| 1 | #20275635 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #20275488 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20273364 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #20273004 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20272616 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20272555 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C53×#1492 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #16810676 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#13133152 | — | 2 | 1 | no | — |
| 10 | C2×C4⋊#88322 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#13133144 | — | 2 | 1 | no | — |
| 12 | C2×#13133144 | — | 2 | 1 | no | — |
| 13 | C4×#11719917 | C22 | 1 | 1 | yes | characteristic |
| 14 | C4×C4⋊Dic53 | C22 | 1 | 1 | yes | characteristic |
| 15 | #16810387 | — | 2 | 1 | no | — |
| 16 | #16810369 | C4 | 1 | 1 | yes | characteristic, complemented |
| 17 | #16810369 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | #16810367 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | #16810367 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | #16810345 | — | 2 | 1 | no | — |
| 21 | #16810344 | — | 2 | 1 | no | — |
| 22 | C53×#532 | C22 | 1 | 1 | yes | characteristic |
| 23 | C53×#423 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×C4×C8×C53 | C22 | 1 | 1 | yes | characteristic |
| 25 | C53×D4⋊C8 | — | 2 | 1 | no | — |
| 26 | C53×D4⋊C8 | — | 2 | 1 | no | — |
| 27 | C2×#11719917 | D4 | 1 | 1 | yes | characteristic |
| 28 | C2×#11719917 | D4 | 1 | 1 | yes | characteristic |
| 29 | C22×#88322 | — | 2 | 1 | no | — |
| 30 | C2×C4⋊Dic53 | — | 2 | 1 | no | — |
| 31 | C2×C4×Dic53 | — | 2 | 1 | no | — |
| 32 | #13133152 | — | 4 | 2 | no | — |
| 33 | C4⋊#88322 | — | 2 | 1 | no | — |
| 34 | C4⋊#88322 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C4⋊#88322 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C4⋊#88322 | C2×C4 | 1 | 1 | yes | characteristic |
| 37 | C4⋊#88322 | C2×C4 | 1 | 1 | yes | characteristic |
| 38 | #13133144 | — | 4 | 2 | no | — |
| 39 | #13133144 | — | 4 | 2 | no | — |
| 40 | C22⋊#88322 | — | 2 | 1 | no | — |
| 41 | #13133128 | — | 2 | 1 | no | — |
| 42 | C4×#88322 | — | 2 | 1 | no | — |
| 43 | C4×#88322 | — | 2 | 1 | no | — |
| 44 | #13133124 | — | 2 | 1 | no | — |
| 45 | C2×#41×C53 | — | 2 | 1 | no | — |
| 46 | C2×M16×C53 | — | 2 | 1 | no | — |
| 47 | C22×C8×C53 | — | 2 | 1 | no | — |
| 48 | C4⋊Q8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | #127×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 50 | #124×C53 | — | 2 | 1 | no | — |
| 51 | #121×C53 | — | 2 | 1 | no | — |
| 52 | #121×C53 | — | 2 | 1 | no | — |
| 53 | C4×D4×C53 | — | 2 | 1 | no | — |
| 54 | C4×D4×C53 | — | 2 | 1 | no | — |
| 55 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 56 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 57 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 58 | C4×C8×C53 | — | 2 | 1 | no | — |
| 59 | C4×C8×C53 | D4 | 1 | 1 | yes | characteristic |
| 60 | C4×C8×C53 | D4 | 1 | 1 | yes | characteristic |
| 61 | #41×C53 | — | 4 | 1 | no | — |
| 62 | #41×C53 | — | 4 | 1 | no | — |
| 63 | #41×C53 | — | 4 | 1 | no | — |
| 64 | #41×C53 | — | 4 | 1 | no | — |
| 65 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 66 | C2×D4×C53 | — | 2 | 1 | no | — |
| 67 | C2×D4×C53 | — | 2 | 1 | no | — |
| 68 | C2×D4×C53 | — | 2 | 1 | no | — |
| 69 | C2×D4×C53 | — | 4 | 1 | no | — |
| 70 | C22×C4×C53 | — | 4 | 1 | no | — |
| 71 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 72 | C22×C4×C53 | #41 | 1 | 1 | yes | characteristic |
| 73 | C22×C4×C53 | #41 | 1 | 1 | yes | characteristic |
| 74 | C22×Dic53 | — | 4 | 1 | no | — |
| 75 | M16×C53 | — | 4 | 1 | no | — |
| 76 | M16×C53 | — | 4 | 1 | no | — |
| 77 | C2×C8×C53 | — | 2 | 1 | no | — |
| 78 | C2×C8×C53 | — | 2 | 1 | no | — |
| 79 | C2×C8×C53 | — | 4 | 2 | no | — |
| 80 | C2×C8×C53 | — | 4 | 1 | no | — |
| 81 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 82 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 83 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 84 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 85 | C42×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 86 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 87 | C42×C53 | #41 | 1 | 1 | yes | characteristic |
| 88 | C42×C53 | #41 | 1 | 1 | yes | characteristic |
| 89 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 90 | C4⋊Dic53 | — | 4 | 1 | no | — |
| 91 | C4×Dic53 | — | 4 | 1 | no | — |
| 92 | C4×Dic53 | — | 4 | 1 | no | — |
| 93 | #11719917 | — | 2 | 1 | no | — |
| 94 | #11719917 | — | 2 | 1 | no | — |
| 95 | #11719917 | — | 2 | 1 | no | — |
| 96 | #11719917 | — | 2 | 1 | no | — |
| 97 | C2×#88322 | — | 2 | 1 | no | — |
| 98 | C2×#88322 | — | 2 | 1 | no | — |
| 99 | C2×#88322 | — | 2 | 1 | no | — |
| 100 | C2×#88322 | — | 2 | 1 | no | — |
| 101 | C2×#88322 | — | 2 | 1 | no | — |
| 102 | C2×#88322 | — | 2 | 1 | no | — |
| 103 | C2×#88322 | — | 4 | 1 | no | — |
| 104 | C2×#88322 | — | 4 | 1 | no | — |
| 105 | C23×C53 | — | 4 | 1 | no | — |
| 106 | C23×C53 | #124 | 1 | 1 | yes | characteristic |
| 107 | Q8×C53 | — | 4 | 1 | no | — |
| 108 | Q8×C53 | — | 4 | 1 | no | — |
| 109 | D4×C53 | — | 4 | 1 | no | — |
| 110 | D4×C53 | — | 4 | 1 | no | — |
| 111 | D4×C53 | — | 4 | 1 | no | — |
| 112 | D4×C53 | — | 4 | 1 | no | — |
| 113 | D4×C53 | — | 8 | 1 | no | — |
| 114 | D4×C53 | — | 8 | 1 | no | — |
| 115 | D4×C53 | — | 8 | 1 | no | — |
| 116 | C2×C4×C53 | — | 2 | 1 | no | — |
| 117 | C2×C4×C53 | — | 2 | 1 | no | — |
| 118 | C2×C4×C53 | — | 4 | 1 | no | — |
| 119 | C2×C4×C53 | — | 4 | 1 | no | — |
| 120 | C2×C4×C53 | — | 8 | 1 | no | — |
| 121 | C2×C4×C53 | — | 8 | 1 | no | — |
| 122 | C2×C4×C53 | #117 | 1 | 1 | yes | characteristic |
| 123 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 124 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 125 | C2×C4×C53 | #121 | 1 | 1 | yes | characteristic |
| 126 | C2×C4×C53 | #123 | 1 | 1 | yes | characteristic |
| 127 | C2×C4×C53 | #126 | 1 | 1 | yes | characteristic |
| 128 | C2×C4×C53 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 129 | C2×C4×C53 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 130 | C2×C4×C53 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 131 | C2×C4×C53 | #137 | 1 | 1 | yes | characteristic |
| 132 | C2×Dic53 | — | 4 | 2 | no | — |
| 133 | C2×Dic53 | — | 8 | 1 | no | — |
| 134 | C2×Dic53 | — | 8 | 1 | no | — |
| 135 | C8×C53 | — | 2 | 2 | no | — |
| 136 | C8×C53 | — | 4 | 1 | no | — |
| 137 | C8×C53 | — | 8 | 1 | no | — |
| 138 | #88322 | — | 4 | 1 | no | — |
| 139 | #88322 | — | 4 | 1 | no | — |
| 140 | #88322 | — | 4 | 1 | no | — |
| 141 | #88322 | — | 4 | 1 | no | — |
| 142 | #88322 | — | 4 | 1 | no | — |
| 143 | #88322 | — | 4 | 1 | no | — |
| 144 | #9592 | — | 53 | 1 | no | maximal, Sylow |
| 145 | C22×C53 | — | 2 | 1 | no | — |
| 146 | C22×C53 | — | 2 | 1 | no | — |
| 147 | C22×C53 | — | 8 | 1 | no | — |
| 148 | C22×C53 | — | 8 | 1 | no | — |
| 149 | C22×C53 | — | 8 | 1 | no | — |
| 150 | C22×C53 | #388 | 1 | 1 | yes | characteristic |
| 151 | C22×C53 | #489 | 1 | 1 | yes | characteristic |
| 152 | C22×C53 | #490 | 1 | 1 | yes | characteristic |
| 153 | C4×C53 | — | 2 | 1 | no | — |
| 154 | C4×C53 | — | 2 | 1 | no | — |
| 155 | C4×C53 | — | 2 | 1 | no | — |
| 156 | C4×C53 | — | 8 | 1 | no | — |
| 157 | C4×C53 | #440 | 1 | 1 | yes | characteristic |
| 158 | C4×C53 | #442 | 1 | 1 | yes | characteristic |
| 159 | C4×C53 | #443 | 1 | 1 | yes | characteristic |
| 160 | C4×C53 | #444 | 1 | 1 | yes | characteristic |
| 161 | C4×C53 | #468 | 1 | 1 | yes | characteristic |
| 162 | C4×C53 | #469 | 1 | 1 | yes | characteristic |
| 163 | Dic53 | — | 8 | 2 | no | — |
| 164 | #1980 | — | 53 | 1 | no | — |
| 165 | #1950 | — | 53 | 1 | no | — |
| 166 | #1540 | — | 53 | 1 | no | — |
| 167 | #1492 | D53 | 1 | 1 | yes | characteristic |
| 168 | #1451 | — | 53 | 1 | no | — |
| 169 | #1303 | — | 53 | 1 | no | — |
| 170 | #1279 | — | 53 | 1 | no | — |
| 171 | C2×C53 | — | 2 | 1 | no | — |
| 172 | C2×C53 | — | 2 | 1 | no | — |
| 173 | C2×C53 | — | 16 | 1 | no | — |
| 174 | C2×C53 | #1929 | 1 | 1 | yes | characteristic |
| 175 | C2×C53 | #1932 | 1 | 1 | yes | characteristic |
| 176 | C2×C53 | #1936 | 1 | 1 | yes | characteristic |
| 177 | #532 | C2×D53 | 1 | 1 | yes | characteristic |
| 178 | #431 | — | 53 | 1 | no | — |
| 179 | C2×#108 | — | 106 | 1 | no | — |
| 180 | #423 | C2×D53 | 1 | 1 | yes | characteristic |
| 181 | C2×C4⋊C8 | — | 53 | 1 | no | — |
| 182 | C2×#104 | — | 106 | 1 | no | — |
| 183 | C2×#104 | — | 106 | 1 | no | — |
| 184 | C4×M16 | — | 53 | 1 | no | — |
| 185 | C2×C4×C8 | C2×D53 | 1 | 1 | yes | characteristic |
| 186 | C4×C4⋊C4 | — | 53 | 1 | no | — |
| 187 | #341 | — | 106 | 1 | no | — |
| 188 | #332 | — | 53 | 1 | no | — |
| 189 | #332 | — | 53 | 1 | no | — |
| 190 | #331 | — | 53 | 1 | no | — |
| 191 | #331 | — | 53 | 1 | no | — |
| 192 | D4⋊C8 | — | 2 | 1 | no | — |
| 193 | D4⋊C8 | — | 2 | 1 | no | — |
| 194 | #322 | — | 106 | 1 | no | — |
| 195 | #322 | — | 106 | 1 | no | — |
| 196 | C53 | #9592 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 197 | C2×#41 | — | 2 | 1 | no | — |
| 198 | C2×M16 | — | 2 | 1 | no | — |
| 199 | C2×M16 | — | 53 | 1 | no | — |
| 200 | C2×M16 | — | 53 | 1 | no | — |
| 201 | C22×C8 | — | 2 | 1 | no | — |
| 202 | C22×C8 | — | 106 | 1 | no | — |
| 203 | C4⋊Q8 | C4×D53 | 1 | 1 | yes | characteristic |
| 204 | #127 | C4×D53 | 1 | 1 | yes | characteristic |
| 205 | #124 | — | 2 | 1 | no | — |
| 206 | #121 | — | 2 | 1 | no | — |
| 207 | #121 | — | 2 | 1 | no | — |
| 208 | C4×D4 | — | 2 | 1 | no | — |
| 209 | C4×D4 | — | 2 | 1 | no | — |
| 210 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 211 | C2×C42 | — | 106 | 1 | no | — |
| 212 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 213 | #108 | — | 212 | 2 | no | — |
| 214 | C4⋊C8 | — | 2 | 1 | no | — |
| 215 | C4⋊C8 | — | 2 | 1 | no | — |
| 216 | C4⋊C8 | — | 53 | 1 | no | — |
| 217 | C4⋊C8 | — | 53 | 1 | no | — |
| 218 | C4⋊C8 | — | 53 | 1 | no | — |
| 219 | C4⋊C8 | — | 53 | 1 | no | — |
| 220 | C4⋊C8 | — | 106 | 1 | no | — |
| 221 | #104 | — | 212 | 2 | no | — |
| 222 | #104 | — | 212 | 2 | no | — |
| 223 | C22⋊C8 | — | 106 | 1 | no | — |
| 224 | #97 | — | 106 | 1 | no | — |
| 225 | C4×C8 | — | 2 | 1 | no | — |
| 226 | C4×C8 | — | 106 | 1 | no | — |
| 227 | C4×C8 | — | 106 | 1 | no | — |
| 228 | C4×C8 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 229 | C4×C8 | C22⋊D53 | 1 | 1 | yes | characteristic |
| 230 | #95 | — | 106 | 1 | no | — |
| 231 | #41 | — | 4 | 1 | no | — |
| 232 | #41 | — | 4 | 1 | no | — |
| 233 | #41 | — | 4 | 1 | no | — |
| 234 | #41 | — | 4 | 1 | no | — |
| 235 | C2×Q8 | — | 2 | 1 | no | — |
| 236 | C2×D4 | — | 2 | 1 | no | — |
| 237 | C2×D4 | — | 2 | 1 | no | — |
| 238 | C2×D4 | — | 2 | 1 | no | — |
| 239 | C2×D4 | — | 4 | 1 | no | — |
| 240 | C22×C4 | — | 4 | 1 | no | — |
| 241 | C22×C4 | — | 212 | 1 | no | — |
| 242 | C22×C4 | #11719945 | 1 | 1 | yes | characteristic |
| 243 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 244 | C22×C4 | #11719947 | 1 | 1 | yes | characteristic |
| 245 | M16 | — | 4 | 1 | no | — |
| 246 | M16 | — | 4 | 1 | no | — |
| 247 | M16 | — | 106 | 1 | no | — |
| 248 | M16 | — | 106 | 1 | no | — |
| 249 | M16 | — | 106 | 1 | no | — |
| 250 | M16 | — | 106 | 1 | no | — |
| 251 | C2×C8 | — | 2 | 1 | no | — |
| 252 | C2×C8 | — | 2 | 1 | no | — |
| 253 | C2×C8 | — | 4 | 2 | no | — |
| 254 | C2×C8 | — | 4 | 1 | no | — |
| 255 | C2×C8 | — | 106 | 1 | no | — |
| 256 | C2×C8 | — | 106 | 1 | no | — |
| 257 | C2×C8 | — | 106 | 1 | no | — |
| 258 | C2×C8 | — | 106 | 1 | no | — |
| 259 | C2×C8 | — | 106 | 1 | no | — |
| 260 | C2×C8 | — | 106 | 1 | no | — |
| 261 | C2×C8 | — | 212 | 1 | no | — |
| 262 | C2×C8 | — | 212 | 1 | no | — |
| 263 | C4⋊C4 | — | 2 | 1 | no | — |
| 264 | C4⋊C4 | — | 2 | 1 | no | — |
| 265 | C4⋊C4 | — | 106 | 2 | no | — |
| 266 | C4⋊C4 | — | 212 | 1 | no | — |
| 267 | C22⋊C4 | — | 4 | 1 | no | — |
| 268 | C22⋊C4 | — | 4 | 1 | no | — |
| 269 | C42 | — | 212 | 1 | no | — |
| 270 | C42 | — | 212 | 1 | no | — |
| 271 | C42 | C2×C4×D53 | 1 | 1 | yes | characteristic |
| 272 | C42 | #11719947 | 1 | 1 | yes | characteristic |
| 273 | C42 | #11719947 | 1 | 1 | yes | characteristic |
| 274 | C42 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 275 | C23 | — | 4 | 1 | no | — |
| 276 | C23 | #13133203 | 1 | 1 | yes | characteristic |
| 277 | Q8 | — | 4 | 1 | no | — |
| 278 | Q8 | — | 4 | 1 | no | — |
| 279 | D4 | — | 4 | 1 | no | — |
| 280 | D4 | — | 4 | 1 | no | — |
| 281 | D4 | — | 4 | 1 | no | — |
| 282 | D4 | — | 4 | 1 | no | — |
| 283 | D4 | — | 8 | 1 | no | — |
| 284 | D4 | — | 8 | 1 | no | — |
| 285 | D4 | — | 8 | 1 | no | — |
| 286 | C2×C4 | — | 2 | 1 | no | — |
| 287 | C2×C4 | — | 2 | 1 | no | — |
| 288 | C2×C4 | — | 4 | 1 | no | — |
| 289 | C2×C4 | — | 4 | 1 | no | — |
| 290 | C2×C4 | — | 8 | 1 | no | — |
| 291 | C2×C4 | — | 8 | 1 | no | — |
| 292 | C2×C4 | — | 424 | 1 | no | — |
| 293 | C2×C4 | — | 424 | 1 | no | — |
| 294 | C2×C4 | — | 212 | 2 | no | — |
| 295 | C2×C4 | #13133173 | 1 | 1 | yes | characteristic |
| 296 | C2×C4 | #13133177 | 1 | 1 | yes | characteristic |
| 297 | C2×C4 | C4×C22⋊D53 | 1 | 1 | yes | characteristic |
| 298 | C2×C4 | #13133188 | 1 | 1 | yes | characteristic |
| 299 | C2×C4 | #13133198 | 1 | 1 | yes | characteristic |
| 300 | C2×C4 | #13133210 | 1 | 1 | yes | characteristic |
| 301 | C2×C4 | #13133241 | 1 | 1 | yes | characteristic |
| 302 | C2×C4 | #13133241 | 1 | 1 | yes | characteristic |
| 303 | C2×C4 | #13133244 | 1 | 1 | yes | characteristic |
| 304 | C2×C4 | #13133246 | 1 | 1 | yes | characteristic |
| 305 | C8 | — | 2 | 2 | no | — |
| 306 | C8 | — | 4 | 1 | no | — |
| 307 | C8 | — | 8 | 1 | no | — |
| 308 | C8 | — | 212 | 1 | no | — |
| 309 | C8 | — | 212 | 1 | no | — |
| 310 | C8 | — | 212 | 1 | no | — |
| 311 | C8 | — | 212 | 1 | no | — |
| 312 | C8 | — | 212 | 1 | no | — |
| 313 | C8 | — | 212 | 1 | no | — |
| 314 | C22 | — | 2 | 1 | no | — |
| 315 | C22 | — | 2 | 1 | no | — |
| 316 | C22 | — | 8 | 1 | no | — |
| 317 | C22 | — | 8 | 1 | no | — |
| 318 | C22 | — | 8 | 1 | no | — |
| 319 | C22 | #16810511 | 1 | 1 | yes | characteristic |
| 320 | C22 | #16810981 | 1 | 1 | yes | characteristic |
| 321 | C22 | #16810986 | 1 | 1 | yes | characteristic |
| 322 | C4 | — | 2 | 1 | no | — |
| 323 | C4 | — | 2 | 1 | no | — |
| 324 | C4 | — | 2 | 1 | no | — |
| 325 | C4 | — | 8 | 1 | no | — |
| 326 | C4 | — | 424 | 2 | no | — |
| 327 | C4 | #16810720 | 1 | 1 | yes | characteristic |
| 328 | C4 | #16810732 | 1 | 1 | yes | characteristic |
| 329 | C4 | #16810738 | 1 | 1 | yes | characteristic |
| 330 | C4 | #16810743 | 1 | 1 | yes | characteristic |
| 331 | C4 | #16810866 | 1 | 1 | yes | characteristic |
| 332 | C4 | #16810873 | 1 | 1 | yes | characteristic |
| 333 | C2 | — | 2 | 1 | no | — |
| 334 | C2 | — | 2 | 1 | no | — |
| 335 | C2 | — | 16 | 1 | no | — |
| 336 | C2 | #20275360 | 1 | 1 | yes | characteristic |
| 337 | C2 | #20275381 | 1 | 1 | yes | characteristic |
| 338 | C2 | #20275409 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta