| 1 | C2×#16837232 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#16837209 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #21424985 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #21423977 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #21422191 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #21422173 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C59×#2138 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C22×C59⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 9 | C2×#14273663 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#14273663 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#14273654 | — | 2 | 1 | no | — |
| 12 | #16837369 | — | 2 | 1 | no | — |
| 13 | #16837358 | — | 2 | 1 | no | — |
| 14 | C2×C8×Dic59 | C22 | 1 | 1 | yes | characteristic |
| 15 | #16837232 | — | 2 | 2 | no | — |
| 16 | #16837209 | — | 2 | 2 | no | — |
| 17 | #16837161 | — | 2 | 1 | no | — |
| 18 | C2×#135×C59 | C22 | 1 | 1 | yes | characteristic |
| 19 | C22×C16×C59 | C22 | 1 | 1 | yes | characteristic |
| 20 | C59×#427 | C22 | 1 | 1 | yes | characteristic |
| 21 | C59×#358 | C4 | 1 | 1 | yes | characteristic, complemented |
| 22 | C59×#358 | C4 | 1 | 1 | yes | characteristic, complemented |
| 23 | C59×#357 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | C59×#357 | C4 | 1 | 1 | yes | characteristic, complemented |
| 25 | C2×#11745664 | — | 2 | 1 | no | — |
| 26 | C2×#11745664 | — | 2 | 1 | no | — |
| 27 | C22×C59⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 28 | C2×C4×Dic59 | D4 | 1 | 1 | yes | characteristic |
| 29 | C2×C59⋊C16 | — | 2 | 1 | no | — |
| 30 | C2×C59⋊C16 | — | 2 | 1 | no | — |
| 31 | C2×C59⋊C16 | — | 2 | 1 | no | — |
| 32 | #14273663 | — | 2 | 1 | no | — |
| 33 | #14273663 | — | 2 | 1 | no | — |
| 34 | #14273663 | — | 2 | 1 | no | — |
| 35 | #14273663 | D4 | 1 | 2 | yes | — |
| 36 | #14273654 | — | 4 | 2 | no | — |
| 37 | C22⋊(C59⋊C8) | — | 4 | 1 | no | — |
| 38 | C22⋊(C59⋊C8) | — | 4 | 1 | no | — |
| 39 | #14273638 | — | 4 | 1 | no | — |
| 40 | C4×C59⋊C8 | — | 4 | 1 | no | — |
| 41 | C8×Dic59 | — | 2 | 1 | no | — |
| 42 | C8×Dic59 | — | 2 | 1 | no | — |
| 43 | C2×#41×C59 | — | 2 | 1 | no | — |
| 44 | #135×C59 | — | 2 | 1 | no | — |
| 45 | #135×C59 | — | 2 | 1 | no | — |
| 46 | #135×C59 | — | 2 | 1 | no | — |
| 47 | #135×C59 | — | 2 | 1 | no | — |
| 48 | C2×Q16×C59 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | C2×SD16×C59 | — | 2 | 1 | no | — |
| 50 | C2×D8×C59 | C2×C4 | 1 | 1 | yes | characteristic |
| 51 | C22×C8×C59 | C23 | 1 | 1 | yes | characteristic |
| 52 | #117×C59 | — | 2 | 1 | no | — |
| 53 | C2×C16×C59 | — | 2 | 1 | no | — |
| 54 | C2×C16×C59 | — | 2 | 1 | no | — |
| 55 | C2×C16×C59 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | C2×C16×C59 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | #107×C59 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | #107×C59 | C2×C4 | 1 | 1 | yes | characteristic |
| 59 | #106×C59 | — | 2 | 1 | no | — |
| 60 | #41×C59 | — | 4 | 1 | no | — |
| 61 | #41×C59 | — | 4 | 1 | no | — |
| 62 | #41×C59 | — | 4 | 1 | no | — |
| 63 | #41×C59 | — | 4 | 1 | no | — |
| 64 | C2×Q8×C59 | — | 2 | 1 | no | — |
| 65 | C2×D4×C59 | — | 2 | 1 | no | — |
| 66 | C2×D4×C59 | — | 4 | 1 | no | — |
| 67 | C22×C4×C59 | — | 4 | 1 | no | — |
| 68 | C22×C4×C59 | C2×D4 | 1 | 1 | yes | characteristic |
| 69 | C22×Dic59 | — | 2 | 1 | no | — |
| 70 | Q16×C59 | — | 2 | 1 | no | — |
| 71 | Q16×C59 | — | 2 | 1 | no | — |
| 72 | SD16×C59 | — | 4 | 1 | no | — |
| 73 | SD16×C59 | — | 4 | 1 | no | — |
| 74 | D8×C59 | — | 2 | 1 | no | — |
| 75 | D8×C59 | — | 2 | 1 | no | — |
| 76 | C2×C8×C59 | C22×C4 | 1 | 1 | yes | characteristic |
| 77 | C2×C8×C59 | C2×D4 | 1 | 1 | yes | characteristic |
| 78 | C2×C8×C59 | #41 | 1 | 1 | yes | characteristic |
| 79 | C2×C8×C59 | #41 | 1 | 1 | yes | characteristic |
| 80 | C2×C8×C59 | #41 | 1 | 1 | yes | characteristic |
| 81 | C2×C8×C59 | #41 | 1 | 1 | yes | characteristic |
| 82 | C4⋊C4×C59 | — | 2 | 1 | no | — |
| 83 | C4⋊C4×C59 | — | 2 | 1 | no | — |
| 84 | C22⋊C4×C59 | — | 4 | 1 | no | — |
| 85 | C42×C59 | — | 4 | 1 | no | — |
| 86 | C4×Dic59 | — | 2 | 1 | no | — |
| 87 | C4×Dic59 | — | 2 | 1 | no | — |
| 88 | #11745664 | — | 2 | 2 | no | — |
| 89 | #11745664 | — | 4 | 1 | no | — |
| 90 | #11745664 | — | 4 | 1 | no | — |
| 91 | #11745664 | — | 4 | 1 | no | — |
| 92 | C2×C59⋊C8 | — | 2 | 1 | no | — |
| 93 | C2×C59⋊C8 | — | 2 | 1 | no | — |
| 94 | C2×C59⋊C8 | — | 4 | 1 | no | — |
| 95 | C2×C59⋊C8 | — | 4 | 1 | no | — |
| 96 | C2×C59⋊C8 | D8 | 1 | 1 | yes | characteristic |
| 97 | C2×C59⋊C8 | D8 | 1 | 1 | yes | characteristic |
| 98 | C16×C59 | — | 2 | 1 | no | — |
| 99 | C16×C59 | — | 2 | 1 | no | — |
| 100 | C59⋊C16 | — | 4 | 1 | no | — |
| 101 | C23×C59 | — | 4 | 1 | no | — |
| 102 | C23×C59 | #135 | 1 | 1 | yes | characteristic |
| 103 | Q8×C59 | — | 4 | 1 | no | — |
| 104 | Q8×C59 | — | 4 | 1 | no | — |
| 105 | D4×C59 | — | 4 | 1 | no | — |
| 106 | D4×C59 | — | 4 | 1 | no | — |
| 107 | D4×C59 | — | 8 | 1 | no | — |
| 108 | D4×C59 | — | 8 | 1 | no | — |
| 109 | C2×C4×C59 | — | 4 | 1 | no | — |
| 110 | C2×C4×C59 | — | 4 | 1 | no | — |
| 111 | C2×C4×C59 | — | 4 | 1 | no | — |
| 112 | C2×C4×C59 | — | 8 | 1 | no | — |
| 113 | C2×C4×C59 | — | 8 | 1 | no | — |
| 114 | C2×C4×C59 | C4×D4 | 1 | 1 | yes | characteristic |
| 115 | C2×C4×C59 | #121 | 1 | 1 | yes | characteristic |
| 116 | C2×C4×C59 | #123 | 1 | 1 | yes | characteristic |
| 117 | C2×C4×C59 | C2×D8 | 1 | 1 | yes | characteristic |
| 118 | C2×C4×C59 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 119 | C2×C4×C59 | #137 | 1 | 1 | yes | characteristic |
| 120 | C2×Dic59 | — | 2 | 2 | no | — |
| 121 | C2×Dic59 | — | 4 | 1 | no | — |
| 122 | C2×Dic59 | — | 4 | 1 | no | — |
| 123 | C8×C59 | #117 | 1 | 1 | yes | characteristic |
| 124 | C8×C59 | C4×D4 | 1 | 1 | yes | characteristic |
| 125 | C8×C59 | #124 | 1 | 1 | yes | characteristic |
| 126 | C8×C59 | #126 | 1 | 1 | yes | characteristic |
| 127 | C59⋊C8 | — | 2 | 1 | no | — |
| 128 | C59⋊C8 | — | 2 | 1 | no | — |
| 129 | C59⋊C8 | — | 4 | 2 | no | — |
| 130 | C59⋊C8 | — | 8 | 1 | no | — |
| 131 | #13134 | — | 59 | 1 | no | maximal, Sylow |
| 132 | C22×C59 | — | 2 | 1 | no | — |
| 133 | C22×C59 | — | 2 | 1 | no | — |
| 134 | C22×C59 | — | 8 | 1 | no | — |
| 135 | C22×C59 | — | 8 | 1 | no | — |
| 136 | C22×C59 | — | 8 | 1 | no | — |
| 137 | C22×C59 | C4×D8 | 1 | 1 | yes | characteristic |
| 138 | C22×C59 | #464 | 1 | 1 | yes | characteristic |
| 139 | C22×C59 | #482 | 1 | 1 | yes | characteristic |
| 140 | C4×C59 | — | 8 | 1 | no | — |
| 141 | C4×C59 | — | 8 | 1 | no | — |
| 142 | C4×C59 | — | 8 | 1 | no | — |
| 143 | C4×C59 | #388 | 1 | 1 | yes | characteristic |
| 144 | C4×C59 | #440 | 1 | 1 | yes | characteristic |
| 145 | C4×C59 | #459 | 1 | 1 | yes | characteristic |
| 146 | C4×C59 | #480 | 1 | 1 | yes | characteristic |
| 147 | Dic59 | — | 4 | 2 | no | — |
| 148 | C2×#368 | — | 59 | 1 | no | — |
| 149 | C2×#359 | — | 59 | 1 | no | — |
| 150 | #2138 | D59 | 1 | 1 | yes | characteristic |
| 151 | #1974 | — | 59 | 1 | no | — |
| 152 | #1772 | — | 59 | 1 | no | — |
| 153 | #1382 | — | 59 | 1 | no | — |
| 154 | #1374 | — | 59 | 1 | no | — |
| 155 | C2×C59 | — | 2 | 1 | no | — |
| 156 | C2×C59 | — | 2 | 1 | no | — |
| 157 | C2×C59 | — | 16 | 1 | no | — |
| 158 | C2×C59 | #1925 | 1 | 1 | yes | characteristic |
| 159 | C2×C59 | #2178 | 1 | 1 | yes | characteristic |
| 160 | C2×C59 | #2179 | 1 | 1 | yes | characteristic |
| 161 | C2×#135 | C2×D59 | 1 | 1 | yes | characteristic |
| 162 | C22×C16 | — | 59 | 1 | no | — |
| 163 | C22×C16 | C2×D59 | 1 | 1 | yes | characteristic |
| 164 | C2×#108 | — | 59 | 1 | no | — |
| 165 | C2×#108 | — | 59 | 1 | no | — |
| 166 | #427 | C2×D59 | 1 | 1 | yes | characteristic |
| 167 | C2×#104 | — | 118 | 1 | no | — |
| 168 | #408 | — | 118 | 1 | no | — |
| 169 | #405 | — | 118 | 1 | no | — |
| 170 | C2×C4×C8 | — | 59 | 1 | no | — |
| 171 | #368 | — | 118 | 2 | no | — |
| 172 | #359 | — | 118 | 2 | no | — |
| 173 | #358 | Dic59 | 1 | 1 | yes | characteristic, complemented |
| 174 | #358 | Dic59 | 1 | 1 | yes | characteristic, complemented |
| 175 | #357 | Dic59 | 1 | 1 | yes | characteristic, complemented |
| 176 | #357 | Dic59 | 1 | 1 | yes | characteristic, complemented |
| 177 | #339 | — | 118 | 1 | no | — |
| 178 | C59 | #13134 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 179 | C2×#41 | — | 2 | 1 | no | — |
| 180 | #135 | — | 2 | 1 | no | — |
| 181 | #135 | — | 2 | 1 | no | — |
| 182 | #135 | — | 2 | 1 | no | — |
| 183 | #135 | — | 2 | 1 | no | — |
| 184 | C2×Q16 | C2×Dic59 | 1 | 1 | yes | characteristic |
| 185 | C2×SD16 | — | 2 | 1 | no | — |
| 186 | C2×D8 | C2×Dic59 | 1 | 1 | yes | characteristic |
| 187 | C2×M16 | — | 118 | 1 | no | — |
| 188 | C2×M16 | — | 118 | 1 | no | — |
| 189 | C22×C8 | — | 59 | 1 | no | — |
| 190 | C22×C8 | C22×D59 | 1 | 1 | yes | characteristic |
| 191 | #117 | — | 2 | 1 | no | — |
| 192 | C2×C42 | — | 59 | 1 | no | — |
| 193 | C2×C16 | — | 2 | 1 | no | — |
| 194 | C2×C16 | — | 2 | 1 | no | — |
| 195 | C2×C16 | — | 118 | 1 | no | — |
| 196 | C2×C16 | — | 118 | 1 | no | — |
| 197 | C2×C16 | — | 118 | 1 | no | — |
| 198 | C2×C16 | C2×Dic59 | 1 | 1 | yes | characteristic |
| 199 | C2×C16 | C2×Dic59 | 1 | 1 | yes | characteristic |
| 200 | #108 | — | 59 | 2 | no | — |
| 201 | #108 | — | 118 | 1 | no | — |
| 202 | #108 | — | 118 | 1 | no | — |
| 203 | #108 | — | 118 | 1 | no | — |
| 204 | #107 | C2×Dic59 | 1 | 1 | yes | characteristic |
| 205 | #107 | C2×Dic59 | 1 | 1 | yes | characteristic |
| 206 | #106 | — | 2 | 1 | no | — |
| 207 | #104 | — | 236 | 2 | no | — |
| 208 | C22⋊C8 | — | 236 | 1 | no | — |
| 209 | C22⋊C8 | — | 236 | 1 | no | — |
| 210 | #97 | — | 236 | 1 | no | — |
| 211 | C4×C8 | — | 118 | 1 | no | — |
| 212 | C4×C8 | — | 118 | 1 | no | — |
| 213 | C4×C8 | — | 236 | 1 | no | — |
| 214 | #41 | — | 4 | 1 | no | — |
| 215 | #41 | — | 4 | 1 | no | — |
| 216 | #41 | — | 4 | 1 | no | — |
| 217 | #41 | — | 4 | 1 | no | — |
| 218 | C2×Q8 | — | 2 | 1 | no | — |
| 219 | C2×D4 | — | 2 | 1 | no | — |
| 220 | C2×D4 | — | 4 | 1 | no | — |
| 221 | C22×C4 | — | 4 | 1 | no | — |
| 222 | C22×C4 | — | 118 | 1 | no | — |
| 223 | C22×C4 | D4×D59 | 1 | 1 | yes | characteristic |
| 224 | Q16 | — | 2 | 1 | no | — |
| 225 | Q16 | — | 2 | 1 | no | — |
| 226 | SD16 | — | 4 | 1 | no | — |
| 227 | SD16 | — | 4 | 1 | no | — |
| 228 | D8 | — | 2 | 1 | no | — |
| 229 | D8 | — | 2 | 1 | no | — |
| 230 | M16 | — | 118 | 2 | no | — |
| 231 | M16 | — | 236 | 1 | no | — |
| 232 | M16 | — | 236 | 1 | no | — |
| 233 | M16 | — | 236 | 1 | no | — |
| 234 | C2×C8 | — | 59 | 1 | no | — |
| 235 | C2×C8 | — | 59 | 1 | no | — |
| 236 | C2×C8 | — | 118 | 1 | no | — |
| 237 | C2×C8 | — | 118 | 1 | no | — |
| 238 | C2×C8 | — | 236 | 1 | no | — |
| 239 | C2×C8 | — | 236 | 1 | no | — |
| 240 | C2×C8 | #11745685 | 1 | 1 | yes | characteristic |
| 241 | C2×C8 | #11745685 | 1 | 1 | yes | characteristic |
| 242 | C2×C8 | D4×D59 | 1 | 1 | yes | characteristic |
| 243 | C2×C8 | #11745687 | 1 | 1 | yes | characteristic |
| 244 | C2×C8 | #11745687 | 1 | 1 | yes | characteristic |
| 245 | C2×C8 | C22×Dic59 | 1 | 1 | yes | characteristic |
| 246 | C4⋊C4 | — | 2 | 1 | no | — |
| 247 | C4⋊C4 | — | 2 | 1 | no | — |
| 248 | C22⋊C4 | — | 4 | 1 | no | — |
| 249 | C42 | — | 4 | 1 | no | — |
| 250 | C42 | — | 118 | 1 | no | — |
| 251 | C42 | — | 118 | 1 | no | — |
| 252 | C16 | — | 2 | 1 | no | — |
| 253 | C16 | — | 2 | 1 | no | — |
| 254 | C16 | — | 236 | 1 | no | — |
| 255 | C23 | — | 4 | 1 | no | — |
| 256 | C23 | #14273746 | 1 | 1 | yes | characteristic |
| 257 | Q8 | — | 4 | 1 | no | — |
| 258 | Q8 | — | 4 | 1 | no | — |
| 259 | D4 | — | 4 | 1 | no | — |
| 260 | D4 | — | 4 | 1 | no | — |
| 261 | D4 | — | 8 | 1 | no | — |
| 262 | D4 | — | 8 | 1 | no | — |
| 263 | C2×C4 | — | 4 | 1 | no | — |
| 264 | C2×C4 | — | 4 | 1 | no | — |
| 265 | C2×C4 | — | 4 | 1 | no | — |
| 266 | C2×C4 | — | 8 | 1 | no | — |
| 267 | C2×C4 | — | 8 | 1 | no | — |
| 268 | C2×C4 | — | 118 | 2 | no | — |
| 269 | C2×C4 | — | 236 | 1 | no | — |
| 270 | C2×C4 | — | 236 | 1 | no | — |
| 271 | C2×C4 | D4×Dic59 | 1 | 1 | yes | characteristic |
| 272 | C2×C4 | #14273700 | 1 | 1 | yes | characteristic |
| 273 | C2×C4 | #14273709 | 1 | 1 | yes | characteristic |
| 274 | C2×C4 | D8×D59 | 1 | 1 | yes | characteristic |
| 275 | C2×C4 | #14273754 | 1 | 1 | yes | characteristic |
| 276 | C2×C4 | #14273756 | 1 | 1 | yes | characteristic |
| 277 | C8 | — | 118 | 1 | no | — |
| 278 | C8 | — | 118 | 1 | no | — |
| 279 | C8 | — | 472 | 1 | no | — |
| 280 | C8 | — | 236 | 2 | no | — |
| 281 | C8 | #14273686 | 1 | 1 | yes | characteristic |
| 282 | C8 | D4×Dic59 | 1 | 1 | yes | characteristic |
| 283 | C8 | #14273713 | 1 | 1 | yes | characteristic |
| 284 | C8 | #14273720 | 1 | 1 | yes | characteristic |
| 285 | C22 | — | 2 | 1 | no | — |
| 286 | C22 | — | 2 | 1 | no | — |
| 287 | C22 | — | 8 | 1 | no | — |
| 288 | C22 | — | 8 | 1 | no | — |
| 289 | C22 | — | 8 | 1 | no | — |
| 290 | C22 | D8×Dic59 | 1 | 1 | yes | characteristic |
| 291 | C22 | #16837623 | 1 | 1 | yes | characteristic |
| 292 | C22 | #16837724 | 1 | 1 | yes | characteristic |
| 293 | C4 | — | 8 | 1 | no | — |
| 294 | C4 | — | 8 | 1 | no | — |
| 295 | C4 | — | 8 | 1 | no | — |
| 296 | C4 | — | 236 | 2 | no | — |
| 297 | C4 | #16837295 | 1 | 1 | yes | characteristic |
| 298 | C4 | #16837503 | 1 | 1 | yes | characteristic |
| 299 | C4 | #16837596 | 1 | 1 | yes | characteristic |
| 300 | C4 | #16837714 | 1 | 1 | yes | characteristic |
| 301 | C2 | — | 2 | 1 | no | — |
| 302 | C2 | — | 2 | 1 | no | — |
| 303 | C2 | — | 16 | 1 | no | — |
| 304 | C2 | #21424718 | 1 | 1 | yes | characteristic |
| 305 | C2 | #21425977 | 1 | 1 | yes | characteristic |
| 306 | C2 | #21425982 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta