| 1 | #20284644 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#16810961 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20283442 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #20276228 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20276158 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20276082 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #20276011 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #20275497 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #20275373 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #20275232 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #20275184 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #20274920 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #20274772 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #20274453 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C53×#3056 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | C2×#13133224 | C22 | 1 | 1 | yes | characteristic |
| 17 | C22×#11719917 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#13133176 | C22 | 1 | 1 | yes | characteristic |
| 19 | #16810961 | — | 2 | 1 | no | — |
| 20 | #16810961 | — | 2 | 1 | no | — |
| 21 | #16810961 | — | 2 | 1 | no | — |
| 22 | #16810961 | — | 2 | 1 | no | — |
| 23 | #16810961 | — | 2 | 1 | no | — |
| 24 | #16810961 | — | 2 | 1 | no | — |
| 25 | #16810944 | — | 2 | 1 | no | — |
| 26 | #16810944 | — | 2 | 1 | no | — |
| 27 | #16810701 | — | 2 | 1 | no | — |
| 28 | #16810695 | — | 2 | 1 | no | — |
| 29 | #16810695 | — | 2 | 1 | no | — |
| 30 | D4×#88322 | — | 2 | 1 | no | — |
| 31 | C2×#13133152 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#13133152 | C22 | 1 | 1 | yes | characteristic |
| 33 | #16810666 | C22 | 1 | 1 | yes | characteristic |
| 34 | #16810666 | C22 | 1 | 1 | yes | characteristic |
| 35 | C2×#13133150 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×#13133148 | C22 | 1 | 1 | yes | characteristic |
| 37 | #16810650 | C22 | 1 | 1 | yes | characteristic |
| 38 | #16810624 | C22 | 1 | 1 | yes | characteristic |
| 39 | #16810624 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#13133141 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#13133141 | C22 | 1 | 1 | yes | characteristic |
| 42 | C2×#13133136 | C22 | 1 | 1 | yes | characteristic |
| 43 | C2×#13133136 | C22 | 1 | 1 | yes | characteristic |
| 44 | #16810590 | C22 | 1 | 1 | yes | characteristic |
| 45 | #16810587 | C22 | 1 | 1 | yes | characteristic |
| 46 | C2×C22⋊#88322 | C22 | 1 | 1 | yes | characteristic |
| 47 | #16810579 | C22 | 1 | 1 | yes | characteristic |
| 48 | #16810392 | C22 | 1 | 1 | yes | characteristic |
| 49 | #16810392 | C22 | 1 | 1 | yes | characteristic |
| 50 | #16810391 | C22 | 1 | 1 | yes | characteristic |
| 51 | #16810391 | C22 | 1 | 1 | yes | characteristic |
| 52 | #16810391 | C22 | 1 | 1 | yes | characteristic |
| 53 | #16810391 | C22 | 1 | 1 | yes | characteristic |
| 54 | #16810387 | C22 | 1 | 1 | yes | characteristic |
| 55 | #16810387 | C22 | 1 | 1 | yes | characteristic |
| 56 | C2×#137×C53 | C22 | 1 | 1 | yes | characteristic |
| 57 | C22×M16×C53 | C22 | 1 | 1 | yes | characteristic |
| 58 | C53×#525 | C22 | 1 | 1 | yes | characteristic |
| 59 | C2×C22⋊Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 60 | C53×#470 | — | 2 | 1 | no | — |
| 61 | C53×#468 | — | 2 | 1 | no | — |
| 62 | C53×#467 | — | 2 | 1 | no | — |
| 63 | C53×#465 | — | 2 | 1 | no | — |
| 64 | C53×#428 | C22 | 1 | 1 | yes | characteristic |
| 65 | C53×#419 | C22 | 1 | 1 | yes | characteristic |
| 66 | C53×#417 | C22 | 1 | 1 | yes | characteristic |
| 67 | #13133224 | — | 2 | 2 | no | — |
| 68 | #13133224 | — | 4 | 1 | no | — |
| 69 | C2×#11719917 | — | 2 | 1 | no | — |
| 70 | C2×#11719917 | — | 2 | 2 | no | — |
| 71 | C2×#11719917 | — | 2 | 1 | no | — |
| 72 | C2×#11719917 | — | 4 | 1 | no | — |
| 73 | C2×#11719917 | C23 | 1 | 1 | yes | characteristic |
| 74 | C2×#11719917 | C23 | 1 | 1 | yes | characteristic |
| 75 | C2×#11719917 | C23 | 1 | 1 | yes | characteristic |
| 76 | C2×#11719917 | C23 | 1 | 1 | yes | characteristic |
| 77 | C22×#88322 | — | 2 | 1 | no | — |
| 78 | C22×#88322 | — | 2 | 1 | no | — |
| 79 | C22×#88322 | C23 | 1 | 1 | yes | characteristic |
| 80 | C22×#88322 | C23 | 1 | 1 | yes | characteristic |
| 81 | #13133176 | — | 2 | 1 | no | — |
| 82 | #13133176 | — | 2 | 1 | no | — |
| 83 | #13133176 | — | 2 | 1 | no | — |
| 84 | #13133176 | — | 2 | 1 | no | — |
| 85 | C2×C4⋊Dic53 | C23 | 1 | 1 | yes | characteristic |
| 86 | C2×C4⋊Dic53 | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×C22⋊Dic53 | — | 2 | 1 | no | — |
| 88 | C2×C4×Dic53 | — | 2 | 1 | no | — |
| 89 | #13133152 | — | 2 | 2 | no | — |
| 90 | #13133152 | — | 4 | 1 | no | — |
| 91 | #13133150 | — | 2 | 1 | no | — |
| 92 | #13133150 | — | 2 | 1 | no | — |
| 93 | #13133150 | — | 2 | 1 | no | — |
| 94 | #13133150 | — | 2 | 1 | no | — |
| 95 | #13133148 | — | 2 | 1 | no | — |
| 96 | #13133148 | — | 2 | 1 | no | — |
| 97 | #13133148 | — | 2 | 1 | no | — |
| 98 | #13133148 | — | 2 | 1 | no | — |
| 99 | C4⋊#88322 | — | 2 | 1 | no | — |
| 100 | C4⋊#88322 | — | 2 | 1 | no | — |
| 101 | #13133141 | — | 2 | 1 | no | — |
| 102 | #13133141 | — | 2 | 1 | no | — |
| 103 | #13133141 | — | 2 | 1 | no | — |
| 104 | #13133141 | — | 2 | 1 | no | — |
| 105 | #13133141 | — | 2 | 1 | no | — |
| 106 | #13133141 | — | 2 | 1 | no | — |
| 107 | #13133138 | — | 2 | 1 | no | — |
| 108 | #13133138 | — | 2 | 1 | no | — |
| 109 | #13133136 | — | 2 | 2 | no | — |
| 110 | #13133136 | — | 4 | 1 | no | — |
| 111 | C22⋊#88322 | — | 2 | 1 | no | — |
| 112 | C22⋊#88322 | — | 2 | 1 | no | — |
| 113 | C22⋊#88322 | — | 2 | 1 | no | — |
| 114 | C22⋊#88322 | — | 2 | 1 | no | — |
| 115 | C22⋊#88322 | D4 | 1 | 1 | yes | characteristic |
| 116 | C22⋊#88322 | D4 | 1 | 1 | yes | characteristic |
| 117 | C22⋊#88322 | D4 | 1 | 1 | yes | characteristic |
| 118 | C22⋊#88322 | D4 | 1 | 1 | yes | characteristic |
| 119 | #13133128 | — | 2 | 1 | no | — |
| 120 | C4×#88322 | — | 2 | 1 | no | — |
| 121 | C2×#41×C53 | C23 | 1 | 1 | yes | characteristic |
| 122 | C22×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 123 | C23×C4×C53 | C23 | 1 | 1 | yes | characteristic |
| 124 | #137×C53 | — | 2 | 2 | no | — |
| 125 | #137×C53 | — | 4 | 1 | no | — |
| 126 | C2×Q16×C53 | — | 2 | 1 | no | — |
| 127 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 128 | C2×M16×C53 | — | 2 | 2 | no | — |
| 129 | C2×M16×C53 | — | 2 | 1 | no | — |
| 130 | C2×M16×C53 | — | 4 | 1 | no | — |
| 131 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 132 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 133 | C22×C8×C53 | — | 2 | 1 | no | — |
| 134 | #123×C53 | — | 2 | 1 | no | — |
| 135 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 136 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 137 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 138 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 139 | C22⋊Q8×C53 | D4 | 1 | 1 | yes | characteristic |
| 140 | C22⋊Q8×C53 | D4 | 1 | 1 | yes | characteristic |
| 141 | #121×C53 | D4 | 1 | 1 | yes | characteristic |
| 142 | #121×C53 | D4 | 1 | 1 | yes | characteristic |
| 143 | #120×C53 | — | 2 | 1 | no | — |
| 144 | C4×D4×C53 | — | 2 | 1 | no | — |
| 145 | C4×D4×C53 | — | 2 | 1 | no | — |
| 146 | #117×C53 | C23 | 1 | 1 | yes | characteristic |
| 147 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 148 | C2×C4⋊C4×C53 | C23 | 1 | 1 | yes | characteristic |
| 149 | C2×C22⋊C4×C53 | — | 2 | 1 | no | — |
| 150 | #107×C53 | — | 2 | 1 | no | — |
| 151 | #106×C53 | — | 2 | 1 | no | — |
| 152 | #103×C53 | — | 2 | 1 | no | — |
| 153 | #103×C53 | — | 2 | 1 | no | — |
| 154 | #103×C53 | — | 2 | 1 | no | — |
| 155 | #102×C53 | — | 2 | 1 | no | — |
| 156 | C24×C53 | #41 | 1 | 1 | yes | characteristic |
| 157 | #41×C53 | — | 2 | 1 | no | — |
| 158 | #41×C53 | — | 2 | 1 | no | — |
| 159 | #41×C53 | — | 2 | 1 | no | — |
| 160 | #41×C53 | — | 2 | 1 | no | — |
| 161 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 162 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 163 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 164 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 165 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 166 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 167 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 168 | C2×D4×C53 | — | 2 | 1 | no | — |
| 169 | C2×D4×C53 | — | 2 | 1 | no | — |
| 170 | C2×D4×C53 | — | 2 | 1 | no | — |
| 171 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | C22×C4×C53 | — | 2 | 1 | no | — |
| 173 | C22×C4×C53 | — | 2 | 1 | no | — |
| 174 | C22×C4×C53 | — | 2 | 1 | no | — |
| 175 | C22×C4×C53 | — | 2 | 1 | no | — |
| 176 | C22×C4×C53 | — | 2 | 1 | no | — |
| 177 | C22×C4×C53 | — | 2 | 1 | no | — |
| 178 | C22×C4×C53 | — | 2 | 1 | no | — |
| 179 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 181 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 183 | C22×C4×C53 | #41 | 1 | 1 | yes | characteristic |
| 184 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 185 | C22×Dic53 | — | 2 | 1 | no | — |
| 186 | C22×Dic53 | — | 2 | 1 | no | — |
| 187 | Q16×C53 | — | 4 | 2 | no | — |
| 188 | SD16×C53 | — | 4 | 2 | no | — |
| 189 | M16×C53 | — | 2 | 1 | no | — |
| 190 | M16×C53 | — | 2 | 1 | no | — |
| 191 | M16×C53 | — | 2 | 1 | no | — |
| 192 | M16×C53 | — | 4 | 2 | no | — |
| 193 | M16×C53 | #41 | 1 | 2 | yes | — |
| 194 | C2×C8×C53 | — | 2 | 1 | no | — |
| 195 | C2×C8×C53 | — | 2 | 1 | no | — |
| 196 | C2×C8×C53 | — | 4 | 2 | no | — |
| 197 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 198 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 199 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 200 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 201 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 202 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 203 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 204 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 205 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 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 | — | 2 | 1 | no | — |
| 210 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 211 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 212 | C42×C53 | — | 2 | 1 | no | — |
| 213 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 214 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 215 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 216 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 217 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 218 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 219 | C4×Dic53 | — | 4 | 1 | no | — |
| 220 | C4×Dic53 | — | 4 | 1 | no | — |
| 221 | #11719917 | — | 2 | 1 | no | — |
| 222 | #11719917 | — | 2 | 1 | no | — |
| 223 | #11719917 | — | 2 | 1 | no | — |
| 224 | #11719917 | — | 2 | 1 | no | — |
| 225 | #11719917 | — | 2 | 1 | no | — |
| 226 | #11719917 | — | 2 | 1 | no | — |
| 227 | #11719917 | — | 2 | 1 | no | — |
| 228 | #11719917 | — | 4 | 2 | no | — |
| 229 | #11719917 | — | 4 | 2 | no | — |
| 230 | #11719917 | #41 | 1 | 2 | yes | — |
| 231 | C2×#88322 | — | 2 | 1 | no | — |
| 232 | C2×#88322 | — | 2 | 1 | no | — |
| 233 | C2×#88322 | — | 2 | 1 | no | — |
| 234 | C2×#88322 | — | 2 | 1 | no | — |
| 235 | C2×#88322 | — | 2 | 1 | no | — |
| 236 | C2×#88322 | — | 2 | 1 | no | — |
| 237 | C2×#88322 | — | 2 | 1 | no | — |
| 238 | C2×#88322 | — | 2 | 1 | no | — |
| 239 | C2×#88322 | — | 4 | 2 | no | — |
| 240 | C2×#88322 | — | 4 | 2 | no | — |
| 241 | C2×#88322 | C2×D4 | 1 | 1 | yes | characteristic |
| 242 | C2×#88322 | C2×D4 | 1 | 1 | yes | characteristic |
| 243 | C2×#88322 | C2×D4 | 1 | 1 | yes | characteristic |
| 244 | C2×#88322 | C2×D4 | 1 | 1 | yes | characteristic |
| 245 | C23×C53 | — | 2 | 1 | no | — |
| 246 | C23×C53 | — | 2 | 1 | no | — |
| 247 | C23×C53 | — | 2 | 1 | no | — |
| 248 | C23×C53 | — | 4 | 1 | no | — |
| 249 | C23×C53 | — | 4 | 1 | no | — |
| 250 | C23×C53 | #121 | 1 | 1 | yes | characteristic |
| 251 | C23×C53 | #121 | 1 | 1 | yes | characteristic |
| 252 | C23×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 253 | Q8×C53 | — | 2 | 1 | no | — |
| 254 | Q8×C53 | — | 2 | 1 | no | — |
| 255 | Q8×C53 | — | 4 | 1 | no | — |
| 256 | Q8×C53 | — | 4 | 1 | no | — |
| 257 | Q8×C53 | — | 4 | 1 | no | — |
| 258 | Q8×C53 | — | 4 | 1 | no | — |
| 259 | D4×C53 | — | 2 | 1 | no | — |
| 260 | D4×C53 | — | 2 | 1 | no | — |
| 261 | D4×C53 | — | 4 | 2 | no | — |
| 262 | D4×C53 | — | 4 | 1 | no | — |
| 263 | D4×C53 | — | 4 | 1 | no | — |
| 264 | D4×C53 | — | 8 | 1 | no | — |
| 265 | C2×C4×C53 | — | 2 | 1 | no | — |
| 266 | C2×C4×C53 | — | 2 | 1 | no | — |
| 267 | C2×C4×C53 | — | 2 | 1 | no | — |
| 268 | C2×C4×C53 | — | 2 | 1 | no | — |
| 269 | C2×C4×C53 | — | 2 | 1 | no | — |
| 270 | C2×C4×C53 | — | 2 | 1 | no | — |
| 271 | C2×C4×C53 | — | 2 | 1 | no | — |
| 272 | C2×C4×C53 | — | 2 | 1 | no | — |
| 273 | C2×C4×C53 | — | 2 | 1 | no | — |
| 274 | C2×C4×C53 | — | 2 | 1 | no | — |
| 275 | C2×C4×C53 | — | 2 | 1 | no | — |
| 276 | C2×C4×C53 | — | 2 | 1 | no | — |
| 277 | C2×C4×C53 | — | 2 | 1 | no | — |
| 278 | C2×C4×C53 | — | 4 | 1 | no | — |
| 279 | C2×C4×C53 | — | 4 | 1 | no | — |
| 280 | C2×C4×C53 | — | 4 | 1 | no | — |
| 281 | C2×C4×C53 | — | 4 | 1 | no | — |
| 282 | C2×C4×C53 | — | 4 | 1 | no | — |
| 283 | C2×C4×C53 | — | 4 | 1 | no | — |
| 284 | C2×C4×C53 | — | 8 | 1 | no | — |
| 285 | C2×C4×C53 | #121 | 1 | 1 | yes | characteristic |
| 286 | C2×C4×C53 | #121 | 1 | 1 | yes | characteristic |
| 287 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 288 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 289 | C2×C4×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 290 | C2×C4×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 291 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 292 | C2×C4×C53 | 2−1+4 | 1 | 1 | yes | characteristic |
| 293 | C2×Dic53 | — | 4 | 1 | no | — |
| 294 | C2×Dic53 | — | 4 | 1 | no | — |
| 295 | C2×Dic53 | — | 8 | 1 | no | — |
| 296 | C2×Dic53 | — | 8 | 1 | no | — |
| 297 | C8×C53 | — | 2 | 2 | no | — |
| 298 | C8×C53 | — | 4 | 1 | no | — |
| 299 | #88322 | — | 2 | 1 | no | — |
| 300 | #88322 | — | 2 | 1 | no | — |
| 301 | #88322 | — | 2 | 2 | no | — |
| 302 | #88322 | — | 2 | 1 | no | — |
| 303 | #88322 | — | 2 | 1 | no | — |
| 304 | #88322 | — | 4 | 1 | no | — |
| 305 | #88322 | — | 4 | 1 | no | — |
| 306 | #88322 | — | 4 | 1 | no | — |
| 307 | #25271 | — | 53 | 1 | no | maximal, Sylow |
| 308 | C22×C53 | — | 2 | 1 | no | — |
| 309 | C22×C53 | — | 2 | 1 | no | — |
| 310 | C22×C53 | — | 2 | 1 | no | — |
| 311 | C22×C53 | — | 2 | 1 | no | — |
| 312 | C22×C53 | — | 2 | 1 | no | — |
| 313 | C22×C53 | — | 2 | 1 | no | — |
| 314 | C22×C53 | — | 2 | 1 | no | — |
| 315 | C22×C53 | — | 2 | 1 | no | — |
| 316 | C22×C53 | — | 4 | 1 | no | — |
| 317 | C22×C53 | — | 4 | 1 | no | — |
| 318 | C22×C53 | — | 4 | 1 | no | — |
| 319 | C22×C53 | — | 8 | 1 | no | — |
| 320 | C22×C53 | — | 8 | 1 | no | — |
| 321 | C22×C53 | C2×#121 | 1 | 1 | yes | characteristic |
| 322 | C22×C53 | #529 | 1 | 1 | yes | characteristic |
| 323 | C22×C53 | #539 | 1 | 1 | yes | characteristic |
| 324 | C4×C53 | — | 2 | 1 | no | — |
| 325 | C4×C53 | — | 2 | 1 | no | — |
| 326 | C4×C53 | — | 4 | 1 | no | — |
| 327 | C4×C53 | — | 4 | 1 | no | — |
| 328 | C4×C53 | — | 4 | 1 | no | — |
| 329 | C4×C53 | — | 8 | 1 | no | — |
| 330 | C4×C53 | — | 8 | 1 | no | — |
| 331 | C4×C53 | #546 | 1 | 1 | yes | characteristic |
| 332 | C4×C53 | #546 | 1 | 1 | yes | characteristic |
| 333 | C4×C53 | #547 | 1 | 1 | yes | characteristic |
| 334 | C4×C53 | #547 | 1 | 1 | yes | characteristic |
| 335 | Dic53 | — | 8 | 1 | no | — |
| 336 | Dic53 | — | 8 | 1 | no | — |
| 337 | #3093 | — | 53 | 1 | no | — |
| 338 | C2×#485 | — | 53 | 1 | no | — |
| 339 | #3056 | D53 | 1 | 1 | yes | characteristic |
| 340 | #2933 | — | 53 | 1 | no | — |
| 341 | #2090 | — | 53 | 1 | no | — |
| 342 | #2078 | — | 53 | 1 | no | — |
| 343 | #2064 | — | 53 | 1 | no | — |
| 344 | #2052 | — | 53 | 1 | no | — |
| 345 | #1952 | — | 53 | 1 | no | — |
| 346 | #1930 | — | 53 | 1 | no | — |
| 347 | #1908 | — | 53 | 1 | no | — |
| 348 | #1901 | — | 53 | 1 | no | — |
| 349 | #1855 | — | 53 | 1 | no | — |
| 350 | #1815 | — | 53 | 1 | no | — |
| 351 | #1742 | — | 53 | 1 | no | — |
| 352 | C2×C53 | — | 2 | 1 | no | — |
| 353 | C2×C53 | — | 2 | 1 | no | — |
| 354 | C2×C53 | — | 4 | 1 | no | — |
| 355 | C2×C53 | — | 4 | 1 | no | — |
| 356 | C2×C53 | — | 8 | 1 | no | — |
| 357 | C2×C53 | #2425 | 1 | 1 | yes | characteristic |
| 358 | C2×C53 | #3067 | 1 | 1 | yes | characteristic |
| 359 | C2×C53 | #3069 | 1 | 1 | yes | characteristic |
| 360 | C2×#137 | C2×D53 | 1 | 1 | yes | characteristic |
| 361 | C2×#131 | — | 53 | 1 | no | — |
| 362 | C22×M16 | — | 53 | 1 | no | — |
| 363 | C22×M16 | C2×D53 | 1 | 1 | yes | characteristic |
| 364 | #525 | C2×D53 | 1 | 1 | yes | characteristic |
| 365 | C2×C22⋊Q8 | C2×D53 | 1 | 1 | yes | characteristic |
| 366 | C2×#117 | — | 53 | 1 | no | — |
| 367 | #485 | — | 106 | 1 | no | — |
| 368 | #485 | — | 106 | 1 | no | — |
| 369 | #485 | — | 106 | 1 | no | — |
| 370 | #485 | — | 106 | 1 | no | — |
| 371 | #485 | — | 106 | 1 | no | — |
| 372 | #485 | — | 106 | 1 | no | — |
| 373 | #482 | — | 106 | 1 | no | — |
| 374 | #482 | — | 106 | 1 | no | — |
| 375 | #470 | — | 2 | 1 | no | — |
| 376 | #468 | — | 2 | 1 | no | — |
| 377 | #467 | — | 2 | 1 | no | — |
| 378 | #465 | — | 2 | 1 | no | — |
| 379 | #436 | — | 106 | 1 | no | — |
| 380 | #435 | — | 106 | 1 | no | — |
| 381 | #435 | — | 106 | 1 | no | — |
| 382 | C8×D4 | — | 106 | 1 | no | — |
| 383 | C2×#108 | — | 53 | 1 | no | — |
| 384 | C2×#108 | — | 53 | 1 | no | — |
| 385 | #428 | — | 53 | 1 | no | — |
| 386 | #428 | — | 53 | 1 | no | — |
| 387 | #428 | C2×D53 | 1 | 1 | yes | characteristic |
| 388 | C2×#107 | — | 53 | 1 | no | — |
| 389 | C2×#106 | — | 53 | 1 | no | — |
| 390 | #424 | — | 53 | 1 | no | — |
| 391 | #419 | C2×D53 | 1 | 1 | yes | characteristic |
| 392 | #417 | — | 53 | 1 | no | — |
| 393 | #417 | — | 53 | 1 | no | — |
| 394 | #417 | C2×D53 | 1 | 1 | yes | characteristic |
| 395 | C2×#103 | — | 53 | 1 | no | — |
| 396 | C2×#103 | — | 53 | 1 | no | — |
| 397 | C2×#101 | — | 53 | 1 | no | — |
| 398 | C2×#101 | — | 53 | 1 | no | — |
| 399 | #408 | — | 53 | 1 | no | — |
| 400 | #407 | — | 53 | 1 | no | — |
| 401 | C2×C22⋊C8 | — | 53 | 1 | no | — |
| 402 | #405 | — | 53 | 1 | no | — |
| 403 | #343 | — | 53 | 1 | no | — |
| 404 | #343 | — | 53 | 1 | no | — |
| 405 | #343 | — | 53 | 1 | no | — |
| 406 | #343 | — | 53 | 1 | no | — |
| 407 | #343 | — | 53 | 1 | no | — |
| 408 | #343 | — | 53 | 1 | no | — |
| 409 | #341 | — | 53 | 1 | no | — |
| 410 | #341 | — | 53 | 1 | no | — |
| 411 | C53 | #25271 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 412 | C2×#41 | C22×D53 | 1 | 1 | yes | characteristic |
| 413 | C22×Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 414 | C23×C4 | C22×D53 | 1 | 1 | yes | characteristic |
| 415 | #137 | — | 2 | 2 | no | — |
| 416 | #137 | — | 4 | 1 | no | — |
| 417 | C2×Q16 | — | 2 | 1 | no | — |
| 418 | C2×SD16 | — | 2 | 1 | no | — |
| 419 | #131 | — | 106 | 2 | no | — |
| 420 | #131 | — | 212 | 1 | no | — |
| 421 | C2×M16 | — | 2 | 1 | no | — |
| 422 | C2×M16 | — | 2 | 2 | no | — |
| 423 | C2×M16 | — | 4 | 1 | no | — |
| 424 | C2×M16 | — | 53 | 1 | no | — |
| 425 | C2×M16 | — | 53 | 1 | no | — |
| 426 | C2×M16 | — | 53 | 1 | no | — |
| 427 | C2×M16 | — | 53 | 1 | no | — |
| 428 | C2×M16 | — | 106 | 1 | no | — |
| 429 | C2×M16 | — | 106 | 1 | no | — |
| 430 | C2×M16 | — | 106 | 2 | no | — |
| 431 | C2×M16 | — | 212 | 1 | no | — |
| 432 | C2×M16 | C22×D53 | 1 | 1 | yes | characteristic |
| 433 | C2×M16 | C22×D53 | 1 | 1 | yes | characteristic |
| 434 | C22×C8 | — | 2 | 1 | no | — |
| 435 | C22×C8 | — | 53 | 1 | no | — |
| 436 | C22×C8 | — | 53 | 1 | no | — |
| 437 | C22×C8 | — | 106 | 1 | no | — |
| 438 | C22×C8 | — | 106 | 1 | no | — |
| 439 | #123 | — | 2 | 1 | no | — |
| 440 | C22⋊Q8 | — | 2 | 1 | no | — |
| 441 | C22⋊Q8 | — | 2 | 1 | no | — |
| 442 | C22⋊Q8 | — | 2 | 1 | no | — |
| 443 | C22⋊Q8 | — | 2 | 1 | no | — |
| 444 | C22⋊Q8 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 445 | C22⋊Q8 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 446 | #121 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 447 | #121 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 448 | #120 | — | 2 | 1 | no | — |
| 449 | C4×D4 | — | 2 | 1 | no | — |
| 450 | C4×D4 | — | 2 | 1 | no | — |
| 451 | #117 | — | 106 | 1 | no | — |
| 452 | #117 | — | 106 | 1 | no | — |
| 453 | #117 | — | 106 | 1 | no | — |
| 454 | #117 | — | 106 | 1 | no | — |
| 455 | #117 | C22×D53 | 1 | 1 | yes | characteristic |
| 456 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 457 | C2×C4⋊C4 | — | 53 | 1 | no | — |
| 458 | C2×C4⋊C4 | — | 53 | 1 | no | — |
| 459 | C2×C4⋊C4 | C22×D53 | 1 | 1 | yes | characteristic |
| 460 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 461 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 462 | C2×C42 | — | 106 | 1 | no | — |
| 463 | #108 | — | 106 | 2 | no | — |
| 464 | #108 | — | 212 | 1 | no | — |
| 465 | #107 | — | 2 | 1 | no | — |
| 466 | #107 | — | 106 | 1 | no | — |
| 467 | #107 | — | 106 | 1 | no | — |
| 468 | #107 | — | 106 | 1 | no | — |
| 469 | #107 | — | 106 | 1 | no | — |
| 470 | #106 | — | 2 | 1 | no | — |
| 471 | #106 | — | 106 | 1 | no | — |
| 472 | #106 | — | 106 | 1 | no | — |
| 473 | #106 | — | 106 | 1 | no | — |
| 474 | #106 | — | 106 | 1 | no | — |
| 475 | C4⋊C8 | — | 106 | 1 | no | — |
| 476 | C4⋊C8 | — | 106 | 1 | no | — |
| 477 | #103 | — | 2 | 1 | no | — |
| 478 | #103 | — | 2 | 1 | no | — |
| 479 | #103 | — | 2 | 1 | no | — |
| 480 | #103 | — | 106 | 1 | no | — |
| 481 | #103 | — | 106 | 1 | no | — |
| 482 | #103 | — | 106 | 1 | no | — |
| 483 | #103 | — | 106 | 1 | no | — |
| 484 | #103 | — | 106 | 1 | no | — |
| 485 | #103 | — | 106 | 1 | no | — |
| 486 | #102 | — | 2 | 1 | no | — |
| 487 | #102 | — | 106 | 1 | no | — |
| 488 | #102 | — | 106 | 1 | no | — |
| 489 | #101 | — | 106 | 2 | no | — |
| 490 | #101 | — | 212 | 1 | no | — |
| 491 | C22⋊C8 | — | 53 | 1 | no | — |
| 492 | C22⋊C8 | — | 53 | 1 | no | — |
| 493 | C22⋊C8 | — | 53 | 1 | no | — |
| 494 | C22⋊C8 | — | 53 | 1 | no | — |
| 495 | C22⋊C8 | — | 106 | 1 | no | — |
| 496 | C22⋊C8 | — | 106 | 1 | no | — |
| 497 | C22⋊C8 | — | 106 | 1 | no | — |
| 498 | C22⋊C8 | — | 106 | 1 | no | — |
| 499 | #97 | — | 106 | 1 | no | — |
| 500 | C4×C8 | — | 106 | 1 | no | — |
| 501 | C24 | #11719947 | 1 | 1 | yes | characteristic |
| 502 | #41 | — | 2 | 1 | no | — |
| 503 | #41 | — | 2 | 1 | no | — |
| 504 | #41 | — | 2 | 1 | no | — |
| 505 | #41 | — | 2 | 1 | no | — |
| 506 | C2×Q8 | — | 2 | 1 | no | — |
| 507 | C2×Q8 | — | 2 | 1 | no | — |
| 508 | C2×Q8 | — | 2 | 1 | no | — |
| 509 | C2×Q8 | — | 2 | 1 | no | — |
| 510 | C2×Q8 | — | 2 | 1 | no | — |
| 511 | C2×Q8 | — | 2 | 1 | no | — |
| 512 | C2×Q8 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 513 | C2×D4 | — | 2 | 1 | no | — |
| 514 | C2×D4 | — | 2 | 1 | no | — |
| 515 | C2×D4 | — | 2 | 1 | no | — |
| 516 | C2×D4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 517 | C22×C4 | — | 2 | 1 | no | — |
| 518 | C22×C4 | — | 2 | 1 | no | — |
| 519 | C22×C4 | — | 2 | 1 | no | — |
| 520 | C22×C4 | — | 2 | 1 | no | — |
| 521 | C22×C4 | — | 2 | 1 | no | — |
| 522 | C22×C4 | — | 2 | 1 | no | — |
| 523 | C22×C4 | — | 2 | 1 | no | — |
| 524 | C22×C4 | — | 106 | 1 | no | — |
| 525 | C22×C4 | — | 106 | 1 | no | — |
| 526 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 527 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 528 | C22×C4 | #11719947 | 1 | 1 | yes | characteristic |
| 529 | C22×C4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 530 | C22×C4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 531 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 532 | Q16 | — | 4 | 2 | no | — |
| 533 | SD16 | — | 4 | 2 | no | — |
| 534 | M16 | — | 2 | 1 | no | — |
| 535 | M16 | — | 2 | 1 | no | — |
| 536 | M16 | — | 2 | 1 | no | — |
| 537 | M16 | — | 4 | 2 | no | — |
| 538 | M16 | — | 53 | 2 | no | — |
| 539 | M16 | — | 106 | 1 | no | — |
| 540 | M16 | — | 106 | 1 | no | — |
| 541 | M16 | — | 106 | 1 | no | — |
| 542 | M16 | — | 106 | 1 | no | — |
| 543 | M16 | — | 106 | 1 | no | — |
| 544 | M16 | — | 106 | 1 | no | — |
| 545 | M16 | — | 106 | 1 | no | — |
| 546 | M16 | — | 212 | 2 | no | — |
| 547 | M16 | — | 212 | 2 | no | — |
| 548 | M16 | #11719947 | 1 | 2 | yes | — |
| 549 | C2×C8 | — | 2 | 1 | no | — |
| 550 | C2×C8 | — | 2 | 1 | no | — |
| 551 | C2×C8 | — | 4 | 2 | no | — |
| 552 | C2×C8 | — | 53 | 1 | no | — |
| 553 | C2×C8 | — | 53 | 1 | no | — |
| 554 | C2×C8 | — | 53 | 1 | no | — |
| 555 | C2×C8 | — | 53 | 1 | no | — |
| 556 | C2×C8 | — | 106 | 1 | no | — |
| 557 | C2×C8 | — | 106 | 1 | no | — |
| 558 | C2×C8 | — | 106 | 1 | no | — |
| 559 | C2×C8 | — | 106 | 1 | no | — |
| 560 | C2×C8 | — | 106 | 1 | no | — |
| 561 | C2×C8 | — | 106 | 1 | no | — |
| 562 | C2×C8 | — | 106 | 1 | no | — |
| 563 | C2×C8 | — | 106 | 1 | no | — |
| 564 | C2×C8 | — | 212 | 2 | no | — |
| 565 | C2×C8 | — | 212 | 2 | no | — |
| 566 | C4⋊C4 | — | 2 | 1 | no | — |
| 567 | C4⋊C4 | — | 2 | 1 | no | — |
| 568 | C4⋊C4 | — | 2 | 1 | no | — |
| 569 | C4⋊C4 | — | 2 | 1 | no | — |
| 570 | C4⋊C4 | — | 4 | 1 | no | — |
| 571 | C4⋊C4 | — | 4 | 1 | no | — |
| 572 | C4⋊C4 | — | 106 | 1 | no | — |
| 573 | C4⋊C4 | — | 106 | 1 | no | — |
| 574 | C4⋊C4 | — | 106 | 1 | no | — |
| 575 | C4⋊C4 | — | 106 | 1 | no | — |
| 576 | C4⋊C4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 577 | C4⋊C4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 578 | C22⋊C4 | — | 2 | 1 | no | — |
| 579 | C22⋊C4 | — | 2 | 1 | no | — |
| 580 | C22⋊C4 | — | 2 | 1 | no | — |
| 581 | C22⋊C4 | — | 2 | 1 | no | — |
| 582 | C22⋊C4 | — | 2 | 1 | no | — |
| 583 | C22⋊C4 | — | 4 | 1 | no | — |
| 584 | C22⋊C4 | — | 4 | 1 | no | — |
| 585 | C22⋊C4 | — | 212 | 1 | no | — |
| 586 | C22⋊C4 | — | 212 | 1 | no | — |
| 587 | C42 | — | 2 | 1 | no | — |
| 588 | C42 | — | 212 | 1 | no | — |
| 589 | C42 | — | 212 | 1 | no | — |
| 590 | C23 | — | 2 | 1 | no | — |
| 591 | C23 | — | 2 | 1 | no | — |
| 592 | C23 | — | 2 | 1 | no | — |
| 593 | C23 | — | 4 | 1 | no | — |
| 594 | C23 | — | 4 | 1 | no | — |
| 595 | C23 | #13133189 | 1 | 1 | yes | characteristic |
| 596 | C23 | #13133189 | 1 | 1 | yes | characteristic |
| 597 | C23 | C2×#11719947 | 1 | 1 | yes | characteristic |
| 598 | Q8 | — | 2 | 1 | no | — |
| 599 | Q8 | — | 2 | 1 | no | — |
| 600 | Q8 | — | 4 | 1 | no | — |
| 601 | Q8 | — | 4 | 1 | no | — |
| 602 | Q8 | — | 4 | 1 | no | — |
| 603 | Q8 | — | 4 | 1 | no | — |
| 604 | D4 | — | 2 | 1 | no | — |
| 605 | D4 | — | 2 | 1 | no | — |
| 606 | D4 | — | 4 | 2 | no | — |
| 607 | D4 | — | 4 | 1 | no | — |
| 608 | D4 | — | 4 | 1 | no | — |
| 609 | D4 | — | 8 | 1 | no | — |
| 610 | C2×C4 | — | 2 | 1 | no | — |
| 611 | C2×C4 | — | 2 | 1 | no | — |
| 612 | C2×C4 | — | 2 | 1 | no | — |
| 613 | C2×C4 | — | 2 | 1 | no | — |
| 614 | C2×C4 | — | 2 | 1 | no | — |
| 615 | C2×C4 | — | 2 | 1 | no | — |
| 616 | C2×C4 | — | 2 | 1 | no | — |
| 617 | C2×C4 | — | 2 | 1 | no | — |
| 618 | C2×C4 | — | 2 | 1 | no | — |
| 619 | C2×C4 | — | 2 | 1 | no | — |
| 620 | C2×C4 | — | 2 | 1 | no | — |
| 621 | C2×C4 | — | 2 | 1 | no | — |
| 622 | C2×C4 | — | 2 | 1 | no | — |
| 623 | C2×C4 | — | 4 | 1 | no | — |
| 624 | C2×C4 | — | 4 | 1 | no | — |
| 625 | C2×C4 | — | 4 | 1 | no | — |
| 626 | C2×C4 | — | 4 | 1 | no | — |
| 627 | C2×C4 | — | 4 | 1 | no | — |
| 628 | C2×C4 | — | 4 | 1 | no | — |
| 629 | C2×C4 | — | 8 | 1 | no | — |
| 630 | C2×C4 | — | 424 | 1 | no | — |
| 631 | C2×C4 | — | 424 | 1 | no | — |
| 632 | C2×C4 | — | 212 | 1 | no | — |
| 633 | C2×C4 | — | 212 | 1 | no | — |
| 634 | C2×C4 | #13133189 | 1 | 1 | yes | characteristic |
| 635 | C2×C4 | #13133189 | 1 | 1 | yes | characteristic |
| 636 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 637 | C2×C4 | C22×C22⋊D53 | 1 | 1 | yes | characteristic |
| 638 | C2×C4 | #41×D53 | 1 | 1 | yes | characteristic |
| 639 | C2×C4 | C2×#11719947 | 1 | 1 | yes | characteristic |
| 640 | C2×C4 | #13133262 | 1 | 1 | yes | characteristic |
| 641 | C2×C4 | #13133264 | 1 | 1 | yes | characteristic |
| 642 | C8 | — | 2 | 2 | no | — |
| 643 | C8 | — | 4 | 1 | no | — |
| 644 | C8 | — | 106 | 1 | no | — |
| 645 | C8 | — | 106 | 1 | no | — |
| 646 | C8 | — | 106 | 1 | no | — |
| 647 | C8 | — | 106 | 1 | no | — |
| 648 | C8 | — | 106 | 2 | no | — |
| 649 | C8 | — | 212 | 1 | no | — |
| 650 | C8 | — | 212 | 1 | no | — |
| 651 | C8 | — | 212 | 1 | no | — |
| 652 | C22 | — | 2 | 1 | no | — |
| 653 | C22 | — | 2 | 1 | no | — |
| 654 | C22 | — | 2 | 1 | no | — |
| 655 | C22 | — | 2 | 1 | no | — |
| 656 | C22 | — | 2 | 1 | no | — |
| 657 | C22 | — | 2 | 1 | no | — |
| 658 | C22 | — | 2 | 1 | no | — |
| 659 | C22 | — | 2 | 1 | no | — |
| 660 | C22 | — | 4 | 1 | no | — |
| 661 | C22 | — | 4 | 1 | no | — |
| 662 | C22 | — | 4 | 1 | no | — |
| 663 | C22 | — | 8 | 1 | no | — |
| 664 | C22 | — | 8 | 1 | no | — |
| 665 | C22 | C2×#13133189 | 1 | 1 | yes | characteristic |
| 666 | C22 | #16811154 | 1 | 1 | yes | characteristic |
| 667 | C22 | #16811218 | 1 | 1 | yes | characteristic |
| 668 | C4 | — | 2 | 1 | no | — |
| 669 | C4 | — | 2 | 1 | no | — |
| 670 | C4 | — | 4 | 1 | no | — |
| 671 | C4 | — | 4 | 1 | no | — |
| 672 | C4 | — | 4 | 1 | no | — |
| 673 | C4 | — | 8 | 1 | no | — |
| 674 | C4 | — | 8 | 1 | no | — |
| 675 | C4 | — | 424 | 1 | no | — |
| 676 | C4 | — | 424 | 1 | no | — |
| 677 | C4 | #16811262 | 1 | 1 | yes | characteristic |
| 678 | C4 | #16811267 | 1 | 1 | yes | characteristic |
| 679 | C4 | #16811272 | 1 | 1 | yes | characteristic |
| 680 | C4 | #16811273 | 1 | 1 | yes | characteristic |
| 681 | C2 | — | 2 | 1 | no | — |
| 682 | C2 | — | 2 | 1 | no | — |
| 683 | C2 | — | 4 | 1 | no | — |
| 684 | C2 | — | 4 | 1 | no | — |
| 685 | C2 | — | 8 | 1 | no | — |
| 686 | C2 | #20278272 | 1 | 1 | yes | characteristic |
| 687 | C2 | #20284432 | 1 | 1 | yes | characteristic |
| 688 | C2 | #20284449 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta