| 1 | C53×#3185 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C53×#2987 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C53×#1537 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C53×#1515 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C53×#1515 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C53×#1291 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C53×#1288 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C53×#533 | C22 | 1 | 1 | yes | characteristic |
| 9 | C53×#533 | C22 | 1 | 1 | yes | characteristic |
| 10 | C53×#498 | C4 | 1 | 1 | yes | characteristic, complemented |
| 11 | C53×#494 | C4 | 1 | 1 | yes | characteristic, complemented |
| 12 | C53×#487 | C4 | 1 | 1 | yes | characteristic, complemented |
| 13 | C53×#487 | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | C53×#470 | — | 2 | 2 | no | — |
| 15 | C53×#446 | — | 2 | 2 | no | — |
| 16 | C53×#446 | — | 2 | 2 | no | — |
| 17 | C53×#441 | — | 2 | 2 | no | — |
| 18 | C53×#433 | — | 2 | 2 | no | — |
| 19 | C53×#432 | C22 | 1 | 1 | yes | characteristic |
| 20 | C53×#432 | C22 | 1 | 1 | yes | characteristic |
| 21 | C53×#432 | C22 | 1 | 1 | yes | characteristic |
| 22 | C4×M16×C53 | C22 | 1 | 1 | yes | characteristic |
| 23 | C53×#383 | C22 | 1 | 1 | yes | characteristic |
| 24 | C53×#330 | — | 2 | 2 | no | — |
| 25 | C53×#328 | — | 2 | 2 | no | — |
| 26 | C53×#328 | — | 2 | 2 | no | — |
| 27 | C2×Q16×C53 | — | 2 | 2 | no | — |
| 28 | C2×M16×C53 | — | 2 | 1 | no | — |
| 29 | C4⋊Q8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 30 | C4⋊Q8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 31 | C4⋊Q8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 32 | C4⋊Q8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 33 | #125×C53 | — | 2 | 1 | no | — |
| 34 | #125×C53 | — | 2 | 1 | no | — |
| 35 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 36 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 37 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 38 | C22⋊Q8×C53 | D4 | 1 | 2 | yes | — |
| 39 | C4×Q8×C53 | — | 2 | 1 | no | — |
| 40 | C4×Q8×C53 | — | 2 | 1 | no | — |
| 41 | C4×Q8×C53 | — | 2 | 1 | no | — |
| 42 | C4×Q8×C53 | D4 | 1 | 2 | yes | — |
| 43 | #117×C53 | — | 2 | 1 | no | — |
| 44 | #117×C53 | — | 2 | 1 | no | — |
| 45 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 46 | #106×C53 | — | 2 | 2 | no | — |
| 47 | C4⋊C8×C53 | — | 2 | 4 | no | — |
| 48 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 49 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 50 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 51 | #103×C53 | — | 2 | 2 | no | — |
| 52 | #103×C53 | — | 2 | 2 | no | — |
| 53 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 54 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 55 | C22⋊C8×C53 | D4 | 1 | 2 | yes | — |
| 56 | #97×C53 | — | 2 | 2 | no | — |
| 57 | #97×C53 | — | 2 | 1 | no | — |
| 58 | #97×C53 | — | 2 | 1 | no | — |
| 59 | #97×C53 | — | 2 | 1 | no | — |
| 60 | #97×C53 | D4 | 1 | 2 | yes | — |
| 61 | C4×C8×C53 | — | 2 | 2 | no | — |
| 62 | C4×C8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 63 | C4×C8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 64 | #95×C53 | — | 2 | 1 | no | — |
| 65 | #95×C53 | — | 2 | 1 | no | — |
| 66 | #95×C53 | — | 2 | 1 | no | — |
| 67 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 68 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 69 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 70 | C2×Q8×C53 | C22⋊C4 | 1 | 2 | yes | — |
| 71 | C22×C4×C53 | — | 4 | 1 | no | — |
| 72 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 73 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 74 | C22×C4×C53 | #41 | 1 | 1 | yes | characteristic |
| 75 | Q16×C53 | — | 4 | 4 | no | — |
| 76 | M16×C53 | — | 4 | 2 | no | — |
| 77 | C2×C8×C53 | — | 2 | 1 | no | — |
| 78 | C2×C8×C53 | — | 2 | 1 | no | — |
| 79 | C2×C8×C53 | — | 2 | 2 | no | — |
| 80 | C2×C8×C53 | — | 2 | 2 | no | — |
| 81 | C2×C8×C53 | — | 4 | 1 | no | — |
| 82 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 83 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 84 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 85 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 86 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 87 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 88 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 89 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 90 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 91 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 92 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 93 | C4⋊C4×C53 | C22⋊C4 | 1 | 2 | yes | — |
| 94 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 95 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 96 | C42×C53 | — | 2 | 2 | no | — |
| 97 | C42×C53 | — | 4 | 1 | no | — |
| 98 | C42×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 99 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 100 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 101 | C42×C53 | #41 | 1 | 1 | yes | characteristic |
| 102 | C23×C53 | #121 | 1 | 1 | yes | characteristic |
| 103 | Q8×C53 | — | 4 | 2 | no | — |
| 104 | Q8×C53 | — | 4 | 2 | no | — |
| 105 | Q8×C53 | — | 8 | 1 | no | — |
| 106 | Q8×C53 | — | 8 | 1 | no | — |
| 107 | C2×C4×C53 | — | 2 | 2 | no | — |
| 108 | C2×C4×C53 | — | 2 | 2 | no | — |
| 109 | C2×C4×C53 | — | 4 | 1 | no | — |
| 110 | C2×C4×C53 | — | 4 | 1 | no | — |
| 111 | C2×C4×C53 | — | 4 | 1 | no | — |
| 112 | C2×C4×C53 | — | 4 | 1 | no | — |
| 113 | C2×C4×C53 | — | 4 | 1 | no | — |
| 114 | C2×C4×C53 | — | 8 | 1 | no | — |
| 115 | C2×C4×C53 | — | 8 | 1 | no | — |
| 116 | C2×C4×C53 | — | 8 | 1 | no | — |
| 117 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 118 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 119 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 120 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 121 | C2×C4×C53 | #121 | 1 | 1 | yes | characteristic |
| 122 | C2×C4×C53 | #123 | 1 | 1 | yes | characteristic |
| 123 | C8×C53 | — | 2 | 2 | no | — |
| 124 | C8×C53 | — | 4 | 2 | no | — |
| 125 | C8×C53 | — | 4 | 2 | no | — |
| 126 | C8×C53 | — | 4 | 1 | no | — |
| 127 | C8×C53 | — | 8 | 1 | no | — |
| 128 | #9416 | C53 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 129 | C22×C53 | — | 2 | 1 | no | — |
| 130 | C22×C53 | — | 2 | 1 | no | — |
| 131 | C22×C53 | — | 2 | 1 | no | — |
| 132 | C22×C53 | #386 | 1 | 1 | yes | characteristic |
| 133 | C4×C53 | — | 2 | 1 | no | — |
| 134 | C4×C53 | — | 2 | 1 | no | — |
| 135 | C4×C53 | — | 2 | 1 | no | — |
| 136 | C4×C53 | — | 2 | 1 | no | — |
| 137 | C4×C53 | — | 2 | 1 | no | — |
| 138 | C4×C53 | — | 2 | 1 | no | — |
| 139 | C4×C53 | — | 4 | 2 | no | — |
| 140 | C4×C53 | — | 4 | 2 | no | — |
| 141 | C4×C53 | — | 8 | 1 | no | — |
| 142 | C4×C53 | — | 8 | 1 | no | — |
| 143 | C4×C53 | — | 16 | 1 | no | — |
| 144 | #3185 | C2×C53 | 1 | 1 | yes | characteristic |
| 145 | #2987 | C2×C53 | 1 | 1 | yes | characteristic |
| 146 | #1537 | C2×C53 | 1 | 1 | yes | characteristic |
| 147 | #1515 | C2×C53 | 1 | 1 | yes | characteristic |
| 148 | #1515 | C2×C53 | 1 | 1 | yes | characteristic |
| 149 | #1291 | C2×C53 | 1 | 1 | yes | characteristic |
| 150 | #1288 | C2×C53 | 1 | 1 | yes | characteristic |
| 151 | C2×C53 | — | 4 | 1 | no | — |
| 152 | C2×C53 | #1884 | 1 | 1 | yes | characteristic |
| 153 | C2×C53 | #1902 | 1 | 1 | yes | characteristic |
| 154 | C2×C53 | #1905 | 1 | 1 | yes | characteristic |
| 155 | #533 | C22×C53 | 1 | 1 | yes | characteristic |
| 156 | #533 | C22×C53 | 1 | 1 | yes | characteristic |
| 157 | #498 | C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 158 | #494 | C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 159 | #487 | C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 160 | #487 | C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 161 | #470 | — | 2 | 2 | no | — |
| 162 | #446 | — | 2 | 2 | no | — |
| 163 | #446 | — | 2 | 2 | no | — |
| 164 | #441 | — | 2 | 2 | no | — |
| 165 | #433 | — | 2 | 2 | no | — |
| 166 | #432 | C22×C53 | 1 | 1 | yes | characteristic |
| 167 | #432 | C22×C53 | 1 | 1 | yes | characteristic |
| 168 | #432 | C22×C53 | 1 | 1 | yes | characteristic |
| 169 | C4×M16 | C22×C53 | 1 | 1 | yes | characteristic |
| 170 | #383 | C22×C53 | 1 | 1 | yes | characteristic |
| 171 | #330 | — | 2 | 2 | no | — |
| 172 | #328 | — | 2 | 2 | no | — |
| 173 | #328 | — | 2 | 2 | no | — |
| 174 | C53 | #9416 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 175 | C2×Q16 | — | 2 | 2 | no | — |
| 176 | C2×M16 | — | 2 | 1 | no | — |
| 177 | C4⋊Q8 | C2×C4×C53 | 1 | 1 | yes | characteristic |
| 178 | C4⋊Q8 | C2×C4×C53 | 1 | 1 | yes | characteristic |
| 179 | C4⋊Q8 | C2×C4×C53 | 1 | 1 | yes | characteristic |
| 180 | C4⋊Q8 | C2×C4×C53 | 1 | 1 | yes | characteristic |
| 181 | #125 | — | 2 | 1 | no | — |
| 182 | #125 | — | 2 | 1 | no | — |
| 183 | C22⋊Q8 | — | 2 | 1 | no | — |
| 184 | C22⋊Q8 | — | 2 | 1 | no | — |
| 185 | C22⋊Q8 | — | 2 | 1 | no | — |
| 186 | C22⋊Q8 | D4×C53 | 1 | 2 | yes | — |
| 187 | C4×Q8 | — | 2 | 1 | no | — |
| 188 | C4×Q8 | — | 2 | 1 | no | — |
| 189 | C4×Q8 | — | 2 | 1 | no | — |
| 190 | C4×Q8 | D4×C53 | 1 | 2 | yes | — |
| 191 | #117 | — | 2 | 1 | no | — |
| 192 | #117 | — | 2 | 1 | no | — |
| 193 | C2×C42 | C23×C53 | 1 | 1 | yes | characteristic |
| 194 | #106 | — | 2 | 2 | no | — |
| 195 | C4⋊C8 | — | 2 | 4 | no | — |
| 196 | C4⋊C8 | — | 2 | 1 | no | — |
| 197 | C4⋊C8 | — | 2 | 1 | no | — |
| 198 | C4⋊C8 | — | 2 | 1 | no | — |
| 199 | #103 | — | 2 | 2 | no | — |
| 200 | #103 | — | 2 | 2 | no | — |
| 201 | C22⋊C8 | — | 2 | 1 | no | — |
| 202 | C22⋊C8 | — | 2 | 1 | no | — |
| 203 | C22⋊C8 | D4×C53 | 1 | 2 | yes | — |
| 204 | #97 | — | 2 | 2 | no | — |
| 205 | #97 | — | 2 | 1 | no | — |
| 206 | #97 | — | 2 | 1 | no | — |
| 207 | #97 | — | 2 | 1 | no | — |
| 208 | #97 | D4×C53 | 1 | 2 | yes | — |
| 209 | C4×C8 | — | 2 | 2 | no | — |
| 210 | C4×C8 | C2×C4×C53 | 1 | 1 | yes | characteristic |
| 211 | C4×C8 | C2×C4×C53 | 1 | 1 | yes | characteristic |
| 212 | #95 | — | 2 | 1 | no | — |
| 213 | #95 | — | 2 | 1 | no | — |
| 214 | #95 | — | 2 | 1 | no | — |
| 215 | C2×Q8 | — | 2 | 1 | no | — |
| 216 | C2×Q8 | — | 2 | 1 | no | — |
| 217 | C2×Q8 | — | 2 | 1 | no | — |
| 218 | C2×Q8 | C22⋊C4×C53 | 1 | 2 | yes | — |
| 219 | C22×C4 | — | 4 | 1 | no | — |
| 220 | C22×C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 221 | C22×C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 222 | C22×C4 | #41×C53 | 1 | 1 | yes | characteristic |
| 223 | Q16 | — | 4 | 4 | no | — |
| 224 | M16 | — | 4 | 2 | no | — |
| 225 | C2×C8 | — | 2 | 1 | no | — |
| 226 | C2×C8 | — | 2 | 1 | no | — |
| 227 | C2×C8 | — | 2 | 2 | no | — |
| 228 | C2×C8 | — | 2 | 2 | no | — |
| 229 | C2×C8 | — | 4 | 1 | no | — |
| 230 | C4⋊C4 | — | 2 | 1 | no | — |
| 231 | C4⋊C4 | — | 2 | 1 | no | — |
| 232 | C4⋊C4 | — | 2 | 1 | no | — |
| 233 | C4⋊C4 | — | 2 | 2 | no | — |
| 234 | C4⋊C4 | — | 2 | 2 | no | — |
| 235 | C4⋊C4 | — | 2 | 1 | no | — |
| 236 | C4⋊C4 | — | 2 | 1 | no | — |
| 237 | C4⋊C4 | — | 2 | 1 | no | — |
| 238 | C4⋊C4 | — | 2 | 1 | no | — |
| 239 | C4⋊C4 | — | 4 | 1 | no | — |
| 240 | C4⋊C4 | — | 4 | 1 | no | — |
| 241 | C4⋊C4 | C22⋊C4×C53 | 1 | 2 | yes | — |
| 242 | C22⋊C4 | — | 2 | 2 | no | — |
| 243 | C22⋊C4 | — | 4 | 1 | no | — |
| 244 | C42 | — | 2 | 2 | no | — |
| 245 | C42 | — | 4 | 1 | no | — |
| 246 | C42 | C22×C4×C53 | 1 | 1 | yes | characteristic |
| 247 | C42 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 248 | C42 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 249 | C42 | #41×C53 | 1 | 1 | yes | characteristic |
| 250 | C23 | #121×C53 | 1 | 1 | yes | characteristic |
| 251 | Q8 | — | 4 | 2 | no | — |
| 252 | Q8 | — | 4 | 2 | no | — |
| 253 | Q8 | — | 8 | 1 | no | — |
| 254 | Q8 | — | 8 | 1 | no | — |
| 255 | C2×C4 | — | 2 | 2 | no | — |
| 256 | C2×C4 | — | 2 | 2 | no | — |
| 257 | C2×C4 | — | 4 | 1 | no | — |
| 258 | C2×C4 | — | 4 | 1 | no | — |
| 259 | C2×C4 | — | 4 | 1 | no | — |
| 260 | C2×C4 | — | 4 | 1 | no | — |
| 261 | C2×C4 | — | 4 | 1 | no | — |
| 262 | C2×C4 | — | 8 | 1 | no | — |
| 263 | C2×C4 | — | 8 | 1 | no | — |
| 264 | C2×C4 | — | 8 | 1 | no | — |
| 265 | C2×C4 | C2×C22⋊C4×C53 | 1 | 1 | yes | characteristic |
| 266 | C2×C4 | C4×D4×C53 | 1 | 1 | yes | characteristic |
| 267 | C2×C4 | C4×D4×C53 | 1 | 1 | yes | characteristic |
| 268 | C2×C4 | #120×C53 | 1 | 1 | yes | characteristic |
| 269 | C2×C4 | #121×C53 | 1 | 1 | yes | characteristic |
| 270 | C2×C4 | #123×C53 | 1 | 1 | yes | characteristic |
| 271 | C8 | — | 2 | 2 | no | — |
| 272 | C8 | — | 4 | 2 | no | — |
| 273 | C8 | — | 4 | 2 | no | — |
| 274 | C8 | — | 4 | 1 | no | — |
| 275 | C8 | — | 8 | 1 | no | — |
| 276 | C22 | — | 2 | 1 | no | — |
| 277 | C22 | — | 2 | 1 | no | — |
| 278 | C22 | — | 2 | 1 | no | — |
| 279 | C22 | C53×#386 | 1 | 1 | yes | characteristic |
| 280 | C4 | — | 2 | 1 | no | — |
| 281 | C4 | — | 2 | 1 | no | — |
| 282 | C4 | — | 2 | 1 | no | — |
| 283 | C4 | — | 2 | 1 | no | — |
| 284 | C4 | — | 2 | 1 | no | — |
| 285 | C4 | — | 2 | 1 | no | — |
| 286 | C4 | — | 4 | 2 | no | — |
| 287 | C4 | — | 4 | 2 | no | — |
| 288 | C4 | — | 8 | 1 | no | — |
| 289 | C4 | — | 8 | 1 | no | — |
| 290 | C4 | — | 16 | 1 | no | — |
| 291 | C2 | — | 4 | 1 | no | — |
| 292 | C2 | C53×#1884 | 1 | 1 | yes | characteristic |
| 293 | C2 | C53×#1902 | 1 | 1 | yes | characteristic |
| 294 | C2 | C53×#1905 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta