120×C53 | — | 2 | 1 | no | — |
| 161 | #120×C53 | — | 2 | 1 | no | — |
| 162 | C4×Q8×C53 | D4 | 1 | 1 | yes | characteristic |
| 163 | C4×Q8×C53 | D4 | 1 | 1 | yes | characteristic |
| 164 | C4×D4×C53 | — | 2 | 1 | no | — |
| 165 | C4×D4×C53 | — | 2 | 1 | no | — |
| 166 | C4×D4×C53 | — | 2 | 1 | no | — |
| 167 | C4×D4×C53 | — | 2 | 1 | no | — |
| 168 | C4×D4×C53 | — | 2 | 1 | no | — |
| 169 | C4×D4×C53 | — | 2 | 1 | no | — |
| 170 | C4×D4×C53 | — | 2 | 1 | no | — |
| 171 | C4×D4×C53 | — | 2 | 1 | no | — |
| 172 | C4×D4×C53 | — | 2 | 1 | no | — |
| 173 | C4×D4×C53 | — | 2 | 1 | no | — |
| 174 | C4×D4×C53 | D4 | 1 | 1 | yes | characteristic |
| 175 | C4×D4×C53 | D4 | 1 | 1 | yes | characteristic |
| 176 | #117×C53 | — | 2 | 1 | no | — |
| 177 | #117×C53 | — | 2 | 1 | no | — |
| 178 | #117×C53 | — | 2 | 1 | no | — |
| 179 | C2×C42×C53 | — | 2 | 1 | no | — |
| 180 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 181 | #107×C53 | — | 2 | 1 | no | — |
| 182 | #106×C53 | — | 2 | 1 | no | — |
| 183 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 184 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 185 | #103×C53 | — | 2 | 1 | no | — |
| 186 | #103×C53 | — | 2 | 1 | no | — |
| 187 | #103×C53 | — | 2 | 1 | no | — |
| 188 | #103×C53 | — | 2 | 1 | no | — |
| 189 | #103×C53 | — | 2 | 1 | no | — |
| 190 | #102×C53 | — | 2 | 1 | no | — |
| 191 | #102×C53 | — | 2 | 1 | no | — |
| 192 | #102×C53 | — | 2 | 1 | no | — |
| 193 | #102×C53 | — | 2 | 1 | no | — |
| 194 | #102×C53 | — | 2 | 1 | no | — |
| 195 | #102×C53 | — | 2 | 1 | no | — |
| 196 | #102×C53 | — | 2 | 1 | no | — |
| 197 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 198 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 199 | #97×C53 | — | 2 | 1 | no | — |
| 200 | #97×C53 | C23 | 1 | 1 | yes | characteristic |
| 201 | #97×C53 | C23 | 1 | 1 | yes | characteristic |
| 202 | #97×C53 | C23 | 1 | 1 | yes | characteristic |
| 203 | #97×C53 | C23 | 1 | 1 | yes | characteristic |
| 204 | #97×C53 | C23 | 1 | 1 | yes | characteristic |
| 205 | #97×C53 | C23 | 1 | 1 | yes | characteristic |
| 206 | C24×C53 | — | 2 | 1 | no | — |
| 207 | #41×C53 | — | 8 | 1 | no | — |
| 208 | #41×C53 | — | 8 | 1 | no | — |
| 209 | #41×C53 | — | 8 | 2 | no | — |
| 210 | #41×C53 | — | 8 | 1 | no | — |
| 211 | #41×C53 | — | 8 | 1 | no | — |
| 212 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 213 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 214 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 215 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 216 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 217 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 218 | C2×D4×C53 | — | 2 | 1 | no | — |
| 219 | C2×D4×C53 | — | 2 | 1 | no | — |
| 220 | C2×D4×C53 | — | 2 | 1 | no | — |
| 221 | C2×D4×C53 | — | 2 | 1 | no | — |
| 222 | C2×D4×C53 | — | 2 | 1 | no | — |
| 223 | C2×D4×C53 | — | 2 | 1 | no | — |
| 224 | C2×D4×C53 | — | 2 | 1 | no | — |
| 225 | C2×D4×C53 | — | 2 | 1 | no | — |
| 226 | C2×D4×C53 | — | 2 | 1 | no | — |
| 227 | C2×D4×C53 | — | 2 | 1 | no | — |
| 228 | C2×D4×C53 | — | 2 | 1 | no | — |
| 229 | C2×D4×C53 | — | 2 | 1 | no | — |
| 230 | C2×D4×C53 | — | 2 | 1 | no | — |
| 231 | C2×D4×C53 | — | 2 | 1 | no | — |
| 232 | C2×D4×C53 | — | 2 | 1 | no | — |
| 233 | C2×D4×C53 | — | 2 | 1 | no | — |
| 234 | C2×D4×C53 | — | 4 | 1 | no | — |
| 235 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 236 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 239 | C22×C4×C53 | — | 2 | 1 | no | — |
| 240 | C22×C4×C53 | — | 2 | 1 | no | — |
| 241 | C22×C4×C53 | — | 2 | 1 | no | — |
| 242 | C22×C4×C53 | — | 2 | 1 | no | — |
| 243 | C22×C4×C53 | — | 2 | 1 | no | — |
| 244 | C22×C4×C53 | — | 2 | 1 | no | — |
| 245 | C22×C4×C53 | — | 2 | 1 | no | — |
| 246 | C22×C4×C53 | — | 2 | 1 | no | — |
| 247 | C22×C4×C53 | — | 2 | 1 | no | — |
| 248 | C22×C4×C53 | — | 4 | 1 | no | — |
| 249 | C22×C4×C53 | — | 8 | 2 | no | — |
| 250 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 251 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 252 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 253 | Q16×C53 | — | 8 | 1 | no | — |
| 254 | SD16×C53 | — | 4 | 2 | no | — |
| 255 | SD16×C53 | — | 8 | 1 | no | — |
| 256 | SD16×C53 | — | 8 | 1 | no | — |
| 257 | SD16×C53 | — | 8 | 1 | no | — |
| 258 | SD16×C53 | — | 8 | 1 | no | — |
| 259 | D8×C53 | — | 4 | 2 | no | — |
| 260 | D8×C53 | — | 8 | 1 | no | — |
| 261 | D8×C53 | — | 8 | 1 | no | — |
| 262 | D8×C53 | — | 8 | 1 | no | — |
| 263 | C2×C8×C53 | — | 2 | 1 | no | — |
| 264 | C2×C8×C53 | — | 2 | 1 | no | — |
| 265 | C2×C8×C53 | — | 2 | 1 | no | — |
| 266 | C2×C8×C53 | — | 2 | 1 | no | — |
| 267 | C2×C8×C53 | — | 2 | 1 | no | — |
| 268 | C2×C8×C53 | — | 2 | 1 | no | — |
| 269 | C2×C8×C53 | — | 4 | 2 | no | — |
| 270 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 271 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 272 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 273 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 274 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 275 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 276 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 277 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 278 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 279 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 280 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 281 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 282 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 283 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 284 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 285 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 286 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 287 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 288 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 289 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 290 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 291 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 292 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 293 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 294 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 295 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 296 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 297 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 298 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 299 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 300 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 301 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 302 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 303 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 304 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 305 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 306 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 307 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 308 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 309 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 310 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 311 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 312 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 313 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 314 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 315 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 316 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 317 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 318 | C42×C53 | — | 2 | 1 | no | — |
| 319 | C42×C53 | — | 2 | 1 | no | — |
| 320 | C42×C53 | — | 2 | 1 | no | — |
| 321 | C42×C53 | — | 2 | 1 | no | — |
| 322 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 323 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 324 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 325 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 326 | C23×C53 | — | 2 | 1 | no | — |
| 327 | C23×C53 | — | 2 | 1 | no | — |
| 328 | C23×C53 | — | 2 | 1 | no | — |
| 329 | C23×C53 | — | 2 | 1 | no | — |
| 330 | C23×C53 | — | 4 | 1 | no | — |
| 331 | C23×C53 | — | 8 | 1 | no | — |
| 332 | C23×C53 | — | 8 | 1 | no | — |
| 333 | C23×C53 | — | 8 | 1 | no | — |
| 334 | C23×C53 | #120 | 1 | 1 | yes | characteristic |
| 335 | Q8×C53 | — | 4 | 1 | no | — |
| 336 | Q8×C53 | — | 4 | 1 | no | — |
| 337 | Q8×C53 | — | 4 | 1 | no | — |
| 338 | Q8×C53 | — | 4 | 1 | no | — |
| 339 | Q8×C53 | — | 4 | 1 | no | — |
| 340 | Q8×C53 | — | 4 | 1 | no | — |
| 341 | Q8×C53 | — | 8 | 1 | no | — |
| 342 | D4×C53 | — | 4 | 1 | no | — |
| 343 | D4×C53 | — | 4 | 1 | no | — |
| 344 | D4×C53 | — | 4 | 1 | no | — |
| 345 | D4×C53 | — | 4 | 1 | no | — |
| 346 | D4×C53 | — | 4 | 1 | no | — |
| 347 | D4×C53 | — | 4 | 1 | no | — |
| 348 | D4×C53 | — | 4 | 1 | no | — |
| 349 | D4×C53 | — | 4 | 1 | no | — |
| 350 | D4×C53 | — | 4 | 1 | no | — |
| 351 | D4×C53 | — | 4 | 1 | no | — |
| 352 | D4×C53 | — | 8 | 1 | no | — |
| 353 | D4×C53 | — | 8 | 1 | no | — |
| 354 | D4×C53 | — | 8 | 1 | no | — |
| 355 | D4×C53 | — | 8 | 1 | no | — |
| 356 | D4×C53 | — | 8 | 1 | no | — |
| 357 | D4×C53 | — | 8 | 1 | no | — |
| 358 | D4×C53 | — | 8 | 1 | no | — |
| 359 | D4×C53 | — | 8 | 1 | no | — |
| 360 | D4×C53 | — | 8 | 1 | no | — |
| 361 | D4×C53 | — | 8 | 1 | no | — |
| 362 | D4×C53 | — | 8 | 1 | no | — |
| 363 | D4×C53 | — | 8 | 1 | no | — |
| 364 | D4×C53 | — | 8 | 1 | no | — |
| 365 | D4×C53 | — | 8 | 2 | no | — |
| 366 | C2×C4×C53 | — | 2 | 1 | no | — |
| 367 | C2×C4×C53 | — | 2 | 1 | no | — |
| 368 | C2×C4×C53 | — | 2 | 1 | no | — |
| 369 | C2×C4×C53 | — | 2 | 1 | no | — |
| 370 | C2×C4×C53 | — | 2 | 1 | no | — |
| 371 | C2×C4×C53 | — | 2 | 1 | no | — |
| 372 | C2×C4×C53 | — | 2 | 1 | no | — |
| 373 | C2×C4×C53 | — | 2 | 1 | no | — |
| 374 | C2×C4×C53 | — | 4 | 1 | no | — |
| 375 | C2×C4×C53 | — | 4 | 1 | no | — |
| 376 | C2×C4×C53 | — | 4 | 1 | no | — |
| 377 | C2×C4×C53 | — | 4 | 2 | no | — |
| 378 | C2×C4×C53 | — | 4 | 2 | no | — |
| 379 | C2×C4×C53 | — | 4 | 2 | no | — |
| 380 | C2×C4×C53 | — | 4 | 2 | no | — |
| 381 | C2×C4×C53 | — | 4 | 1 | no | — |
| 382 | C2×C4×C53 | — | 8 | 2 | no | — |
| 383 | C2×C4×C53 | — | 8 | 1 | no | — |
| 384 | C2×C4×C53 | — | 8 | 1 | no | — |
| 385 | C2×C4×C53 | — | 8 | 1 | no | — |
| 386 | C2×C4×C53 | — | 8 | 1 | no | — |
| 387 | C2×C4×C53 | — | 8 | 1 | no | — |
| 388 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 389 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 390 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 391 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 392 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 393 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 394 | C8×C53 | — | 2 | 2 | no | — |
| 395 | C8×C53 | — | 4 | 1 | no | — |
| 396 | C8×C53 | — | 4 | 1 | no | — |
| 397 | C8×C53 | — | 4 | 1 | no | — |
| 398 | C8×C53 | — | 4 | 1 | no | — |
| 399 | C8×C53 | — | 4 | 1 | no | — |
| 400 | #19010 | C53 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 401 | C22×C53 | — | 2 | 1 | no | — |
| 402 | C22×C53 | — | 2 | 1 | no | — |
| 403 | C22×C53 | — | 2 | 1 | no | — |
| 404 | C22×C53 | — | 4 | 1 | no | — |
| 405 | C22×C53 | — | 4 | 1 | no | — |
| 406 | C22×C53 | — | 4 | 1 | no | — |
| 407 | C22×C53 | — | 4 | 1 | no | — |
| 408 | C22×C53 | — | 4 | 1 | no | — |
| 409 | C22×C53 | — | 4 | 1 | no | — |
| 410 | C22×C53 | — | 4 | 1 | no | — |
| 411 | C22×C53 | — | 4 | 1 | no | — |
| 412 | C22×C53 | — | 4 | 1 | no | — |
| 413 | C22×C53 | — | 4 | 1 | no | — |
| 414 | C22×C53 | — | 4 | 1 | no | — |
| 415 | C22×C53 | — | 4 | 1 | no | — |
| 416 | C22×C53 | — | 8 | 4 | no | — |
| 417 | C22×C53 | — | 8 | 1 | no | — |
| 418 | C22×C53 | — | 8 | 1 | no | — |
| 419 | C22×C53 | — | 8 | 1 | no | — |
| 420 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 421 | C4×C53 | — | 2 | 1 | no | — |
| 422 | C4×C53 | — | 2 | 1 | no | — |
| 423 | C4×C53 | — | 2 | 1 | no | — |
| 424 | C4×C53 | — | 2 | 1 | no | — |
| 425 | C4×C53 | — | 2 | 1 | no | — |
| 426 | C4×C53 | — | 2 | 1 | no | — |
| 427 | C4×C53 | — | 4 | 1 | no | — |
| 428 | C4×C53 | — | 4 | 1 | no | — |
| 429 | C4×C53 | — | 4 | 1 | no | — |
| 430 | C4×C53 | — | 4 | 1 | no | — |
| 431 | C4×C53 | — | 4 | 1 | no | — |
| 432 | C4×C53 | — | 4 | 1 | no | — |
| 433 | C4×C53 | — | 4 | 1 | no | — |
| 434 | C4×C53 | — | 4 | 1 | no | — |
| 435 | C4×C53 | — | 8 | 1 | no | — |
| 436 | #3529 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 437 | #3219 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 438 | #3214 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 439 | #3180 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 440 | #1664 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 441 | #1662 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 442 | #1661 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 443 | #1659 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 444 | #1657 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 445 | #1656 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 446 | #1656 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 447 | #1655 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 448 | #1535 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 449 | #1532 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 450 | #1530 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 451 | C2×C53 | — | 4 | 1 | no | — |
| 452 | C2×C53 | — | 8 | 1 | no | — |
| 453 | C2×C53 | — | 8 | 1 | no | — |
| 454 | C2×C53 | — | 8 | 1 | no | — |
| 455 | C2×C53 | — | 8 | 1 | no | — |
| 456 | C2×C53 | — | 16 | 1 | no | — |
| 457 | C2×C53 | #3018 | 1 | 1 | yes | characteristic |
| 458 | C2×C53 | #3019 | 1 | 1 | yes | characteristic |
| 459 | C2×C53 | #3021 | 1 | 1 | yes | characteristic |
| 460 | #563 | — | 2 | 1 | no | — |
| 461 | #563 | C22×C53 | 1 | 1 | yes | characteristic |
| 462 | #562 | — | 2 | 1 | no | — |
| 463 | #562 | — | 2 | 1 | no | — |
| 464 | #562 | C22×C53 | 1 | 1 | yes | characteristic |
| 465 | #562 | C22×C53 | 1 | 1 | yes | characteristic |
| 466 | H(3,𝔽4) | C22×C53 | 1 | 1 | yes | characteristic |
| 467 | #560 | — | 2 | 1 | no | — |
| 468 | #560 | — | 2 | 1 | no | — |
| 469 | #560 | — | 2 | 1 | no | — |
| 470 | #532 | — | 2 | 1 | no | — |
| 471 | #532 | C22×C53 | 1 | 1 | yes | characteristic |
| 472 | #532 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 473 | #529 | — | 2 | 1 | no | — |
| 474 | #529 | — | 2 | 1 | no | — |
| 475 | #529 | C22×C53 | 1 | 1 | yes | characteristic |
| 476 | #529 | C22×C53 | 1 | 1 | yes | characteristic |
| 477 | #525 | — | 2 | 1 | no | — |
| 478 | #525 | — | 2 | 1 | no | — |
| 479 | #525 | — | 2 | 1 | no | — |
| 480 | #501 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 481 | #497 | C22×C53 | 1 | 1 | yes | characteristic |
| 482 | #496 | C22×C53 | 1 | 1 | yes | characteristic |
| 483 | #496 | C22×C53 | 1 | 1 | yes | characteristic |
| 484 | #496 | C22×C53 | 1 | 1 | yes | characteristic |
| 485 | #496 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 486 | #491 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 487 | #490 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 488 | #490 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 489 | #489 | C22×C53 | 1 | 1 | yes | characteristic |
| 490 | #489 | C22×C53 | 1 | 1 | yes | characteristic |
| 491 | #489 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 492 | #466 | — | 2 | 1 | no | — |
| 493 | #465 | — | 2 | 1 | no | — |
| 494 | #464 | — | 2 | 1 | no | — |
| 495 | #463 | — | 2 | 1 | no | — |
| 496 | #461 | — | 2 | 1 | no | — |
| 497 | #459 | — | 2 | 1 | no | — |
| 498 | #452 | — | 2 | 1 | no | — |
| 499 | #449 | — | 2 | 1 | no | — |
| 500 | #449 | — | 2 | 1 | no | — |
| 501 | #449 | — | 2 | 1 | no | — |
| 502 | #442 | — | 2 | 1 | no | — |
| 503 | #440 | — | 2 | 1 | no | — |
| 504 | #432 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 505 | #432 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 506 | C2×#97 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 507 | #330 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 508 | #330 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 509 | #330 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 510 | #330 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 511 | #329 | C22×C53 | 1 | 1 | yes | characteristic |
| 512 | #329 | C22×C53 | 1 | 1 | yes | characteristic |
| 513 | #329 | C22×C53 | 1 | 1 | yes | characteristic |
| 514 | #329 | C22×C53 | 1 | 1 | yes | characteristic |
| 515 | #329 | C22×C53 | 1 | 1 | yes | characteristic |
| 516 | #329 | C22×C53 | 1 | 1 | yes | characteristic |
| 517 | #329 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 518 | #329 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 519 | C53 | #19010 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 520 | C2×#41 | — | 2 | 1 | no | — |
| 521 | C2×#41 | — | 2 | 1 | no | — |
| 522 | C2×#41 | D4×C53 | 1 | 1 | yes | characteristic |
| 523 | C2×#41 | D4×C53 | 1 | 1 | yes | characteristic |
| 524 | C23×C4 | — | 2 | 1 | no | — |
| 525 | C2×Q16 | — | 2 | 1 | no | — |
| 526 | C2×SD16 | — | 2 | 1 | no | — |
| 527 | C2×SD16 | — | 2 | 1 | no | — |
| 528 | C2×SD16 | — | 2 | 1 | no | — |
| 529 | C2×SD16 | — | 2 | 1 | no | — |
| 530 | C2×SD16 | — | 2 | 1 | no | — |
| 531 | C2×D8 | — | 2 | 1 | no | — |
| 532 | C2×D8 | — | 2 | 1 | no | — |
| 533 | C2×D8 | — | 2 | 1 | no | — |
| 534 | C2×D8 | — | 2 | 1 | no | — |
| 535 | C22×C8 | — | 2 | 1 | no | — |
| 536 | C4⋊Q8 | — | 2 | 1 | no | — |
| 537 | C4⋊Q8 | D4×C53 | 1 | 1 | yes | characteristic |
| 538 | C4⋊Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 539 | #127 | — | 2 | 1 | no | — |
| 540 | #127 | D4×C53 | 1 | 1 | yes | characteristic |
| 541 | #127 | C23×C53 | 1 | 1 | yes | characteristic |
| 542 | #126 | — | 2 | 1 | no | — |
| 543 | #126 | — | 2 | 1 | no | — |
| 544 | #126 | — | 2 | 1 | no | — |
| 545 | #126 | — | 2 | 1 | no | — |
| 546 | #126 | — | 2 | 1 | no | — |
| 547 | #126 | — | 2 | 1 | no | — |
| 548 | #125 | — | 2 | 1 | no | — |
| 549 | #125 | — | 2 | 1 | no | — |
| 550 | #125 | C23×C53 | 1 | 1 | yes | characteristic |
| 551 | #125 | C23×C53 | 1 | 1 | yes | characteristic |
| 552 | #124 | — | 2 | 1 | no | — |
| 553 | #124 | — | 2 | 1 | no | — |
| 554 | #124 | — | 2 | 1 | no | — |
| 555 | #124 | — | 2 | 1 | no | — |
| 556 | #124 | — | 2 | 1 | no | — |
| 557 | #124 | C23×C53 | 1 | 1 | yes | characteristic |
| 558 | #124 | C23×C53 | 1 | 1 | yes | characteristic |
| 559 | #124 | C23×C53 | 1 | 1 | yes | characteristic |
| 560 | #124 | C23×C53 | 1 | 1 | yes | characteristic |
| 561 | #123 | — | 2 | 1 | no | — |
| 562 | #123 | — | 2 | 1 | no | — |
| 563 | #123 | — | 2 | 1 | no | — |
| 564 | #123 | — | 2 | 1 | no | — |
| 565 | #123 | — | 2 | 1 | no | — |
| 566 | #123 | — | 2 | 1 | no | — |
| 567 | #123 | — | 2 | 1 | no | — |
| 568 | #123 | — | 2 | 1 | no | — |
| 569 | #123 | — | 2 | 1 | no | — |
| 570 | #123 | — | 2 | 1 | no | — |
| 571 | #123 | — | 2 | 1 | no | — |
| 572 | #123 | — | 2 | 1 | no | — |
| 573 | C22⋊Q8 | — | 2 | 1 | no | — |
| 574 | C22⋊Q8 | — | 2 | 1 | no | — |
| 575 | C22⋊Q8 | — | 2 | 1 | no | — |
| 576 | C22⋊Q8 | — | 2 | 1 | no | — |
| 577 | C22⋊Q8 | — | 2 | 1 | no | — |
| 578 | C22⋊Q8 | — | 2 | 1 | no | — |
| 579 | C22⋊Q8 | — | 2 | 1 | no | — |
| 580 | C22⋊Q8 | — | 2 | 1 | no | — |
| 581 | C22⋊Q8 | D4×C53 | 1 | 1 | yes | characteristic |
| 582 | C22⋊Q8 | D4×C53 | 1 | 1 | yes | characteristic |
| 583 | #121 | — | 2 | 1 | no | — |
| 584 | #121 | — | 2 | 1 | no | — |
| 585 | #121 | — | 2 | 1 | no | — |
| 586 | #121 | — | 2 | 1 | no | — |
| 587 | #121 | — | 2 | 1 | no | — |
| 588 | #121 | — | 2 | 1 | no | — |
| 589 | #121 | — | 2 | 1 | no | — |
| 590 | #121 | — | 2 | 1 | no | — |
| 591 | #121 | — | 2 | 1 | no | — |
| 592 | #121 | — | 2 | 1 | no | — |
| 593 | #121 | — | 2 | 1 | no | — |
| 594 | #121 | — | 2 | 1 | no | — |
| 595 | #121 | — | 2 | 1 | no | — |
| 596 | #121 | — | 2 | 1 | no | — |
| 597 | #121 | — | 2 | 1 | no | — |
| 598 | #121 | — | 2 | 1 | no | — |
| 599 | #121 | D4×C53 | 1 | 1 | yes | characteristic |
| 600 | #121 | D4×C53 | 1 | 1 | yes | characteristic |
| 601 | #120 | — | 2 | 1 | no | — |
| 602 | #120 | — | 2 | 1 | no | — |
| 603 | #120 | — | 2 | 1 | no | — |
| 604 | #120 | — | 2 | 1 | no | — |
| 605 | #120 | — | 2 | 1 | no | — |
| 606 | #120 | — | 2 | 1 | no | — |
| 607 | C4×Q8 | D4×C53 | 1 | 1 | yes | characteristic |
| 608 | C4×Q8 | D4×C53 | 1 | 1 | yes | characteristic |
| 609 | C4×D4 | — | 2 | 1 | no | — |
| 610 | C4×D4 | — | 2 | 1 | no | — |
| 611 | C4×D4 | — | 2 | 1 | no | — |
| 612 | C4×D4 | — | 2 | 1 | no | — |
| 613 | C4×D4 | — | 2 | 1 | no | — |
| 614 | C4×D4 | — | 2 | 1 | no | — |
| 615 | C4×D4 | — | 2 | 1 | no | — |
| 616 | C4×D4 | — | 2 | 1 | no | — |
| 617 | C4×D4 | — | 2 | 1 | no | — |
| 618 | C4×D4 | — | 2 | 1 | no | — |
| 619 | C4×D4 | D4×C53 | 1 | 1 | yes | characteristic |
| 620 | C4×D4 | D4×C53 | 1 | 1 | yes | characteristic |
| 621 | #117 | — | 2 | 1 | no | — |
| 622 | #117 | — | 2 | 1 | no | — |
| 623 | #117 | — | 2 | 1 | no | — |
| 624 | C2×C42 | — | 2 | 1 | no | — |
| 625 | C2×C42 | C23×C53 | 1 | 1 | yes | characteristic |
| 626 | #107 | — | 2 | 1 | no | — |
| 627 | #106 | — | 2 | 1 | no | — |
| 628 | C4⋊C8 | — | 2 | 1 | no | — |
| 629 | C4⋊C8 | — | 2 | 1 | no | — |
| 630 | #103 | — | 2 | 1 | no | — |
| 631 | #103 | — | 2 | 1 | no | — |
| 632 | #103 | — | 2 | 1 | no | — |
| 633 | #103 | — | 2 | 1 | no | — |
| 634 | #103 | — | 2 | 1 | no | — |
| 635 | #102 | — | 2 | 1 | no | — |
| 636 | #102 | — | 2 | 1 | no | — |
| 637 | #102 | — | 2 | 1 | no | — |
| 638 | #102 | — | 2 | 1 | no | — |
| 639 | #102 | — | 2 | 1 | no | — |
| 640 | #102 | — | 2 | 1 | no | — |
| 641 | #102 | — | 2 | 1 | no | — |
| 642 | C22⋊C8 | — | 2 | 1 | no | — |
| 643 | C22⋊C8 | — | 2 | 1 | no | — |
| 644 | #97 | — | 2 | 1 | no | — |
| 645 | #97 | C23×C53 | 1 | 1 | yes | characteristic |
| 646 | #97 | C23×C53 | 1 | 1 | yes | characteristic |
| 647 | #97 | C23×C53 | 1 | 1 | yes | characteristic |
| 648 | #97 | C23×C53 | 1 | 1 | yes | characteristic |
| 649 | #97 | C23×C53 | 1 | 1 | yes | characteristic |
| 650 | #97 | C23×C53 | 1 | 1 | yes | characteristic |
| 651 | C24 | — | 2 | 1 | no | — |
| 652 | #41 | — | 8 | 1 | no | — |
| 653 | #41 | — | 8 | 1 | no | — |
| 654 | #41 | — | 8 | 2 | no | — |
| 655 | #41 | — | 8 | 1 | no | — |
| 656 | #41 | — | 8 | 1 | no | — |
| 657 | C2×Q8 | — | 2 | 1 | no | — |
| 658 | C2×Q8 | — | 2 | 1 | no | — |
| 659 | C2×Q8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 660 | C2×Q8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 661 | C2×Q8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 662 | C2×Q8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 663 | C2×D4 | — | 2 | 1 | no | — |
| 664 | C2×D4 | — | 2 | 1 | no | — |
| 665 | C2×D4 | — | 2 | 1 | no | — |
| 666 | C2×D4 | — | 2 | 1 | no | — |
| 667 | C2×D4 | — | 2 | 1 | no | — |
| 668 | C2×D4 | — | 2 | 1 | no | — |
| 669 | C2×D4 | — | 2 | 1 | no | — |
| 670 | C2×D4 | — | 2 | 1 | no | — |
| 671 | C2×D4 | — | 2 | 1 | no | — |
| 672 | C2×D4 | — | 2 | 1 | no | — |
| 673 | C2×D4 | — | 2 | 1 | no | — |
| 674 | C2×D4 | — | 2 | 1 | no | — |
| 675 | C2×D4 | — | 2 | 1 | no | — |
| 676 | C2×D4 | — | 2 | 1 | no | — |
| 677 | C2×D4 | — | 2 | 1 | no | — |
| 678 | C2×D4 | — | 2 | 1 | no | — |
| 679 | C2×D4 | — | 4 | 1 | no | — |
| 680 | C2×D4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 681 | C2×D4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 682 | C2×D4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 683 | C2×D4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 684 | C22×C4 | — | 2 | 1 | no | — |
| 685 | C22×C4 | — | 2 | 1 | no | — |
| 686 | C22×C4 | — | 2 | 1 | no | — |
| 687 | C22×C4 | — | 2 | 1 | no | — |
| 688 | C22×C4 | — | 2 | 1 | no | — |
| 689 | C22×C4 | — | 2 | 1 | no | — |
| 690 | C22×C4 | — | 2 | 1 | no | — |
| 691 | C22×C4 | — | 2 | 1 | no | — |
| 692 | C22×C4 | — | 2 | 1 | no | — |
| 693 | C22×C4 | — | 4 | 1 | no | — |
| 694 | C22×C4 | — | 8 | 2 | no | — |
| 695 | C22×C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 696 | C22×C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 697 | C22×C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 698 | Q16 | — | 8 | 1 | no | — |
| 699 | SD16 | — | 4 | 2 | no | — |
| 700 | SD16 | — | 8 | 1 | no | — |
| 701 | SD16 | — | 8 | 1 | no | — |
| 702 | SD16 | — | 8 | 1 | no | — |
| 703 | SD16 | — | 8 | 1 | no | — |
| 704 | D8 | — | 4 | 2 | no | — |
| 705 | D8 | — | 8 | 1 | no | — |
| 706 | D8 | — | 8 | 1 | no | — |
| 707 | D8 | — | 8 | 1 | no | — |
| 708 | C2×C8 | — | 2 | 1 | no | — |
| 709 | C2×C8 | — | 2 | 1 | no | — |
| 710 | C2×C8 | — | 2 | 1 | no | — |
| 711 | C2×C8 | — | 2 | 1 | no | — |
| 712 | C2×C8 | — | 2 | 1 | no | — |
| 713 | C2×C8 | — | 2 | 1 | no | — |
| 714 | C2×C8 | — | 4 | 2 | no | — |
| 715 | C4⋊C4 | — | 2 | 1 | no | — |
| 716 | C4⋊C4 | — | 2 | 1 | no | — |
| 717 | C4⋊C4 | — | 2 | 1 | no | — |
| 718 | C4⋊C4 | — | 2 | 1 | no | — |
| 719 | C4⋊C4 | — | 2 | 1 | no | — |
| 720 | C4⋊C4 | — | 2 | 1 | no | — |
| 721 | C4⋊C4 | — | 2 | 1 | no | — |
| 722 | C4⋊C4 | — | 2 | 1 | no | — |
| 723 | C4⋊C4 | — | 2 | 1 | no | — |
| 724 | C4⋊C4 | — | 2 | 1 | no | — |
| 725 | C4⋊C4 | — | 2 | 1 | no | — |
| 726 | C4⋊C4 | — | 2 | 1 | no | — |
| 727 | C4⋊C4 | — | 2 | 1 | no | — |
| 728 | C4⋊C4 | — | 2 | 1 | no | — |
| 729 | C4⋊C4 | — | 2 | 1 | no | — |
| 730 | C4⋊C4 | — | 2 | 1 | no | — |
| 731 | C4⋊C4 | — | 2 | 1 | no | — |
| 732 | C4⋊C4 | — | 2 | 1 | no | — |
| 733 | C4⋊C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 734 | C4⋊C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 735 | C4⋊C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 736 | C4⋊C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 737 | C22⋊C4 | — | 2 | 1 | no | — |
| 738 | C22⋊C4 | — | 2 | 1 | no | — |
| 739 | C22⋊C4 | — | 2 | 1 | no | — |
| 740 | C22⋊C4 | — | 2 | 1 | no | — |
| 741 | C22⋊C4 | — | 2 | 1 | no | — |
| 742 | C22⋊C4 | — | 2 | 1 | no | — |
| 743 | C22⋊C4 | — | 2 | 1 | no | — |
| 744 | C22⋊C4 | — | 2 | 1 | no | — |
| 745 | C22⋊C4 | — | 2 | 1 | no | — |
| 746 | C22⋊C4 | — | 2 | 1 | no | — |
| 747 | C22⋊C4 | — | 2 | 1 | no | — |
| 748 | C22⋊C4 | — | 2 | 1 | no | — |
| 749 | C22⋊C4 | — | 2 | 1 | no | — |
| 750 | C22⋊C4 | — | 2 | 1 | no | — |
| 751 | C22⋊C4 | — | 2 | 1 | no | — |
| 752 | C22⋊C4 | — | 2 | 1 | no | — |
| 753 | C22⋊C4 | — | 2 | 1 | no | — |
| 754 | C22⋊C4 | — | 2 | 1 | no | — |
| 755 | C22⋊C4 | — | 2 | 1 | no | — |
| 756 | C22⋊C4 | — | 2 | 1 | no | — |
| 757 | C22⋊C4 | — | 2 | 1 | no | — |
| 758 | C22⋊C4 | — | 2 | 1 | no | — |
| 759 | C22⋊C4 | — | 2 | 1 | no | — |
| 760 | C22⋊C4 | — | 2 | 1 | no | — |
| 761 | C22⋊C4 | — | 4 | 1 | no | — |
| 762 | C22⋊C4 | — | 4 | 1 | no | — |
| 763 | C42 | — | 2 | 1 | no | — |
| 764 | C42 | — | 2 | 1 | no | — |
| 765 | C42 | — | 2 | 1 | no | — |
| 766 | C42 | — | 2 | 1 | no | — |
| 767 | C42 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 768 | C42 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 769 | C42 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 770 | C42 | C24×C53 | 1 | 1 | yes | characteristic |
| 771 | C23 | — | 2 | 1 | no | — |
| 772 | C23 | — | 2 | 1 | no | — |
| 773 | C23 | — | 2 | 1 | no | — |
| 774 | C23 | — | 2 | 1 | no | — |
| 775 | C23 | — | 4 | 1 | no | — |
| 776 | C23 | — | 8 | 1 | no | — |
| 777 | C23 | — | 8 | 1 | no | — |
| 778 | C23 | — | 8 | 1 | no | — |
| 779 | C23 | #120×C53 | 1 | 1 | yes | characteristic |
| 780 | Q8 | — | 4 | 1 | no | — |
| 781 | Q8 | — | 4 | 1 | no | — |
| 782 | Q8 | — | 4 | 1 | no | — |
| 783 | Q8 | — | 4 | 1 | no | — |
| 784 | Q8 | — | 4 | 1 | no | — |
| 785 | Q8 | — | 4 | 1 | no | — |
| 786 | Q8 | — | 8 | 1 | no | — |
| 787 | D4 | — | 4 | 1 | no | — |
| 788 | D4 | — | 4 | 1 | no | — |
| 789 | D4 | — | 4 | 1 | no | — |
| 790 | D4 | — | 4 | 1 | no | — |
| 791 | D4 | — | 4 | 1 | no | — |
| 792 | D4 | — | 4 | 1 | no | — |
| 793 | D4 | — | 4 | 1 | no | — |
| 794 | D4 | — | 4 | 1 | no | — |
| 795 | D4 | — | 4 | 1 | no | — |
| 796 | D4 | — | 4 | 1 | no | — |
| 797 | D4 | — | 8 | 1 | no | — |
| 798 | D4 | — | 8 | 1 | no | — |
| 799 | D4 | — | 8 | 1 | no | — |
| 800 | D4 | — | 8 | 1 | no | — |
| 801 | D4 | — | 8 | 1 | no | — |
| 802 | D4 | — | 8 | 1 | no | — |
| 803 | D4 | — | 8 | 1 | no | — |
| 804 | D4 | — | 8 | 1 | no | — |
| 805 | D4 | — | 8 | 1 | no | — |
| 806 | D4 | — | 8 | 1 | no | — |
| 807 | D4 | — | 8 | 1 | no | — |
| 808 | D4 | — | 8 | 1 | no | — |
| 809 | D4 | — | 8 | 1 | no | — |
| 810 | D4 | — | 8 | 2 | no | — |
| 811 | C2×C4 | — | 2 | 1 | no | — |
| 812 | C2×C4 | — | 2 | 1 | no | — |
| 813 | C2×C4 | — | 2 | 1 | no | — |
| 814 | C2×C4 | — | 2 | 1 | no | — |
| 815 | C2×C4 | — | 2 | 1 | no | — |
| 816 | C2×C4 | — | 2 | 1 | no | — |
| 817 | C2×C4 | — | 2 | 1 | no | — |
| 818 | C2×C4 | — | 2 | 1 | no | — |
| 819 | C2×C4 | — | 4 | 1 | no | — |
| 820 | C2×C4 | — | 4 | 1 | no | — |
| 821 | C2×C4 | — | 4 | 1 | no | — |
| 822 | C2×C4 | — | 4 | 2 | no | — |
| 823 | C2×C4 | — | 4 | 2 | no | — |
| 824 | C2×C4 | — | 4 | 2 | no | — |
| 825 | C2×C4 | — | 4 | 2 | no | — |
| 826 | C2×C4 | — | 4 | 1 | no | — |
| 827 | C2×C4 | — | 8 | 2 | no | — |
| 828 | C2×C4 | — | 8 | 1 | no | — |
| 829 | C2×C4 | — | 8 | 1 | no | — |
| 830 | C2×C4 | — | 8 | 1 | no | — |
| 831 | C2×C4 | — | 8 | 1 | no | — |
| 832 | C2×C4 | — | 8 | 1 | no | — |
| 833 | C2×C4 | #120×C53 | 1 | 1 | yes | characteristic |
| 834 | C2×C4 | #120×C53 | 1 | 1 | yes | characteristic |
| 835 | C2×C4 | #120×C53 | 1 | 1 | yes | characteristic |
| 836 | C2×C4 | C22×D4×C53 | 1 | 1 | yes | characteristic |
| 837 | C2×C4 | C22×D4×C53 | 1 | 1 | yes | characteristic |
| 838 | C2×C4 | C22×D4×C53 | 1 | 1 | yes | characteristic |
| 839 | C8 | — | 2 | 2 | no | — |
| 840 | C8 | — | 4 | 1 | no | — |
| 841 | C8 | — | 4 | 1 | no | — |
| 842 | C8 | — | 4 | 1 | no | — |
| 843 | C8 | — | 4 | 1 | no | — |
| 844 | C8 | — | 4 | 1 | no | — |
| 845 | C22 | — | 2 | 1 | no | — |
| 846 | C22 | — | 2 | 1 | no | — |
| 847 | C22 | — | 2 | 1 | no | — |
| 848 | C22 | — | 4 | 1 | no | — |
| 849 | C22 | — | 4 | 1 | no | — |
| 850 | C22 | — | 4 | 1 | no | — |
| 851 | C22 | — | 4 | 1 | no | — |
| 852 | C22 | — | 4 | 1 | no | — |
| 853 | C22 | — | 4 | 1 | no | — |
| 854 | C22 | — | 4 | 1 | no | — |
| 855 | C22 | — | 4 | 1 | no | — |
| 856 | C22 | — | 4 | 1 | no | — |
| 857 | C22 | — | 4 | 1 | no | — |
| 858 | C22 | — | 4 | 1 | no | — |
| 859 | C22 | — | 4 | 1 | no | — |
| 860 | C22 | — | 8 | 4 | no | — |
| 861 | C22 | — | 8 | 1 | no | — |
| 862 | C22 | — | 8 | 1 | no | — |
| 863 | C22 | — | 8 | 1 | no | — |
| 864 | C22 | C2×#120×C53 | 1 | 1 | yes | characteristic |
| 865 | C4 | — | 2 | 1 | no | — |
| 866 | C4 | — | 2 | 1 | no | — |
| 867 | C4 | — | 2 | 1 | no | — |
| 868 | C4 | — | 2 | 1 | no | — |
| 869 | C4 | — | 2 | 1 | no | — |
| 870 | C4 | — | 2 | 1 | no | — |
| 871 | C4 | — | 4 | 1 | no | — |
| 872 | C4 | — | 4 | 1 | no | — |
| 873 | C4 | — | 4 | 1 | no | — |
| 874 | C4 | — | 4 | 1 | no | — |
| 875 | C4 | — | 4 | 1 | no | — |
| 876 | C4 | — | 4 | 1 | no | — |
| 877 | C4 | — | 4 | 1 | no | — |
| 878 | C4 | — | 4 | 1 | no | — |
| 879 | C4 | — | 8 | 1 | no | — |
| 880 | C2 | — | 4 | 1 | no | — |
| 881 | C2 | — | 8 | 1 | no | — |
| 882 | C2 | — | 8 | 1 | no | — |
| 883 | C2 | — | 8 | 1 | no | — |
| 884 | C2 | — | 8 | 1 | no | — |
| 885 | C2 | — | 16 | 1 | no | — |
| 886 | C2 | C53×#3018 | 1 | 1 | yes | characteristic |
| 887 | C2 | C53×#3019 | 1 | 1 | yes | characteristic |
| 888 | C2 | C53×#3021 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta