| 1 | #30632487 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #30632485 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#22548735 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#22548723 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #30631961 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #30631956 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #30631953 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #30631949 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | C2×#22548650 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #30631669 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #413×C251 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#16860810 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#16860810 | C22 | 1 | 1 | yes | characteristic |
| 14 | #22548748 | — | 2 | 1 | no | — |
| 15 | #22548748 | C22 | 1 | 2 | yes | — |
| 16 | #22548746 | C22 | 1 | 2 | yes | — |
| 17 | #22548745 | — | 2 | 1 | no | — |
| 18 | #22548743 | — | 2 | 1 | no | — |
| 19 | #22548743 | C22 | 1 | 2 | yes | — |
| 20 | #22548741 | C22 | 1 | 2 | yes | — |
| 21 | #22548740 | — | 2 | 1 | no | — |
| 22 | #22548737 | — | 2 | 2 | no | — |
| 23 | #22548735 | — | 2 | 2 | no | — |
| 24 | #22548735 | — | 2 | 1 | no | — |
| 25 | #22548735 | — | 2 | 1 | no | — |
| 26 | #22548735 | — | 2 | 1 | no | — |
| 27 | #22548735 | — | 2 | 1 | no | — |
| 28 | C2×#16860800 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C2×#16860798 | C22 | 1 | 1 | yes | characteristic, complemented |
| 30 | C2×#16860797 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | C2×#16860795 | C22 | 1 | 1 | yes | characteristic, complemented |
| 32 | #22548723 | — | 2 | 1 | no | — |
| 33 | #22548723 | — | 2 | 1 | no | — |
| 34 | #22548723 | C22 | 1 | 2 | yes | — |
| 35 | #22548723 | C22 | 1 | 2 | yes | — |
| 36 | C2×#16860794 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×#16860793 | — | 2 | 1 | no | — |
| 38 | C22×C251⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×C8×D251 | — | 2 | 1 | no | — |
| 40 | #22548650 | C22 | 1 | 2 | yes | complemented |
| 41 | #22548650 | C22 | 1 | 2 | yes | complemented |
| 42 | #22548633 | C22 | 1 | 2 | yes | complemented |
| 43 | #22548631 | C22 | 1 | 2 | yes | complemented |
| 44 | C2×#41×C251 | C22 | 1 | 1 | yes | characteristic |
| 45 | C2×M16×C251 | C22 | 1 | 1 | yes | characteristic |
| 46 | C2×M16×C251 | C22 | 1 | 1 | yes | characteristic |
| 47 | #101×C251 | C22 | 1 | 2 | yes | complemented |
| 48 | #100×C251 | C22 | 1 | 2 | yes | complemented |
| 49 | #16860810 | — | 2 | 1 | no | — |
| 50 | #16860810 | — | 2 | 1 | no | — |
| 51 | #16860810 | — | 2 | 1 | no | — |
| 52 | #16860810 | — | 2 | 1 | no | — |
| 53 | #16860810 | — | 2 | 1 | no | — |
| 54 | #16860810 | — | 2 | 1 | no | — |
| 55 | #16860810 | D4 | 1 | 2 | yes | — |
| 56 | #16860810 | C23 | 1 | 2 | yes | — |
| 57 | C2×Dic502 | D4 | 1 | 1 | yes | characteristic |
| 58 | C2×Dic502 | C23 | 1 | 1 | yes | characteristic |
| 59 | C2×D1004 | D4 | 1 | 1 | yes | characteristic |
| 60 | C2×D1004 | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×C22⋊D251 | — | 2 | 1 | no | — |
| 62 | C2×C22⋊D251 | — | 2 | 1 | no | — |
| 63 | C2×C4×D251 | — | 2 | 1 | no | — |
| 64 | C2×C4×D251 | — | 2 | 1 | no | — |
| 65 | Dic1004 | — | 2 | 2 | no | — |
| 66 | #16860800 | — | 2 | 2 | no | — |
| 67 | #16860800 | — | 2 | 1 | no | — |
| 68 | #16860800 | — | 2 | 1 | no | — |
| 69 | #16860799 | — | 2 | 2 | no | — |
| 70 | #16860799 | — | 2 | 2 | no | — |
| 71 | #16860798 | — | 2 | 2 | no | — |
| 72 | #16860798 | — | 2 | 1 | no | — |
| 73 | #16860798 | — | 2 | 1 | no | — |
| 74 | #16860797 | — | 2 | 2 | no | — |
| 75 | #16860797 | — | 2 | 1 | no | — |
| 76 | #16860797 | — | 2 | 1 | no | — |
| 77 | D2008 | — | 2 | 2 | no | — |
| 78 | #16860795 | — | 2 | 2 | no | — |
| 79 | #16860795 | — | 2 | 1 | no | — |
| 80 | #16860795 | — | 2 | 1 | no | — |
| 81 | #16860794 | — | 2 | 1 | no | — |
| 82 | #16860794 | C23 | 1 | 2 | yes | — |
| 83 | #16860793 | — | 2 | 2 | no | — |
| 84 | #16860793 | — | 2 | 2 | no | — |
| 85 | C2×C251⋊C8 | — | 2 | 1 | no | — |
| 86 | C2×C251⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 87 | C2×C251⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 88 | C2×C251⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 89 | C2×C251⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 90 | C2×C251⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 91 | C2×C251⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 92 | C8×D251 | — | 2 | 2 | no | — |
| 93 | C8×D251 | — | 2 | 2 | no | — |
| 94 | #41×C251 | — | 2 | 1 | no | — |
| 95 | #41×C251 | — | 2 | 1 | no | — |
| 96 | #41×C251 | — | 2 | 1 | no | — |
| 97 | #41×C251 | — | 2 | 1 | no | — |
| 98 | C2×Q8×C251 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×D4×C251 | — | 2 | 1 | no | — |
| 100 | C2×D4×C251 | C23 | 1 | 1 | yes | characteristic |
| 101 | C22×C4×C251 | — | 2 | 1 | no | — |
| 102 | C22×C4×C251 | C23 | 1 | 1 | yes | characteristic |
| 103 | M16×C251 | — | 2 | 1 | no | — |
| 104 | M16×C251 | — | 2 | 1 | no | — |
| 105 | M16×C251 | C23 | 1 | 2 | yes | — |
| 106 | M16×C251 | C23 | 1 | 2 | yes | — |
| 107 | C2×C8×C251 | — | 2 | 1 | no | — |
| 108 | C2×C8×C251 | — | 2 | 1 | no | — |
| 109 | C22×D251 | — | 2 | 1 | no | — |
| 110 | C22×D251 | — | 2 | 1 | no | — |
| 111 | Dic502 | — | 2 | 1 | no | — |
| 112 | Dic502 | — | 2 | 1 | no | — |
| 113 | Dic502 | — | 2 | 1 | no | — |
| 114 | Dic502 | C2×D4 | 1 | 2 | yes | — |
| 115 | D1004 | — | 2 | 1 | no | — |
| 116 | D1004 | — | 2 | 1 | no | — |
| 117 | D1004 | — | 2 | 1 | no | — |
| 118 | D1004 | C2×D4 | 1 | 2 | yes | — |
| 119 | C22⋊D251 | — | 2 | 2 | no | — |
| 120 | C22⋊D251 | — | 2 | 2 | no | — |
| 121 | C22⋊D251 | — | 4 | 1 | no | — |
| 122 | C22⋊D251 | — | 4 | 1 | no | — |
| 123 | C2×Dic251 | — | 2 | 1 | no | — |
| 124 | C2×Dic251 | — | 2 | 1 | no | — |
| 125 | C4×D251 | — | 2 | 2 | no | — |
| 126 | C4×D251 | — | 2 | 2 | no | — |
| 127 | C4×D251 | — | 4 | 1 | no | — |
| 128 | C4×D251 | — | 4 | 1 | no | — |
| 129 | C251⋊C8 | — | 2 | 2 | no | — |
| 130 | C251⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 131 | C251⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | C251⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | C251⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 134 | C23×C251 | — | 2 | 1 | no | — |
| 135 | C23×C251 | #41 | 1 | 1 | yes | characteristic |
| 136 | Q8×C251 | — | 2 | 1 | no | — |
| 137 | Q8×C251 | — | 2 | 1 | no | — |
| 138 | D4×C251 | — | 2 | 1 | no | — |
| 139 | D4×C251 | — | 2 | 1 | no | — |
| 140 | D4×C251 | — | 4 | 1 | no | — |
| 141 | D4×C251 | — | 4 | 1 | no | — |
| 142 | C2×C4×C251 | — | 2 | 1 | no | — |
| 143 | C2×C4×C251 | — | 4 | 1 | no | — |
| 144 | C2×C4×C251 | — | 4 | 1 | no | — |
| 145 | C2×C4×C251 | C2×D4 | 1 | 1 | yes | characteristic |
| 146 | C2×C4×C251 | C2×D4 | 1 | 1 | yes | characteristic |
| 147 | C2×C4×C251 | C2×D4 | 1 | 1 | yes | characteristic |
| 148 | C2×C4×C251 | C2×D4 | 1 | 1 | yes | characteristic |
| 149 | C2×C4×C251 | #41 | 1 | 1 | yes | characteristic |
| 150 | C2×C4×C251 | C24 | 1 | 1 | yes | characteristic |
| 151 | C8×C251 | — | 2 | 2 | no | — |
| 152 | C8×C251 | — | 2 | 2 | no | — |
| 153 | C22×C251 | — | 4 | 1 | no | — |
| 154 | C22×C251 | — | 4 | 1 | no | — |
| 155 | C22×C251 | — | 8 | 1 | no | — |
| 156 | C22×C251 | #121 | 1 | 1 | yes | characteristic |
| 157 | C22×C251 | #121 | 1 | 1 | yes | characteristic |
| 158 | C22×C251 | C2×#41 | 1 | 1 | yes | characteristic |
| 159 | C2×D251 | — | 2 | 2 | no | — |
| 160 | C2×D251 | — | 4 | 2 | no | — |
| 161 | C2×D251 | — | 4 | 1 | no | — |
| 162 | C2×D251 | — | 8 | 1 | no | — |
| 163 | C4×C251 | — | 4 | 1 | no | — |
| 164 | C4×C251 | #121 | 1 | 1 | yes | characteristic |
| 165 | C4×C251 | #121 | 1 | 1 | yes | characteristic |
| 166 | C4×C251 | C22×D4 | 1 | 1 | yes | characteristic |
| 167 | C4×C251 | C22×D4 | 1 | 1 | yes | characteristic |
| 168 | Dic251 | — | 2 | 2 | no | — |
| 169 | Dic251 | — | 4 | 1 | no | — |
| 170 | C2×C251 | — | 2 | 1 | no | — |
| 171 | C2×C251 | — | 2 | 1 | no | — |
| 172 | C2×C251 | — | 2 | 1 | no | — |
| 173 | C2×C251 | — | 8 | 1 | no | — |
| 174 | C2×C251 | C2×#121 | 1 | 1 | yes | characteristic |
| 175 | D251 | — | 4 | 2 | no | — |
| 176 | D251 | — | 8 | 1 | no | — |
| 177 | C251 | #3067 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 178 | #3067 | — | 251 | 1 | no | maximal, Sylow |
| 179 | #575 | — | 251 | 1 | no | — |
| 180 | #575 | — | 251 | 1 | no | — |
| 181 | C2×#135 | — | 251 | 1 | no | — |
| 182 | C2×#131 | — | 251 | 1 | no | — |
| 183 | #473 | — | 251 | 2 | no | — |
| 184 | #472 | — | 251 | 2 | no | — |
| 185 | #471 | — | 251 | 2 | no | — |
| 186 | #471 | — | 251 | 2 | no | — |
| 187 | C2×#108 | — | 251 | 1 | no | — |
| 188 | #413 | — | 251 | 1 | no | — |
| 189 | #413 | D251 | 1 | 1 | yes | characteristic, complemented |
| 190 | C2×#41 | — | 251 | 1 | no | — |
| 191 | C2×#41 | — | 251 | 1 | no | — |
| 192 | C2×#41 | C2×D251 | 1 | 1 | yes | characteristic |
| 193 | #137 | — | 502 | 1 | no | — |
| 194 | #137 | — | 502 | 1 | no | — |
| 195 | #137 | — | 251 | 2 | no | — |
| 196 | #137 | — | 251 | 2 | no | — |
| 197 | AGL(1,ℤ/8) | — | 502 | 1 | no | — |
| 198 | AGL(1,ℤ/8) | — | 502 | 1 | no | — |
| 199 | AGL(1,ℤ/8) | — | 251 | 2 | no | — |
| 200 | AGL(1,ℤ/8) | — | 251 | 2 | no | — |
| 201 | #135 | — | 502 | 2 | no | — |
| 202 | #135 | — | 502 | 2 | no | — |
| 203 | #135 | — | 502 | 1 | no | — |
| 204 | #135 | — | 502 | 1 | no | — |
| 205 | #135 | — | 502 | 1 | no | — |
| 206 | #135 | — | 502 | 1 | no | — |
| 207 | C2×Q16 | — | 251 | 1 | no | — |
| 208 | C2×SD16 | — | 251 | 1 | no | — |
| 209 | C2×SD16 | — | 251 | 1 | no | — |
| 210 | C2×D8 | — | 251 | 1 | no | — |
| 211 | #131 | — | 502 | 1 | no | — |
| 212 | #131 | — | 502 | 1 | no | — |
| 213 | #131 | — | 251 | 2 | no | — |
| 214 | #131 | — | 251 | 2 | no | — |
| 215 | C2×M16 | — | 502 | 1 | no | — |
| 216 | C2×M16 | — | 251 | 1 | no | — |
| 217 | C2×M16 | C2×D251 | 1 | 1 | yes | characteristic |
| 218 | C2×M16 | C2×D251 | 1 | 1 | yes | characteristic |
| 219 | C22×C8 | — | 502 | 1 | no | — |
| 220 | C22×C8 | — | 251 | 1 | no | — |
| 221 | #108 | — | 251 | 2 | no | — |
| 222 | #108 | — | 251 | 2 | no | — |
| 223 | #101 | — | 251 | 2 | no | — |
| 224 | #101 | C2×D251 | 1 | 2 | yes | complemented |
| 225 | #100 | — | 251 | 2 | no | — |
| 226 | #100 | C2×D251 | 1 | 2 | yes | complemented |
| 227 | #41 | — | 2 | 1 | no | — |
| 228 | #41 | — | 2 | 1 | no | — |
| 229 | #41 | — | 2 | 1 | no | — |
| 230 | #41 | — | 2 | 1 | no | — |
| 231 | #41 | — | 502 | 1 | no | — |
| 232 | #41 | — | 502 | 1 | no | — |
| 233 | #41 | — | 502 | 1 | no | — |
| 234 | #41 | — | 502 | 1 | no | — |
| 235 | #41 | — | 502 | 1 | no | — |
| 236 | #41 | — | 502 | 1 | no | — |
| 237 | #41 | — | 251 | 2 | no | — |
| 238 | #41 | — | 251 | 2 | no | — |
| 239 | C2×Q8 | — | 251 | 1 | no | — |
| 240 | C2×Q8 | — | 251 | 1 | no | — |
| 241 | C2×Q8 | C22×D251 | 1 | 1 | yes | characteristic |
| 242 | C2×D4 | — | 2 | 1 | no | — |
| 243 | C2×D4 | — | 502 | 1 | no | — |
| 244 | C2×D4 | — | 502 | 1 | no | — |
| 245 | C2×D4 | — | 251 | 1 | no | — |
| 246 | C2×D4 | — | 251 | 1 | no | — |
| 247 | C2×D4 | C22×D251 | 1 | 1 | yes | characteristic |
| 248 | C22×C4 | — | 2 | 1 | no | — |
| 249 | C22×C4 | — | 502 | 1 | no | — |
| 250 | C22×C4 | — | 502 | 1 | no | — |
| 251 | C22×C4 | C22×D251 | 1 | 1 | yes | characteristic |
| 252 | Q16 | — | 502 | 2 | no | — |
| 253 | Q16 | — | 502 | 2 | no | — |
| 254 | Q16 | — | 502 | 1 | no | — |
| 255 | Q16 | — | 502 | 1 | no | — |
| 256 | SD16 | — | 502 | 2 | no | — |
| 257 | SD16 | — | 502 | 2 | no | — |
| 258 | SD16 | — | 502 | 2 | no | — |
| 259 | SD16 | — | 502 | 2 | no | — |
| 260 | SD16 | — | 502 | 1 | no | — |
| 261 | SD16 | — | 502 | 1 | no | — |
| 262 | SD16 | — | 502 | 1 | no | — |
| 263 | SD16 | — | 502 | 1 | no | — |
| 264 | D8 | — | 502 | 2 | no | — |
| 265 | D8 | — | 502 | 2 | no | — |
| 266 | D8 | — | 502 | 1 | no | — |
| 267 | D8 | — | 502 | 1 | no | — |
| 268 | M16 | — | 2 | 1 | no | — |
| 269 | M16 | — | 2 | 1 | no | — |
| 270 | M16 | — | 502 | 2 | no | — |
| 271 | M16 | — | 502 | 2 | no | — |
| 272 | M16 | — | 502 | 1 | no | — |
| 273 | M16 | — | 251 | 2 | no | — |
| 274 | M16 | C22×D251 | 1 | 2 | yes | — |
| 275 | M16 | C22×D251 | 1 | 2 | yes | — |
| 276 | C2×C8 | — | 2 | 1 | no | — |
| 277 | C2×C8 | — | 2 | 1 | no | — |
| 278 | C2×C8 | — | 502 | 2 | no | — |
| 279 | C2×C8 | — | 502 | 2 | no | — |
| 280 | C2×C8 | — | 502 | 1 | no | — |
| 281 | C2×C8 | — | 251 | 1 | no | — |
| 282 | C2×C8 | — | 251 | 1 | no | — |
| 283 | C2×C8 | — | 251 | 1 | no | — |
| 284 | C2×C8 | — | 251 | 1 | no | — |
| 285 | C2×C8 | — | 251 | 1 | no | — |
| 286 | C2×C8 | — | 251 | 1 | no | — |
| 287 | C23 | — | 2 | 1 | no | — |
| 288 | C23 | — | 502 | 1 | no | — |
| 289 | C23 | — | 502 | 1 | no | — |
| 290 | C23 | #16860810 | 1 | 1 | yes | characteristic |
| 291 | Q8 | — | 2 | 1 | no | — |
| 292 | Q8 | — | 2 | 1 | no | — |
| 293 | Q8 | — | 502 | 1 | no | — |
| 294 | Q8 | — | 502 | 1 | no | — |
| 295 | Q8 | — | 502 | 1 | no | — |
| 296 | Q8 | — | 251 | 2 | no | — |
| 297 | D4 | — | 2 | 1 | no | — |
| 298 | D4 | — | 2 | 1 | no | — |
| 299 | D4 | — | 4 | 1 | no | — |
| 300 | D4 | — | 4 | 1 | no | — |
| 301 | D4 | — | 1004 | 1 | no | — |
| 302 | D4 | — | 1004 | 1 | no | — |
| 303 | D4 | — | 502 | 2 | no | — |
| 304 | D4 | — | 502 | 2 | no | — |
| 305 | D4 | — | 502 | 1 | no | — |
| 306 | D4 | — | 502 | 1 | no | — |
| 307 | D4 | — | 502 | 1 | no | — |
| 308 | D4 | — | 251 | 2 | no | — |
| 309 | C2×C4 | — | 2 | 1 | no | — |
| 310 | C2×C4 | — | 4 | 1 | no | — |
| 311 | C2×C4 | — | 4 | 1 | no | — |
| 312 | C2×C4 | — | 1004 | 1 | no | — |
| 313 | C2×C4 | — | 1004 | 1 | no | — |
| 314 | C2×C4 | — | 502 | 1 | no | — |
| 315 | C2×C4 | — | 502 | 1 | no | — |
| 316 | C2×C4 | — | 502 | 2 | no | — |
| 317 | C2×C4 | — | 502 | 2 | no | — |
| 318 | C2×C4 | D4×D251 | 1 | 1 | yes | characteristic |
| 319 | C2×C4 | D4×D251 | 1 | 1 | yes | characteristic |
| 320 | C2×C4 | D4×D251 | 1 | 1 | yes | characteristic |
| 321 | C2×C4 | D4×D251 | 1 | 1 | yes | characteristic |
| 322 | C2×C4 | #16860810 | 1 | 1 | yes | characteristic |
| 323 | C2×C4 | C23×D251 | 1 | 1 | yes | characteristic |
| 324 | C8 | — | 2 | 2 | no | — |
| 325 | C8 | — | 2 | 2 | no | — |
| 326 | C8 | — | 502 | 2 | no | — |
| 327 | C8 | — | 251 | 1 | no | — |
| 328 | C8 | — | 251 | 1 | no | — |
| 329 | C8 | — | 251 | 1 | no | — |
| 330 | C8 | — | 251 | 1 | no | — |
| 331 | C22 | — | 4 | 1 | no | — |
| 332 | C22 | — | 4 | 1 | no | — |
| 333 | C22 | — | 8 | 1 | no | — |
| 334 | C22 | — | 2008 | 1 | no | — |
| 335 | C22 | — | 1004 | 2 | no | — |
| 336 | C22 | — | 1004 | 1 | no | — |
| 337 | C22 | — | 502 | 2 | no | — |
| 338 | C22 | #22548688 | 1 | 1 | yes | characteristic |
| 339 | C22 | #22548688 | 1 | 1 | yes | characteristic |
| 340 | C22 | C2×#16860810 | 1 | 1 | yes | characteristic |
| 341 | C4 | — | 4 | 1 | no | — |
| 342 | C4 | — | 1004 | 1 | no | — |
| 343 | C4 | — | 502 | 2 | no | — |
| 344 | C4 | #22548688 | 1 | 1 | yes | characteristic |
| 345 | C4 | #22548688 | 1 | 1 | yes | characteristic |
| 346 | C4 | C2×D4×D251 | 1 | 1 | yes | characteristic |
| 347 | C4 | C2×D4×D251 | 1 | 1 | yes | characteristic |
| 348 | C2 | — | 2 | 1 | no | — |
| 349 | C2 | — | 2 | 1 | no | — |
| 350 | C2 | — | 2 | 1 | no | — |
| 351 | C2 | — | 8 | 1 | no | — |
| 352 | C2 | — | 2008 | 1 | no | — |
| 353 | C2 | — | 1004 | 2 | no | — |
| 354 | C2 | C2×#22548688 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta