| 1 | C53×#3002 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×C53×#443 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C53×#2933 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C22×#104×C53 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C53×#2880 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C53×#1974 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C53×#1937 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C53×#1929 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C53×#1896 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C53×#1876 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C53×#1876 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C53×#1866 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C53×#1855 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C53×#1764 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C4×C22⋊C8×C53 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C22×#41×C53 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#135×C53 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#135×C53 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#131×C53 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#131×C53 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#131×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | C22×M16×C53 | C22 | 1 | 1 | yes | characteristic |
| 23 | C53×#525 | C22 | 1 | 1 | yes | characteristic |
| 24 | C22×C42×C53 | C22 | 1 | 1 | yes | characteristic |
| 25 | C53×#452 | C4 | 1 | 1 | yes | characteristic, complemented |
| 26 | C53×#452 | C4 | 1 | 1 | yes | characteristic, complemented |
| 27 | C53×#451 | C4 | 1 | 1 | yes | characteristic, complemented |
| 28 | C53×#450 | C4 | 1 | 1 | yes | characteristic, complemented |
| 29 | C53×#449 | C4 | 1 | 1 | yes | characteristic, complemented |
| 30 | C53×#449 | C4 | 1 | 1 | yes | characteristic, complemented |
| 31 | C53×#448 | C4 | 1 | 1 | yes | characteristic, complemented |
| 32 | C53×#447 | C4 | 1 | 1 | yes | characteristic, complemented |
| 33 | C53×#443 | — | 2 | 4 | no | — |
| 34 | C53×#436 | — | 2 | 1 | no | — |
| 35 | C53×#435 | — | 2 | 1 | no | — |
| 36 | C53×#435 | — | 2 | 1 | no | — |
| 37 | C8×D4×C53 | — | 2 | 1 | no | — |
| 38 | C2×#108×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 39 | C2×#108×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | C53×#424 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | C2×#104×C53 | — | 2 | 4 | no | — |
| 42 | C2×#104×C53 | C22 | 1 | 1 | yes | characteristic |
| 43 | C2×#104×C53 | C22 | 1 | 1 | yes | characteristic |
| 44 | C2×#104×C53 | C22 | 1 | 1 | yes | characteristic |
| 45 | C2×#104×C53 | C22 | 1 | 1 | yes | characteristic |
| 46 | C2×#104×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 47 | C2×#104×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 48 | C53×#416 | C22 | 1 | 1 | yes | characteristic |
| 49 | C53×#416 | C22 | 1 | 1 | yes | characteristic |
| 50 | C53×#408 | — | 2 | 1 | no | — |
| 51 | C53×#408 | — | 2 | 1 | no | — |
| 52 | C53×#408 | C22 | 1 | 1 | yes | characteristic |
| 53 | C53×#408 | C22 | 1 | 1 | yes | characteristic |
| 54 | C53×#408 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | C53×#407 | — | 2 | 1 | no | — |
| 56 | C53×#407 | C22 | 1 | 1 | yes | characteristic |
| 57 | C2×C22⋊C8×C53 | — | 2 | 1 | no | — |
| 58 | C2×C22⋊C8×C53 | C22 | 1 | 1 | yes | characteristic |
| 59 | C2×C22⋊C8×C53 | C22 | 1 | 1 | yes | characteristic |
| 60 | C53×#405 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | C2×C4×C8×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | C2×C4×C8×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | C53×#341 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | C53×#341 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | C53×#339 | C22 | 1 | 1 | yes | characteristic, complemented |
| 66 | C53×#339 | C22 | 1 | 1 | yes | characteristic, complemented |
| 67 | C53×#336 | C22 | 1 | 1 | yes | characteristic, complemented |
| 68 | C53×#336 | C22 | 1 | 1 | yes | characteristic, complemented |
| 69 | C2×#41×C53 | — | 2 | 1 | no | — |
| 70 | C2×#41×C53 | — | 2 | 1 | no | — |
| 71 | C2×#41×C53 | — | 2 | 2 | no | — |
| 72 | C2×#41×C53 | — | 2 | 2 | no | — |
| 73 | C2×#41×C53 | — | 4 | 1 | no | — |
| 74 | C2×#41×C53 | — | 4 | 1 | no | — |
| 75 | C2×#41×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 76 | C2×#41×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 77 | C2×#41×C53 | C23 | 1 | 1 | yes | characteristic |
| 78 | C2×#41×C53 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×#41×C53 | C23 | 1 | 1 | yes | characteristic |
| 80 | C22×Q8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 81 | C22×D4×C53 | — | 2 | 1 | no | — |
| 82 | C22×D4×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 83 | C23×C4×C53 | — | 2 | 1 | no | — |
| 84 | C23×C4×C53 | — | 2 | 1 | no | — |
| 85 | C23×C4×C53 | C23 | 1 | 1 | yes | characteristic |
| 86 | #135×C53 | — | 2 | 2 | no | — |
| 87 | #135×C53 | — | 2 | 2 | no | — |
| 88 | #135×C53 | — | 4 | 1 | no | — |
| 89 | #135×C53 | — | 4 | 1 | no | — |
| 90 | C2×Q16×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 91 | C2×Q16×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 92 | C2×SD16×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 93 | C2×SD16×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 94 | C2×SD16×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 95 | C2×SD16×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 96 | C2×D8×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 97 | C2×D8×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 98 | #131×C53 | — | 2 | 2 | no | — |
| 99 | #131×C53 | — | 2 | 2 | no | — |
| 100 | #131×C53 | — | 2 | 2 | no | — |
| 101 | #131×C53 | — | 4 | 1 | no | — |
| 102 | #131×C53 | — | 4 | 1 | no | — |
| 103 | #131×C53 | — | 4 | 1 | no | — |
| 104 | C2×M16×C53 | — | 2 | 1 | no | — |
| 105 | C2×M16×C53 | — | 2 | 1 | no | — |
| 106 | C2×M16×C53 | — | 2 | 1 | no | — |
| 107 | C2×M16×C53 | — | 2 | 2 | no | — |
| 108 | C2×M16×C53 | — | 2 | 1 | no | — |
| 109 | C2×M16×C53 | — | 4 | 1 | no | — |
| 110 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 111 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 112 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 113 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 114 | C22×C8×C53 | — | 2 | 1 | no | — |
| 115 | C22×C8×C53 | — | 2 | 1 | no | — |
| 116 | C22×C8×C53 | — | 2 | 1 | no | — |
| 117 | C22×C8×C53 | — | 2 | 1 | no | — |
| 118 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 119 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 120 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 121 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 122 | #123×C53 | — | 2 | 1 | no | — |
| 123 | C22⋊Q8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 124 | C22⋊Q8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 125 | #121×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 126 | #121×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 127 | #120×C53 | — | 2 | 1 | no | — |
| 128 | C4×D4×C53 | — | 2 | 1 | no | — |
| 129 | C4×D4×C53 | — | 2 | 1 | no | — |
| 130 | #117×C53 | C23 | 1 | 1 | yes | characteristic |
| 131 | C2×C42×C53 | — | 2 | 1 | no | — |
| 132 | C2×C42×C53 | — | 2 | 2 | no | — |
| 133 | C2×C42×C53 | — | 4 | 1 | no | — |
| 134 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 135 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 136 | #108×C53 | — | 2 | 2 | no | — |
| 137 | #108×C53 | — | 4 | 1 | no | — |
| 138 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 139 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 140 | #104×C53 | — | 2 | 2 | no | — |
| 141 | #104×C53 | — | 2 | 2 | no | — |
| 142 | #104×C53 | — | 2 | 2 | no | — |
| 143 | #104×C53 | — | 2 | 2 | no | — |
| 144 | #104×C53 | — | 4 | 1 | no | — |
| 145 | #104×C53 | D4 | 1 | 4 | yes | complemented |
| 146 | #103×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 147 | #103×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 148 | #103×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 149 | #103×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 150 | #102×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 151 | #102×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 152 | #102×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 153 | #102×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 154 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 155 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 156 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 157 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 158 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 159 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 160 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 161 | C22⋊C8×C53 | — | 2 | 1 | no | — |
| 162 | C22⋊C8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 163 | C22⋊C8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 164 | C22⋊C8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 165 | C22⋊C8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 166 | C22⋊C8×C53 | D4 | 1 | 1 | yes | characteristic |
| 167 | C22⋊C8×C53 | D4 | 1 | 1 | yes | characteristic |
| 168 | C22⋊C8×C53 | D4 | 1 | 1 | yes | characteristic |
| 169 | C22⋊C8×C53 | D4 | 1 | 1 | yes | characteristic |
| 170 | #97×C53 | — | 2 | 1 | no | — |
| 171 | C4×C8×C53 | — | 2 | 1 | no | — |
| 172 | C4×C8×C53 | — | 2 | 2 | no | — |
| 173 | C4×C8×C53 | — | 4 | 1 | no | — |
| 174 | C24×C53 | — | 2 | 1 | no | — |
| 175 | C24×C53 | #41 | 1 | 1 | yes | characteristic |
| 176 | #41×C53 | — | 2 | 1 | no | — |
| 177 | #41×C53 | — | 2 | 1 | no | — |
| 178 | #41×C53 | — | 2 | 2 | no | — |
| 179 | #41×C53 | — | 2 | 2 | no | — |
| 180 | #41×C53 | — | 2 | 1 | no | — |
| 181 | #41×C53 | — | 2 | 1 | no | — |
| 182 | #41×C53 | — | 2 | 1 | no | — |
| 183 | #41×C53 | — | 2 | 1 | no | — |
| 184 | #41×C53 | — | 2 | 1 | no | — |
| 185 | #41×C53 | — | 2 | 1 | no | — |
| 186 | #41×C53 | — | 2 | 1 | no | — |
| 187 | #41×C53 | — | 2 | 1 | no | — |
| 188 | #41×C53 | — | 4 | 2 | no | — |
| 189 | #41×C53 | — | 4 | 2 | no | — |
| 190 | #41×C53 | — | 4 | 1 | no | — |
| 191 | #41×C53 | — | 4 | 1 | no | — |
| 192 | #41×C53 | — | 4 | 2 | no | — |
| 193 | #41×C53 | — | 4 | 2 | no | — |
| 194 | #41×C53 | C2×D4 | 1 | 2 | yes | — |
| 195 | #41×C53 | #41 | 1 | 2 | yes | — |
| 196 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 197 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 198 | C2×Q8×C53 | — | 4 | 1 | no | — |
| 199 | C2×Q8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 200 | C2×Q8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 201 | C2×Q8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 202 | C2×D4×C53 | — | 2 | 1 | no | — |
| 203 | C2×D4×C53 | — | 2 | 2 | no | — |
| 204 | C2×D4×C53 | — | 2 | 1 | no | — |
| 205 | C2×D4×C53 | — | 2 | 1 | no | — |
| 206 | C2×D4×C53 | — | 2 | 1 | no | — |
| 207 | C2×D4×C53 | — | 2 | 1 | no | — |
| 208 | C2×D4×C53 | — | 2 | 1 | no | — |
| 209 | C2×D4×C53 | — | 2 | 1 | no | — |
| 210 | C2×D4×C53 | — | 2 | 1 | no | — |
| 211 | C2×D4×C53 | — | 4 | 1 | no | — |
| 212 | C2×D4×C53 | — | 4 | 2 | no | — |
| 213 | C2×D4×C53 | — | 4 | 2 | no | — |
| 214 | C2×D4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 215 | C2×D4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 216 | C2×D4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 217 | C22×C4×C53 | — | 2 | 1 | no | — |
| 218 | C22×C4×C53 | — | 2 | 1 | no | — |
| 219 | C22×C4×C53 | — | 2 | 1 | no | — |
| 220 | C22×C4×C53 | — | 2 | 1 | no | — |
| 221 | C22×C4×C53 | — | 2 | 1 | no | — |
| 222 | C22×C4×C53 | — | 2 | 1 | no | — |
| 223 | C22×C4×C53 | — | 2 | 4 | no | — |
| 224 | C22×C4×C53 | — | 2 | 1 | no | — |
| 225 | C22×C4×C53 | — | 2 | 1 | no | — |
| 226 | C22×C4×C53 | — | 2 | 1 | no | — |
| 227 | C22×C4×C53 | — | 2 | 1 | no | — |
| 228 | C22×C4×C53 | — | 2 | 1 | no | — |
| 229 | C22×C4×C53 | — | 2 | 1 | no | — |
| 230 | C22×C4×C53 | — | 4 | 2 | no | — |
| 231 | C22×C4×C53 | — | 4 | 2 | no | — |
| 232 | C22×C4×C53 | — | 4 | 2 | no | — |
| 233 | C22×C4×C53 | — | 4 | 2 | no | — |
| 234 | C22×C4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 235 | C22×C4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 236 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 238 | C22×C4×C53 | #41 | 1 | 1 | yes | characteristic |
| 239 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 240 | Q16×C53 | — | 2 | 2 | no | — |
| 241 | Q16×C53 | — | 4 | 1 | no | — |
| 242 | SD16×C53 | — | 2 | 2 | no | — |
| 243 | SD16×C53 | — | 2 | 2 | no | — |
| 244 | SD16×C53 | — | 4 | 1 | no | — |
| 245 | SD16×C53 | — | 4 | 1 | no | — |
| 246 | D8×C53 | — | 2 | 2 | no | — |
| 247 | D8×C53 | — | 4 | 1 | no | — |
| 248 | M16×C53 | — | 2 | 1 | no | — |
| 249 | M16×C53 | — | 2 | 1 | no | — |
| 250 | M16×C53 | — | 2 | 1 | no | — |
| 251 | M16×C53 | — | 2 | 1 | no | — |
| 252 | M16×C53 | — | 2 | 1 | no | — |
| 253 | M16×C53 | — | 2 | 1 | no | — |
| 254 | M16×C53 | — | 2 | 1 | no | — |
| 255 | M16×C53 | — | 4 | 2 | no | — |
| 256 | M16×C53 | — | 4 | 2 | no | — |
| 257 | M16×C53 | — | 4 | 2 | no | — |
| 258 | M16×C53 | — | 4 | 2 | no | — |
| 259 | M16×C53 | C2×D4 | 1 | 2 | yes | — |
| 260 | C2×C8×C53 | — | 2 | 1 | no | — |
| 261 | C2×C8×C53 | — | 2 | 1 | no | — |
| 262 | C2×C8×C53 | — | 2 | 1 | no | — |
| 263 | C2×C8×C53 | — | 2 | 1 | no | — |
| 264 | C2×C8×C53 | — | 2 | 1 | no | — |
| 265 | C2×C8×C53 | — | 2 | 1 | no | — |
| 266 | C2×C8×C53 | — | 2 | 1 | no | — |
| 267 | C2×C8×C53 | — | 2 | 1 | no | — |
| 268 | C2×C8×C53 | — | 2 | 1 | no | — |
| 269 | C2×C8×C53 | — | 2 | 1 | no | — |
| 270 | C2×C8×C53 | — | 2 | 1 | no | — |
| 271 | C2×C8×C53 | — | 2 | 1 | no | — |
| 272 | C2×C8×C53 | — | 4 | 2 | no | — |
| 273 | C2×C8×C53 | — | 4 | 2 | no | — |
| 274 | C2×C8×C53 | — | 4 | 2 | no | — |
| 275 | C2×C8×C53 | — | 4 | 2 | no | — |
| 276 | C2×C8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 277 | C2×C8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 278 | C2×C8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 279 | C2×C8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 280 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 281 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 282 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 283 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 284 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 285 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 286 | C4⋊C4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 287 | C4⋊C4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 288 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 289 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 290 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 291 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 292 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 293 | C42×C53 | — | 2 | 1 | no | — |
| 294 | C42×C53 | — | 2 | 1 | no | — |
| 295 | C42×C53 | — | 2 | 1 | no | — |
| 296 | C42×C53 | — | 2 | 1 | no | — |
| 297 | C42×C53 | — | 4 | 2 | no | — |
| 298 | C42×C53 | C2×D4 | 1 | 2 | yes | — |
| 299 | C23×C53 | — | 2 | 1 | no | — |
| 300 | C23×C53 | — | 2 | 1 | no | — |
| 301 | C23×C53 | — | 2 | 1 | no | — |
| 302 | C23×C53 | — | 2 | 2 | no | — |
| 303 | C23×C53 | — | 2 | 1 | no | — |
| 304 | C23×C53 | — | 2 | 1 | no | — |
| 305 | C23×C53 | — | 4 | 1 | no | — |
| 306 | C23×C53 | — | 4 | 2 | no | — |
| 307 | C23×C53 | — | 4 | 2 | no | — |
| 308 | C23×C53 | — | 8 | 1 | no | — |
| 309 | C23×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 310 | C23×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 311 | C23×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 312 | Q8×C53 | — | 2 | 1 | no | — |
| 313 | Q8×C53 | — | 2 | 1 | no | — |
| 314 | Q8×C53 | — | 2 | 1 | no | — |
| 315 | Q8×C53 | — | 2 | 1 | no | — |
| 316 | Q8×C53 | — | 2 | 1 | no | — |
| 317 | Q8×C53 | — | 4 | 2 | no | — |
| 318 | Q8×C53 | C4×D4 | 1 | 2 | yes | — |
| 319 | D4×C53 | — | 2 | 2 | no | — |
| 320 | D4×C53 | — | 2 | 2 | no | — |
| 321 | D4×C53 | — | 2 | 1 | no | — |
| 322 | D4×C53 | — | 2 | 1 | no | — |
| 323 | D4×C53 | — | 2 | 1 | no | — |
| 324 | D4×C53 | — | 2 | 1 | no | — |
| 325 | D4×C53 | — | 2 | 1 | no | — |
| 326 | D4×C53 | — | 4 | 2 | no | — |
| 327 | D4×C53 | — | 4 | 2 | no | — |
| 328 | D4×C53 | — | 4 | 2 | no | — |
| 329 | D4×C53 | — | 4 | 1 | no | — |
| 330 | D4×C53 | — | 4 | 1 | no | — |
| 331 | D4×C53 | — | 4 | 1 | no | — |
| 332 | D4×C53 | — | 4 | 1 | no | — |
| 333 | D4×C53 | — | 4 | 2 | no | — |
| 334 | D4×C53 | — | 8 | 1 | no | — |
| 335 | D4×C53 | C4×D4 | 1 | 2 | yes | — |
| 336 | C2×C4×C53 | — | 2 | 2 | no | — |
| 337 | C2×C4×C53 | — | 2 | 2 | no | — |
| 338 | C2×C4×C53 | — | 2 | 1 | no | — |
| 339 | C2×C4×C53 | — | 2 | 1 | no | — |
| 340 | C2×C4×C53 | — | 2 | 2 | no | — |
| 341 | C2×C4×C53 | — | 2 | 1 | no | — |
| 342 | C2×C4×C53 | — | 2 | 1 | no | — |
| 343 | C2×C4×C53 | — | 2 | 1 | no | — |
| 344 | C2×C4×C53 | — | 2 | 1 | no | — |
| 345 | C2×C4×C53 | — | 2 | 1 | no | — |
| 346 | C2×C4×C53 | — | 2 | 1 | no | — |
| 347 | C2×C4×C53 | — | 2 | 1 | no | — |
| 348 | C2×C4×C53 | — | 2 | 2 | no | — |
| 349 | C2×C4×C53 | — | 2 | 1 | no | — |
| 350 | C2×C4×C53 | — | 2 | 1 | no | — |
| 351 | C2×C4×C53 | — | 2 | 2 | no | — |
| 352 | C2×C4×C53 | — | 2 | 2 | no | — |
| 353 | C2×C4×C53 | — | 2 | 1 | no | — |
| 354 | C2×C4×C53 | — | 2 | 1 | no | — |
| 355 | C2×C4×C53 | — | 2 | 1 | no | — |
| 356 | C2×C4×C53 | — | 2 | 1 | no | — |
| 357 | C2×C4×C53 | — | 4 | 2 | no | — |
| 358 | C2×C4×C53 | — | 4 | 2 | no | — |
| 359 | C2×C4×C53 | — | 4 | 2 | no | — |
| 360 | C2×C4×C53 | — | 4 | 8 | no | — |
| 361 | C2×C4×C53 | — | 4 | 1 | no | — |
| 362 | C2×C4×C53 | — | 4 | 1 | no | — |
| 363 | C2×C4×C53 | — | 4 | 1 | no | — |
| 364 | C2×C4×C53 | — | 4 | 1 | no | — |
| 365 | C2×C4×C53 | — | 4 | 1 | no | — |
| 366 | C2×C4×C53 | — | 4 | 1 | no | — |
| 367 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 368 | C2×C4×C53 | C4×D4 | 1 | 1 | yes | characteristic |
| 369 | C2×C4×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 370 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 371 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 372 | C2×C4×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 373 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 374 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 375 | C8×C53 | — | 2 | 1 | no | — |
| 376 | C8×C53 | — | 2 | 1 | no | — |
| 377 | C8×C53 | — | 2 | 1 | no | — |
| 378 | C8×C53 | — | 2 | 1 | no | — |
| 379 | C8×C53 | — | 2 | 1 | no | — |
| 380 | C8×C53 | — | 2 | 1 | no | — |
| 381 | C8×C53 | — | 2 | 2 | no | — |
| 382 | C8×C53 | — | 2 | 1 | no | — |
| 383 | C8×C53 | — | 2 | 1 | no | — |
| 384 | C8×C53 | — | 4 | 1 | no | — |
| 385 | C8×C53 | — | 4 | 1 | no | — |
| 386 | C8×C53 | — | 4 | 1 | no | — |
| 387 | #22888 | C53 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 388 | C22×C53 | — | 2 | 1 | no | — |
| 389 | C22×C53 | — | 2 | 1 | no | — |
| 390 | C22×C53 | — | 2 | 1 | no | — |
| 391 | C22×C53 | — | 2 | 1 | no | — |
| 392 | C22×C53 | — | 2 | 1 | no | — |
| 393 | C22×C53 | — | 2 | 2 | no | — |
| 394 | C22×C53 | — | 2 | 1 | no | — |
| 395 | C22×C53 | — | 2 | 1 | no | — |
| 396 | C22×C53 | — | 4 | 2 | no | — |
| 397 | C22×C53 | — | 4 | 2 | no | — |
| 398 | C22×C53 | — | 4 | 1 | no | — |
| 399 | C22×C53 | — | 4 | 1 | no | — |
| 400 | C22×C53 | — | 4 | 1 | no | — |
| 401 | C22×C53 | — | 4 | 1 | no | — |
| 402 | C22×C53 | — | 4 | 1 | no | — |
| 403 | C22×C53 | — | 4 | 1 | no | — |
| 404 | C22×C53 | — | 4 | 1 | no | — |
| 405 | C22×C53 | — | 4 | 1 | no | — |
| 406 | C22×C53 | — | 8 | 4 | no | — |
| 407 | C22×C53 | #443 | 1 | 2 | yes | complemented |
| 408 | C22×C53 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 409 | C22×C53 | #546 | 1 | 1 | yes | characteristic |
| 410 | C22×C53 | #551 | 1 | 1 | yes | characteristic |
| 411 | C4×C53 | — | 2 | 4 | no | — |
| 412 | C4×C53 | — | 2 | 1 | no | — |
| 413 | C4×C53 | — | 2 | 1 | no | — |
| 414 | C4×C53 | — | 2 | 2 | no | — |
| 415 | C4×C53 | — | 4 | 2 | no | — |
| 416 | C4×C53 | — | 4 | 1 | no | — |
| 417 | C4×C53 | — | 4 | 1 | no | — |
| 418 | C4×C53 | — | 4 | 1 | no | — |
| 419 | C4×C53 | — | 4 | 1 | no | — |
| 420 | C4×C53 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 421 | C4×C53 | #518 | 1 | 1 | yes | characteristic |
| 422 | C4×C53 | D42 | 1 | 1 | yes | characteristic |
| 423 | C4×C53 | #546 | 1 | 1 | yes | characteristic |
| 424 | #3002 | C2×C53 | 1 | 1 | yes | characteristic |
| 425 | C2×#443 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 426 | #2933 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 427 | C22×#104 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 428 | #2880 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 429 | #1974 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 430 | #1937 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 431 | #1929 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 432 | #1896 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 433 | #1876 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 434 | #1876 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 435 | #1866 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 436 | #1855 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 437 | #1764 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 438 | C4×C22⋊C8 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 439 | C2×C53 | — | 2 | 1 | no | — |
| 440 | C2×C53 | — | 2 | 2 | no | — |
| 441 | C2×C53 | — | 2 | 1 | no | — |
| 442 | C2×C53 | — | 4 | 1 | no | — |
| 443 | C2×C53 | — | 4 | 2 | no | — |
| 444 | C2×C53 | — | 8 | 1 | no | — |
| 445 | C2×C53 | — | 8 | 1 | no | — |
| 446 | C2×C53 | #2358 | 1 | 1 | yes | characteristic |
| 447 | C2×C53 | C2×#443 | 1 | 1 | yes | characteristic |
| 448 | C2×C53 | #2956 | 1 | 1 | yes | characteristic |
| 449 | C22×#41 | C22×C53 | 1 | 1 | yes | characteristic |
| 450 | C2×#135 | C22×C53 | 1 | 1 | yes | characteristic |
| 451 | C2×#135 | C22×C53 | 1 | 1 | yes | characteristic |
| 452 | C2×#131 | C22×C53 | 1 | 1 | yes | characteristic |
| 453 | C2×#131 | C22×C53 | 1 | 1 | yes | characteristic |
| 454 | C2×#131 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 455 | C22×M16 | C22×C53 | 1 | 1 | yes | characteristic |
| 456 | #525 | C22×C53 | 1 | 1 | yes | characteristic |
| 457 | C22×C42 | C22×C53 | 1 | 1 | yes | characteristic |
| 458 | #452 | C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 459 | #452 | C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 460 | #451 | C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 461 | #450 | C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 462 | #449 | C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 463 | #449 | C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 464 | #448 | C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 465 | #447 | C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 466 | #443 | — | 2 | 4 | no | — |
| 467 | #436 | — | 2 | 1 | no | — |
| 468 | #435 | — | 2 | 1 | no | — |
| 469 | #435 | — | 2 | 1 | no | — |
| 470 | C8×D4 | — | 2 | 1 | no | — |
| 471 | C2×#108 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 472 | C2×#108 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 473 | #424 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 474 | C2×#104 | — | 2 | 4 | no | — |
| 475 | C2×#104 | C22×C53 | 1 | 1 | yes | characteristic |
| 476 | C2×#104 | C22×C53 | 1 | 1 | yes | characteristic |
| 477 | C2×#104 | C22×C53 | 1 | 1 | yes | characteristic |
| 478 | C2×#104 | C22×C53 | 1 | 1 | yes | characteristic |
| 479 | C2×#104 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 480 | C2×#104 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 481 | #416 | C22×C53 | 1 | 1 | yes | characteristic |
| 482 | #416 | C22×C53 | 1 | 1 | yes | characteristic |
| 483 | #408 | — | 2 | 1 | no | — |
| 484 | #408 | — | 2 | 1 | no | — |
| 485 | #408 | C22×C53 | 1 | 1 | yes | characteristic |
| 486 | #408 | C22×C53 | 1 | 1 | yes | characteristic |
| 487 | #408 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 488 | #407 | — | 2 | 1 | no | — |
| 489 | #407 | C22×C53 | 1 | 1 | yes | characteristic |
| 490 | C2×C22⋊C8 | — | 2 | 1 | no | — |
| 491 | C2×C22⋊C8 | C22×C53 | 1 | 1 | yes | characteristic |
| 492 | C2×C22⋊C8 | C22×C53 | 1 | 1 | yes | characteristic |
| 493 | #405 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 494 | C2×C4×C8 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 495 | C2×C4×C8 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 496 | #341 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 497 | #341 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 498 | #339 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 499 | #339 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 500 | #336 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 501 | #336 | C22×C53 | 1 | 1 | yes | characteristic, complemented |
| 502 | C53 | #22888 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 503 | C2×#41 | — | 2 | 1 | no | — |
| 504 | C2×#41 | — | 2 | 1 | no | — |
| 505 | C2×#41 | — | 2 | 2 | no | — |
| 506 | C2×#41 | — | 2 | 2 | no | — |
| 507 | C2×#41 | — | 4 | 1 | no | — |
| 508 | C2×#41 | — | 4 | 1 | no | — |
| 509 | C2×#41 | C2×C4×C53 | 1 | 1 | yes | characteristic |
| 510 | C2×#41 | C2×C4×C53 | 1 | 1 | yes | characteristic |
| 511 | C2×#41 | C23×C53 | 1 | 1 | yes | characteristic |
| 512 | C2×#41 | C23×C53 | 1 | 1 | yes | characteristic |
| 513 | C2×#41 | C23×C53 | 1 | 1 | yes | characteristic |
| 514 | C22×Q8 | C2×C4×C53 | 1 | 1 | yes | characteristic |
| 515 | C22×D4 | — | 2 | 1 | no | — |
| 516 | C22×D4 | C2×C4×C53 | 1 | 1 | yes | characteristic |
| 517 | C23×C4 | — | 2 | 1 | no | — |
| 518 | C23×C4 | — | 2 | 1 | no | — |
| 519 | C23×C4 | C23×C53 | 1 | 1 | yes | characteristic |
| 520 | #135 | — | 2 | 2 | no | — |
| 521 | #135 | — | 2 | 2 | no | — |
| 522 | #135 | — | 4 | 1 | no | — |
| 523 | #135 | — | 4 | 1 | no | — |
| 524 | C2×Q16 | C2×C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 525 | C2×Q16 | C2×C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 526 | C2×SD16 | C2×C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 527 | C2×SD16 | C2×C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 528 | C2×SD16 | C2×C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 529 | C2×SD16 | C2×C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 530 | C2×D8 | C2×C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 531 | C2×D8 | C2×C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 532 | #131 | — | 2 | 2 | no | — |
| 533 | #131 | — | 2 | 2 | no | — |
| 534 | #131 | — | 2 | 2 | no | — |
| 535 | #131 | — | 4 | 1 | no | — |
| 536 | #131 | — | 4 | 1 | no | — |
| 537 | #131 | — | 4 | 1 | no | — |
| 538 | C2×M16 | — | 2 | 1 | no | — |
| 539 | C2×M16 | — | 2 | 1 | no | — |
| 540 | C2×M16 | — | 2 | 1 | no | — |
| 541 | C2×M16 | — | 2 | 1 | no | — |
| 542 | C2×M16 | — | 2 | 2 | no | — |
| 543 | C2×M16 | — | 4 | 1 | no | — |
| 544 | C2×M16 | C23×C53 | 1 | 1 | yes | characteristic |
| 545 | C2×M16 | C23×C53 | 1 | 1 | yes | characteristic |
| 546 | C2×M16 | C23×C53 | 1 | 1 | yes | characteristic |
| 547 | C2×M16 | C23×C53 | 1 | 1 | yes | characteristic |
| 548 | C22×C8 | — | 2 | 1 | no | — |
| 549 | C22×C8 | — | 2 | 1 | no | — |
| 550 | C22×C8 | — | 2 | 1 | no | — |
| 551 | C22×C8 | — | 2 | 1 | no | — |
| 552 | C22×C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 553 | C22×C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 554 | C22×C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 555 | C22×C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 556 | #123 | — | 2 | 1 | no | — |
| 557 | C22⋊Q8 | C2×C4×C53 | 1 | 1 | yes | characteristic |
| 558 | C22⋊Q8 | C2×C4×C53 | 1 | 1 | yes | characteristic |
| 559 | #121 | C2×C4×C53 | 1 | 1 | yes | characteristic |
| 560 | #121 | C2×C4×C53 | 1 | 1 | yes | characteristic |
| 561 | #120 | — | 2 | 1 | no | — |
| 562 | C4×D4 | — | 2 | 1 | no | — |
| 563 | C4×D4 | — | 2 | 1 | no | — |
| 564 | #117 | C23×C53 | 1 | 1 | yes | characteristic |
| 565 | C2×C42 | — | 2 | 2 | no | — |
| 566 | C2×C42 | — | 2 | 1 | no | — |
| 567 | C2×C42 | — | 4 | 1 | no | — |
| 568 | C2×C42 | C23×C53 | 1 | 1 | yes | characteristic |
| 569 | C2×C42 | C23×C53 | 1 | 1 | yes | characteristic |
| 570 | #108 | — | 2 | 2 | no | — |
| 571 | #108 | — | 4 | 1 | no | — |
| 572 | C4⋊C8 | — | 2 | 1 | no | — |
| 573 | C4⋊C8 | — | 2 | 1 | no | — |
| 574 | #104 | — | 2 | 2 | no | — |
| 575 | #104 | — | 2 | 2 | no | — |
| 576 | #104 | — | 2 | 2 | no | — |
| 577 | #104 | — | 2 | 2 | no | — |
| 578 | #104 | — | 4 | 1 | no | — |
| 579 | #104 | D4×C53 | 1 | 4 | yes | complemented |
| 580 | #103 | C2×C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 581 | #103 | C2×C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 582 | #103 | C2×C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 583 | #103 | C2×C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 584 | #102 | C2×C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 585 | #102 | C2×C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 586 | #102 | C2×C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 587 | #102 | C2×C4×C53 | 1 | 1 | yes | characteristic, complemented |
| 588 | C22⋊C8 | — | 2 | 1 | no | — |
| 589 | C22⋊C8 | — | 2 | 1 | no | — |
| 590 | C22⋊C8 | — | 2 | 1 | no | — |
| 591 | C22⋊C8 | — | 2 | 1 | no | — |
| 592 | C22⋊C8 | — | 2 | 1 | no | — |
| 593 | C22⋊C8 | — | 2 | 1 | no | — |
| 594 | C22⋊C8 | — | 2 | 1 | no | — |
| 595 | C22⋊C8 | — | 2 | 1 | no | — |
| 596 | C22⋊C8 | C2×C4×C53 | 1 | 1 | yes | characteristic |
| 597 | C22⋊C8 | C2×C4×C53 | 1 | 1 | yes | characteristic |
| 598 | C22⋊C8 | C2×C4×C53 | 1 | 1 | yes | characteristic |
| 599 | C22⋊C8 | C2×C4×C53 | 1 | 1 | yes | characteristic |
| 600 | C22⋊C8 | D4×C53 | 1 | 1 | yes | characteristic |
| 601 | C22⋊C8 | D4×C53 | 1 | 1 | yes | characteristic |
| 602 | C22⋊C8 | D4×C53 | 1 | 1 | yes | characteristic |
| 603 | C22⋊C8 | D4×C53 | 1 | 1 | yes | characteristic |
| 604 | #97 | — | 2 | 1 | no | — |
| 605 | C4×C8 | — | 2 | 1 | no | — |
| 606 | C4×C8 | — | 2 | 2 | no | — |
| 607 | C4×C8 | — | 4 | 1 | no | — |
| 608 | C24 | — | 2 | 1 | no | — |
| 609 | C24 | #41×C53 | 1 | 1 | yes | characteristic |
| 610 | #41 | — | 2 | 1 | no | — |
| 611 | #41 | — | 2 | 1 | no | — |
| 612 | #41 | — | 2 | 2 | no | — |
| 613 | #41 | — | 2 | 2 | no | — |
| 614 | #41 | — | 2 | 1 | no | — |
| 615 | #41 | — | 2 | 1 | no | — |
| 616 | #41 | — | 2 | 1 | no | — |
| 617 | #41 | — | 2 | 1 | no | — |
| 618 | #41 | — | 2 | 1 | no | — |
| 619 | #41 | — | 2 | 1 | no | — |
| 620 | #41 | — | 2 | 1 | no | — |
| 621 | #41 | — | 2 | 1 | no | — |
| 622 | #41 | — | 4 | 2 | no | — |
| 623 | #41 | — | 4 | 2 | no | — |
| 624 | #41 | — | 4 | 1 | no | — |
| 625 | #41 | — | 4 | 1 | no | — |
| 626 | #41 | — | 4 | 2 | no | — |
| 627 | #41 | — | 4 | 2 | no | — |
| 628 | #41 | C2×D4×C53 | 1 | 2 | yes | — |
| 629 | #41 | #41×C53 | 1 | 2 | yes | — |
| 630 | C2×Q8 | — | 2 | 1 | no | — |
| 631 | C2×Q8 | — | 2 | 2 | no | — |
| 632 | C2×Q8 | — | 4 | 1 | no | — |
| 633 | C2×Q8 | C22×C4×C53 | 1 | 1 | yes | characteristic |
| 634 | C2×Q8 | C22×C4×C53 | 1 | 1 | yes | characteristic |
| 635 | C2×Q8 | C22×C4×C53 | 1 | 1 | yes | characteristic |
| 636 | C2×D4 | — | 2 | 1 | no | — |
| 637 | C2×D4 | — | 2 | 2 | no | — |
| 638 | C2×D4 | — | 2 | 1 | no | — |
| 639 | C2×D4 | — | 2 | 1 | no | — |
| 640 | C2×D4 | — | 2 | 1 | no | — |
| 641 | C2×D4 | — | 2 | 1 | no | — |
| 642 | C2×D4 | — | 2 | 1 | no | — |
| 643 | C2×D4 | — | 2 | 1 | no | — |
| 644 | C2×D4 | — | 2 | 1 | no | — |
| 645 | C2×D4 | — | 4 | 1 | no | — |
| 646 | C2×D4 | — | 4 | 2 | no | — |
| 647 | C2×D4 | — | 4 | 2 | no | — |
| 648 | C2×D4 | C22×C4×C53 | 1 | 1 | yes | characteristic |
| 649 | C2×D4 | C22×C4×C53 | 1 | 1 | yes | characteristic |
| 650 | C2×D4 | C22×C4×C53 | 1 | 1 | yes | characteristic |
| 651 | C22×C4 | — | 2 | 1 | no | — |
| 652 | C22×C4 | — | 2 | 1 | no | — |
| 653 | C22×C4 | — | 2 | 1 | no | — |
| 654 | C22×C4 | — | 2 | 1 | no | — |
| 655 | C22×C4 | — | 2 | 1 | no | — |
| 656 | C22×C4 | — | 2 | 1 | no | — |
| 657 | C22×C4 | — | 2 | 4 | no | — |
| 658 | C22×C4 | — | 2 | 1 | no | — |
| 659 | C22×C4 | — | 2 | 1 | no | — |
| 660 | C22×C4 | — | 2 | 1 | no | — |
| 661 | C22×C4 | — | 2 | 1 | no | — |
| 662 | C22×C4 | — | 2 | 1 | no | — |
| 663 | C22×C4 | — | 2 | 1 | no | — |
| 664 | C22×C4 | — | 4 | 2 | no | — |
| 665 | C22×C4 | — | 4 | 2 | no | — |
| 666 | C22×C4 | — | 4 | 2 | no | — |
| 667 | C22×C4 | — | 4 | 2 | no | — |
| 668 | C22×C4 | C22×C4×C53 | 1 | 1 | yes | characteristic |
| 669 | C22×C4 | C22×C4×C53 | 1 | 1 | yes | characteristic |
| 670 | C22×C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 671 | C22×C4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 672 | C22×C4 | #41×C53 | 1 | 1 | yes | characteristic |
| 673 | C22×C4 | C24×C53 | 1 | 1 | yes | characteristic |
| 674 | Q16 | — | 2 | 2 | no | — |
| 675 | Q16 | — | 4 | 1 | no | — |
| 676 | SD16 | — | 2 | 2 | no | — |
| 677 | SD16 | — | 2 | 2 | no | — |
| 678 | SD16 | — | 4 | 1 | no | — |
| 679 | SD16 | — | 4 | 1 | no | — |
| 680 | D8 | — | 2 | 2 | no | — |
| 681 | D8 | — | 4 | 1 | no | — |
| 682 | M16 | — | 2 | 1 | no | — |
| 683 | M16 | — | 2 | 1 | no | — |
| 684 | M16 | — | 2 | 1 | no | — |
| 685 | M16 | — | 2 | 1 | no | — |
| 686 | M16 | — | 2 | 1 | no | — |
| 687 | M16 | — | 2 | 1 | no | — |
| 688 | M16 | — | 2 | 1 | no | — |
| 689 | M16 | — | 4 | 2 | no | — |
| 690 | M16 | — | 4 | 2 | no | — |
| 691 | M16 | — | 4 | 2 | no | — |
| 692 | M16 | — | 4 | 2 | no | — |
| 693 | M16 | C2×D4×C53 | 1 | 2 | yes | — |
| 694 | C2×C8 | — | 2 | 1 | no | — |
| 695 | C2×C8 | — | 2 | 1 | no | — |
| 696 | C2×C8 | — | 2 | 1 | no | — |
| 697 | C2×C8 | — | 2 | 1 | no | — |
| 698 | C2×C8 | — | 2 | 1 | no | — |
| 699 | C2×C8 | — | 2 | 1 | no | — |
| 700 | C2×C8 | — | 2 | 1 | no | — |
| 701 | C2×C8 | — | 2 | 1 | no | — |
| 702 | C2×C8 | — | 2 | 1 | no | — |
| 703 | C2×C8 | — | 2 | 1 | no | — |
| 704 | C2×C8 | — | 2 | 1 | no | — |
| 705 | C2×C8 | — | 2 | 1 | no | — |
| 706 | C2×C8 | — | 4 | 2 | no | — |
| 707 | C2×C8 | — | 4 | 2 | no | — |
| 708 | C2×C8 | — | 4 | 2 | no | — |
| 709 | C2×C8 | — | 4 | 2 | no | — |
| 710 | C2×C8 | C22×C4×C53 | 1 | 1 | yes | characteristic |
| 711 | C2×C8 | C22×C4×C53 | 1 | 1 | yes | characteristic |
| 712 | C2×C8 | C22×C4×C53 | 1 | 1 | yes | characteristic |
| 713 | C2×C8 | C22×C4×C53 | 1 | 1 | yes | characteristic |
| 714 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 715 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 716 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 717 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 718 | C4⋊C4 | — | 2 | 1 | no | — |
| 719 | C4⋊C4 | — | 2 | 1 | no | — |
| 720 | C4⋊C4 | C22×C4×C53 | 1 | 1 | yes | characteristic |
| 721 | C4⋊C4 | C22×C4×C53 | 1 | 1 | yes | characteristic |
| 722 | C22⋊C4 | — | 2 | 1 | no | — |
| 723 | C22⋊C4 | — | 2 | 1 | no | — |
| 724 | C22⋊C4 | — | 2 | 1 | no | — |
| 725 | C22⋊C4 | — | 2 | 1 | no | — |
| 726 | C22⋊C4 | — | 2 | 1 | no | — |
| 727 | C42 | — | 2 | 1 | no | — |
| 728 | C42 | — | 2 | 1 | no | — |
| 729 | C42 | — | 2 | 1 | no | — |
| 730 | C42 | — | 2 | 1 | no | — |
| 731 | C42 | — | 4 | 2 | no | — |
| 732 | C42 | C2×D4×C53 | 1 | 2 | yes | — |
| 733 | C23 | — | 2 | 1 | no | — |
| 734 | C23 | — | 2 | 1 | no | — |
| 735 | C23 | — | 2 | 1 | no | — |
| 736 | C23 | — | 2 | 2 | no | — |
| 737 | C23 | — | 2 | 1 | no | — |
| 738 | C23 | — | 2 | 1 | no | — |
| 739 | C23 | — | 4 | 1 | no | — |
| 740 | C23 | — | 4 | 2 | no | — |
| 741 | C23 | — | 4 | 2 | no | — |
| 742 | C23 | — | 8 | 1 | no | — |
| 743 | C23 | C4×D4×C53 | 1 | 1 | yes | characteristic |
| 744 | C23 | C4×D4×C53 | 1 | 1 | yes | characteristic |
| 745 | C23 | C2×#41×C53 | 1 | 1 | yes | characteristic |
| 746 | Q8 | — | 2 | 1 | no | — |
| 747 | Q8 | — | 2 | 1 | no | — |
| 748 | Q8 | — | 2 | 1 | no | — |
| 749 | Q8 | — | 2 | 1 | no | — |
| 750 | Q8 | — | 2 | 1 | no | — |
| 751 | Q8 | — | 4 | 2 | no | — |
| 752 | Q8 | C4×D4×C53 | 1 | 2 | yes | — |
| 753 | D4 | — | 2 | 2 | no | — |
| 754 | D4 | — | 2 | 2 | no | — |
| 755 | D4 | — | 2 | 1 | no | — |
| 756 | D4 | — | 2 | 1 | no | — |
| 757 | D4 | — | 2 | 1 | no | — |
| 758 | D4 | — | 2 | 1 | no | — |
| 759 | D4 | — | 2 | 1 | no | — |
| 760 | D4 | — | 4 | 2 | no | — |
| 761 | D4 | — | 4 | 2 | no | — |
| 762 | D4 | — | 4 | 2 | no | — |
| 763 | D4 | — | 4 | 1 | no | — |
| 764 | D4 | — | 4 | 1 | no | — |
| 765 | D4 | — | 4 | 1 | no | — |
| 766 | D4 | — | 4 | 1 | no | — |
| 767 | D4 | — | 4 | 2 | no | — |
| 768 | D4 | — | 8 | 1 | no | — |
| 769 | D4 | C4×D4×C53 | 1 | 2 | yes | — |
| 770 | C2×C4 | — | 2 | 2 | no | — |
| 771 | C2×C4 | — | 2 | 2 | no | — |
| 772 | C2×C4 | — | 2 | 1 | no | — |
| 773 | C2×C4 | — | 2 | 2 | no | — |
| 774 | C2×C4 | — | 2 | 1 | no | — |
| 775 | C2×C4 | — | 2 | 1 | no | — |
| 776 | C2×C4 | — | 2 | 1 | no | — |
| 777 | C2×C4 | — | 2 | 1 | no | — |
| 778 | C2×C4 | — | 2 | 1 | no | — |
| 779 | C2×C4 | — | 2 | 1 | no | — |
| 780 | C2×C4 | — | 2 | 1 | no | — |
| 781 | C2×C4 | — | 2 | 2 | no | — |
| 782 | C2×C4 | — | 2 | 1 | no | — |
| 783 | C2×C4 | — | 2 | 2 | no | — |
| 784 | C2×C4 | — | 2 | 1 | no | — |
| 785 | C2×C4 | — | 2 | 1 | no | — |
| 786 | C2×C4 | — | 2 | 2 | no | — |
| 787 | C2×C4 | — | 2 | 1 | no | — |
| 788 | C2×C4 | — | 2 | 1 | no | — |
| 789 | C2×C4 | — | 2 | 1 | no | — |
| 790 | C2×C4 | — | 2 | 1 | no | — |
| 791 | C2×C4 | — | 4 | 2 | no | — |
| 792 | C2×C4 | — | 4 | 2 | no | — |
| 793 | C2×C4 | — | 4 | 2 | no | — |
| 794 | C2×C4 | — | 4 | 8 | no | — |
| 795 | C2×C4 | — | 4 | 1 | no | — |
| 796 | C2×C4 | — | 4 | 1 | no | — |
| 797 | C2×C4 | — | 4 | 1 | no | — |
| 798 | C2×C4 | — | 4 | 1 | no | — |
| 799 | C2×C4 | — | 4 | 1 | no | — |
| 800 | C2×C4 | — | 4 | 1 | no | — |
| 801 | C2×C4 | C4×D4×C53 | 1 | 1 | yes | characteristic |
| 802 | C2×C4 | C4×D4×C53 | 1 | 1 | yes | characteristic |
| 803 | C2×C4 | C23×C4×C53 | 1 | 1 | yes | characteristic |
| 804 | C2×C4 | C22×D4×C53 | 1 | 1 | yes | characteristic |
| 805 | C2×C4 | C22×D4×C53 | 1 | 1 | yes | characteristic |
| 806 | C2×C4 | C2×#41×C53 | 1 | 1 | yes | characteristic |
| 807 | C2×C4 | H(5,𝔽2)×C53 | 1 | 1 | yes | characteristic |
| 808 | C2×C4 | H(5,𝔽2)×C53 | 1 | 1 | yes | characteristic |
| 809 | C8 | — | 2 | 1 | no | — |
| 810 | C8 | — | 2 | 1 | no | — |
| 811 | C8 | — | 2 | 1 | no | — |
| 812 | C8 | — | 2 | 1 | no | — |
| 813 | C8 | — | 2 | 1 | no | — |
| 814 | C8 | — | 2 | 1 | no | — |
| 815 | C8 | — | 2 | 2 | no | — |
| 816 | C8 | — | 2 | 1 | no | — |
| 817 | C8 | — | 2 | 1 | no | — |
| 818 | C8 | — | 4 | 1 | no | — |
| 819 | C8 | — | 4 | 1 | no | — |
| 820 | C8 | — | 4 | 1 | no | — |
| 821 | C22 | — | 2 | 1 | no | — |
| 822 | C22 | — | 2 | 1 | no | — |
| 823 | C22 | — | 2 | 1 | no | — |
| 824 | C22 | — | 2 | 1 | no | — |
| 825 | C22 | — | 2 | 1 | no | — |
| 826 | C22 | — | 2 | 1 | no | — |
| 827 | C22 | — | 2 | 1 | no | — |
| 828 | C22 | — | 2 | 2 | no | — |
| 829 | C22 | — | 4 | 2 | no | — |
| 830 | C22 | — | 4 | 2 | no | — |
| 831 | C22 | — | 4 | 1 | no | — |
| 832 | C22 | — | 4 | 1 | no | — |
| 833 | C22 | — | 4 | 1 | no | — |
| 834 | C22 | — | 4 | 1 | no | — |
| 835 | C22 | — | 4 | 1 | no | — |
| 836 | C22 | — | 4 | 1 | no | — |
| 837 | C22 | — | 4 | 1 | no | — |
| 838 | C22 | — | 4 | 1 | no | — |
| 839 | C22 | — | 8 | 4 | no | — |
| 840 | C22 | C53×#443 | 1 | 2 | yes | complemented |
| 841 | C22 | C2×C4×D4×C53 | 1 | 1 | yes | characteristic |
| 842 | C22 | C53×#546 | 1 | 1 | yes | characteristic |
| 843 | C22 | C53×#551 | 1 | 1 | yes | characteristic |
| 844 | C4 | — | 2 | 4 | no | — |
| 845 | C4 | — | 2 | 1 | no | — |
| 846 | C4 | — | 2 | 1 | no | — |
| 847 | C4 | — | 2 | 2 | no | — |
| 848 | C4 | — | 4 | 2 | no | — |
| 849 | C4 | — | 4 | 1 | no | — |
| 850 | C4 | — | 4 | 1 | no | — |
| 851 | C4 | — | 4 | 1 | no | — |
| 852 | C4 | — | 4 | 1 | no | — |
| 853 | C4 | C2×C4×D4×C53 | 1 | 1 | yes | characteristic |
| 854 | C4 | C53×#518 | 1 | 1 | yes | characteristic |
| 855 | C4 | D42×C53 | 1 | 1 | yes | characteristic |
| 856 | C4 | C53×#546 | 1 | 1 | yes | characteristic |
| 857 | C2 | — | 2 | 1 | no | — |
| 858 | C2 | — | 2 | 2 | no | — |
| 859 | C2 | — | 2 | 1 | no | — |
| 860 | C2 | — | 4 | 1 | no | — |
| 861 | C2 | — | 4 | 2 | no | — |
| 862 | C2 | — | 8 | 1 | no | — |
| 863 | C2 | — | 8 | 1 | no | — |
| 864 | C2 | C53×#2358 | 1 | 1 | yes | characteristic |
| 865 | C2 | C2×C53×#443 | 1 | 1 | yes | characteristic |
| 866 | C2 | C53×#2956 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta