| 1 | #16811355 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #16811348 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #16811016 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #16810994 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #16810847 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #16810842 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #16810831 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #16810826 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #16810825 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #16810821 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #16810751 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #16810725 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #16810724 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | Q16×Dic53 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C53×#497 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#11719925 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#11719913 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#11719923 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#11719924 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#11719924 | C22 | 1 | 1 | yes | characteristic |
| 21 | #13133215 | C22 | 1 | 1 | yes | characteristic |
| 22 | #13133215 | C22 | 1 | 1 | yes | characteristic |
| 23 | #13133213 | C22 | 1 | 1 | yes | characteristic |
| 24 | #13133208 | — | 2 | 1 | no | — |
| 25 | #13133207 | — | 2 | 1 | no | — |
| 26 | #13133207 | — | 2 | 1 | no | — |
| 27 | #13133206 | C22 | 1 | 1 | yes | characteristic |
| 28 | #13133203 | — | 2 | 1 | no | — |
| 29 | #13133201 | — | 2 | 1 | no | — |
| 30 | #13133199 | — | 2 | 1 | no | — |
| 31 | Q8×Dic53 | C22 | 1 | 1 | yes | characteristic |
| 32 | Q8×Dic53 | C22 | 1 | 1 | yes | characteristic |
| 33 | Q8×Dic53 | C22 | 1 | 1 | yes | characteristic |
| 34 | C4×Dic106 | C22 | 1 | 1 | yes | characteristic |
| 35 | C4×Dic106 | C22 | 1 | 1 | yes | characteristic |
| 36 | #13133182 | — | 2 | 1 | no | — |
| 37 | C4×D212 | C22 | 1 | 1 | yes | characteristic |
| 38 | D4×Dic53 | C22 | 1 | 1 | yes | characteristic |
| 39 | #13133177 | — | 2 | 1 | no | — |
| 40 | #13133151 | C22 | 1 | 1 | yes | characteristic |
| 41 | C4⋊#88322 | C22 | 1 | 1 | yes | characteristic |
| 42 | #13133146 | C22 | 1 | 1 | yes | characteristic |
| 43 | #13133146 | C22 | 1 | 1 | yes | characteristic |
| 44 | #13133142 | C22 | 1 | 1 | yes | characteristic |
| 45 | #13133141 | C22 | 1 | 1 | yes | characteristic |
| 46 | #13133141 | C22 | 1 | 1 | yes | characteristic |
| 47 | #13133141 | C22 | 1 | 1 | yes | characteristic |
| 48 | #13133139 | C22 | 1 | 1 | yes | characteristic |
| 49 | #13133138 | C22 | 1 | 1 | yes | characteristic |
| 50 | #13133127 | C22 | 1 | 1 | yes | characteristic |
| 51 | C8×Dic53 | C22 | 1 | 1 | yes | characteristic |
| 52 | C2×Q16×C53 | C22 | 1 | 1 | yes | characteristic |
| 53 | C2×Q16×C53 | C22 | 1 | 1 | yes | characteristic |
| 54 | C2×SD16×C53 | C22 | 1 | 1 | yes | characteristic |
| 55 | C2×SD16×C53 | C22 | 1 | 1 | yes | characteristic |
| 56 | C4⋊Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 57 | #124×C53 | C22 | 1 | 1 | yes | characteristic |
| 58 | #97×C53 | C22 | 1 | 1 | yes | characteristic |
| 59 | C2×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×D4×C53 | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 64 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 65 | C22×Dic53 | — | 2 | 1 | no | — |
| 66 | C2×D212 | C23 | 1 | 1 | yes | characteristic |
| 67 | C2×C4×D53 | — | 2 | 1 | no | — |
| 68 | C2×Dic106 | D4 | 1 | 1 | yes | characteristic |
| 69 | C2×Dic106 | C23 | 1 | 1 | yes | characteristic |
| 70 | Q16×C53 | — | 2 | 2 | no | — |
| 71 | Q16×C53 | — | 4 | 1 | no | — |
| 72 | SD16×C53 | — | 2 | 2 | no | — |
| 73 | SD16×C53 | — | 4 | 1 | no | — |
| 74 | C2×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 75 | C2×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 76 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 77 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 78 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 79 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 80 | C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 81 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 82 | #11719925 | — | 4 | 1 | no | — |
| 83 | #11719924 | — | 4 | 1 | no | — |
| 84 | #11719924 | — | 4 | 1 | no | — |
| 85 | #11719923 | — | 4 | 1 | no | — |
| 86 | #11719921 | — | 2 | 1 | no | — |
| 87 | #11719921 | — | 2 | 1 | no | — |
| 88 | #11719921 | — | 2 | 1 | no | — |
| 89 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 90 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 91 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 92 | C4⋊Dic53 | D4 | 1 | 1 | yes | characteristic |
| 93 | C4⋊Dic53 | C23 | 1 | 1 | yes | characteristic |
| 94 | C4⋊Dic53 | C23 | 1 | 1 | yes | characteristic |
| 95 | #11719919 | — | 2 | 1 | no | — |
| 96 | #11719919 | — | 2 | 1 | no | — |
| 97 | #11719919 | — | 2 | 1 | no | — |
| 98 | #11719919 | — | 2 | 1 | no | — |
| 99 | #11719919 | — | 2 | 1 | no | — |
| 100 | #11719919 | D4 | 1 | 1 | yes | characteristic |
| 101 | #11719919 | D4 | 1 | 1 | yes | characteristic |
| 102 | C4×Dic53 | — | 2 | 1 | no | — |
| 103 | C4×Dic53 | — | 2 | 1 | no | — |
| 104 | C4×Dic53 | — | 2 | 1 | no | — |
| 105 | C4×Dic53 | — | 2 | 1 | no | — |
| 106 | C4×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 107 | C4×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 108 | C2×#88322 | C23 | 1 | 1 | yes | characteristic |
| 109 | C2×#88322 | C23 | 1 | 1 | yes | characteristic |
| 110 | #11719913 | — | 2 | 2 | no | — |
| 111 | C23×C53 | — | 2 | 1 | no | — |
| 112 | C22×D53 | — | 2 | 1 | no | — |
| 113 | Q8×C53 | — | 2 | 1 | no | — |
| 114 | Q8×C53 | — | 2 | 1 | no | — |
| 115 | Q8×C53 | — | 2 | 1 | no | — |
| 116 | Q8×C53 | — | 2 | 1 | no | — |
| 117 | Q8×C53 | — | 2 | 1 | no | — |
| 118 | Q8×C53 | — | 2 | 1 | no | — |
| 119 | D4×C53 | — | 2 | 1 | no | — |
| 120 | D4×C53 | — | 2 | 1 | no | — |
| 121 | C2×C4×C53 | — | 2 | 1 | no | — |
| 122 | C2×C4×C53 | — | 2 | 1 | no | — |
| 123 | C2×C4×C53 | — | 2 | 1 | no | — |
| 124 | C2×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 125 | C2×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 126 | C2×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 127 | C22⋊D53 | — | 4 | 2 | no | — |
| 128 | C22⋊D53 | — | 8 | 1 | no | — |
| 129 | C2×Dic53 | — | 2 | 1 | no | — |
| 130 | C2×Dic53 | — | 2 | 1 | no | — |
| 131 | C2×Dic53 | — | 2 | 1 | no | — |
| 132 | C2×Dic53 | — | 8 | 1 | no | — |
| 133 | C2×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 134 | C2×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | C2×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 136 | C2×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 137 | D212 | — | 2 | 1 | no | — |
| 138 | D212 | — | 2 | 1 | no | — |
| 139 | C4×D53 | — | 8 | 1 | no | — |
| 140 | Dic106 | — | 2 | 2 | no | — |
| 141 | Dic106 | — | 2 | 1 | no | — |
| 142 | Dic106 | — | 2 | 1 | no | — |
| 143 | C8×C53 | — | 2 | 1 | no | — |
| 144 | C8×C53 | #41 | 1 | 2 | yes | — |
| 145 | #88322 | — | 2 | 1 | no | — |
| 146 | #88322 | — | 2 | 1 | no | — |
| 147 | C22×C53 | — | 4 | 1 | no | — |
| 148 | C22×C53 | — | 4 | 1 | no | — |
| 149 | C22×C53 | — | 4 | 1 | no | — |
| 150 | C22×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 151 | C2×D53 | — | 4 | 1 | no | — |
| 152 | C2×D53 | — | 4 | 1 | no | — |
| 153 | C2×D53 | — | 4 | 1 | no | — |
| 154 | C4×C53 | — | 2 | 1 | no | — |
| 155 | C4×C53 | — | 2 | 1 | no | — |
| 156 | C4×C53 | — | 4 | 1 | no | — |
| 157 | C4×C53 | — | 4 | 1 | no | — |
| 158 | C4×C53 | — | 4 | 1 | no | — |
| 159 | C4×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 160 | C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 161 | Dic53 | — | 2 | 1 | no | — |
| 162 | Dic53 | — | 2 | 1 | no | — |
| 163 | Dic53 | — | 2 | 1 | no | — |
| 164 | Dic53 | — | 4 | 1 | no | — |
| 165 | Dic53 | — | 4 | 1 | no | — |
| 166 | Dic53 | — | 4 | 1 | no | — |
| 167 | Dic53 | #137 | 1 | 2 | yes | — |
| 168 | #3400 | — | 53 | 1 | no | maximal, Sylow |
| 169 | C2×C53 | — | 8 | 1 | no | — |
| 170 | C2×C53 | #550 | 1 | 1 | yes | characteristic |
| 171 | C2×C53 | C2×#137 | 1 | 1 | yes | characteristic |
| 172 | C2×C53 | #577 | 1 | 1 | yes | characteristic |
| 173 | D53 | — | 8 | 1 | no | — |
| 174 | #559 | — | 53 | 1 | no | — |
| 175 | #557 | — | 53 | 1 | no | — |
| 176 | #497 | — | 53 | 1 | no | — |
| 177 | #497 | D53 | 1 | 1 | yes | characteristic, complemented |
| 178 | #492 | — | 53 | 1 | no | — |
| 179 | #464 | — | 53 | 1 | no | — |
| 180 | #464 | — | 53 | 1 | no | — |
| 181 | #462 | — | 53 | 1 | no | — |
| 182 | #461 | — | 53 | 1 | no | — |
| 183 | #461 | — | 53 | 1 | no | — |
| 184 | #460 | — | 53 | 1 | no | — |
| 185 | #446 | — | 53 | 1 | no | — |
| 186 | #440 | — | 53 | 1 | no | — |
| 187 | #440 | — | 53 | 1 | no | — |
| 188 | C4×Q16 | — | 53 | 1 | no | — |
| 189 | C53 | #3400 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 190 | C2×Q16 | — | 53 | 1 | no | — |
| 191 | C2×Q16 | C2×D53 | 1 | 1 | yes | characteristic |
| 192 | C2×Q16 | C2×D53 | 1 | 1 | yes | characteristic |
| 193 | C2×SD16 | — | 53 | 1 | no | — |
| 194 | C2×SD16 | — | 53 | 1 | no | — |
| 195 | C2×SD16 | — | 53 | 1 | no | — |
| 196 | C2×SD16 | — | 53 | 1 | no | — |
| 197 | C2×SD16 | C2×D53 | 1 | 1 | yes | characteristic |
| 198 | C2×SD16 | C2×D53 | 1 | 1 | yes | characteristic |
| 199 | C4⋊Q8 | — | 53 | 1 | no | — |
| 200 | C4⋊Q8 | — | 53 | 1 | no | — |
| 201 | C4⋊Q8 | C2×D53 | 1 | 1 | yes | characteristic |
| 202 | #127 | — | 53 | 1 | no | — |
| 203 | #125 | — | 106 | 1 | no | — |
| 204 | #125 | — | 106 | 1 | no | — |
| 205 | #125 | — | 106 | 1 | no | — |
| 206 | #124 | — | 53 | 1 | no | — |
| 207 | #124 | — | 106 | 1 | no | — |
| 208 | #124 | C2×D53 | 1 | 1 | yes | characteristic |
| 209 | #123 | — | 106 | 1 | no | — |
| 210 | #123 | — | 106 | 1 | no | — |
| 211 | C4×Q8 | — | 53 | 1 | no | — |
| 212 | C4×Q8 | — | 53 | 1 | no | — |
| 213 | C4×Q8 | — | 53 | 1 | no | — |
| 214 | C4×Q8 | — | 53 | 1 | no | — |
| 215 | C4×Q8 | — | 53 | 1 | no | — |
| 216 | C4×Q8 | — | 106 | 1 | no | — |
| 217 | C4×D4 | — | 53 | 1 | no | — |
| 218 | C4×D4 | — | 53 | 1 | no | — |
| 219 | C4×D4 | — | 106 | 1 | no | — |
| 220 | #107 | — | 53 | 1 | no | — |
| 221 | C4⋊C8 | — | 53 | 1 | no | — |
| 222 | C4⋊C8 | — | 53 | 1 | no | — |
| 223 | C4⋊C8 | — | 53 | 1 | no | — |
| 224 | #103 | — | 53 | 1 | no | — |
| 225 | #103 | — | 53 | 1 | no | — |
| 226 | #103 | — | 53 | 1 | no | — |
| 227 | #103 | — | 53 | 1 | no | — |
| 228 | #102 | — | 53 | 1 | no | — |
| 229 | #102 | — | 53 | 1 | no | — |
| 230 | #97 | — | 53 | 1 | no | — |
| 231 | #97 | C2×D53 | 1 | 1 | yes | characteristic |
| 232 | C4×C8 | — | 53 | 1 | no | — |
| 233 | C2×Q8 | — | 53 | 1 | no | — |
| 234 | C2×Q8 | — | 53 | 1 | no | — |
| 235 | C2×Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 236 | C2×Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 237 | C2×Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 238 | C2×D4 | — | 53 | 1 | no | — |
| 239 | C2×D4 | — | 106 | 1 | no | — |
| 240 | C2×D4 | — | 106 | 1 | no | — |
| 241 | C2×D4 | C22×D53 | 1 | 1 | yes | characteristic |
| 242 | C22×C4 | — | 106 | 1 | no | — |
| 243 | C22×C4 | — | 106 | 1 | no | — |
| 244 | Q16 | — | 2 | 2 | no | — |
| 245 | Q16 | — | 4 | 1 | no | — |
| 246 | Q16 | — | 212 | 1 | no | — |
| 247 | SD16 | — | 2 | 2 | no | — |
| 248 | SD16 | — | 4 | 1 | no | — |
| 249 | SD16 | — | 106 | 2 | no | — |
| 250 | SD16 | — | 212 | 1 | no | — |
| 251 | SD16 | — | 212 | 1 | no | — |
| 252 | SD16 | — | 212 | 1 | no | — |
| 253 | C2×C8 | — | 53 | 1 | no | — |
| 254 | C2×C8 | — | 53 | 1 | no | — |
| 255 | C2×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 256 | C2×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 257 | C4⋊C4 | — | 2 | 1 | no | — |
| 258 | C4⋊C4 | — | 2 | 1 | no | — |
| 259 | C4⋊C4 | — | 53 | 1 | no | — |
| 260 | C4⋊C4 | — | 53 | 1 | no | — |
| 261 | C4⋊C4 | — | 53 | 1 | no | — |
| 262 | C4⋊C4 | — | 53 | 1 | no | — |
| 263 | C4⋊C4 | — | 53 | 1 | no | — |
| 264 | C4⋊C4 | — | 106 | 1 | no | — |
| 265 | C4⋊C4 | — | 106 | 1 | no | — |
| 266 | C4⋊C4 | — | 106 | 1 | no | — |
| 267 | C4⋊C4 | — | 106 | 1 | no | — |
| 268 | C4⋊C4 | — | 106 | 1 | no | — |
| 269 | C4⋊C4 | — | 106 | 1 | no | — |
| 270 | C4⋊C4 | — | 106 | 1 | no | — |
| 271 | C4⋊C4 | — | 106 | 1 | no | — |
| 272 | C22⋊C4 | — | 2 | 1 | no | — |
| 273 | C22⋊C4 | — | 2 | 1 | no | — |
| 274 | C22⋊C4 | — | 106 | 1 | no | — |
| 275 | C22⋊C4 | — | 106 | 1 | no | — |
| 276 | C22⋊C4 | — | 106 | 1 | no | — |
| 277 | C22⋊C4 | — | 106 | 1 | no | — |
| 278 | C42 | — | 53 | 1 | no | — |
| 279 | C42 | — | 53 | 1 | no | — |
| 280 | C42 | — | 106 | 1 | no | — |
| 281 | C42 | — | 106 | 1 | no | — |
| 282 | C42 | — | 106 | 1 | no | — |
| 283 | C42 | — | 106 | 1 | no | — |
| 284 | C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 285 | C23 | — | 2 | 1 | no | — |
| 286 | C23 | — | 106 | 1 | no | — |
| 287 | Q8 | — | 2 | 1 | no | — |
| 288 | Q8 | — | 2 | 1 | no | — |
| 289 | Q8 | — | 2 | 1 | no | — |
| 290 | Q8 | — | 2 | 1 | no | — |
| 291 | Q8 | — | 2 | 1 | no | — |
| 292 | Q8 | — | 2 | 1 | no | — |
| 293 | Q8 | — | 106 | 2 | no | — |
| 294 | Q8 | — | 106 | 1 | no | — |
| 295 | Q8 | — | 106 | 1 | no | — |
| 296 | D4 | — | 2 | 1 | no | — |
| 297 | D4 | — | 2 | 1 | no | — |
| 298 | D4 | — | 106 | 1 | no | — |
| 299 | D4 | — | 106 | 1 | no | — |
| 300 | D4 | — | 424 | 1 | no | — |
| 301 | D4 | — | 212 | 2 | no | — |
| 302 | C2×C4 | — | 2 | 1 | no | — |
| 303 | C2×C4 | — | 2 | 1 | no | — |
| 304 | C2×C4 | — | 2 | 1 | no | — |
| 305 | C2×C4 | — | 53 | 1 | no | — |
| 306 | C2×C4 | — | 53 | 1 | no | — |
| 307 | C2×C4 | — | 53 | 1 | no | — |
| 308 | C2×C4 | — | 53 | 1 | no | — |
| 309 | C2×C4 | — | 106 | 1 | no | — |
| 310 | C2×C4 | — | 106 | 1 | no | — |
| 311 | C2×C4 | — | 106 | 1 | no | — |
| 312 | C2×C4 | — | 424 | 1 | no | — |
| 313 | C2×C4 | — | 424 | 1 | no | — |
| 314 | C2×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 315 | C2×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 316 | C2×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 317 | C8 | — | 2 | 1 | no | — |
| 318 | C8 | — | 106 | 1 | no | — |
| 319 | C8 | — | 106 | 1 | no | — |
| 320 | C8 | #11719947 | 1 | 2 | yes | — |
| 321 | C22 | — | 4 | 1 | no | — |
| 322 | C22 | — | 4 | 1 | no | — |
| 323 | C22 | — | 4 | 1 | no | — |
| 324 | C22 | — | 212 | 1 | no | — |
| 325 | C22 | — | 212 | 1 | no | — |
| 326 | C22 | — | 212 | 1 | no | — |
| 327 | C22 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 328 | C4 | — | 2 | 1 | no | — |
| 329 | C4 | — | 2 | 1 | no | — |
| 330 | C4 | — | 4 | 1 | no | — |
| 331 | C4 | — | 4 | 1 | no | — |
| 332 | C4 | — | 4 | 1 | no | — |
| 333 | C4 | — | 53 | 2 | no | — |
| 334 | C4 | — | 106 | 1 | no | — |
| 335 | C4 | — | 106 | 1 | no | — |
| 336 | C4 | — | 106 | 1 | no | — |
| 337 | C4 | — | 212 | 1 | no | — |
| 338 | C4 | — | 212 | 1 | no | — |
| 339 | C4 | — | 212 | 1 | no | — |
| 340 | C4 | C2×#11719947 | 1 | 1 | yes | characteristic |
| 341 | C4 | #13133262 | 1 | 1 | yes | characteristic |
| 342 | C2 | — | 8 | 1 | no | — |
| 343 | C2 | — | 424 | 1 | no | — |
| 344 | C2 | #16811293 | 1 | 1 | yes | characteristic |
| 345 | C2 | #137×D53 | 1 | 1 | yes | characteristic |
| 346 | C2 | #16811432 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta