| 1 | C2×C59×#471 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C59×#2949 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C59×#2082 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C59×#2081 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C59×#2049 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C59×#2048 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C59×#1977 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C59×#1953 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C59×#1905 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C59×#1904 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | C59×#1833 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C59×#1830 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C59×#1829 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C59×#1814 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C59×#1757 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#137×C59 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×AGL(1,ℤ/8)×C59 | C22 | 1 | 1 | yes | characteristic |
| 18 | C22×SD16×C59 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#131×C59 | C22 | 1 | 1 | yes | characteristic |
| 20 | C59×#519 | C22 | 1 | 1 | yes | characteristic |
| 21 | C59×#518 | C22 | 1 | 1 | yes | characteristic |
| 22 | C59×#471 | — | 2 | 2 | no | — |
| 23 | C59×#471 | — | 2 | 2 | no | — |
| 24 | C59×#440 | — | 2 | 2 | no | — |
| 25 | C4×SD16×C59 | — | 2 | 2 | no | — |
| 26 | C59×#430 | C22 | 1 | 1 | yes | characteristic |
| 27 | C59×#430 | C22 | 1 | 1 | yes | characteristic |
| 28 | C2×#108×C59 | C22 | 1 | 1 | yes | characteristic |
| 29 | C2×#108×C59 | C22 | 1 | 1 | yes | characteristic |
| 30 | C59×#427 | C22 | 1 | 1 | yes | characteristic |
| 31 | C59×#421 | C22 | 1 | 1 | yes | characteristic |
| 32 | C59×#421 | C22 | 1 | 1 | yes | characteristic |
| 33 | C59×#419 | C22 | 1 | 1 | yes | characteristic |
| 34 | C59×#419 | C22 | 1 | 1 | yes | characteristic |
| 35 | C59×#418 | C22 | 1 | 1 | yes | characteristic |
| 36 | C59×#418 | C22 | 1 | 1 | yes | characteristic |
| 37 | C59×#413 | C22 | 1 | 1 | yes | characteristic |
| 38 | C2×#101×C59 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#101×C59 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#100×C59 | C22 | 1 | 1 | yes | characteristic |
| 41 | C2×#100×C59 | C22 | 1 | 1 | yes | characteristic |
| 42 | C59×#410 | C22 | 1 | 1 | yes | characteristic |
| 43 | C59×#405 | C22 | 1 | 1 | yes | characteristic |
| 44 | C59×#405 | C22 | 1 | 1 | yes | characteristic |
| 45 | C59×#344 | C22 | 1 | 1 | yes | characteristic |
| 46 | C59×#344 | C22 | 1 | 1 | yes | characteristic |
| 47 | C59×#344 | C22 | 1 | 1 | yes | characteristic |
| 48 | C59×#344 | C22 | 1 | 1 | yes | characteristic |
| 49 | C59×#344 | C22 | 1 | 1 | yes | characteristic |
| 50 | C59×#344 | C22 | 1 | 1 | yes | characteristic |
| 51 | C59×#344 | C22 | 1 | 1 | yes | characteristic |
| 52 | C59×#344 | C22 | 1 | 1 | yes | characteristic |
| 53 | C59×H(3,ℤ/4) | C22 | 1 | 1 | yes | characteristic |
| 54 | C59×H(3,ℤ/4) | C22 | 1 | 1 | yes | characteristic |
| 55 | C2×#41×C59 | C23 | 1 | 1 | yes | characteristic |
| 56 | C22×Q8×C59 | C23 | 1 | 1 | yes | characteristic |
| 57 | C22×D4×C59 | C23 | 1 | 1 | yes | characteristic |
| 58 | #137×C59 | — | 2 | 2 | no | — |
| 59 | #137×C59 | — | 4 | 1 | no | — |
| 60 | AGL(1,ℤ/8)×C59 | — | 2 | 2 | no | — |
| 61 | AGL(1,ℤ/8)×C59 | — | 4 | 1 | no | — |
| 62 | C2×Q16×C59 | — | 2 | 1 | no | — |
| 63 | C2×SD16×C59 | — | 2 | 1 | no | — |
| 64 | C2×SD16×C59 | — | 2 | 1 | no | — |
| 65 | C2×SD16×C59 | — | 2 | 1 | no | — |
| 66 | C2×SD16×C59 | — | 2 | 1 | no | — |
| 67 | C2×SD16×C59 | — | 2 | 1 | no | — |
| 68 | C2×SD16×C59 | — | 2 | 1 | no | — |
| 69 | C2×SD16×C59 | D4 | 1 | 2 | yes | — |
| 70 | C2×SD16×C59 | D4 | 1 | 2 | yes | — |
| 71 | C2×D8×C59 | — | 2 | 1 | no | — |
| 72 | #131×C59 | — | 2 | 1 | no | — |
| 73 | #131×C59 | — | 2 | 1 | no | — |
| 74 | #131×C59 | — | 2 | 1 | no | — |
| 75 | #131×C59 | — | 2 | 1 | no | — |
| 76 | C2×M16×C59 | — | 2 | 1 | no | — |
| 77 | C2×M16×C59 | C23 | 1 | 1 | yes | characteristic |
| 78 | C2×M16×C59 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×M16×C59 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×M16×C59 | C23 | 1 | 1 | yes | characteristic |
| 81 | C2×M16×C59 | C23 | 1 | 1 | yes | characteristic |
| 82 | C2×M16×C59 | C23 | 1 | 1 | yes | characteristic |
| 83 | C2×M16×C59 | C23 | 1 | 1 | yes | characteristic |
| 84 | C22×C8×C59 | — | 2 | 1 | no | — |
| 85 | C22×C8×C59 | C23 | 1 | 1 | yes | characteristic |
| 86 | C4×Q8×C59 | — | 2 | 2 | no | — |
| 87 | C4×Q8×C59 | — | 4 | 1 | no | — |
| 88 | C4×D4×C59 | — | 2 | 2 | no | — |
| 89 | C4×D4×C59 | — | 4 | 1 | no | — |
| 90 | #117×C59 | — | 2 | 2 | no | — |
| 91 | #117×C59 | C23 | 1 | 1 | yes | characteristic |
| 92 | #117×C59 | C23 | 1 | 1 | yes | characteristic |
| 93 | #117×C59 | C23 | 1 | 1 | yes | characteristic |
| 94 | #117×C59 | C23 | 1 | 1 | yes | characteristic |
| 95 | C2×C22⋊C4×C59 | — | 2 | 2 | no | — |
| 96 | #108×C59 | — | 2 | 1 | no | — |
| 97 | #108×C59 | — | 2 | 1 | no | — |
| 98 | #108×C59 | — | 2 | 1 | no | — |
| 99 | #108×C59 | — | 2 | 1 | no | — |
| 100 | #108×C59 | — | 4 | 1 | no | — |
| 101 | #108×C59 | — | 4 | 1 | no | — |
| 102 | #107×C59 | — | 2 | 1 | no | — |
| 103 | #106×C59 | — | 2 | 1 | no | — |
| 104 | #104×C59 | — | 4 | 1 | no | — |
| 105 | #104×C59 | — | 4 | 1 | no | — |
| 106 | #103×C59 | — | 2 | 2 | no | — |
| 107 | #103×C59 | — | 4 | 1 | no | — |
| 108 | #102×C59 | — | 2 | 2 | no | — |
| 109 | #102×C59 | — | 4 | 1 | no | — |
| 110 | #101×C59 | — | 2 | 2 | no | — |
| 111 | #101×C59 | — | 2 | 1 | no | — |
| 112 | #101×C59 | — | 4 | 1 | no | — |
| 113 | #100×C59 | — | 2 | 2 | no | — |
| 114 | #100×C59 | — | 2 | 1 | no | — |
| 115 | #100×C59 | — | 4 | 1 | no | — |
| 116 | #99×C59 | — | 2 | 2 | no | — |
| 117 | #97×C59 | — | 2 | 1 | no | — |
| 118 | #97×C59 | — | 2 | 1 | no | — |
| 119 | C4×C8×C59 | — | 2 | 1 | no | — |
| 120 | C4×C8×C59 | — | 2 | 1 | no | — |
| 121 | C24×C59 | — | 2 | 1 | no | — |
| 122 | #41×C59 | — | 2 | 1 | no | — |
| 123 | #41×C59 | — | 2 | 1 | no | — |
| 124 | #41×C59 | — | 2 | 1 | no | — |
| 125 | #41×C59 | — | 2 | 1 | no | — |
| 126 | C2×Q8×C59 | — | 2 | 1 | no | — |
| 127 | C2×Q8×C59 | — | 2 | 1 | no | — |
| 128 | C2×Q8×C59 | — | 2 | 1 | no | — |
| 129 | C2×Q8×C59 | — | 2 | 1 | no | — |
| 130 | C2×Q8×C59 | — | 2 | 1 | no | — |
| 131 | C2×Q8×C59 | C2×D4 | 1 | 2 | yes | — |
| 132 | C2×Q8×C59 | #41 | 1 | 1 | yes | characteristic |
| 133 | C2×D4×C59 | — | 2 | 1 | no | — |
| 134 | C2×D4×C59 | — | 2 | 1 | no | — |
| 135 | C2×D4×C59 | — | 2 | 1 | no | — |
| 136 | C2×D4×C59 | — | 2 | 1 | no | — |
| 137 | C2×D4×C59 | — | 2 | 1 | no | — |
| 138 | C2×D4×C59 | — | 2 | 1 | no | — |
| 139 | C2×D4×C59 | C2×D4 | 1 | 2 | yes | — |
| 140 | C2×D4×C59 | #41 | 1 | 1 | yes | characteristic |
| 141 | C22×C4×C59 | — | 2 | 1 | no | — |
| 142 | C22×C4×C59 | — | 2 | 1 | no | — |
| 143 | C22×C4×C59 | — | 4 | 2 | no | — |
| 144 | C22×C4×C59 | C24 | 1 | 1 | yes | characteristic |
| 145 | Q16×C59 | — | 4 | 2 | no | — |
| 146 | SD16×C59 | — | 2 | 2 | no | — |
| 147 | SD16×C59 | — | 2 | 2 | no | — |
| 148 | SD16×C59 | — | 2 | 2 | no | — |
| 149 | SD16×C59 | — | 2 | 2 | no | — |
| 150 | SD16×C59 | — | 4 | 2 | no | — |
| 151 | SD16×C59 | — | 4 | 2 | no | — |
| 152 | D8×C59 | — | 4 | 2 | no | — |
| 153 | M16×C59 | — | 2 | 1 | no | — |
| 154 | M16×C59 | — | 2 | 1 | no | — |
| 155 | M16×C59 | — | 2 | 1 | no | — |
| 156 | M16×C59 | — | 2 | 1 | no | — |
| 157 | M16×C59 | — | 2 | 1 | no | — |
| 158 | M16×C59 | — | 2 | 1 | no | — |
| 159 | M16×C59 | — | 2 | 1 | no | — |
| 160 | M16×C59 | — | 2 | 1 | no | — |
| 161 | M16×C59 | — | 2 | 1 | no | — |
| 162 | M16×C59 | — | 2 | 1 | no | — |
| 163 | M16×C59 | — | 2 | 1 | no | — |
| 164 | M16×C59 | — | 2 | 1 | no | — |
| 165 | M16×C59 | — | 2 | 1 | no | — |
| 166 | M16×C59 | — | 2 | 1 | no | — |
| 167 | M16×C59 | — | 4 | 1 | no | — |
| 168 | M16×C59 | — | 4 | 1 | no | — |
| 169 | C2×C8×C59 | — | 2 | 1 | no | — |
| 170 | C2×C8×C59 | — | 2 | 1 | no | — |
| 171 | C2×C8×C59 | — | 2 | 1 | no | — |
| 172 | C2×C8×C59 | — | 2 | 1 | no | — |
| 173 | C2×C8×C59 | — | 2 | 1 | no | — |
| 174 | C2×C8×C59 | — | 2 | 1 | no | — |
| 175 | C2×C8×C59 | — | 2 | 1 | no | — |
| 176 | C2×C8×C59 | — | 4 | 1 | no | — |
| 177 | C2×C8×C59 | — | 4 | 1 | no | — |
| 178 | C2×C8×C59 | C2×D4 | 1 | 1 | yes | characteristic |
| 179 | C2×C8×C59 | C2×D4 | 1 | 1 | yes | characteristic |
| 180 | C2×C8×C59 | #41 | 1 | 1 | yes | characteristic |
| 181 | C2×C8×C59 | #41 | 1 | 1 | yes | characteristic |
| 182 | C2×C8×C59 | #41 | 1 | 1 | yes | characteristic |
| 183 | C2×C8×C59 | #41 | 1 | 1 | yes | characteristic |
| 184 | C4⋊C4×C59 | — | 2 | 1 | no | — |
| 185 | C4⋊C4×C59 | — | 2 | 1 | no | — |
| 186 | C4⋊C4×C59 | — | 2 | 1 | no | — |
| 187 | C4⋊C4×C59 | — | 2 | 1 | no | — |
| 188 | C4⋊C4×C59 | — | 4 | 2 | no | — |
| 189 | C22⋊C4×C59 | — | 2 | 1 | no | — |
| 190 | C22⋊C4×C59 | — | 2 | 1 | no | — |
| 191 | C22⋊C4×C59 | — | 2 | 1 | no | — |
| 192 | C22⋊C4×C59 | — | 4 | 2 | no | — |
| 193 | C22⋊C4×C59 | #41 | 1 | 2 | yes | — |
| 194 | C42×C59 | — | 2 | 1 | no | — |
| 195 | C42×C59 | — | 2 | 1 | no | — |
| 196 | C42×C59 | — | 2 | 1 | no | — |
| 197 | C42×C59 | — | 2 | 1 | no | — |
| 198 | C42×C59 | — | 4 | 2 | no | — |
| 199 | C23×C59 | — | 2 | 1 | no | — |
| 200 | C23×C59 | — | 2 | 2 | no | — |
| 201 | C23×C59 | — | 4 | 1 | no | — |
| 202 | C23×C59 | — | 4 | 1 | no | — |
| 203 | C23×C59 | — | 16 | 1 | no | — |
| 204 | C23×C59 | C2×#41 | 1 | 1 | yes | characteristic |
| 205 | Q8×C59 | — | 2 | 2 | no | — |
| 206 | Q8×C59 | — | 2 | 1 | no | — |
| 207 | Q8×C59 | — | 2 | 2 | no | — |
| 208 | Q8×C59 | — | 2 | 1 | no | — |
| 209 | Q8×C59 | — | 4 | 1 | no | — |
| 210 | Q8×C59 | — | 4 | 1 | no | — |
| 211 | D4×C59 | — | 2 | 2 | no | — |
| 212 | D4×C59 | — | 2 | 1 | no | — |
| 213 | D4×C59 | — | 2 | 2 | no | — |
| 214 | D4×C59 | — | 2 | 1 | no | — |
| 215 | D4×C59 | — | 4 | 1 | no | — |
| 216 | D4×C59 | — | 4 | 1 | no | — |
| 217 | D4×C59 | — | 4 | 1 | no | — |
| 218 | D4×C59 | — | 4 | 1 | no | — |
| 219 | C2×C4×C59 | — | 2 | 1 | no | — |
| 220 | C2×C4×C59 | — | 2 | 2 | no | — |
| 221 | C2×C4×C59 | — | 2 | 2 | no | — |
| 222 | C2×C4×C59 | — | 4 | 1 | no | — |
| 223 | C2×C4×C59 | — | 4 | 1 | no | — |
| 224 | C2×C4×C59 | — | 4 | 1 | no | — |
| 225 | C2×C4×C59 | — | 4 | 1 | no | — |
| 226 | C2×C4×C59 | — | 4 | 1 | no | — |
| 227 | C2×C4×C59 | — | 4 | 1 | no | — |
| 228 | C2×C4×C59 | — | 4 | 1 | no | — |
| 229 | C2×C4×C59 | — | 16 | 2 | no | — |
| 230 | C2×C4×C59 | C22×D4 | 1 | 1 | yes | characteristic |
| 231 | C2×C4×C59 | C2×#41 | 1 | 1 | yes | characteristic |
| 232 | C2×C4×C59 | C2×#41 | 1 | 1 | yes | characteristic |
| 233 | C2×C4×C59 | C2×#41 | 1 | 1 | yes | characteristic |
| 234 | C2×C4×C59 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 235 | C2×C4×C59 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 236 | C8×C59 | — | 4 | 1 | no | — |
| 237 | C8×C59 | — | 4 | 1 | no | — |
| 238 | C8×C59 | — | 4 | 1 | no | — |
| 239 | C8×C59 | — | 4 | 1 | no | — |
| 240 | C8×C59 | — | 4 | 1 | no | — |
| 241 | C8×C59 | — | 4 | 1 | no | — |
| 242 | C8×C59 | — | 4 | 1 | no | — |
| 243 | C8×C59 | #123 | 1 | 1 | yes | characteristic |
| 244 | C8×C59 | #123 | 1 | 1 | yes | characteristic |
| 245 | C8×C59 | #123 | 1 | 1 | yes | characteristic |
| 246 | C8×C59 | #123 | 1 | 1 | yes | characteristic |
| 247 | #24987 | C59 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 248 | C22×C59 | — | 4 | 1 | no | — |
| 249 | C22×C59 | — | 4 | 1 | no | — |
| 250 | C22×C59 | — | 4 | 2 | no | — |
| 251 | C22×C59 | — | 8 | 2 | no | — |
| 252 | C22×C59 | — | 8 | 1 | no | — |
| 253 | C22×C59 | — | 16 | 1 | no | — |
| 254 | C22×C59 | — | 16 | 1 | no | — |
| 255 | C22×C59 | #529 | 1 | 1 | yes | characteristic |
| 256 | C22×C59 | #546 | 1 | 1 | yes | characteristic |
| 257 | C22×C59 | #555 | 1 | 1 | yes | characteristic |
| 258 | C4×C59 | — | 4 | 2 | no | — |
| 259 | C4×C59 | — | 4 | 1 | no | — |
| 260 | C4×C59 | — | 4 | 2 | no | — |
| 261 | C4×C59 | — | 8 | 1 | no | — |
| 262 | C4×C59 | — | 8 | 1 | no | — |
| 263 | C4×C59 | — | 8 | 1 | no | — |
| 264 | C4×C59 | C2×#123 | 1 | 1 | yes | characteristic |
| 265 | C4×C59 | #540 | 1 | 1 | yes | characteristic |
| 266 | C4×C59 | #546 | 1 | 1 | yes | characteristic |
| 267 | C4×C59 | #553 | 1 | 1 | yes | characteristic |
| 268 | C2×#471 | C2×C59 | 1 | 1 | yes | characteristic |
| 269 | #2949 | C2×C59 | 1 | 1 | yes | characteristic, complemented |
| 270 | #2082 | C2×C59 | 1 | 1 | yes | characteristic, complemented |
| 271 | #2081 | C2×C59 | 1 | 1 | yes | characteristic, complemented |
| 272 | #2049 | C2×C59 | 1 | 1 | yes | characteristic, complemented |
| 273 | #2048 | C2×C59 | 1 | 1 | yes | characteristic |
| 274 | #1977 | C2×C59 | 1 | 1 | yes | characteristic, complemented |
| 275 | #1953 | C2×C59 | 1 | 1 | yes | characteristic, complemented |
| 276 | #1905 | C2×C59 | 1 | 1 | yes | characteristic, complemented |
| 277 | #1904 | C2×C59 | 1 | 1 | yes | characteristic |
| 278 | #1833 | C2×C59 | 1 | 1 | yes | characteristic, complemented |
| 279 | #1830 | C2×C59 | 1 | 1 | yes | characteristic, complemented |
| 280 | #1829 | C2×C59 | 1 | 1 | yes | characteristic, complemented |
| 281 | #1814 | C2×C59 | 1 | 1 | yes | characteristic, complemented |
| 282 | #1757 | C2×C59 | 1 | 1 | yes | characteristic, complemented |
| 283 | C2×C59 | — | 2 | 1 | no | — |
| 284 | C2×C59 | — | 2 | 1 | no | — |
| 285 | C2×C59 | — | 2 | 1 | no | — |
| 286 | C2×C59 | — | 8 | 1 | no | — |
| 287 | C2×C59 | — | 8 | 2 | no | — |
| 288 | C2×C59 | #2420 | 1 | 1 | yes | characteristic |
| 289 | C2×#137 | C22×C59 | 1 | 1 | yes | characteristic |
| 290 | C2×AGL(1,ℤ/8) | C22×C59 | 1 | 1 | yes | characteristic |
| 291 | C22×SD16 | C22×C59 | 1 | 1 | yes | characteristic |
| 292 | C2×#131 | C22×C59 | 1 | 1 | yes | characteristic |
| 293 | #519 | C22×C59 | 1 | 1 | yes | characteristic |
| 294 | #518 | C22×C59 | 1 | 1 | yes | characteristic |
| 295 | #471 | — | 2 | 2 | no | — |
| 296 | #471 | — | 2 | 2 | no | — |
| 297 | #440 | — | 2 | 2 | no | — |
| 298 | C4×SD16 | — | 2 | 2 | no | — |
| 299 | #430 | C22×C59 | 1 | 1 | yes | characteristic |
| 300 | #430 | C22×C59 | 1 | 1 | yes | characteristic |
| 301 | C2×#108 | C22×C59 | 1 | 1 | yes | characteristic |
| 302 | C2×#108 | C22×C59 | 1 | 1 | yes | characteristic |
| 303 | #427 | C22×C59 | 1 | 1 | yes | characteristic |
| 304 | #421 | C22×C59 | 1 | 1 | yes | characteristic |
| 305 | #421 | C22×C59 | 1 | 1 | yes | characteristic |
| 306 | #419 | C22×C59 | 1 | 1 | yes | characteristic |
| 307 | #419 | C22×C59 | 1 | 1 | yes | characteristic |
| 308 | #418 | C22×C59 | 1 | 1 | yes | characteristic |
| 309 | #418 | C22×C59 | 1 | 1 | yes | characteristic |
| 310 | #413 | C22×C59 | 1 | 1 | yes | characteristic |
| 311 | C2×#101 | C22×C59 | 1 | 1 | yes | characteristic |
| 312 | C2×#101 | C22×C59 | 1 | 1 | yes | characteristic |
| 313 | C2×#100 | C22×C59 | 1 | 1 | yes | characteristic |
| 314 | C2×#100 | C22×C59 | 1 | 1 | yes | characteristic |
| 315 | #410 | C22×C59 | 1 | 1 | yes | characteristic |
| 316 | #405 | C22×C59 | 1 | 1 | yes | characteristic |
| 317 | #405 | C22×C59 | 1 | 1 | yes | characteristic |
| 318 | #344 | C22×C59 | 1 | 1 | yes | characteristic |
| 319 | #344 | C22×C59 | 1 | 1 | yes | characteristic |
| 320 | #344 | C22×C59 | 1 | 1 | yes | characteristic |
| 321 | #344 | C22×C59 | 1 | 1 | yes | characteristic |
| 322 | #344 | C22×C59 | 1 | 1 | yes | characteristic |
| 323 | #344 | C22×C59 | 1 | 1 | yes | characteristic |
| 324 | #344 | C22×C59 | 1 | 1 | yes | characteristic |
| 325 | #344 | C22×C59 | 1 | 1 | yes | characteristic |
| 326 | H(3,ℤ/4) | C22×C59 | 1 | 1 | yes | characteristic |
| 327 | H(3,ℤ/4) | C22×C59 | 1 | 1 | yes | characteristic |
| 328 | C59 | #24987 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 329 | C2×#41 | C23×C59 | 1 | 1 | yes | characteristic |
| 330 | C22×Q8 | C23×C59 | 1 | 1 | yes | characteristic |
| 331 | C22×D4 | C23×C59 | 1 | 1 | yes | characteristic |
| 332 | #137 | — | 2 | 2 | no | — |
| 333 | #137 | — | 4 | 1 | no | — |
| 334 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 335 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 336 | C2×Q16 | — | 2 | 1 | no | — |
| 337 | C2×SD16 | — | 2 | 1 | no | — |
| 338 | C2×SD16 | — | 2 | 1 | no | — |
| 339 | C2×SD16 | — | 2 | 1 | no | — |
| 340 | C2×SD16 | — | 2 | 1 | no | — |
| 341 | C2×SD16 | — | 2 | 1 | no | — |
| 342 | C2×SD16 | — | 2 | 1 | no | — |
| 343 | C2×SD16 | D4×C59 | 1 | 2 | yes | — |
| 344 | C2×SD16 | D4×C59 | 1 | 2 | yes | — |
| 345 | C2×D8 | — | 2 | 1 | no | — |
| 346 | #131 | — | 2 | 1 | no | — |
| 347 | #131 | — | 2 | 1 | no | — |
| 348 | #131 | — | 2 | 1 | no | — |
| 349 | #131 | — | 2 | 1 | no | — |
| 350 | C2×M16 | — | 2 | 1 | no | — |
| 351 | C2×M16 | C23×C59 | 1 | 1 | yes | characteristic |
| 352 | C2×M16 | C23×C59 | 1 | 1 | yes | characteristic |
| 353 | C2×M16 | C23×C59 | 1 | 1 | yes | characteristic |
| 354 | C2×M16 | C23×C59 | 1 | 1 | yes | characteristic |
| 355 | C2×M16 | C23×C59 | 1 | 1 | yes | characteristic |
| 356 | C2×M16 | C23×C59 | 1 | 1 | yes | characteristic |
| 357 | C2×M16 | C23×C59 | 1 | 1 | yes | characteristic |
| 358 | C22×C8 | — | 2 | 1 | no | — |
| 359 | C22×C8 | C23×C59 | 1 | 1 | yes | characteristic |
| 360 | C4×Q8 | — | 2 | 2 | no | — |
| 361 | C4×Q8 | — | 4 | 1 | no | — |
| 362 | C4×D4 | — | 2 | 2 | no | — |
| 363 | C4×D4 | — | 4 | 1 | no | — |
| 364 | #117 | — | 2 | 2 | no | — |
| 365 | #117 | C23×C59 | 1 | 1 | yes | characteristic |
| 366 | #117 | C23×C59 | 1 | 1 | yes | characteristic |
| 367 | #117 | C23×C59 | 1 | 1 | yes | characteristic |
| 368 | #117 | C23×C59 | 1 | 1 | yes | characteristic |
| 369 | C2×C22⋊C4 | — | 2 | 2 | no | — |
| 370 | #108 | — | 2 | 1 | no | — |
| 371 | #108 | — | 2 | 1 | no | — |
| 372 | #108 | — | 2 | 1 | no | — |
| 373 | #108 | — | 2 | 1 | no | — |
| 374 | #108 | — | 4 | 1 | no | — |
| 375 | #108 | — | 4 | 1 | no | — |
| 376 | #107 | — | 2 | 1 | no | — |
| 377 | #106 | — | 2 | 1 | no | — |
| 378 | #104 | — | 4 | 1 | no | — |
| 379 | #104 | — | 4 | 1 | no | — |
| 380 | #103 | — | 2 | 2 | no | — |
| 381 | #103 | — | 4 | 1 | no | — |
| 382 | #102 | — | 2 | 2 | no | — |
| 383 | #102 | — | 4 | 1 | no | — |
| 384 | #101 | — | 2 | 2 | no | — |
| 385 | #101 | — | 2 | 1 | no | — |
| 386 | #101 | — | 4 | 1 | no | — |
| 387 | #100 | — | 2 | 2 | no | — |
| 388 | #100 | — | 2 | 1 | no | — |
| 389 | #100 | — | 4 | 1 | no | — |
| 390 | #99 | — | 2 | 2 | no | — |
| 391 | #97 | — | 2 | 1 | no | — |
| 392 | #97 | — | 2 | 1 | no | — |
| 393 | C4×C8 | — | 2 | 1 | no | — |
| 394 | C4×C8 | — | 2 | 1 | no | — |
| 395 | C24 | — | 2 | 1 | no | — |
| 396 | #41 | — | 2 | 1 | no | — |
| 397 | #41 | — | 2 | 1 | no | — |
| 398 | #41 | — | 2 | 1 | no | — |
| 399 | #41 | — | 2 | 1 | no | — |
| 400 | C2×Q8 | — | 2 | 1 | no | — |
| 401 | C2×Q8 | — | 2 | 1 | no | — |
| 402 | C2×Q8 | — | 2 | 1 | no | — |
| 403 | C2×Q8 | — | 2 | 1 | no | — |
| 404 | C2×Q8 | — | 2 | 1 | no | — |
| 405 | C2×Q8 | C2×D4×C59 | 1 | 2 | yes | — |
| 406 | C2×Q8 | #41×C59 | 1 | 1 | yes | characteristic |
| 407 | C2×D4 | — | 2 | 1 | no | — |
| 408 | C2×D4 | — | 2 | 1 | no | — |
| 409 | C2×D4 | — | 2 | 1 | no | — |
| 410 | C2×D4 | — | 2 | 1 | no | — |
| 411 | C2×D4 | — | 2 | 1 | no | — |
| 412 | C2×D4 | — | 2 | 1 | no | — |
| 413 | C2×D4 | C2×D4×C59 | 1 | 2 | yes | — |
| 414 | C2×D4 | #41×C59 | 1 | 1 | yes | characteristic |
| 415 | C22×C4 | — | 2 | 1 | no | — |
| 416 | C22×C4 | — | 2 | 1 | no | — |
| 417 | C22×C4 | — | 4 | 2 | no | — |
| 418 | C22×C4 | C24×C59 | 1 | 1 | yes | characteristic |
| 419 | Q16 | — | 4 | 2 | no | — |
| 420 | SD16 | — | 2 | 2 | no | — |
| 421 | SD16 | — | 2 | 2 | no | — |
| 422 | SD16 | — | 2 | 2 | no | — |
| 423 | SD16 | — | 2 | 2 | no | — |
| 424 | SD16 | — | 4 | 2 | no | — |
| 425 | SD16 | — | 4 | 2 | no | — |
| 426 | D8 | — | 4 | 2 | no | — |
| 427 | M16 | — | 2 | 1 | no | — |
| 428 | M16 | — | 2 | 1 | no | — |
| 429 | M16 | — | 2 | 1 | no | — |
| 430 | M16 | — | 2 | 1 | no | — |
| 431 | M16 | — | 2 | 1 | no | — |
| 432 | M16 | — | 2 | 1 | no | — |
| 433 | M16 | — | 2 | 1 | no | — |
| 434 | M16 | — | 2 | 1 | no | — |
| 435 | M16 | — | 2 | 1 | no | — |
| 436 | M16 | — | 2 | 1 | no | — |
| 437 | M16 | — | 2 | 1 | no | — |
| 438 | M16 | — | 2 | 1 | no | — |
| 439 | M16 | — | 2 | 1 | no | — |
| 440 | M16 | — | 2 | 1 | no | — |
| 441 | M16 | — | 4 | 1 | no | — |
| 442 | M16 | — | 4 | 1 | no | — |
| 443 | C2×C8 | — | 2 | 1 | no | — |
| 444 | C2×C8 | — | 2 | 1 | no | — |
| 445 | C2×C8 | — | 2 | 1 | no | — |
| 446 | C2×C8 | — | 2 | 1 | no | — |
| 447 | C2×C8 | — | 2 | 1 | no | — |
| 448 | C2×C8 | — | 2 | 1 | no | — |
| 449 | C2×C8 | — | 2 | 1 | no | — |
| 450 | C2×C8 | — | 4 | 1 | no | — |
| 451 | C2×C8 | — | 4 | 1 | no | — |
| 452 | C2×C8 | C2×D4×C59 | 1 | 1 | yes | characteristic |
| 453 | C2×C8 | C2×D4×C59 | 1 | 1 | yes | characteristic |
| 454 | C2×C8 | #41×C59 | 1 | 1 | yes | characteristic |
| 455 | C2×C8 | #41×C59 | 1 | 1 | yes | characteristic |
| 456 | C2×C8 | #41×C59 | 1 | 1 | yes | characteristic |
| 457 | C2×C8 | #41×C59 | 1 | 1 | yes | characteristic |
| 458 | C4⋊C4 | — | 2 | 1 | no | — |
| 459 | C4⋊C4 | — | 2 | 1 | no | — |
| 460 | C4⋊C4 | — | 2 | 1 | no | — |
| 461 | C4⋊C4 | — | 2 | 1 | no | — |
| 462 | C4⋊C4 | — | 4 | 2 | no | — |
| 463 | C22⋊C4 | — | 2 | 1 | no | — |
| 464 | C22⋊C4 | — | 2 | 1 | no | — |
| 465 | C22⋊C4 | — | 2 | 1 | no | — |
| 466 | C22⋊C4 | — | 4 | 2 | no | — |
| 467 | C22⋊C4 | #41×C59 | 1 | 2 | yes | — |
| 468 | C42 | — | 2 | 1 | no | — |
| 469 | C42 | — | 2 | 1 | no | — |
| 470 | C42 | — | 2 | 1 | no | — |
| 471 | C42 | — | 2 | 1 | no | — |
| 472 | C42 | — | 4 | 2 | no | — |
| 473 | C23 | — | 2 | 1 | no | — |
| 474 | C23 | — | 2 | 2 | no | — |
| 475 | C23 | — | 4 | 1 | no | — |
| 476 | C23 | — | 4 | 1 | no | — |
| 477 | C23 | — | 16 | 1 | no | — |
| 478 | C23 | C2×#41×C59 | 1 | 1 | yes | characteristic |
| 479 | Q8 | — | 2 | 2 | no | — |
| 480 | Q8 | — | 2 | 1 | no | — |
| 481 | Q8 | — | 2 | 2 | no | — |
| 482 | Q8 | — | 2 | 1 | no | — |
| 483 | Q8 | — | 4 | 1 | no | — |
| 484 | Q8 | — | 4 | 1 | no | — |
| 485 | D4 | — | 2 | 2 | no | — |
| 486 | D4 | — | 2 | 1 | no | — |
| 487 | D4 | — | 2 | 2 | no | — |
| 488 | D4 | — | 2 | 1 | no | — |
| 489 | D4 | — | 4 | 1 | no | — |
| 490 | D4 | — | 4 | 1 | no | — |
| 491 | D4 | — | 4 | 1 | no | — |
| 492 | D4 | — | 4 | 1 | no | — |
| 493 | C2×C4 | — | 2 | 1 | no | — |
| 494 | C2×C4 | — | 2 | 2 | no | — |
| 495 | C2×C4 | — | 2 | 2 | no | — |
| 496 | C2×C4 | — | 4 | 1 | no | — |
| 497 | C2×C4 | — | 4 | 1 | no | — |
| 498 | C2×C4 | — | 4 | 1 | no | — |
| 499 | C2×C4 | — | 4 | 1 | no | — |
| 500 | C2×C4 | — | 4 | 1 | no | — |
| 501 | C2×C4 | — | 4 | 1 | no | — |
| 502 | C2×C4 | — | 4 | 1 | no | — |
| 503 | C2×C4 | — | 16 | 2 | no | — |
| 504 | C2×C4 | C22×D4×C59 | 1 | 1 | yes | characteristic |
| 505 | C2×C4 | C2×#41×C59 | 1 | 1 | yes | characteristic |
| 506 | C2×C4 | C2×#41×C59 | 1 | 1 | yes | characteristic |
| 507 | C2×C4 | C2×#41×C59 | 1 | 1 | yes | characteristic |
| 508 | C2×C4 | H(5,𝔽2)×C59 | 1 | 1 | yes | characteristic |
| 509 | C2×C4 | H(5,𝔽2)×C59 | 1 | 1 | yes | characteristic |
| 510 | C8 | — | 4 | 1 | no | — |
| 511 | C8 | — | 4 | 1 | no | — |
| 512 | C8 | — | 4 | 1 | no | — |
| 513 | C8 | — | 4 | 1 | no | — |
| 514 | C8 | — | 4 | 1 | no | — |
| 515 | C8 | — | 4 | 1 | no | — |
| 516 | C8 | — | 4 | 1 | no | — |
| 517 | C8 | #123×C59 | 1 | 1 | yes | characteristic |
| 518 | C8 | #123×C59 | 1 | 1 | yes | characteristic |
| 519 | C8 | #123×C59 | 1 | 1 | yes | characteristic |
| 520 | C8 | #123×C59 | 1 | 1 | yes | characteristic |
| 521 | C22 | — | 4 | 1 | no | — |
| 522 | C22 | — | 4 | 1 | no | — |
| 523 | C22 | — | 4 | 2 | no | — |
| 524 | C22 | — | 8 | 2 | no | — |
| 525 | C22 | — | 8 | 1 | no | — |
| 526 | C22 | — | 16 | 1 | no | — |
| 527 | C22 | — | 16 | 1 | no | — |
| 528 | C22 | C59×#529 | 1 | 1 | yes | characteristic |
| 529 | C22 | C59×#546 | 1 | 1 | yes | characteristic |
| 530 | C22 | C59×#555 | 1 | 1 | yes | characteristic |
| 531 | C4 | — | 4 | 2 | no | — |
| 532 | C4 | — | 4 | 1 | no | — |
| 533 | C4 | — | 4 | 2 | no | — |
| 534 | C4 | — | 8 | 1 | no | — |
| 535 | C4 | — | 8 | 1 | no | — |
| 536 | C4 | — | 8 | 1 | no | — |
| 537 | C4 | C2×#123×C59 | 1 | 1 | yes | characteristic |
| 538 | C4 | C59×#540 | 1 | 1 | yes | characteristic |
| 539 | C4 | C59×#546 | 1 | 1 | yes | characteristic |
| 540 | C4 | C59×#553 | 1 | 1 | yes | characteristic |
| 541 | C2 | — | 2 | 1 | no | — |
| 542 | C2 | — | 2 | 1 | no | — |
| 543 | C2 | — | 2 | 1 | no | — |
| 544 | C2 | — | 8 | 2 | no | — |
| 545 | C2 | — | 8 | 1 | no | — |
| 546 | C2 | C59×#2420 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta