| 1 | C59×#2159 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×C59×#361 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C59×#2140 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C59×#1970 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C59×#1772 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C59×#1387 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C59×#1376 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×D8×C59 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×M32×C59 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×M32×C59 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#108×C59 | C22 | 1 | 1 | yes | characteristic |
| 12 | C59×#427 | C22 | 1 | 1 | yes | characteristic |
| 13 | C2×#107×C59 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×#102×C59 | — | 2 | 1 | no | — |
| 15 | C59×#405 | — | 2 | 1 | no | — |
| 16 | C2×C4×C8×C59 | C22 | 1 | 1 | yes | characteristic |
| 17 | C59×#390 | — | 2 | 1 | no | — |
| 18 | C59×#367 | — | 2 | 1 | no | — |
| 19 | C59×#366 | — | 2 | 1 | no | — |
| 20 | C59×#361 | C4 | 1 | 4 | yes | complemented |
| 21 | C59×#357 | — | 2 | 1 | no | — |
| 22 | C59×#357 | — | 2 | 1 | no | — |
| 23 | C59×#339 | — | 2 | 1 | no | — |
| 24 | C22×D4×C59 | — | 2 | 1 | no | — |
| 25 | C2×D8×C59 | — | 2 | 1 | no | — |
| 26 | C2×D8×C59 | — | 2 | 1 | no | — |
| 27 | C2×D8×C59 | — | 2 | 1 | no | — |
| 28 | C2×D8×C59 | — | 2 | 1 | no | — |
| 29 | C2×D8×C59 | — | 2 | 1 | no | — |
| 30 | C2×D8×C59 | C2×C4 | 1 | 2 | yes | — |
| 31 | C2×M16×C59 | — | 2 | 1 | no | — |
| 32 | C22×C8×C59 | D4 | 1 | 1 | yes | characteristic |
| 33 | C22×C8×C59 | C23 | 1 | 1 | yes | characteristic |
| 34 | #117×C59 | — | 2 | 1 | no | — |
| 35 | C2×C4⋊C4×C59 | — | 2 | 1 | no | — |
| 36 | C2×C22⋊C4×C59 | — | 4 | 2 | no | — |
| 37 | C2×C42×C59 | D4 | 1 | 1 | yes | characteristic |
| 38 | M32×C59 | — | 2 | 1 | no | — |
| 39 | M32×C59 | — | 2 | 1 | no | — |
| 40 | M32×C59 | — | 2 | 1 | no | — |
| 41 | M32×C59 | C2×C4 | 1 | 2 | yes | — |
| 42 | C2×C16×C59 | — | 2 | 1 | no | — |
| 43 | C2×C16×C59 | — | 2 | 1 | no | — |
| 44 | #108×C59 | — | 2 | 1 | no | — |
| 45 | #108×C59 | C2×C4 | 1 | 2 | yes | — |
| 46 | #107×C59 | — | 2 | 1 | no | — |
| 47 | #107×C59 | — | 2 | 1 | no | — |
| 48 | #107×C59 | D4 | 1 | 1 | yes | characteristic |
| 49 | #107×C59 | D4 | 1 | 1 | yes | characteristic |
| 50 | #106×C59 | — | 2 | 1 | no | — |
| 51 | #102×C59 | — | 4 | 1 | no | — |
| 52 | #102×C59 | — | 4 | 1 | no | — |
| 53 | #97×C59 | — | 4 | 1 | no | — |
| 54 | C4×C8×C59 | — | 2 | 1 | no | — |
| 55 | C4×C8×C59 | — | 2 | 1 | no | — |
| 56 | C4×C8×C59 | — | 4 | 1 | no | — |
| 57 | C24×C59 | — | 4 | 1 | no | — |
| 58 | C2×D4×C59 | — | 2 | 2 | no | — |
| 59 | C2×D4×C59 | — | 4 | 1 | no | — |
| 60 | C2×D4×C59 | — | 4 | 1 | no | — |
| 61 | C2×D4×C59 | — | 4 | 1 | no | — |
| 62 | C2×D4×C59 | — | 4 | 1 | no | — |
| 63 | C2×D4×C59 | — | 4 | 1 | no | — |
| 64 | C22×C4×C59 | — | 2 | 1 | no | — |
| 65 | C22×C4×C59 | — | 4 | 1 | no | — |
| 66 | C22×C4×C59 | C2×D4 | 1 | 1 | yes | characteristic |
| 67 | D8×C59 | — | 2 | 2 | no | — |
| 68 | D8×C59 | — | 2 | 2 | no | — |
| 69 | D8×C59 | — | 4 | 1 | no | — |
| 70 | D8×C59 | — | 4 | 1 | no | — |
| 71 | M16×C59 | — | 2 | 2 | no | — |
| 72 | M16×C59 | — | 4 | 1 | no | — |
| 73 | C2×C8×C59 | — | 2 | 1 | no | — |
| 74 | C2×C8×C59 | — | 2 | 1 | no | — |
| 75 | C2×C8×C59 | — | 4 | 1 | no | — |
| 76 | C2×C8×C59 | D8 | 1 | 1 | yes | characteristic |
| 77 | C2×C8×C59 | D8 | 1 | 1 | yes | characteristic |
| 78 | C2×C8×C59 | C22×C4 | 1 | 1 | yes | characteristic |
| 79 | C2×C8×C59 | C2×D4 | 1 | 1 | yes | characteristic |
| 80 | C2×C8×C59 | #41 | 1 | 1 | yes | characteristic |
| 81 | C2×C8×C59 | #41 | 1 | 1 | yes | characteristic |
| 82 | C2×C8×C59 | #41 | 1 | 1 | yes | characteristic |
| 83 | C2×C8×C59 | #41 | 1 | 1 | yes | characteristic |
| 84 | C4⋊C4×C59 | — | 2 | 1 | no | — |
| 85 | C4⋊C4×C59 | — | 2 | 1 | no | — |
| 86 | C4⋊C4×C59 | — | 4 | 1 | no | — |
| 87 | C4⋊C4×C59 | — | 4 | 1 | no | — |
| 88 | C22⋊C4×C59 | — | 4 | 1 | no | — |
| 89 | C22⋊C4×C59 | — | 8 | 4 | no | — |
| 90 | C42×C59 | — | 2 | 1 | no | — |
| 91 | C42×C59 | — | 2 | 1 | no | — |
| 92 | C42×C59 | — | 4 | 1 | no | — |
| 93 | C16×C59 | — | 2 | 2 | no | — |
| 94 | C16×C59 | — | 4 | 1 | no | — |
| 95 | C23×C59 | — | 4 | 2 | no | — |
| 96 | C23×C59 | — | 8 | 2 | no | — |
| 97 | C23×C59 | — | 8 | 2 | no | — |
| 98 | C23×C59 | — | 8 | 1 | no | — |
| 99 | C23×C59 | — | 8 | 1 | no | — |
| 100 | C23×C59 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 101 | D4×C59 | — | 4 | 2 | no | — |
| 102 | D4×C59 | — | 4 | 2 | no | — |
| 103 | D4×C59 | — | 8 | 1 | no | — |
| 104 | D4×C59 | — | 8 | 1 | no | — |
| 105 | C2×C4×C59 | — | 2 | 2 | no | — |
| 106 | C2×C4×C59 | — | 4 | 1 | no | — |
| 107 | C2×C4×C59 | — | 4 | 1 | no | — |
| 108 | C2×C4×C59 | — | 4 | 1 | no | — |
| 109 | C2×C4×C59 | — | 4 | 1 | no | — |
| 110 | C2×C4×C59 | — | 8 | 2 | no | — |
| 111 | C2×C4×C59 | — | 8 | 1 | no | — |
| 112 | C2×C4×C59 | C4×D4 | 1 | 1 | yes | characteristic |
| 113 | C2×C4×C59 | #121 | 1 | 1 | yes | characteristic |
| 114 | C2×C4×C59 | #123 | 1 | 1 | yes | characteristic |
| 115 | C2×C4×C59 | C2×D8 | 1 | 1 | yes | characteristic |
| 116 | C2×C4×C59 | #135 | 1 | 1 | yes | characteristic |
| 117 | C2×C4×C59 | #137 | 1 | 1 | yes | characteristic |
| 118 | C8×C59 | — | 2 | 1 | no | — |
| 119 | C8×C59 | — | 2 | 1 | no | — |
| 120 | C8×C59 | — | 4 | 2 | no | — |
| 121 | C8×C59 | #117 | 1 | 1 | yes | characteristic |
| 122 | C8×C59 | C4×D4 | 1 | 1 | yes | characteristic |
| 123 | C8×C59 | #124 | 1 | 1 | yes | characteristic |
| 124 | C8×C59 | #126 | 1 | 1 | yes | characteristic |
| 125 | #13136 | C59 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 126 | C22×C59 | — | 2 | 1 | no | — |
| 127 | C22×C59 | — | 2 | 1 | no | — |
| 128 | C22×C59 | — | 8 | 4 | no | — |
| 129 | C22×C59 | — | 8 | 2 | no | — |
| 130 | C22×C59 | — | 16 | 2 | no | — |
| 131 | C22×C59 | — | 16 | 1 | no | — |
| 132 | C22×C59 | — | 16 | 1 | no | — |
| 133 | C22×C59 | #440 | 1 | 1 | yes | characteristic |
| 134 | C22×C59 | #459 | 1 | 1 | yes | characteristic |
| 135 | C22×C59 | #482 | 1 | 1 | yes | characteristic |
| 136 | C4×C59 | — | 4 | 2 | no | — |
| 137 | C4×C59 | — | 8 | 1 | no | — |
| 138 | C4×C59 | — | 8 | 1 | no | — |
| 139 | C4×C59 | — | 16 | 1 | no | — |
| 140 | C4×C59 | #388 | 1 | 1 | yes | characteristic |
| 141 | C4×C59 | C4×D8 | 1 | 1 | yes | characteristic |
| 142 | C4×C59 | #464 | 1 | 1 | yes | characteristic |
| 143 | C4×C59 | #480 | 1 | 1 | yes | characteristic |
| 144 | #2159 | C2×C59 | 1 | 1 | yes | characteristic, complemented |
| 145 | C2×#361 | C2×C59 | 1 | 1 | yes | characteristic |
| 146 | #2140 | C2×C59 | 1 | 1 | yes | characteristic |
| 147 | #1970 | C2×C59 | 1 | 1 | yes | characteristic |
| 148 | #1772 | C2×C59 | 1 | 1 | yes | characteristic, complemented |
| 149 | #1387 | C2×C59 | 1 | 1 | yes | characteristic, complemented |
| 150 | #1376 | C2×C59 | 1 | 1 | yes | characteristic, complemented |
| 151 | C2×C59 | — | 2 | 1 | no | — |
| 152 | C2×C59 | — | 2 | 1 | no | — |
| 153 | C2×C59 | — | 16 | 2 | no | — |
| 154 | C2×C59 | #1925 | 1 | 1 | yes | characteristic |
| 155 | C2×C59 | #2212 | 1 | 1 | yes | characteristic |
| 156 | C2×C59 | #2213 | 1 | 1 | yes | characteristic |
| 157 | C22×D8 | C22×C59 | 1 | 1 | yes | characteristic |
| 158 | C2×M32 | C22×C59 | 1 | 1 | yes | characteristic |
| 159 | C2×M32 | C22×C59 | 1 | 1 | yes | characteristic |
| 160 | C2×#108 | C22×C59 | 1 | 1 | yes | characteristic |
| 161 | #427 | C22×C59 | 1 | 1 | yes | characteristic |
| 162 | C2×#107 | C22×C59 | 1 | 1 | yes | characteristic |
| 163 | C2×#102 | — | 2 | 1 | no | — |
| 164 | #405 | — | 2 | 1 | no | — |
| 165 | C2×C4×C8 | C22×C59 | 1 | 1 | yes | characteristic |
| 166 | #390 | — | 2 | 1 | no | — |
| 167 | #367 | — | 2 | 1 | no | — |
| 168 | #366 | — | 2 | 1 | no | — |
| 169 | #361 | C4×C59 | 1 | 4 | yes | complemented |
| 170 | #357 | — | 2 | 1 | no | — |
| 171 | #357 | — | 2 | 1 | no | — |
| 172 | #339 | — | 2 | 1 | no | — |
| 173 | C59 | #13136 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 174 | C22×D4 | — | 2 | 1 | no | — |
| 175 | C2×D8 | — | 2 | 1 | no | — |
| 176 | C2×D8 | — | 2 | 1 | no | — |
| 177 | C2×D8 | — | 2 | 1 | no | — |
| 178 | C2×D8 | — | 2 | 1 | no | — |
| 179 | C2×D8 | — | 2 | 1 | no | — |
| 180 | C2×D8 | C2×C4×C59 | 1 | 2 | yes | — |
| 181 | C2×M16 | — | 2 | 1 | no | — |
| 182 | C22×C8 | D4×C59 | 1 | 1 | yes | characteristic |
| 183 | C22×C8 | C23×C59 | 1 | 1 | yes | characteristic |
| 184 | #117 | — | 2 | 1 | no | — |
| 185 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 186 | C2×C22⋊C4 | — | 4 | 2 | no | — |
| 187 | C2×C42 | D4×C59 | 1 | 1 | yes | characteristic |
| 188 | M32 | — | 2 | 1 | no | — |
| 189 | M32 | — | 2 | 1 | no | — |
| 190 | M32 | — | 2 | 1 | no | — |
| 191 | M32 | C2×C4×C59 | 1 | 2 | yes | — |
| 192 | C2×C16 | — | 2 | 1 | no | — |
| 193 | C2×C16 | — | 2 | 1 | no | — |
| 194 | #108 | — | 2 | 1 | no | — |
| 195 | #108 | C2×C4×C59 | 1 | 2 | yes | — |
| 196 | #107 | — | 2 | 1 | no | — |
| 197 | #107 | — | 2 | 1 | no | — |
| 198 | #107 | D4×C59 | 1 | 1 | yes | characteristic |
| 199 | #107 | D4×C59 | 1 | 1 | yes | characteristic |
| 200 | #106 | — | 2 | 1 | no | — |
| 201 | #102 | — | 4 | 1 | no | — |
| 202 | #102 | — | 4 | 1 | no | — |
| 203 | #97 | — | 4 | 1 | no | — |
| 204 | C4×C8 | — | 2 | 1 | no | — |
| 205 | C4×C8 | — | 2 | 1 | no | — |
| 206 | C4×C8 | — | 4 | 1 | no | — |
| 207 | C24 | — | 4 | 1 | no | — |
| 208 | C2×D4 | — | 2 | 2 | no | — |
| 209 | C2×D4 | — | 4 | 1 | no | — |
| 210 | C2×D4 | — | 4 | 1 | no | — |
| 211 | C2×D4 | — | 4 | 1 | no | — |
| 212 | C2×D4 | — | 4 | 1 | no | — |
| 213 | C2×D4 | — | 4 | 1 | no | — |
| 214 | C22×C4 | — | 2 | 1 | no | — |
| 215 | C22×C4 | — | 4 | 1 | no | — |
| 216 | C22×C4 | C2×D4×C59 | 1 | 1 | yes | characteristic |
| 217 | D8 | — | 2 | 2 | no | — |
| 218 | D8 | — | 2 | 2 | no | — |
| 219 | D8 | — | 4 | 1 | no | — |
| 220 | D8 | — | 4 | 1 | no | — |
| 221 | M16 | — | 2 | 2 | no | — |
| 222 | M16 | — | 4 | 1 | no | — |
| 223 | C2×C8 | — | 2 | 1 | no | — |
| 224 | C2×C8 | — | 2 | 1 | no | — |
| 225 | C2×C8 | — | 4 | 1 | no | — |
| 226 | C2×C8 | D8×C59 | 1 | 1 | yes | characteristic |
| 227 | C2×C8 | D8×C59 | 1 | 1 | yes | characteristic |
| 228 | C2×C8 | C22×C4×C59 | 1 | 1 | yes | characteristic |
| 229 | C2×C8 | C2×D4×C59 | 1 | 1 | yes | characteristic |
| 230 | C2×C8 | #41×C59 | 1 | 1 | yes | characteristic |
| 231 | C2×C8 | #41×C59 | 1 | 1 | yes | characteristic |
| 232 | C2×C8 | #41×C59 | 1 | 1 | yes | characteristic |
| 233 | C2×C8 | #41×C59 | 1 | 1 | yes | characteristic |
| 234 | C4⋊C4 | — | 2 | 1 | no | — |
| 235 | C4⋊C4 | — | 2 | 1 | no | — |
| 236 | C4⋊C4 | — | 4 | 1 | no | — |
| 237 | C4⋊C4 | — | 4 | 1 | no | — |
| 238 | C22⋊C4 | — | 4 | 1 | no | — |
| 239 | C22⋊C4 | — | 8 | 4 | no | — |
| 240 | C42 | — | 2 | 1 | no | — |
| 241 | C42 | — | 2 | 1 | no | — |
| 242 | C42 | — | 4 | 1 | no | — |
| 243 | C16 | — | 2 | 2 | no | — |
| 244 | C16 | — | 4 | 1 | no | — |
| 245 | C23 | — | 4 | 2 | no | — |
| 246 | C23 | — | 8 | 2 | no | — |
| 247 | C23 | — | 8 | 2 | no | — |
| 248 | C23 | — | 8 | 1 | no | — |
| 249 | C23 | — | 8 | 1 | no | — |
| 250 | C23 | AGL(1,ℤ/8)×C59 | 1 | 1 | yes | characteristic |
| 251 | D4 | — | 4 | 2 | no | — |
| 252 | D4 | — | 4 | 2 | no | — |
| 253 | D4 | — | 8 | 1 | no | — |
| 254 | D4 | — | 8 | 1 | no | — |
| 255 | C2×C4 | — | 2 | 2 | no | — |
| 256 | C2×C4 | — | 4 | 1 | no | — |
| 257 | C2×C4 | — | 4 | 1 | no | — |
| 258 | C2×C4 | — | 4 | 1 | no | — |
| 259 | C2×C4 | — | 4 | 1 | no | — |
| 260 | C2×C4 | — | 8 | 2 | no | — |
| 261 | C2×C4 | — | 8 | 1 | no | — |
| 262 | C2×C4 | C4×D4×C59 | 1 | 1 | yes | characteristic |
| 263 | C2×C4 | #121×C59 | 1 | 1 | yes | characteristic |
| 264 | C2×C4 | #123×C59 | 1 | 1 | yes | characteristic |
| 265 | C2×C4 | C2×D8×C59 | 1 | 1 | yes | characteristic |
| 266 | C2×C4 | #135×C59 | 1 | 1 | yes | characteristic |
| 267 | C2×C4 | #137×C59 | 1 | 1 | yes | characteristic |
| 268 | C8 | — | 2 | 1 | no | — |
| 269 | C8 | — | 2 | 1 | no | — |
| 270 | C8 | — | 4 | 2 | no | — |
| 271 | C8 | #117×C59 | 1 | 1 | yes | characteristic |
| 272 | C8 | C4×D4×C59 | 1 | 1 | yes | characteristic |
| 273 | C8 | #124×C59 | 1 | 1 | yes | characteristic |
| 274 | C8 | #126×C59 | 1 | 1 | yes | characteristic |
| 275 | C22 | — | 2 | 1 | no | — |
| 276 | C22 | — | 2 | 1 | no | — |
| 277 | C22 | — | 8 | 4 | no | — |
| 278 | C22 | — | 8 | 2 | no | — |
| 279 | C22 | — | 16 | 2 | no | — |
| 280 | C22 | — | 16 | 1 | no | — |
| 281 | C22 | — | 16 | 1 | no | — |
| 282 | C22 | C59×#440 | 1 | 1 | yes | characteristic |
| 283 | C22 | C59×#459 | 1 | 1 | yes | characteristic |
| 284 | C22 | C59×#482 | 1 | 1 | yes | characteristic |
| 285 | C4 | — | 4 | 2 | no | — |
| 286 | C4 | — | 8 | 1 | no | — |
| 287 | C4 | — | 8 | 1 | no | — |
| 288 | C4 | — | 16 | 1 | no | — |
| 289 | C4 | C59×#388 | 1 | 1 | yes | characteristic |
| 290 | C4 | C4×D8×C59 | 1 | 1 | yes | characteristic |
| 291 | C4 | C59×#464 | 1 | 1 | yes | characteristic |
| 292 | C4 | C59×#480 | 1 | 1 | yes | characteristic |
| 293 | C2 | — | 2 | 1 | no | — |
| 294 | C2 | — | 2 | 1 | no | — |
| 295 | C2 | — | 16 | 2 | no | — |
| 296 | C2 | C59×#1925 | 1 | 1 | yes | characteristic |
| 297 | C2 | C59×#2212 | 1 | 1 | yes | characteristic |
| 298 | C2 | C59×#2213 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta