| 1 | #14521781 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #14521777 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #14521444 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #14521442 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #14521420 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #14521274 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #14521257 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #14521255 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #14521252 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #14521248 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #14521178 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #14521147 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #14521146 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #14521141 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C31×#464 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×Q16×C31 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×SD16×C31 | C22 | 1 | 1 | yes | characteristic |
| 18 | C31×#124 | C22 | 1 | 1 | yes | characteristic |
| 19 | C4×Q8×C31 | C22 | 1 | 1 | yes | characteristic |
| 20 | #11758524 | C22 | 1 | 1 | yes | characteristic |
| 21 | Q8×Dic31 | C22 | 1 | 1 | yes | characteristic |
| 22 | #11758521 | C22 | 1 | 1 | yes | characteristic |
| 23 | #11758521 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#92482 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#92482 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#92481 | C22 | 1 | 1 | yes | characteristic |
| 27 | #11758517 | C22 | 1 | 1 | yes | characteristic |
| 28 | D4×Dic31 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×#92480 | C22 | 1 | 1 | yes | characteristic |
| 30 | C2×#92480 | C22 | 1 | 1 | yes | characteristic |
| 31 | C2×#92470 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#92470 | C22 | 1 | 1 | yes | characteristic |
| 33 | #11758466 | — | 2 | 1 | no | — |
| 34 | #11758466 | — | 2 | 1 | no | — |
| 35 | #11758464 | C22 | 1 | 1 | yes | characteristic |
| 36 | #11758464 | C22 | 1 | 1 | yes | characteristic |
| 37 | #11758463 | — | 2 | 1 | no | — |
| 38 | #11758462 | — | 2 | 1 | no | — |
| 39 | #11758460 | — | 2 | 1 | no | — |
| 40 | (C22⋊D31)⋊C4 | — | 2 | 1 | no | — |
| 41 | C4×D124 | C22 | 1 | 1 | yes | characteristic |
| 42 | #11758447 | — | 2 | 1 | no | — |
| 43 | #11758446 | C22 | 1 | 1 | yes | characteristic |
| 44 | C4×Dic62 | — | 2 | 1 | no | — |
| 45 | C4×Dic62 | C22 | 1 | 1 | yes | characteristic |
| 46 | C31×C4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 47 | C31×#103 | C22 | 1 | 1 | yes | characteristic |
| 48 | C31×#102 | C22 | 1 | 1 | yes | characteristic |
| 49 | #11758423 | C22 | 1 | 1 | yes | characteristic |
| 50 | #11758404 | C22 | 1 | 1 | yes | characteristic |
| 51 | #11758404 | C22 | 1 | 1 | yes | characteristic |
| 52 | #11758403 | C22 | 1 | 1 | yes | characteristic |
| 53 | Dic31⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 54 | Dic31⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 55 | C8×Dic31 | C22 | 1 | 1 | yes | characteristic |
| 56 | #11758397 | C22 | 1 | 1 | yes | characteristic |
| 57 | #11758395 | C22 | 1 | 1 | yes | characteristic |
| 58 | #11758391 | C22 | 1 | 1 | yes | characteristic |
| 59 | C2×Q8×C31 | C23 | 1 | 1 | yes | characteristic |
| 60 | C2×Q8×C31 | C23 | 1 | 1 | yes | characteristic |
| 61 | C2×D4×C31 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×C22⋊D31 | — | 2 | 1 | no | — |
| 63 | C2×C22⋊D31 | — | 2 | 1 | no | — |
| 64 | C22×Dic31 | — | 2 | 1 | no | — |
| 65 | C2×D124 | C23 | 1 | 1 | yes | characteristic |
| 66 | C2×C4×D31 | — | 2 | 1 | no | — |
| 67 | C2×Dic62 | D4 | 1 | 1 | yes | characteristic |
| 68 | C2×Dic62 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×Dic62 | C23 | 1 | 1 | yes | characteristic |
| 70 | Q16×C31 | — | 4 | 1 | no | — |
| 71 | SD16×C31 | — | 4 | 1 | no | — |
| 72 | C2×C8×C31 | C23 | 1 | 1 | yes | characteristic |
| 73 | C2×C8×C31 | C23 | 1 | 1 | yes | characteristic |
| 74 | C4⋊C4×C31 | — | 2 | 1 | no | — |
| 75 | C4⋊C4×C31 | C23 | 1 | 1 | yes | characteristic |
| 76 | C22⋊C4×C31 | — | 2 | 1 | no | — |
| 77 | C22⋊C4×C31 | — | 2 | 1 | no | — |
| 78 | C42×C31 | — | 2 | 1 | no | — |
| 79 | C42×C31 | C23 | 1 | 1 | yes | characteristic |
| 80 | C22⋊Dic31 | — | 2 | 1 | no | — |
| 81 | #92482 | — | 2 | 2 | no | — |
| 82 | #92482 | — | 4 | 1 | no | — |
| 83 | #92481 | — | 2 | 2 | no | — |
| 84 | #92480 | — | 2 | 2 | no | — |
| 85 | #92480 | — | 4 | 1 | no | — |
| 86 | (C2×D31)⋊C4 | — | 2 | 1 | no | — |
| 87 | (C2×D31)⋊C4 | — | 2 | 1 | no | — |
| 88 | (C2×D31)⋊C4 | — | 2 | 1 | no | — |
| 89 | C4⋊Dic31 | — | 2 | 1 | no | — |
| 90 | C4⋊Dic31 | — | 2 | 1 | no | — |
| 91 | C4⋊Dic31 | — | 2 | 1 | no | — |
| 92 | C4⋊Dic31 | D4 | 1 | 1 | yes | characteristic |
| 93 | C4⋊Dic31 | C23 | 1 | 1 | yes | characteristic |
| 94 | Dic31⋊C4 | — | 2 | 1 | no | — |
| 95 | Dic31⋊C4 | — | 2 | 1 | no | — |
| 96 | Dic31⋊C4 | — | 2 | 1 | no | — |
| 97 | Dic31⋊C4 | — | 2 | 1 | no | — |
| 98 | Dic31⋊C4 | — | 2 | 1 | no | — |
| 99 | Dic31⋊C4 | — | 2 | 1 | no | — |
| 100 | Dic31⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 101 | Dic31⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 102 | C4×Dic31 | — | 2 | 1 | no | — |
| 103 | C4×Dic31 | — | 2 | 1 | no | — |
| 104 | C4×Dic31 | — | 2 | 1 | no | — |
| 105 | C4×Dic31 | C23 | 1 | 1 | yes | characteristic |
| 106 | C4×Dic31 | C23 | 1 | 1 | yes | characteristic |
| 107 | C2×C31⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 108 | C2×C31⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 109 | #92470 | — | 4 | 1 | no | — |
| 110 | #92470 | — | 4 | 1 | no | — |
| 111 | C23×C31 | — | 2 | 1 | no | — |
| 112 | C22×D31 | — | 2 | 1 | no | — |
| 113 | Q8×C31 | — | 2 | 1 | no | — |
| 114 | Q8×C31 | — | 2 | 1 | no | — |
| 115 | Q8×C31 | — | 2 | 1 | no | — |
| 116 | Q8×C31 | — | 2 | 1 | no | — |
| 117 | D4×C31 | — | 2 | 1 | no | — |
| 118 | D4×C31 | — | 2 | 1 | no | — |
| 119 | C2×C4×C31 | — | 2 | 1 | no | — |
| 120 | C2×C4×C31 | — | 2 | 1 | no | — |
| 121 | C2×C4×C31 | — | 2 | 1 | no | — |
| 122 | C2×C4×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 123 | C2×C4×C31 | C2×D4 | 1 | 1 | yes | characteristic |
| 124 | C2×C4×C31 | C24 | 1 | 1 | yes | characteristic |
| 125 | C22⋊D31 | — | 4 | 2 | no | — |
| 126 | C22⋊D31 | — | 8 | 1 | no | — |
| 127 | C2×Dic31 | — | 2 | 1 | no | — |
| 128 | C2×Dic31 | — | 2 | 1 | no | — |
| 129 | C2×Dic31 | — | 2 | 1 | no | — |
| 130 | C2×Dic31 | — | 8 | 1 | no | — |
| 131 | C2×Dic31 | C2×D4 | 1 | 1 | yes | characteristic |
| 132 | C2×Dic31 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | C2×Dic31 | C2×D4 | 1 | 1 | yes | characteristic |
| 134 | C2×Dic31 | C2×D4 | 1 | 1 | yes | characteristic |
| 135 | D124 | — | 2 | 1 | no | — |
| 136 | D124 | — | 2 | 1 | no | — |
| 137 | C4×D31 | — | 8 | 1 | no | — |
| 138 | Dic62 | — | 2 | 2 | no | — |
| 139 | Dic62 | — | 2 | 1 | no | — |
| 140 | Dic62 | — | 2 | 1 | no | — |
| 141 | Dic62 | — | 2 | 1 | no | — |
| 142 | Dic62 | — | 2 | 1 | no | — |
| 143 | C8×C31 | — | 2 | 1 | no | — |
| 144 | C8×C31 | — | 2 | 1 | no | — |
| 145 | C31⋊C8 | — | 2 | 1 | no | — |
| 146 | C31⋊C8 | #41 | 1 | 2 | yes | — |
| 147 | #3400 | — | 31 | 1 | no | maximal, Sylow |
| 148 | C22×C31 | — | 4 | 1 | no | — |
| 149 | C22×C31 | — | 4 | 1 | no | — |
| 150 | C22×C31 | — | 4 | 1 | no | — |
| 151 | C22×C31 | C22×D4 | 1 | 1 | yes | characteristic |
| 152 | C2×D31 | — | 4 | 1 | no | — |
| 153 | C2×D31 | — | 4 | 1 | no | — |
| 154 | C2×D31 | — | 4 | 1 | no | — |
| 155 | C4×C31 | — | 2 | 1 | no | — |
| 156 | C4×C31 | — | 2 | 1 | no | — |
| 157 | C4×C31 | — | 4 | 1 | no | — |
| 158 | C4×C31 | — | 4 | 1 | no | — |
| 159 | C4×C31 | — | 4 | 1 | no | — |
| 160 | C4×C31 | C2×#41 | 1 | 1 | yes | characteristic |
| 161 | C4×C31 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 162 | Dic31 | — | 2 | 1 | no | — |
| 163 | Dic31 | — | 2 | 1 | no | — |
| 164 | Dic31 | — | 2 | 1 | no | — |
| 165 | Dic31 | — | 4 | 1 | no | — |
| 166 | Dic31 | — | 4 | 1 | no | — |
| 167 | Dic31 | — | 4 | 1 | no | — |
| 168 | Dic31 | #137 | 1 | 2 | yes | — |
| 169 | #559 | — | 31 | 1 | no | — |
| 170 | #557 | — | 31 | 1 | no | — |
| 171 | #497 | — | 31 | 1 | no | — |
| 172 | #497 | — | 31 | 1 | no | — |
| 173 | #492 | — | 31 | 1 | no | — |
| 174 | #464 | — | 31 | 1 | no | — |
| 175 | #464 | D31 | 1 | 1 | yes | characteristic, complemented |
| 176 | #462 | — | 31 | 1 | no | — |
| 177 | #461 | — | 31 | 1 | no | — |
| 178 | #461 | — | 31 | 1 | no | — |
| 179 | #460 | — | 31 | 1 | no | — |
| 180 | #446 | — | 31 | 1 | no | — |
| 181 | #440 | — | 31 | 1 | no | — |
| 182 | #440 | — | 31 | 1 | no | — |
| 183 | C4×Q16 | — | 31 | 1 | no | — |
| 184 | C2×C31 | — | 8 | 1 | no | — |
| 185 | C2×C31 | #550 | 1 | 1 | yes | characteristic |
| 186 | C2×C31 | C2×#137 | 1 | 1 | yes | characteristic |
| 187 | C2×C31 | #577 | 1 | 1 | yes | characteristic |
| 188 | D31 | — | 8 | 1 | no | — |
| 189 | C2×Q16 | — | 31 | 1 | no | — |
| 190 | C2×Q16 | — | 31 | 1 | no | — |
| 191 | C2×Q16 | C2×D31 | 1 | 1 | yes | characteristic |
| 192 | C2×SD16 | — | 31 | 1 | no | — |
| 193 | C2×SD16 | — | 31 | 1 | no | — |
| 194 | C2×SD16 | — | 31 | 1 | no | — |
| 195 | C2×SD16 | — | 31 | 1 | no | — |
| 196 | C2×SD16 | — | 31 | 1 | no | — |
| 197 | C2×SD16 | C2×D31 | 1 | 1 | yes | characteristic |
| 198 | C4⋊Q8 | — | 31 | 1 | no | — |
| 199 | C4⋊Q8 | — | 31 | 1 | no | — |
| 200 | C4⋊Q8 | — | 31 | 1 | no | — |
| 201 | #127 | — | 31 | 1 | no | — |
| 202 | #125 | — | 62 | 1 | no | — |
| 203 | #125 | — | 62 | 1 | no | — |
| 204 | #125 | — | 62 | 1 | no | — |
| 205 | #124 | — | 31 | 1 | no | — |
| 206 | #124 | — | 62 | 1 | no | — |
| 207 | #124 | C2×D31 | 1 | 1 | yes | characteristic |
| 208 | #123 | — | 62 | 1 | no | — |
| 209 | #123 | — | 62 | 1 | no | — |
| 210 | C4×Q8 | — | 31 | 1 | no | — |
| 211 | C4×Q8 | — | 31 | 1 | no | — |
| 212 | C4×Q8 | — | 31 | 1 | no | — |
| 213 | C4×Q8 | — | 31 | 1 | no | — |
| 214 | C4×Q8 | — | 62 | 1 | no | — |
| 215 | C4×Q8 | C2×D31 | 1 | 1 | yes | characteristic |
| 216 | C4×D4 | — | 31 | 1 | no | — |
| 217 | C4×D4 | — | 31 | 1 | no | — |
| 218 | C4×D4 | — | 62 | 1 | no | — |
| 219 | #107 | — | 31 | 1 | no | — |
| 220 | C4⋊C8 | — | 31 | 1 | no | — |
| 221 | C4⋊C8 | — | 31 | 1 | no | — |
| 222 | C4⋊C8 | C2×D31 | 1 | 1 | yes | characteristic |
| 223 | #103 | — | 31 | 1 | no | — |
| 224 | #103 | — | 31 | 1 | no | — |
| 225 | #103 | — | 31 | 1 | no | — |
| 226 | #103 | C2×D31 | 1 | 1 | yes | characteristic |
| 227 | #102 | — | 31 | 1 | no | — |
| 228 | #102 | C2×D31 | 1 | 1 | yes | characteristic |
| 229 | #97 | — | 31 | 1 | no | — |
| 230 | #97 | — | 31 | 1 | no | — |
| 231 | C4×C8 | — | 31 | 1 | no | — |
| 232 | C31 | #3400 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 233 | C2×Q8 | — | 31 | 1 | no | — |
| 234 | C2×Q8 | — | 31 | 1 | no | — |
| 235 | C2×Q8 | — | 31 | 1 | no | — |
| 236 | C2×Q8 | C22×D31 | 1 | 1 | yes | characteristic |
| 237 | C2×Q8 | C22×D31 | 1 | 1 | yes | characteristic |
| 238 | C2×D4 | — | 31 | 1 | no | — |
| 239 | C2×D4 | — | 62 | 1 | no | — |
| 240 | C2×D4 | — | 62 | 1 | no | — |
| 241 | C2×D4 | C22×D31 | 1 | 1 | yes | characteristic |
| 242 | C22×C4 | — | 62 | 1 | no | — |
| 243 | C22×C4 | — | 62 | 1 | no | — |
| 244 | Q16 | — | 4 | 1 | no | — |
| 245 | Q16 | — | 62 | 2 | no | — |
| 246 | Q16 | — | 124 | 1 | no | — |
| 247 | SD16 | — | 4 | 1 | no | — |
| 248 | SD16 | — | 62 | 2 | no | — |
| 249 | SD16 | — | 62 | 2 | no | — |
| 250 | SD16 | — | 124 | 1 | no | — |
| 251 | SD16 | — | 124 | 1 | no | — |
| 252 | SD16 | — | 124 | 1 | no | — |
| 253 | C2×C8 | — | 31 | 1 | no | — |
| 254 | C2×C8 | — | 31 | 1 | no | — |
| 255 | C2×C8 | C22×D31 | 1 | 1 | yes | characteristic |
| 256 | C2×C8 | C22×D31 | 1 | 1 | yes | characteristic |
| 257 | C4⋊C4 | — | 2 | 1 | no | — |
| 258 | C4⋊C4 | — | 31 | 1 | no | — |
| 259 | C4⋊C4 | — | 31 | 1 | no | — |
| 260 | C4⋊C4 | — | 31 | 1 | no | — |
| 261 | C4⋊C4 | — | 31 | 1 | no | — |
| 262 | C4⋊C4 | — | 62 | 1 | no | — |
| 263 | C4⋊C4 | — | 62 | 1 | no | — |
| 264 | C4⋊C4 | — | 62 | 1 | no | — |
| 265 | C4⋊C4 | — | 62 | 1 | no | — |
| 266 | C4⋊C4 | — | 62 | 1 | no | — |
| 267 | C4⋊C4 | — | 62 | 1 | no | — |
| 268 | C4⋊C4 | — | 62 | 1 | no | — |
| 269 | C4⋊C4 | — | 62 | 1 | no | — |
| 270 | C4⋊C4 | — | 62 | 1 | no | — |
| 271 | C4⋊C4 | C22×D31 | 1 | 1 | yes | characteristic |
| 272 | C22⋊C4 | — | 2 | 1 | no | — |
| 273 | C22⋊C4 | — | 2 | 1 | no | — |
| 274 | C22⋊C4 | — | 62 | 1 | no | — |
| 275 | C22⋊C4 | — | 62 | 1 | no | — |
| 276 | C22⋊C4 | — | 62 | 1 | no | — |
| 277 | C22⋊C4 | — | 62 | 1 | no | — |
| 278 | C42 | — | 2 | 1 | no | — |
| 279 | C42 | — | 31 | 1 | no | — |
| 280 | C42 | — | 31 | 1 | no | — |
| 281 | C42 | — | 62 | 1 | no | — |
| 282 | C42 | — | 62 | 1 | no | — |
| 283 | C42 | — | 62 | 1 | no | — |
| 284 | C42 | C22×D31 | 1 | 1 | yes | characteristic |
| 285 | C23 | — | 2 | 1 | no | — |
| 286 | C23 | — | 62 | 1 | no | — |
| 287 | Q8 | — | 2 | 1 | no | — |
| 288 | Q8 | — | 2 | 1 | no | — |
| 289 | Q8 | — | 2 | 1 | no | — |
| 290 | Q8 | — | 2 | 1 | no | — |
| 291 | Q8 | — | 62 | 2 | no | — |
| 292 | Q8 | — | 62 | 1 | no | — |
| 293 | Q8 | — | 62 | 1 | no | — |
| 294 | Q8 | — | 62 | 1 | no | — |
| 295 | Q8 | — | 62 | 1 | no | — |
| 296 | D4 | — | 2 | 1 | no | — |
| 297 | D4 | — | 2 | 1 | no | — |
| 298 | D4 | — | 62 | 1 | no | — |
| 299 | D4 | — | 62 | 1 | no | — |
| 300 | D4 | — | 124 | 2 | no | — |
| 301 | D4 | — | 248 | 1 | no | — |
| 302 | C2×C4 | — | 2 | 1 | no | — |
| 303 | C2×C4 | — | 2 | 1 | no | — |
| 304 | C2×C4 | — | 2 | 1 | no | — |
| 305 | C2×C4 | — | 31 | 1 | no | — |
| 306 | C2×C4 | — | 31 | 1 | no | — |
| 307 | C2×C4 | — | 31 | 1 | no | — |
| 308 | C2×C4 | — | 31 | 1 | no | — |
| 309 | C2×C4 | — | 62 | 1 | no | — |
| 310 | C2×C4 | — | 62 | 1 | no | — |
| 311 | C2×C4 | — | 62 | 1 | no | — |
| 312 | C2×C4 | — | 248 | 1 | no | — |
| 313 | C2×C4 | — | 248 | 1 | no | — |
| 314 | C2×C4 | D4×D31 | 1 | 1 | yes | characteristic |
| 315 | C2×C4 | D4×D31 | 1 | 1 | yes | characteristic |
| 316 | C2×C4 | C23×D31 | 1 | 1 | yes | characteristic |
| 317 | C8 | — | 2 | 1 | no | — |
| 318 | C8 | — | 2 | 1 | no | — |
| 319 | C8 | — | 31 | 2 | no | — |
| 320 | C8 | — | 62 | 1 | no | — |
| 321 | C22 | — | 4 | 1 | no | — |
| 322 | C22 | — | 4 | 1 | no | — |
| 323 | C22 | — | 4 | 1 | no | — |
| 324 | C22 | — | 124 | 1 | no | — |
| 325 | C22 | — | 124 | 1 | no | — |
| 326 | C22 | — | 124 | 1 | no | — |
| 327 | C22 | C2×D4×D31 | 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 | — | 31 | 2 | no | — |
| 334 | C4 | — | 62 | 1 | no | — |
| 335 | C4 | — | 62 | 1 | no | — |
| 336 | C4 | — | 62 | 1 | no | — |
| 337 | C4 | — | 124 | 1 | no | — |
| 338 | C4 | — | 124 | 1 | no | — |
| 339 | C4 | — | 124 | 1 | no | — |
| 340 | C4 | #11758561 | 1 | 1 | yes | characteristic |
| 341 | C4 | #41×D31 | 1 | 1 | yes | characteristic |
| 342 | C2 | — | 8 | 1 | no | — |
| 343 | C2 | — | 248 | 1 | no | — |
| 344 | C2 | #14521717 | 1 | 1 | yes | characteristic |
| 345 | C2 | #137×D31 | 1 | 1 | yes | characteristic |
| 346 | C2 | #14521856 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta