| 1 | C53×#3336 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D4×D8×C53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C53×#2244 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C53×#2234 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C53×#2232 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C53×#2228 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C53×#2220 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C53×#2217 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C53×#2207 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C53×#2187 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C53×#2187 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C53×#2175 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C53×#2168 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C53×#2140 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C2×C53×#357 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C22×D8×C53 | C22 | 1 | 1 | yes | characteristic |
| 17 | C22×D8×C53 | C22 | 1 | 1 | yes | characteristic |
| 18 | C53×#552 | — | 2 | 1 | no | — |
| 19 | D42×C53 | — | 2 | 1 | no | — |
| 20 | C2×SD32×C53 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×SD32×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C2×SD32×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | C2×M32×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C22×C16×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | C53×#499 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C53×#493 | C22 | 1 | 1 | yes | characteristic |
| 27 | C53×#485 | — | 2 | 1 | no | — |
| 28 | C53×#483 | — | 2 | 1 | no | — |
| 29 | C53×#479 | — | 2 | 1 | no | — |
| 30 | C53×#467 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | C53×#467 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | C53×#466 | C22 | 1 | 1 | yes | characteristic |
| 33 | C53×#466 | C22 | 1 | 1 | yes | characteristic |
| 34 | C53×#459 | — | 2 | 1 | no | — |
| 35 | C53×#447 | — | 2 | 1 | no | — |
| 36 | C53×#447 | — | 2 | 1 | no | — |
| 37 | C4×Q16×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | C4×D8×C53 | C22 | 1 | 1 | yes | characteristic |
| 39 | C8×D4×C53 | C22 | 1 | 1 | yes | characteristic |
| 40 | C53×#427 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C2×#107×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | C53×#367 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | C53×#366 | C22 | 1 | 1 | yes | characteristic, complemented |
| 44 | C53×#366 | C22 | 1 | 1 | yes | characteristic, complemented |
| 45 | C53×C4⋊C16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 46 | C53×#358 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | C53×#357 | C22 | 1 | 1 | yes | characteristic |
| 48 | C53×#357 | C22 | 1 | 1 | yes | characteristic |
| 49 | C53×#357 | C22 | 1 | 1 | yes | characteristic |
| 50 | C53×#357 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | C53×#357 | C22 | 1 | 1 | yes | characteristic, complemented |
| 52 | C53×#357 | C22 | 1 | 1 | yes | characteristic, complemented |
| 53 | C53×#357 | C22 | 1 | 1 | yes | characteristic, complemented |
| 54 | C53×#357 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | C53×#357 | C22 | 1 | 1 | yes | characteristic, complemented |
| 56 | C53×C22⋊C16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | C53×C22⋊C16 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | C53×#346 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | C22×D4×C53 | — | 2 | 1 | no | — |
| 60 | C22×D4×C53 | — | 2 | 1 | no | — |
| 61 | C22×D4×C53 | — | 4 | 1 | no | — |
| 62 | C2×Q16×C53 | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×D8×C53 | — | 2 | 1 | no | — |
| 64 | C2×D8×C53 | — | 2 | 1 | no | — |
| 65 | C2×D8×C53 | — | 2 | 1 | no | — |
| 66 | C2×D8×C53 | — | 2 | 2 | no | — |
| 67 | C2×D8×C53 | — | 2 | 2 | no | — |
| 68 | C2×D8×C53 | — | 4 | 1 | no | — |
| 69 | C2×D8×C53 | — | 4 | 1 | no | — |
| 70 | C2×D8×C53 | C23 | 1 | 1 | yes | characteristic |
| 71 | C2×D8×C53 | C23 | 1 | 1 | yes | characteristic |
| 72 | C2×D8×C53 | C23 | 1 | 1 | yes | characteristic |
| 73 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 74 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 75 | #127×C53 | — | 2 | 1 | no | — |
| 76 | #126×C53 | — | 4 | 1 | no | — |
| 77 | #125×C53 | — | 2 | 1 | no | — |
| 78 | #125×C53 | — | 4 | 1 | no | — |
| 79 | #123×C53 | — | 4 | 1 | no | — |
| 80 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 81 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 82 | #121×C53 | — | 2 | 1 | no | — |
| 83 | #121×C53 | — | 2 | 1 | no | — |
| 84 | #121×C53 | — | 4 | 1 | no | — |
| 85 | #120×C53 | — | 4 | 1 | no | — |
| 86 | #120×C53 | — | 4 | 1 | no | — |
| 87 | C4×Q8×C53 | — | 2 | 1 | no | — |
| 88 | C4×D4×C53 | — | 2 | 1 | no | — |
| 89 | C4×D4×C53 | D4 | 1 | 1 | yes | characteristic |
| 90 | #117×C53 | — | 2 | 1 | no | — |
| 91 | #117×C53 | — | 4 | 1 | no | — |
| 92 | C2×C4⋊C4×C53 | — | 2 | 1 | no | — |
| 93 | SD32×C53 | — | 2 | 2 | no | — |
| 94 | SD32×C53 | — | 4 | 1 | no | — |
| 95 | SD32×C53 | — | 4 | 1 | no | — |
| 96 | M32×C53 | — | 4 | 1 | no | — |
| 97 | C2×C16×C53 | — | 4 | 1 | no | — |
| 98 | C2×C16×C53 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×C16×C53 | C23 | 1 | 1 | yes | characteristic |
| 100 | C2×C16×C53 | C23 | 1 | 1 | yes | characteristic |
| 101 | C2×C16×C53 | C23 | 1 | 1 | yes | characteristic |
| 102 | #107×C53 | — | 2 | 1 | no | — |
| 103 | #107×C53 | C23 | 1 | 1 | yes | characteristic |
| 104 | #107×C53 | C23 | 1 | 1 | yes | characteristic |
| 105 | #107×C53 | C23 | 1 | 1 | yes | characteristic |
| 106 | #107×C53 | C23 | 1 | 1 | yes | characteristic |
| 107 | #106×C53 | — | 2 | 1 | no | — |
| 108 | #106×C53 | — | 2 | 1 | no | — |
| 109 | C4⋊C8×C53 | D4 | 1 | 1 | yes | characteristic |
| 110 | #103×C53 | — | 2 | 1 | no | — |
| 111 | #103×C53 | — | 2 | 1 | no | — |
| 112 | #103×C53 | — | 2 | 1 | no | — |
| 113 | #102×C53 | — | 2 | 1 | no | — |
| 114 | #102×C53 | — | 2 | 1 | no | — |
| 115 | #102×C53 | — | 2 | 1 | no | — |
| 116 | C22⋊C8×C53 | D4 | 1 | 1 | yes | characteristic |
| 117 | C22⋊C8×C53 | D4 | 1 | 1 | yes | characteristic |
| 118 | C4×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 119 | C24×C53 | — | 4 | 1 | no | — |
| 120 | C24×C53 | — | 4 | 1 | no | — |
| 121 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 122 | C2×D4×C53 | — | 2 | 1 | no | — |
| 123 | C2×D4×C53 | — | 2 | 1 | no | — |
| 124 | C2×D4×C53 | — | 2 | 1 | no | — |
| 125 | C2×D4×C53 | — | 4 | 2 | no | — |
| 126 | C2×D4×C53 | — | 4 | 2 | no | — |
| 127 | C2×D4×C53 | — | 4 | 1 | no | — |
| 128 | C2×D4×C53 | — | 4 | 1 | no | — |
| 129 | C2×D4×C53 | — | 4 | 1 | no | — |
| 130 | C2×D4×C53 | — | 4 | 1 | no | — |
| 131 | C2×D4×C53 | — | 4 | 1 | no | — |
| 132 | C2×D4×C53 | — | 4 | 1 | no | — |
| 133 | C2×D4×C53 | — | 8 | 1 | no | — |
| 134 | C2×D4×C53 | — | 8 | 1 | no | — |
| 135 | C2×D4×C53 | — | 8 | 4 | no | — |
| 136 | C2×D4×C53 | D8 | 1 | 1 | yes | characteristic |
| 137 | C22×C4×C53 | — | 4 | 1 | no | — |
| 138 | C22×C4×C53 | — | 4 | 1 | no | — |
| 139 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 140 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 141 | Q16×C53 | — | 2 | 1 | no | — |
| 142 | Q16×C53 | — | 2 | 1 | no | — |
| 143 | D8×C53 | — | 2 | 1 | no | — |
| 144 | D8×C53 | — | 2 | 1 | no | — |
| 145 | D8×C53 | — | 2 | 1 | no | — |
| 146 | D8×C53 | — | 2 | 1 | no | — |
| 147 | D8×C53 | — | 2 | 1 | no | — |
| 148 | D8×C53 | — | 4 | 2 | no | — |
| 149 | D8×C53 | — | 4 | 2 | no | — |
| 150 | D8×C53 | — | 8 | 1 | no | — |
| 151 | D8×C53 | #41 | 1 | 2 | yes | — |
| 152 | C2×C8×C53 | — | 2 | 1 | no | — |
| 153 | C2×C8×C53 | — | 2 | 1 | no | — |
| 154 | C2×C8×C53 | — | 2 | 1 | no | — |
| 155 | C2×C8×C53 | — | 2 | 1 | no | — |
| 156 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 157 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 158 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C2×C8×C53 | C24 | 1 | 1 | yes | characteristic |
| 160 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 161 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 162 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 163 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 164 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 165 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 166 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 167 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 168 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 169 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 170 | C4⋊C4×C53 | D8 | 1 | 1 | yes | characteristic |
| 171 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 172 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 173 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 174 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 175 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 176 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 177 | C22⋊C4×C53 | D8 | 1 | 1 | yes | characteristic |
| 178 | C22⋊C4×C53 | D8 | 1 | 1 | yes | characteristic |
| 179 | C42×C53 | — | 4 | 1 | no | — |
| 180 | C42×C53 | — | 4 | 1 | no | — |
| 181 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 182 | C16×C53 | — | 2 | 1 | no | — |
| 183 | C16×C53 | — | 2 | 1 | no | — |
| 184 | C16×C53 | — | 2 | 1 | no | — |
| 185 | C16×C53 | — | 2 | 1 | no | — |
| 186 | C23×C53 | — | 4 | 1 | no | — |
| 187 | C23×C53 | — | 4 | 1 | no | — |
| 188 | C23×C53 | — | 4 | 1 | no | — |
| 189 | C23×C53 | — | 8 | 2 | no | — |
| 190 | C23×C53 | — | 8 | 2 | no | — |
| 191 | C23×C53 | — | 8 | 2 | no | — |
| 192 | C23×C53 | — | 8 | 2 | no | — |
| 193 | C23×C53 | — | 16 | 1 | no | — |
| 194 | C23×C53 | — | 16 | 1 | no | — |
| 195 | C23×C53 | C2×D8 | 1 | 1 | yes | characteristic |
| 196 | C23×C53 | C2×D8 | 1 | 1 | yes | characteristic |
| 197 | Q8×C53 | — | 4 | 1 | no | — |
| 198 | Q8×C53 | — | 4 | 1 | no | — |
| 199 | D4×C53 | — | 2 | 2 | no | — |
| 200 | D4×C53 | — | 2 | 2 | no | — |
| 201 | D4×C53 | — | 4 | 1 | no | — |
| 202 | D4×C53 | — | 4 | 1 | no | — |
| 203 | D4×C53 | — | 4 | 1 | no | — |
| 204 | D4×C53 | — | 4 | 1 | no | — |
| 205 | D4×C53 | — | 4 | 1 | no | — |
| 206 | D4×C53 | — | 8 | 2 | no | — |
| 207 | D4×C53 | — | 8 | 2 | no | — |
| 208 | D4×C53 | — | 8 | 2 | no | — |
| 209 | D4×C53 | — | 8 | 2 | no | — |
| 210 | D4×C53 | — | 8 | 2 | no | — |
| 211 | D4×C53 | — | 16 | 1 | no | — |
| 212 | C2×C4×C53 | — | 2 | 1 | no | — |
| 213 | C2×C4×C53 | — | 2 | 1 | no | — |
| 214 | C2×C4×C53 | — | 2 | 1 | no | — |
| 215 | C2×C4×C53 | — | 2 | 1 | no | — |
| 216 | C2×C4×C53 | — | 4 | 1 | no | — |
| 217 | C2×C4×C53 | — | 4 | 1 | no | — |
| 218 | C2×C4×C53 | — | 4 | 1 | no | — |
| 219 | C2×C4×C53 | — | 4 | 1 | no | — |
| 220 | C2×C4×C53 | — | 4 | 1 | no | — |
| 221 | C2×C4×C53 | — | 8 | 2 | no | — |
| 222 | C2×C4×C53 | — | 8 | 2 | no | — |
| 223 | C2×C4×C53 | C2×D8 | 1 | 1 | yes | characteristic |
| 224 | C2×C4×C53 | C2×D8 | 1 | 1 | yes | characteristic |
| 225 | C2×C4×C53 | C2×D8 | 1 | 1 | yes | characteristic |
| 226 | C2×C4×C53 | C2×D8 | 1 | 1 | yes | characteristic |
| 227 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 228 | C8×C53 | — | 2 | 1 | no | — |
| 229 | C8×C53 | — | 2 | 1 | no | — |
| 230 | C8×C53 | — | 2 | 1 | no | — |
| 231 | C8×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 232 | C8×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 233 | #33877 | C53 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 234 | C22×C53 | — | 2 | 1 | no | — |
| 235 | C22×C53 | — | 2 | 1 | no | — |
| 236 | C22×C53 | — | 2 | 1 | no | — |
| 237 | C22×C53 | — | 2 | 1 | no | — |
| 238 | C22×C53 | — | 2 | 1 | no | — |
| 239 | C22×C53 | — | 4 | 2 | no | — |
| 240 | C22×C53 | — | 8 | 1 | no | — |
| 241 | C22×C53 | — | 8 | 1 | no | — |
| 242 | C22×C53 | — | 8 | 1 | no | — |
| 243 | C22×C53 | — | 8 | 1 | no | — |
| 244 | C22×C53 | — | 8 | 1 | no | — |
| 245 | C22×C53 | — | 8 | 1 | no | — |
| 246 | C22×C53 | — | 8 | 1 | no | — |
| 247 | C22×C53 | — | 8 | 1 | no | — |
| 248 | C22×C53 | — | 16 | 4 | no | — |
| 249 | C22×C53 | — | 16 | 4 | no | — |
| 250 | C22×C53 | #509 | 1 | 2 | yes | — |
| 251 | C22×C53 | C22×D8 | 1 | 1 | yes | characteristic |
| 252 | C4×C53 | — | 2 | 1 | no | — |
| 253 | C4×C53 | — | 2 | 1 | no | — |
| 254 | C4×C53 | — | 2 | 1 | no | — |
| 255 | C4×C53 | — | 2 | 1 | no | — |
| 256 | C4×C53 | — | 8 | 1 | no | — |
| 257 | C4×C53 | — | 8 | 1 | no | — |
| 258 | C4×C53 | — | 8 | 1 | no | — |
| 259 | C4×C53 | — | 8 | 1 | no | — |
| 260 | C4×C53 | — | 8 | 1 | no | — |
| 261 | C4×C53 | #546 | 1 | 1 | yes | characteristic |
| 262 | C4×C53 | #577 | 1 | 1 | yes | characteristic |
| 263 | #3336 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 264 | D4×D8 | C2×C53 | 1 | 1 | yes | characteristic |
| 265 | #2244 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 266 | #2234 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 267 | #2232 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 268 | #2228 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 269 | #2220 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 270 | #2217 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 271 | #2207 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 272 | #2187 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 273 | #2187 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 274 | #2175 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 275 | #2168 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 276 | #2140 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 277 | C2×#357 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 278 | C2×C53 | — | 2 | 2 | no | — |
| 279 | C2×C53 | — | 4 | 1 | no | — |
| 280 | C2×C53 | — | 8 | 2 | no | — |
| 281 | C2×C53 | — | 16 | 1 | no | — |
| 282 | C2×C53 | — | 16 | 1 | no | — |
| 283 | C2×C53 | #3294 | 1 | 1 | yes | characteristic |
| 284 | C2×C53 | C2×#509 | 1 | 1 | yes | characteristic |
| 285 | C2×C53 | #3416 | 1 | 1 | yes | characteristic |
| 286 | C22×D8 | C22×C53 | 1 | 1 | yes | characteristic |
| 287 | C22×D8 | C22×C53 | 1 | 1 | yes | characteristic |
| 288 | #552 | — | 2 | 1 | no | — |
| 289 | D42 | — | 2 | 1 | no | — |
| 290 | C2×SD32 | C22×C53 | 1 | 1 | yes | characteristic |
| 291 | C2×SD32 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 292 | C2×SD32 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 293 | C2×M32 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 294 | C22×C16 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 295 | #499 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 296 | #493 | C22×C53 | 1 | 1 | yes | characteristic |
| 297 | #485 | — | 2 | 1 | no | — |
| 298 | #483 | — | 2 | 1 | no | — |
| 299 | #479 | — | 2 | 1 | no | — |
| 300 | #467 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 301 | #467 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 302 | #466 | C22×C53 | 1 | 1 | yes | characteristic |
| 303 | #466 | C22×C53 | 1 | 1 | yes | characteristic |
| 304 | #459 | — | 2 | 1 | no | — |
| 305 | #447 | — | 2 | 1 | no | — |
| 306 | #447 | — | 2 | 1 | no | — |
| 307 | C4×Q16 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 308 | C4×D8 | C22×C53 | 1 | 1 | yes | characteristic |
| 309 | C8×D4 | C22×C53 | 1 | 1 | yes | characteristic |
| 310 | #427 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 311 | C2×#107 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 312 | #367 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 313 | #366 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 314 | #366 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 315 | C4⋊C16 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 316 | #358 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 317 | #357 | C22×C53 | 1 | 1 | yes | characteristic |
| 318 | #357 | C22×C53 | 1 | 1 | yes | characteristic |
| 319 | #357 | C22×C53 | 1 | 1 | yes | characteristic |
| 320 | #357 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 321 | #357 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 322 | #357 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 323 | #357 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 324 | #357 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 325 | #357 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 326 | C22⋊C16 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 327 | C22⋊C16 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 328 | #346 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 329 | C53 | #33877 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 330 | C22×D4 | — | 2 | 1 | no | — |
| 331 | C22×D4 | — | 2 | 1 | no | — |
| 332 | C22×D4 | — | 4 | 1 | no | — |
| 333 | C2×Q16 | C23×C53 | 1 | 1 | yes | characteristic |
| 334 | C2×D8 | — | 2 | 2 | no | — |
| 335 | C2×D8 | — | 2 | 2 | no | — |
| 336 | C2×D8 | — | 2 | 1 | no | — |
| 337 | C2×D8 | — | 2 | 1 | no | — |
| 338 | C2×D8 | — | 2 | 1 | no | — |
| 339 | C2×D8 | — | 4 | 1 | no | — |
| 340 | C2×D8 | — | 4 | 1 | no | — |
| 341 | C2×D8 | C23×C53 | 1 | 1 | yes | characteristic |
| 342 | C2×D8 | C23×C53 | 1 | 1 | yes | characteristic |
| 343 | C2×D8 | C23×C53 | 1 | 1 | yes | characteristic |
| 344 | C22×C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 345 | C22×C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 346 | #127 | — | 2 | 1 | no | — |
| 347 | #126 | — | 4 | 1 | no | — |
| 348 | #125 | — | 2 | 1 | no | — |
| 349 | #125 | — | 4 | 1 | no | — |
| 350 | #123 | — | 4 | 1 | no | — |
| 351 | C22⋊Q8 | — | 2 | 1 | no | — |
| 352 | C22⋊Q8 | — | 2 | 1 | no | — |
| 353 | #121 | — | 2 | 1 | no | — |
| 354 | #121 | — | 2 | 1 | no | — |
| 355 | #121 | — | 4 | 1 | no | — |
| 356 | #120 | — | 4 | 1 | no | — |
| 357 | #120 | — | 4 | 1 | no | — |
| 358 | C4×Q8 | — | 2 | 1 | no | — |
| 359 | C4×D4 | — | 2 | 1 | no | — |
| 360 | C4×D4 | D4×C53 | 1 | 1 | yes | characteristic |
| 361 | #117 | — | 2 | 1 | no | — |
| 362 | #117 | — | 4 | 1 | no | — |
| 363 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 364 | SD32 | — | 2 | 2 | no | — |
| 365 | SD32 | — | 4 | 1 | no | — |
| 366 | SD32 | — | 4 | 1 | no | — |
| 367 | M32 | — | 4 | 1 | no | — |
| 368 | C2×C16 | — | 4 | 1 | no | — |
| 369 | C2×C16 | C23×C53 | 1 | 1 | yes | characteristic |
| 370 | C2×C16 | C23×C53 | 1 | 1 | yes | characteristic |
| 371 | C2×C16 | C23×C53 | 1 | 1 | yes | characteristic |
| 372 | C2×C16 | C23×C53 | 1 | 1 | yes | characteristic |
| 373 | #107 | — | 2 | 1 | no | — |
| 374 | #107 | C23×C53 | 1 | 1 | yes | characteristic |
| 375 | #107 | C23×C53 | 1 | 1 | yes | characteristic |
| 376 | #107 | C23×C53 | 1 | 1 | yes | characteristic |
| 377 | #107 | C23×C53 | 1 | 1 | yes | characteristic |
| 378 | #106 | — | 2 | 1 | no | — |
| 379 | #106 | — | 2 | 1 | no | — |
| 380 | C4⋊C8 | D4×C53 | 1 | 1 | yes | characteristic |
| 381 | #103 | — | 2 | 1 | no | — |
| 382 | #103 | — | 2 | 1 | no | — |
| 383 | #103 | — | 2 | 1 | no | — |
| 384 | #102 | — | 2 | 1 | no | — |
| 385 | #102 | — | 2 | 1 | no | — |
| 386 | #102 | — | 2 | 1 | no | — |
| 387 | C22⋊C8 | D4×C53 | 1 | 1 | yes | characteristic |
| 388 | C22⋊C8 | D4×C53 | 1 | 1 | yes | characteristic |
| 389 | C4×C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 390 | C24 | — | 4 | 1 | no | — |
| 391 | C24 | — | 4 | 1 | no | — |
| 392 | C2×Q8 | — | 2 | 1 | no | — |
| 393 | C2×D4 | — | 2 | 1 | no | — |
| 394 | C2×D4 | — | 2 | 1 | no | — |
| 395 | C2×D4 | — | 2 | 1 | no | — |
| 396 | C2×D4 | — | 4 | 2 | no | — |
| 397 | C2×D4 | — | 4 | 2 | no | — |
| 398 | C2×D4 | — | 4 | 1 | no | — |
| 399 | C2×D4 | — | 4 | 1 | no | — |
| 400 | C2×D4 | — | 4 | 1 | no | — |
| 401 | C2×D4 | — | 4 | 1 | no | — |
| 402 | C2×D4 | — | 4 | 1 | no | — |
| 403 | C2×D4 | — | 4 | 1 | no | — |
| 404 | C2×D4 | — | 8 | 1 | no | — |
| 405 | C2×D4 | — | 8 | 1 | no | — |
| 406 | C2×D4 | — | 8 | 4 | no | — |
| 407 | C2×D4 | D8×C53 | 1 | 1 | yes | characteristic |
| 408 | C22×C4 | — | 4 | 1 | no | — |
| 409 | C22×C4 | — | 4 | 1 | no | — |
| 410 | C22×C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 411 | C22×C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 412 | Q16 | — | 2 | 1 | no | — |
| 413 | Q16 | — | 2 | 1 | no | — |
| 414 | D8 | — | 2 | 1 | no | — |
| 415 | D8 | — | 2 | 1 | no | — |
| 416 | D8 | — | 2 | 1 | no | — |
| 417 | D8 | — | 2 | 1 | no | — |
| 418 | D8 | — | 2 | 1 | no | — |
| 419 | D8 | — | 4 | 2 | no | — |
| 420 | D8 | — | 4 | 2 | no | — |
| 421 | D8 | — | 8 | 1 | no | — |
| 422 | D8 | #41×C53 | 1 | 2 | yes | — |
| 423 | C2×C8 | — | 2 | 1 | no | — |
| 424 | C2×C8 | — | 2 | 1 | no | — |
| 425 | C2×C8 | — | 2 | 1 | no | — |
| 426 | C2×C8 | — | 2 | 1 | no | — |
| 427 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 428 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 429 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 430 | C2×C8 | C24×C53 | 1 | 1 | yes | characteristic |
| 431 | C4⋊C4 | — | 2 | 1 | no | — |
| 432 | C4⋊C4 | — | 2 | 1 | no | — |
| 433 | C4⋊C4 | — | 2 | 1 | no | — |
| 434 | C4⋊C4 | — | 2 | 1 | no | — |
| 435 | C4⋊C4 | — | 4 | 1 | no | — |
| 436 | C4⋊C4 | — | 4 | 1 | no | — |
| 437 | C4⋊C4 | — | 4 | 1 | no | — |
| 438 | C4⋊C4 | — | 4 | 1 | no | — |
| 439 | C4⋊C4 | — | 4 | 1 | no | — |
| 440 | C4⋊C4 | — | 4 | 1 | no | — |
| 441 | C4⋊C4 | D8×C53 | 1 | 1 | yes | characteristic |
| 442 | C22⋊C4 | — | 4 | 1 | no | — |
| 443 | C22⋊C4 | — | 4 | 1 | no | — |
| 444 | C22⋊C4 | — | 4 | 1 | no | — |
| 445 | C22⋊C4 | — | 4 | 1 | no | — |
| 446 | C22⋊C4 | — | 4 | 1 | no | — |
| 447 | C22⋊C4 | — | 4 | 1 | no | — |
| 448 | C22⋊C4 | D8×C53 | 1 | 1 | yes | characteristic |
| 449 | C22⋊C4 | D8×C53 | 1 | 1 | yes | characteristic |
| 450 | C42 | — | 4 | 1 | no | — |
| 451 | C42 | — | 4 | 1 | no | — |
| 452 | C42 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 453 | C16 | — | 2 | 1 | no | — |
| 454 | C16 | — | 2 | 1 | no | — |
| 455 | C16 | — | 2 | 1 | no | — |
| 456 | C16 | — | 2 | 1 | no | — |
| 457 | C23 | — | 4 | 1 | no | — |
| 458 | C23 | — | 4 | 1 | no | — |
| 459 | C23 | — | 4 | 1 | no | — |
| 460 | C23 | — | 8 | 2 | no | — |
| 461 | C23 | — | 8 | 2 | no | — |
| 462 | C23 | — | 8 | 2 | no | — |
| 463 | C23 | — | 8 | 2 | no | — |
| 464 | C23 | — | 16 | 1 | no | — |
| 465 | C23 | — | 16 | 1 | no | — |
| 466 | C23 | C2×D8×C53 | 1 | 1 | yes | characteristic |
| 467 | C23 | C2×D8×C53 | 1 | 1 | yes | characteristic |
| 468 | Q8 | — | 4 | 1 | no | — |
| 469 | Q8 | — | 4 | 1 | no | — |
| 470 | D4 | — | 2 | 2 | no | — |
| 471 | D4 | — | 2 | 2 | no | — |
| 472 | D4 | — | 4 | 1 | no | — |
| 473 | D4 | — | 4 | 1 | no | — |
| 474 | D4 | — | 4 | 1 | no | — |
| 475 | D4 | — | 4 | 1 | no | — |
| 476 | D4 | — | 4 | 1 | no | — |
| 477 | D4 | — | 8 | 2 | no | — |
| 478 | D4 | — | 8 | 2 | no | — |
| 479 | D4 | — | 8 | 2 | no | — |
| 480 | D4 | — | 8 | 2 | no | — |
| 481 | D4 | — | 8 | 2 | no | — |
| 482 | D4 | — | 16 | 1 | no | — |
| 483 | C2×C4 | — | 2 | 1 | no | — |
| 484 | C2×C4 | — | 2 | 1 | no | — |
| 485 | C2×C4 | — | 2 | 1 | no | — |
| 486 | C2×C4 | — | 2 | 1 | no | — |
| 487 | C2×C4 | — | 4 | 1 | no | — |
| 488 | C2×C4 | — | 4 | 1 | no | — |
| 489 | C2×C4 | — | 4 | 1 | no | — |
| 490 | C2×C4 | — | 4 | 1 | no | — |
| 491 | C2×C4 | — | 4 | 1 | no | — |
| 492 | C2×C4 | — | 8 | 2 | no | — |
| 493 | C2×C4 | — | 8 | 2 | no | — |
| 494 | C2×C4 | C2×D8×C53 | 1 | 1 | yes | characteristic |
| 495 | C2×C4 | C2×D8×C53 | 1 | 1 | yes | characteristic |
| 496 | C2×C4 | C2×D8×C53 | 1 | 1 | yes | characteristic |
| 497 | C2×C4 | C2×D8×C53 | 1 | 1 | yes | characteristic |
| 498 | C2×C4 | C22×D4×C53 | 1 | 1 | yes | characteristic |
| 499 | C8 | — | 2 | 1 | no | — |
| 500 | C8 | — | 2 | 1 | no | — |
| 501 | C8 | — | 2 | 1 | no | — |
| 502 | C8 | C2×#41×C53 | 1 | 1 | yes | characteristic |
| 503 | C8 | H(5,𝔽2)×C53 | 1 | 1 | yes | characteristic |
| 504 | C22 | — | 2 | 1 | no | — |
| 505 | C22 | — | 2 | 1 | no | — |
| 506 | C22 | — | 2 | 1 | no | — |
| 507 | C22 | — | 2 | 1 | no | — |
| 508 | C22 | — | 2 | 1 | no | — |
| 509 | C22 | — | 4 | 2 | no | — |
| 510 | C22 | — | 8 | 1 | no | — |
| 511 | C22 | — | 8 | 1 | no | — |
| 512 | C22 | — | 8 | 1 | no | — |
| 513 | C22 | — | 8 | 1 | no | — |
| 514 | C22 | — | 8 | 1 | no | — |
| 515 | C22 | — | 8 | 1 | no | — |
| 516 | C22 | — | 8 | 1 | no | — |
| 517 | C22 | — | 8 | 1 | no | — |
| 518 | C22 | — | 16 | 4 | no | — |
| 519 | C22 | — | 16 | 4 | no | — |
| 520 | C22 | C53×#509 | 1 | 2 | yes | — |
| 521 | C22 | C22×D8×C53 | 1 | 1 | yes | characteristic |
| 522 | C4 | — | 2 | 1 | no | — |
| 523 | C4 | — | 2 | 1 | no | — |
| 524 | C4 | — | 2 | 1 | no | — |
| 525 | C4 | — | 2 | 1 | no | — |
| 526 | C4 | — | 8 | 1 | no | — |
| 527 | C4 | — | 8 | 1 | no | — |
| 528 | C4 | — | 8 | 1 | no | — |
| 529 | C4 | — | 8 | 1 | no | — |
| 530 | C4 | — | 8 | 1 | no | — |
| 531 | C4 | C53×#546 | 1 | 1 | yes | characteristic |
| 532 | C4 | C53×#577 | 1 | 1 | yes | characteristic |
| 533 | C2 | — | 2 | 2 | no | — |
| 534 | C2 | — | 4 | 1 | no | — |
| 535 | C2 | — | 8 | 2 | no | — |
| 536 | C2 | — | 16 | 1 | no | — |
| 537 | C2 | — | 16 | 1 | no | — |
| 538 | C2 | C53×#3294 | 1 | 1 | yes | characteristic |
| 539 | C2 | C2×C53×#509 | 1 | 1 | yes | characteristic |
| 540 | C2 | C53×#3416 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta