| 1 | C53×#3154 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C53×#3069 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C53×#3068 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C53×#3067 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×C53×#471 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C53×#2957 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C53×#2049 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C53×#2048 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C53×#2009 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C53×#2008 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C53×#1977 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C53×#1953 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C53×#1915 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C53×#1914 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C53×#1757 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C53×#575 | C22 | 1 | 1 | yes | characteristic |
| 17 | C53×#575 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#137×C53 | C22 | 1 | 1 | yes | characteristic |
| 19 | C2×#137×C53 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×AGL(1,ℤ/8)×C53 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×AGL(1,ℤ/8)×C53 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#135×C53 | C22 | 1 | 1 | yes | characteristic |
| 23 | C22×SD16×C53 | C22 | 1 | 1 | yes | characteristic |
| 24 | C53×#568 | C22 | 1 | 1 | yes | characteristic |
| 25 | C53×#568 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#131×C53 | C22 | 1 | 1 | yes | characteristic |
| 27 | C53×#536 | C22 | 1 | 1 | yes | characteristic |
| 28 | C53×#535 | C22 | 1 | 1 | yes | characteristic |
| 29 | C53×#497 | — | 2 | 1 | no | — |
| 30 | C53×#496 | — | 2 | 1 | no | — |
| 31 | C53×#495 | — | 2 | 1 | no | — |
| 32 | C53×#492 | — | 2 | 1 | no | — |
| 33 | C53×#473 | — | 2 | 1 | no | — |
| 34 | C53×#473 | — | 2 | 2 | no | — |
| 35 | C53×#472 | — | 2 | 1 | no | — |
| 36 | C53×#472 | — | 2 | 2 | no | — |
| 37 | C53×#471 | — | 2 | 1 | no | — |
| 38 | C53×#471 | — | 2 | 1 | no | — |
| 39 | C53×#471 | — | 2 | 2 | no | — |
| 40 | C53×#471 | — | 2 | 2 | no | — |
| 41 | C53×#471 | — | 2 | 2 | no | — |
| 42 | C53×#471 | — | 2 | 2 | no | — |
| 43 | C53×#444 | — | 2 | 2 | no | — |
| 44 | C53×#443 | — | 2 | 2 | no | — |
| 45 | C53×#430 | C22 | 1 | 1 | yes | characteristic |
| 46 | C53×#430 | C22 | 1 | 1 | yes | characteristic |
| 47 | C2×#108×C53 | C22 | 1 | 1 | yes | characteristic |
| 48 | C2×#108×C53 | C22 | 1 | 1 | yes | characteristic |
| 49 | C53×#421 | C22 | 1 | 1 | yes | characteristic |
| 50 | C53×#421 | C22 | 1 | 1 | yes | characteristic |
| 51 | C53×#419 | C22 | 1 | 1 | yes | characteristic |
| 52 | C53×#418 | C22 | 1 | 1 | yes | characteristic |
| 53 | C53×#413 | C22 | 1 | 1 | yes | characteristic |
| 54 | C53×#413 | C22 | 1 | 1 | yes | characteristic |
| 55 | C53×#413 | C22 | 1 | 1 | yes | characteristic |
| 56 | C2×#101×C53 | C22 | 1 | 1 | yes | characteristic |
| 57 | C2×#101×C53 | C22 | 1 | 1 | yes | characteristic |
| 58 | C2×#100×C53 | C22 | 1 | 1 | yes | characteristic |
| 59 | C2×#100×C53 | C22 | 1 | 1 | yes | characteristic |
| 60 | C53×#410 | C22 | 1 | 1 | yes | characteristic |
| 61 | C53×#405 | C22 | 1 | 1 | yes | characteristic |
| 62 | C53×#405 | C22 | 1 | 1 | yes | characteristic |
| 63 | C53×#344 | C22 | 1 | 1 | yes | characteristic |
| 64 | C53×#344 | C22 | 1 | 1 | yes | characteristic |
| 65 | C53×#344 | C22 | 1 | 1 | yes | characteristic |
| 66 | C53×#344 | C22 | 1 | 1 | yes | characteristic |
| 67 | C2×#41×C53 | C23 | 1 | 1 | yes | characteristic |
| 68 | C2×#41×C53 | C23 | 1 | 1 | yes | characteristic |
| 69 | C2×#41×C53 | C23 | 1 | 1 | yes | characteristic |
| 70 | C22×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 71 | C22×D4×C53 | C23 | 1 | 1 | yes | characteristic |
| 72 | #137×C53 | — | 2 | 2 | no | — |
| 73 | #137×C53 | — | 2 | 2 | no | — |
| 74 | #137×C53 | — | 2 | 1 | no | — |
| 75 | #137×C53 | — | 2 | 1 | no | — |
| 76 | #137×C53 | — | 2 | 1 | no | — |
| 77 | #137×C53 | — | 2 | 1 | no | — |
| 78 | #137×C53 | — | 4 | 1 | no | — |
| 79 | #137×C53 | — | 4 | 1 | no | — |
| 80 | AGL(1,ℤ/8)×C53 | — | 2 | 2 | no | — |
| 81 | AGL(1,ℤ/8)×C53 | — | 2 | 2 | no | — |
| 82 | AGL(1,ℤ/8)×C53 | — | 2 | 1 | no | — |
| 83 | AGL(1,ℤ/8)×C53 | — | 2 | 1 | no | — |
| 84 | AGL(1,ℤ/8)×C53 | — | 2 | 1 | no | — |
| 85 | AGL(1,ℤ/8)×C53 | — | 2 | 1 | no | — |
| 86 | AGL(1,ℤ/8)×C53 | — | 4 | 1 | no | — |
| 87 | AGL(1,ℤ/8)×C53 | — | 4 | 1 | no | — |
| 88 | #135×C53 | — | 2 | 1 | no | — |
| 89 | #135×C53 | — | 2 | 1 | no | — |
| 90 | #135×C53 | — | 2 | 1 | no | — |
| 91 | #135×C53 | — | 2 | 1 | no | — |
| 92 | #135×C53 | — | 4 | 1 | no | — |
| 93 | #135×C53 | — | 4 | 1 | no | — |
| 94 | C2×Q16×C53 | — | 2 | 1 | no | — |
| 95 | C2×Q16×C53 | — | 2 | 1 | no | — |
| 96 | C2×Q16×C53 | D4 | 1 | 1 | yes | characteristic |
| 97 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 98 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 99 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 100 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 101 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 102 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 103 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 104 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 105 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 106 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 107 | C2×SD16×C53 | D4 | 1 | 1 | yes | characteristic |
| 108 | C2×SD16×C53 | D4 | 1 | 1 | yes | characteristic |
| 109 | C2×D8×C53 | — | 2 | 1 | no | — |
| 110 | C2×D8×C53 | — | 2 | 1 | no | — |
| 111 | C2×D8×C53 | D4 | 1 | 1 | yes | characteristic |
| 112 | #131×C53 | — | 2 | 2 | no | — |
| 113 | #131×C53 | — | 2 | 2 | no | — |
| 114 | #131×C53 | — | 2 | 2 | no | — |
| 115 | #131×C53 | — | 2 | 2 | no | — |
| 116 | #131×C53 | — | 2 | 1 | no | — |
| 117 | #131×C53 | — | 2 | 1 | no | — |
| 118 | #131×C53 | — | 2 | 1 | no | — |
| 119 | #131×C53 | — | 2 | 1 | no | — |
| 120 | C2×M16×C53 | — | 2 | 1 | no | — |
| 121 | C2×M16×C53 | — | 4 | 1 | no | — |
| 122 | C2×M16×C53 | — | 4 | 1 | no | — |
| 123 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 124 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 125 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 126 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 127 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 128 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 129 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 130 | C22×C8×C53 | — | 2 | 1 | no | — |
| 131 | C22×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 132 | C4⋊Q8×C53 | — | 2 | 1 | no | — |
| 133 | #127×C53 | — | 2 | 1 | no | — |
| 134 | #124×C53 | — | 2 | 1 | no | — |
| 135 | #124×C53 | — | 2 | 1 | no | — |
| 136 | #123×C53 | — | 2 | 2 | no | — |
| 137 | C22⋊Q8×C53 | — | 4 | 1 | no | — |
| 138 | #121×C53 | — | 4 | 1 | no | — |
| 139 | #120×C53 | — | 2 | 2 | no | — |
| 140 | #117×C53 | C23 | 1 | 1 | yes | characteristic |
| 141 | #117×C53 | C23 | 1 | 1 | yes | characteristic |
| 142 | #108×C53 | — | 2 | 2 | no | — |
| 143 | #108×C53 | — | 2 | 2 | no | — |
| 144 | #108×C53 | — | 2 | 1 | no | — |
| 145 | #108×C53 | — | 2 | 1 | no | — |
| 146 | #108×C53 | D4 | 1 | 2 | yes | complemented |
| 147 | #108×C53 | D4 | 1 | 2 | yes | complemented |
| 148 | #104×C53 | — | 2 | 2 | no | — |
| 149 | #104×C53 | — | 2 | 2 | no | — |
| 150 | #103×C53 | — | 4 | 1 | no | — |
| 151 | #102×C53 | — | 4 | 1 | no | — |
| 152 | #101×C53 | — | 2 | 2 | no | — |
| 153 | #101×C53 | — | 2 | 2 | no | — |
| 154 | #101×C53 | — | 2 | 1 | no | — |
| 155 | #101×C53 | — | 2 | 1 | no | — |
| 156 | #101×C53 | D4 | 1 | 2 | yes | complemented |
| 157 | #100×C53 | — | 2 | 2 | no | — |
| 158 | #100×C53 | — | 2 | 2 | no | — |
| 159 | #100×C53 | — | 2 | 1 | no | — |
| 160 | #100×C53 | — | 2 | 1 | no | — |
| 161 | #100×C53 | D4 | 1 | 2 | yes | complemented |
| 162 | #99×C53 | — | 2 | 2 | no | — |
| 163 | #97×C53 | — | 2 | 1 | no | — |
| 164 | #97×C53 | — | 2 | 1 | no | — |
| 165 | C4×C8×C53 | — | 2 | 1 | no | — |
| 166 | C4×C8×C53 | — | 2 | 1 | no | — |
| 167 | C24×C53 | — | 2 | 1 | no | — |
| 168 | #41×C53 | — | 2 | 1 | no | — |
| 169 | #41×C53 | — | 2 | 1 | no | — |
| 170 | #41×C53 | — | 2 | 1 | no | — |
| 171 | #41×C53 | — | 2 | 1 | no | — |
| 172 | #41×C53 | — | 2 | 1 | no | — |
| 173 | #41×C53 | — | 2 | 1 | no | — |
| 174 | #41×C53 | — | 2 | 1 | no | — |
| 175 | #41×C53 | — | 2 | 1 | no | — |
| 176 | #41×C53 | — | 2 | 1 | no | — |
| 177 | #41×C53 | — | 2 | 1 | no | — |
| 178 | #41×C53 | — | 2 | 1 | no | — |
| 179 | #41×C53 | — | 2 | 1 | no | — |
| 180 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 181 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 182 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 183 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 184 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 185 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 186 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C2×D4×C53 | — | 2 | 1 | no | — |
| 190 | C2×D4×C53 | — | 2 | 1 | no | — |
| 191 | C2×D4×C53 | — | 2 | 1 | no | — |
| 192 | C2×D4×C53 | — | 2 | 1 | no | — |
| 193 | C2×D4×C53 | — | 2 | 1 | no | — |
| 194 | C2×D4×C53 | — | 2 | 1 | no | — |
| 195 | C2×D4×C53 | — | 2 | 1 | no | — |
| 196 | C2×D4×C53 | — | 2 | 1 | no | — |
| 197 | C2×D4×C53 | — | 2 | 1 | no | — |
| 198 | C2×D4×C53 | — | 4 | 2 | no | — |
| 199 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 200 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 201 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 202 | C22×C4×C53 | — | 2 | 1 | no | — |
| 203 | C22×C4×C53 | — | 2 | 1 | no | — |
| 204 | C22×C4×C53 | — | 2 | 1 | no | — |
| 205 | C22×C4×C53 | — | 2 | 1 | no | — |
| 206 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 207 | Q16×C53 | — | 2 | 1 | no | — |
| 208 | Q16×C53 | — | 2 | 1 | no | — |
| 209 | Q16×C53 | — | 4 | 2 | no | — |
| 210 | Q16×C53 | — | 4 | 2 | no | — |
| 211 | Q16×C53 | — | 4 | 1 | no | — |
| 212 | Q16×C53 | — | 4 | 1 | no | — |
| 213 | SD16×C53 | — | 2 | 1 | no | — |
| 214 | SD16×C53 | — | 2 | 1 | no | — |
| 215 | SD16×C53 | — | 2 | 1 | no | — |
| 216 | SD16×C53 | — | 2 | 1 | no | — |
| 217 | SD16×C53 | — | 4 | 2 | no | — |
| 218 | SD16×C53 | — | 4 | 2 | no | — |
| 219 | SD16×C53 | — | 4 | 2 | no | — |
| 220 | SD16×C53 | — | 4 | 2 | no | — |
| 221 | SD16×C53 | — | 4 | 1 | no | — |
| 222 | SD16×C53 | — | 4 | 1 | no | — |
| 223 | SD16×C53 | — | 4 | 1 | no | — |
| 224 | SD16×C53 | — | 4 | 1 | no | — |
| 225 | SD16×C53 | — | 4 | 1 | no | — |
| 226 | SD16×C53 | — | 4 | 1 | no | — |
| 227 | SD16×C53 | — | 4 | 1 | no | — |
| 228 | SD16×C53 | — | 4 | 1 | no | — |
| 229 | D8×C53 | — | 2 | 1 | no | — |
| 230 | D8×C53 | — | 2 | 1 | no | — |
| 231 | D8×C53 | — | 4 | 2 | no | — |
| 232 | D8×C53 | — | 4 | 2 | no | — |
| 233 | D8×C53 | — | 4 | 1 | no | — |
| 234 | D8×C53 | — | 4 | 1 | no | — |
| 235 | M16×C53 | — | 2 | 1 | no | — |
| 236 | M16×C53 | — | 2 | 1 | no | — |
| 237 | M16×C53 | — | 2 | 1 | no | — |
| 238 | M16×C53 | — | 2 | 1 | no | — |
| 239 | M16×C53 | — | 2 | 1 | no | — |
| 240 | M16×C53 | — | 2 | 1 | no | — |
| 241 | M16×C53 | — | 2 | 1 | no | — |
| 242 | M16×C53 | — | 2 | 1 | no | — |
| 243 | M16×C53 | — | 2 | 1 | no | — |
| 244 | M16×C53 | — | 2 | 1 | no | — |
| 245 | M16×C53 | — | 4 | 2 | no | — |
| 246 | M16×C53 | — | 4 | 2 | no | — |
| 247 | M16×C53 | — | 4 | 1 | no | — |
| 248 | M16×C53 | — | 4 | 1 | no | — |
| 249 | M16×C53 | C2×D4 | 1 | 2 | yes | — |
| 250 | M16×C53 | C2×D4 | 1 | 2 | yes | — |
| 251 | M16×C53 | C2×D4 | 1 | 2 | yes | — |
| 252 | M16×C53 | C2×D4 | 1 | 2 | yes | — |
| 253 | C2×C8×C53 | — | 2 | 1 | no | — |
| 254 | C2×C8×C53 | — | 2 | 1 | no | — |
| 255 | C2×C8×C53 | — | 2 | 1 | no | — |
| 256 | C2×C8×C53 | — | 2 | 1 | no | — |
| 257 | C2×C8×C53 | — | 2 | 1 | no | — |
| 258 | C2×C8×C53 | — | 2 | 1 | no | — |
| 259 | C2×C8×C53 | — | 2 | 1 | no | — |
| 260 | C2×C8×C53 | — | 4 | 2 | no | — |
| 261 | C2×C8×C53 | — | 4 | 2 | no | — |
| 262 | C2×C8×C53 | — | 4 | 1 | no | — |
| 263 | C2×C8×C53 | — | 4 | 1 | no | — |
| 264 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 265 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 266 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 267 | C2×C8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 268 | C2×C8×C53 | #41 | 1 | 1 | yes | characteristic |
| 269 | C2×C8×C53 | #41 | 1 | 1 | yes | characteristic |
| 270 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 271 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 272 | C4⋊C4×C53 | — | 4 | 2 | no | — |
| 273 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 274 | C22⋊C4×C53 | — | 4 | 2 | no | — |
| 275 | C22⋊C4×C53 | — | 4 | 2 | no | — |
| 276 | C22⋊C4×C53 | #41 | 1 | 2 | yes | — |
| 277 | C42×C53 | — | 2 | 1 | no | — |
| 278 | C42×C53 | — | 2 | 1 | no | — |
| 279 | C23×C53 | — | 2 | 1 | no | — |
| 280 | C23×C53 | — | 2 | 1 | no | — |
| 281 | C23×C53 | — | 2 | 1 | no | — |
| 282 | C23×C53 | — | 4 | 1 | no | — |
| 283 | C23×C53 | — | 4 | 1 | no | — |
| 284 | C23×C53 | — | 4 | 1 | no | — |
| 285 | C23×C53 | — | 16 | 1 | no | — |
| 286 | C23×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 287 | Q8×C53 | — | 2 | 1 | no | — |
| 288 | Q8×C53 | — | 2 | 1 | no | — |
| 289 | Q8×C53 | — | 2 | 1 | no | — |
| 290 | Q8×C53 | — | 2 | 1 | no | — |
| 291 | Q8×C53 | — | 2 | 1 | no | — |
| 292 | Q8×C53 | — | 2 | 1 | no | — |
| 293 | Q8×C53 | — | 4 | 1 | no | — |
| 294 | Q8×C53 | — | 4 | 1 | no | — |
| 295 | Q8×C53 | — | 4 | 1 | no | — |
| 296 | Q8×C53 | — | 4 | 1 | no | — |
| 297 | D4×C53 | — | 2 | 1 | no | — |
| 298 | D4×C53 | — | 2 | 1 | no | — |
| 299 | D4×C53 | — | 2 | 1 | no | — |
| 300 | D4×C53 | — | 2 | 1 | no | — |
| 301 | D4×C53 | — | 2 | 1 | no | — |
| 302 | D4×C53 | — | 2 | 1 | no | — |
| 303 | D4×C53 | — | 4 | 1 | no | — |
| 304 | D4×C53 | — | 4 | 1 | no | — |
| 305 | D4×C53 | — | 4 | 1 | no | — |
| 306 | D4×C53 | — | 4 | 1 | no | — |
| 307 | D4×C53 | — | 4 | 1 | no | — |
| 308 | D4×C53 | — | 4 | 1 | no | — |
| 309 | D4×C53 | — | 4 | 1 | no | — |
| 310 | D4×C53 | — | 4 | 1 | no | — |
| 311 | D4×C53 | — | 4 | 1 | no | — |
| 312 | D4×C53 | — | 4 | 1 | no | — |
| 313 | D4×C53 | — | 16 | 2 | no | — |
| 314 | C2×C4×C53 | — | 2 | 1 | no | — |
| 315 | C2×C4×C53 | — | 2 | 1 | no | — |
| 316 | C2×C4×C53 | — | 2 | 1 | no | — |
| 317 | C2×C4×C53 | — | 2 | 2 | no | — |
| 318 | C2×C4×C53 | — | 4 | 1 | no | — |
| 319 | C2×C4×C53 | — | 4 | 1 | no | — |
| 320 | C2×C4×C53 | — | 4 | 1 | no | — |
| 321 | C2×C4×C53 | — | 4 | 1 | no | — |
| 322 | C2×C4×C53 | — | 4 | 1 | no | — |
| 323 | C2×C4×C53 | — | 4 | 1 | no | — |
| 324 | C2×C4×C53 | — | 4 | 1 | no | — |
| 325 | C2×C4×C53 | — | 4 | 1 | no | — |
| 326 | C2×C4×C53 | — | 4 | 1 | no | — |
| 327 | C2×C4×C53 | — | 4 | 1 | no | — |
| 328 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 329 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 330 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 331 | C2×C4×C53 | C2×#41 | 1 | 1 | yes | characteristic |
| 332 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 333 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 334 | C8×C53 | — | 2 | 2 | no | — |
| 335 | C8×C53 | — | 2 | 2 | no | — |
| 336 | C8×C53 | — | 2 | 2 | no | — |
| 337 | C8×C53 | — | 2 | 2 | no | — |
| 338 | C8×C53 | — | 4 | 1 | no | — |
| 339 | C8×C53 | — | 4 | 1 | no | — |
| 340 | C8×C53 | — | 4 | 1 | no | — |
| 341 | C8×C53 | #121 | 1 | 1 | yes | characteristic |
| 342 | C8×C53 | #121 | 1 | 1 | yes | characteristic |
| 343 | C8×C53 | #121 | 1 | 1 | yes | characteristic |
| 344 | C8×C53 | #121 | 1 | 1 | yes | characteristic |
| 345 | #25446 | C53 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 346 | C22×C53 | — | 4 | 1 | no | — |
| 347 | C22×C53 | — | 4 | 1 | no | — |
| 348 | C22×C53 | — | 4 | 1 | no | — |
| 349 | C22×C53 | — | 4 | 1 | no | — |
| 350 | C22×C53 | — | 8 | 1 | no | — |
| 351 | C22×C53 | — | 8 | 1 | no | — |
| 352 | C22×C53 | — | 8 | 1 | no | — |
| 353 | C22×C53 | — | 8 | 2 | no | — |
| 354 | C22×C53 | — | 8 | 1 | no | — |
| 355 | C22×C53 | — | 16 | 1 | no | — |
| 356 | C22×C53 | — | 16 | 1 | no | — |
| 357 | C22×C53 | #532 | 1 | 1 | yes | characteristic |
| 358 | C22×C53 | #546 | 1 | 1 | yes | characteristic |
| 359 | C22×C53 | #550 | 1 | 1 | yes | characteristic |
| 360 | C4×C53 | — | 4 | 2 | no | — |
| 361 | C4×C53 | — | 4 | 1 | no | — |
| 362 | C4×C53 | — | 4 | 1 | no | — |
| 363 | C4×C53 | — | 4 | 1 | no | — |
| 364 | C4×C53 | — | 8 | 1 | no | — |
| 365 | C4×C53 | — | 8 | 1 | no | — |
| 366 | C4×C53 | C2×#121 | 1 | 1 | yes | characteristic |
| 367 | C4×C53 | #540 | 1 | 1 | yes | characteristic |
| 368 | C4×C53 | D42 | 1 | 1 | yes | characteristic |
| 369 | C4×C53 | D42 | 1 | 1 | yes | characteristic |
| 370 | #3154 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 371 | #3069 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 372 | #3068 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 373 | #3067 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 374 | C2×#471 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 375 | #2957 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 376 | #2049 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 377 | #2048 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 378 | #2009 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 379 | #2008 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 380 | #1977 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 381 | #1953 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 382 | #1915 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 383 | #1914 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 384 | #1757 | C2×C53 | 1 | 1 | yes | characteristic, complemented |
| 385 | C2×C53 | — | 2 | 1 | no | — |
| 386 | C2×C53 | — | 2 | 1 | no | — |
| 387 | C2×C53 | — | 2 | 1 | no | — |
| 388 | C2×C53 | — | 8 | 1 | no | — |
| 389 | C2×C53 | — | 8 | 1 | no | — |
| 390 | C2×C53 | — | 8 | 1 | no | — |
| 391 | C2×C53 | — | 16 | 1 | no | — |
| 392 | C2×C53 | #2428 | 1 | 1 | yes | characteristic |
| 393 | #575 | C22×C53 | 1 | 1 | yes | characteristic |
| 394 | #575 | C22×C53 | 1 | 1 | yes | characteristic |
| 395 | C2×#137 | C22×C53 | 1 | 1 | yes | characteristic |
| 396 | C2×#137 | C22×C53 | 1 | 1 | yes | characteristic |
| 397 | C2×AGL(1,ℤ/8) | C22×C53 | 1 | 1 | yes | characteristic |
| 398 | C2×AGL(1,ℤ/8) | C22×C53 | 1 | 1 | yes | characteristic |
| 399 | C2×#135 | C22×C53 | 1 | 1 | yes | characteristic |
| 400 | C22×SD16 | C22×C53 | 1 | 1 | yes | characteristic |
| 401 | #568 | C22×C53 | 1 | 1 | yes | characteristic |
| 402 | #568 | C22×C53 | 1 | 1 | yes | characteristic |
| 403 | C2×#131 | C22×C53 | 1 | 1 | yes | characteristic |
| 404 | #536 | C22×C53 | 1 | 1 | yes | characteristic |
| 405 | #535 | C22×C53 | 1 | 1 | yes | characteristic |
| 406 | #497 | — | 2 | 1 | no | — |
| 407 | #496 | — | 2 | 1 | no | — |
| 408 | #495 | — | 2 | 1 | no | — |
| 409 | #492 | — | 2 | 1 | no | — |
| 410 | #473 | — | 2 | 1 | no | — |
| 411 | #473 | — | 2 | 2 | no | — |
| 412 | #472 | — | 2 | 1 | no | — |
| 413 | #472 | — | 2 | 2 | no | — |
| 414 | #471 | — | 2 | 1 | no | — |
| 415 | #471 | — | 2 | 1 | no | — |
| 416 | #471 | — | 2 | 2 | no | — |
| 417 | #471 | — | 2 | 2 | no | — |
| 418 | #471 | — | 2 | 2 | no | — |
| 419 | #471 | — | 2 | 2 | no | — |
| 420 | #444 | — | 2 | 2 | no | — |
| 421 | #443 | — | 2 | 2 | no | — |
| 422 | #430 | C22×C53 | 1 | 1 | yes | characteristic |
| 423 | #430 | C22×C53 | 1 | 1 | yes | characteristic |
| 424 | C2×#108 | C22×C53 | 1 | 1 | yes | characteristic |
| 425 | C2×#108 | C22×C53 | 1 | 1 | yes | characteristic |
| 426 | #421 | C22×C53 | 1 | 1 | yes | characteristic |
| 427 | #421 | C22×C53 | 1 | 1 | yes | characteristic |
| 428 | #419 | C22×C53 | 1 | 1 | yes | characteristic |
| 429 | #418 | C22×C53 | 1 | 1 | yes | characteristic |
| 430 | #413 | C22×C53 | 1 | 1 | yes | characteristic |
| 431 | #413 | C22×C53 | 1 | 1 | yes | characteristic |
| 432 | #413 | C22×C53 | 1 | 1 | yes | characteristic |
| 433 | C2×#101 | C22×C53 | 1 | 1 | yes | characteristic |
| 434 | C2×#101 | C22×C53 | 1 | 1 | yes | characteristic |
| 435 | C2×#100 | C22×C53 | 1 | 1 | yes | characteristic |
| 436 | C2×#100 | C22×C53 | 1 | 1 | yes | characteristic |
| 437 | #410 | C22×C53 | 1 | 1 | yes | characteristic |
| 438 | #405 | C22×C53 | 1 | 1 | yes | characteristic |
| 439 | #405 | C22×C53 | 1 | 1 | yes | characteristic |
| 440 | #344 | C22×C53 | 1 | 1 | yes | characteristic |
| 441 | #344 | C22×C53 | 1 | 1 | yes | characteristic |
| 442 | #344 | C22×C53 | 1 | 1 | yes | characteristic |
| 443 | #344 | C22×C53 | 1 | 1 | yes | characteristic |
| 444 | C53 | #25446 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 445 | C2×#41 | C23×C53 | 1 | 1 | yes | characteristic |
| 446 | C2×#41 | C23×C53 | 1 | 1 | yes | characteristic |
| 447 | C2×#41 | C23×C53 | 1 | 1 | yes | characteristic |
| 448 | C22×Q8 | C23×C53 | 1 | 1 | yes | characteristic |
| 449 | C22×D4 | C23×C53 | 1 | 1 | yes | characteristic |
| 450 | #137 | — | 2 | 1 | no | — |
| 451 | #137 | — | 2 | 1 | no | — |
| 452 | #137 | — | 2 | 1 | no | — |
| 453 | #137 | — | 2 | 1 | no | — |
| 454 | #137 | — | 2 | 2 | no | — |
| 455 | #137 | — | 2 | 2 | no | — |
| 456 | #137 | — | 4 | 1 | no | — |
| 457 | #137 | — | 4 | 1 | no | — |
| 458 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 459 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 460 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 461 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 462 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 463 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 464 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 465 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 466 | #135 | — | 2 | 1 | no | — |
| 467 | #135 | — | 2 | 1 | no | — |
| 468 | #135 | — | 2 | 1 | no | — |
| 469 | #135 | — | 2 | 1 | no | — |
| 470 | #135 | — | 4 | 1 | no | — |
| 471 | #135 | — | 4 | 1 | no | — |
| 472 | C2×Q16 | — | 2 | 1 | no | — |
| 473 | C2×Q16 | — | 2 | 1 | no | — |
| 474 | C2×Q16 | D4×C53 | 1 | 1 | yes | characteristic |
| 475 | C2×SD16 | — | 2 | 1 | no | — |
| 476 | C2×SD16 | — | 2 | 1 | no | — |
| 477 | C2×SD16 | — | 2 | 1 | no | — |
| 478 | C2×SD16 | — | 2 | 1 | no | — |
| 479 | C2×SD16 | — | 2 | 1 | no | — |
| 480 | C2×SD16 | — | 2 | 1 | no | — |
| 481 | C2×SD16 | — | 2 | 1 | no | — |
| 482 | C2×SD16 | — | 2 | 1 | no | — |
| 483 | C2×SD16 | — | 2 | 1 | no | — |
| 484 | C2×SD16 | — | 2 | 1 | no | — |
| 485 | C2×SD16 | D4×C53 | 1 | 1 | yes | characteristic |
| 486 | C2×SD16 | D4×C53 | 1 | 1 | yes | characteristic |
| 487 | C2×D8 | — | 2 | 1 | no | — |
| 488 | C2×D8 | — | 2 | 1 | no | — |
| 489 | C2×D8 | D4×C53 | 1 | 1 | yes | characteristic |
| 490 | #131 | — | 2 | 2 | no | — |
| 491 | #131 | — | 2 | 2 | no | — |
| 492 | #131 | — | 2 | 2 | no | — |
| 493 | #131 | — | 2 | 2 | no | — |
| 494 | #131 | — | 2 | 1 | no | — |
| 495 | #131 | — | 2 | 1 | no | — |
| 496 | #131 | — | 2 | 1 | no | — |
| 497 | #131 | — | 2 | 1 | no | — |
| 498 | C2×M16 | — | 2 | 1 | no | — |
| 499 | C2×M16 | — | 4 | 1 | no | — |
| 500 | C2×M16 | — | 4 | 1 | no | — |
| 501 | C2×M16 | C23×C53 | 1 | 1 | yes | characteristic |
| 502 | C2×M16 | C23×C53 | 1 | 1 | yes | characteristic |
| 503 | C2×M16 | C23×C53 | 1 | 1 | yes | characteristic |
| 504 | C2×M16 | C23×C53 | 1 | 1 | yes | characteristic |
| 505 | C2×M16 | C23×C53 | 1 | 1 | yes | characteristic |
| 506 | C2×M16 | C23×C53 | 1 | 1 | yes | characteristic |
| 507 | C2×M16 | C23×C53 | 1 | 1 | yes | characteristic |
| 508 | C22×C8 | — | 2 | 1 | no | — |
| 509 | C22×C8 | C23×C53 | 1 | 1 | yes | characteristic |
| 510 | C4⋊Q8 | — | 2 | 1 | no | — |
| 511 | #127 | — | 2 | 1 | no | — |
| 512 | #124 | — | 2 | 1 | no | — |
| 513 | #124 | — | 2 | 1 | no | — |
| 514 | #123 | — | 2 | 2 | no | — |
| 515 | C22⋊Q8 | — | 4 | 1 | no | — |
| 516 | #121 | — | 4 | 1 | no | — |
| 517 | #120 | — | 2 | 2 | no | — |
| 518 | #117 | C23×C53 | 1 | 1 | yes | characteristic |
| 519 | #117 | C23×C53 | 1 | 1 | yes | characteristic |
| 520 | #108 | — | 2 | 2 | no | — |
| 521 | #108 | — | 2 | 2 | no | — |
| 522 | #108 | — | 2 | 1 | no | — |
| 523 | #108 | — | 2 | 1 | no | — |
| 524 | #108 | D4×C53 | 1 | 2 | yes | complemented |
| 525 | #108 | D4×C53 | 1 | 2 | yes | complemented |
| 526 | #104 | — | 2 | 2 | no | — |
| 527 | #104 | — | 2 | 2 | no | — |
| 528 | #103 | — | 4 | 1 | no | — |
| 529 | #102 | — | 4 | 1 | no | — |
| 530 | #101 | — | 2 | 1 | no | — |
| 531 | #101 | — | 2 | 1 | no | — |
| 532 | #101 | — | 2 | 2 | no | — |
| 533 | #101 | — | 2 | 2 | no | — |
| 534 | #101 | D4×C53 | 1 | 2 | yes | complemented |
| 535 | #100 | — | 2 | 1 | no | — |
| 536 | #100 | — | 2 | 1 | no | — |
| 537 | #100 | — | 2 | 2 | no | — |
| 538 | #100 | — | 2 | 2 | no | — |
| 539 | #100 | D4×C53 | 1 | 2 | yes | complemented |
| 540 | #99 | — | 2 | 2 | no | — |
| 541 | #97 | — | 2 | 1 | no | — |
| 542 | #97 | — | 2 | 1 | no | — |
| 543 | C4×C8 | — | 2 | 1 | no | — |
| 544 | C4×C8 | — | 2 | 1 | no | — |
| 545 | C24 | — | 2 | 1 | no | — |
| 546 | #41 | — | 2 | 1 | no | — |
| 547 | #41 | — | 2 | 1 | no | — |
| 548 | #41 | — | 2 | 1 | no | — |
| 549 | #41 | — | 2 | 1 | no | — |
| 550 | #41 | — | 2 | 1 | no | — |
| 551 | #41 | — | 2 | 1 | no | — |
| 552 | #41 | — | 2 | 1 | no | — |
| 553 | #41 | — | 2 | 1 | no | — |
| 554 | #41 | — | 2 | 1 | no | — |
| 555 | #41 | — | 2 | 1 | no | — |
| 556 | #41 | — | 2 | 1 | no | — |
| 557 | #41 | — | 2 | 1 | no | — |
| 558 | C2×Q8 | — | 2 | 1 | no | — |
| 559 | C2×Q8 | — | 2 | 1 | no | — |
| 560 | C2×Q8 | — | 2 | 1 | no | — |
| 561 | C2×Q8 | — | 2 | 1 | no | — |
| 562 | C2×Q8 | — | 2 | 1 | no | — |
| 563 | C2×Q8 | — | 2 | 1 | no | — |
| 564 | C2×Q8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 565 | C2×Q8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 566 | C2×Q8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 567 | C2×D4 | — | 2 | 1 | no | — |
| 568 | C2×D4 | — | 2 | 1 | no | — |
| 569 | C2×D4 | — | 2 | 1 | no | — |
| 570 | C2×D4 | — | 2 | 1 | no | — |
| 571 | C2×D4 | — | 2 | 1 | no | — |
| 572 | C2×D4 | — | 2 | 1 | no | — |
| 573 | C2×D4 | — | 2 | 1 | no | — |
| 574 | C2×D4 | — | 2 | 1 | no | — |
| 575 | C2×D4 | — | 2 | 1 | no | — |
| 576 | C2×D4 | — | 4 | 2 | no | — |
| 577 | C2×D4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 578 | C2×D4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 579 | C2×D4 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 580 | C22×C4 | — | 2 | 1 | no | — |
| 581 | C22×C4 | — | 2 | 1 | no | — |
| 582 | C22×C4 | — | 2 | 1 | no | — |
| 583 | C22×C4 | — | 2 | 1 | no | — |
| 584 | C22×C4 | C24×C53 | 1 | 1 | yes | characteristic |
| 585 | Q16 | — | 2 | 1 | no | — |
| 586 | Q16 | — | 2 | 1 | no | — |
| 587 | Q16 | — | 4 | 2 | no | — |
| 588 | Q16 | — | 4 | 2 | no | — |
| 589 | Q16 | — | 4 | 1 | no | — |
| 590 | Q16 | — | 4 | 1 | no | — |
| 591 | SD16 | — | 2 | 1 | no | — |
| 592 | SD16 | — | 2 | 1 | no | — |
| 593 | SD16 | — | 2 | 1 | no | — |
| 594 | SD16 | — | 2 | 1 | no | — |
| 595 | SD16 | — | 4 | 2 | no | — |
| 596 | SD16 | — | 4 | 2 | no | — |
| 597 | SD16 | — | 4 | 2 | no | — |
| 598 | SD16 | — | 4 | 2 | no | — |
| 599 | SD16 | — | 4 | 1 | no | — |
| 600 | SD16 | — | 4 | 1 | no | — |
| 601 | SD16 | — | 4 | 1 | no | — |
| 602 | SD16 | — | 4 | 1 | no | — |
| 603 | SD16 | — | 4 | 1 | no | — |
| 604 | SD16 | — | 4 | 1 | no | — |
| 605 | SD16 | — | 4 | 1 | no | — |
| 606 | SD16 | — | 4 | 1 | no | — |
| 607 | D8 | — | 2 | 1 | no | — |
| 608 | D8 | — | 2 | 1 | no | — |
| 609 | D8 | — | 4 | 2 | no | — |
| 610 | D8 | — | 4 | 2 | no | — |
| 611 | D8 | — | 4 | 1 | no | — |
| 612 | D8 | — | 4 | 1 | no | — |
| 613 | M16 | — | 2 | 1 | no | — |
| 614 | M16 | — | 2 | 1 | no | — |
| 615 | M16 | — | 2 | 1 | no | — |
| 616 | M16 | — | 2 | 1 | no | — |
| 617 | M16 | — | 2 | 1 | no | — |
| 618 | M16 | — | 2 | 1 | no | — |
| 619 | M16 | — | 2 | 1 | no | — |
| 620 | M16 | — | 2 | 1 | no | — |
| 621 | M16 | — | 2 | 1 | no | — |
| 622 | M16 | — | 2 | 1 | no | — |
| 623 | M16 | — | 4 | 2 | no | — |
| 624 | M16 | — | 4 | 2 | no | — |
| 625 | M16 | — | 4 | 1 | no | — |
| 626 | M16 | — | 4 | 1 | no | — |
| 627 | M16 | C2×D4×C53 | 1 | 2 | yes | — |
| 628 | M16 | C2×D4×C53 | 1 | 2 | yes | — |
| 629 | M16 | C2×D4×C53 | 1 | 2 | yes | — |
| 630 | M16 | C2×D4×C53 | 1 | 2 | yes | — |
| 631 | C2×C8 | — | 2 | 1 | no | — |
| 632 | C2×C8 | — | 2 | 1 | no | — |
| 633 | C2×C8 | — | 2 | 1 | no | — |
| 634 | C2×C8 | — | 2 | 1 | no | — |
| 635 | C2×C8 | — | 2 | 1 | no | — |
| 636 | C2×C8 | — | 2 | 1 | no | — |
| 637 | C2×C8 | — | 2 | 1 | no | — |
| 638 | C2×C8 | — | 4 | 2 | no | — |
| 639 | C2×C8 | — | 4 | 2 | no | — |
| 640 | C2×C8 | — | 4 | 1 | no | — |
| 641 | C2×C8 | — | 4 | 1 | no | — |
| 642 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 643 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 644 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 645 | C2×C8 | C2×D4×C53 | 1 | 1 | yes | characteristic |
| 646 | C2×C8 | #41×C53 | 1 | 1 | yes | characteristic |
| 647 | C2×C8 | #41×C53 | 1 | 1 | yes | characteristic |
| 648 | C4⋊C4 | — | 2 | 1 | no | — |
| 649 | C4⋊C4 | — | 2 | 1 | no | — |
| 650 | C4⋊C4 | — | 4 | 2 | no | — |
| 651 | C22⋊C4 | — | 2 | 1 | no | — |
| 652 | C22⋊C4 | — | 4 | 2 | no | — |
| 653 | C22⋊C4 | — | 4 | 2 | no | — |
| 654 | C22⋊C4 | #41×C53 | 1 | 2 | yes | — |
| 655 | C42 | — | 2 | 1 | no | — |
| 656 | C42 | — | 2 | 1 | no | — |
| 657 | C23 | — | 2 | 1 | no | — |
| 658 | C23 | — | 2 | 1 | no | — |
| 659 | C23 | — | 2 | 1 | no | — |
| 660 | C23 | — | 4 | 1 | no | — |
| 661 | C23 | — | 4 | 1 | no | — |
| 662 | C23 | — | 4 | 1 | no | — |
| 663 | C23 | — | 16 | 1 | no | — |
| 664 | C23 | C2×#41×C53 | 1 | 1 | yes | characteristic |
| 665 | Q8 | — | 2 | 1 | no | — |
| 666 | Q8 | — | 2 | 1 | no | — |
| 667 | Q8 | — | 2 | 1 | no | — |
| 668 | Q8 | — | 2 | 1 | no | — |
| 669 | Q8 | — | 2 | 1 | no | — |
| 670 | Q8 | — | 2 | 1 | no | — |
| 671 | Q8 | — | 4 | 1 | no | — |
| 672 | Q8 | — | 4 | 1 | no | — |
| 673 | Q8 | — | 4 | 1 | no | — |
| 674 | Q8 | — | 4 | 1 | no | — |
| 675 | D4 | — | 2 | 1 | no | — |
| 676 | D4 | — | 2 | 1 | no | — |
| 677 | D4 | — | 2 | 1 | no | — |
| 678 | D4 | — | 2 | 1 | no | — |
| 679 | D4 | — | 2 | 1 | no | — |
| 680 | D4 | — | 2 | 1 | no | — |
| 681 | D4 | — | 4 | 1 | no | — |
| 682 | D4 | — | 4 | 1 | no | — |
| 683 | D4 | — | 4 | 1 | no | — |
| 684 | D4 | — | 4 | 1 | no | — |
| 685 | D4 | — | 4 | 1 | no | — |
| 686 | D4 | — | 4 | 1 | no | — |
| 687 | D4 | — | 4 | 1 | no | — |
| 688 | D4 | — | 4 | 1 | no | — |
| 689 | D4 | — | 4 | 1 | no | — |
| 690 | D4 | — | 4 | 1 | no | — |
| 691 | D4 | — | 16 | 2 | no | — |
| 692 | C2×C4 | — | 2 | 1 | no | — |
| 693 | C2×C4 | — | 2 | 2 | no | — |
| 694 | C2×C4 | — | 2 | 1 | no | — |
| 695 | C2×C4 | — | 2 | 1 | no | — |
| 696 | C2×C4 | — | 4 | 1 | no | — |
| 697 | C2×C4 | — | 4 | 1 | no | — |
| 698 | C2×C4 | — | 4 | 1 | no | — |
| 699 | C2×C4 | — | 4 | 1 | no | — |
| 700 | C2×C4 | — | 4 | 1 | no | — |
| 701 | C2×C4 | — | 4 | 1 | no | — |
| 702 | C2×C4 | — | 4 | 1 | no | — |
| 703 | C2×C4 | — | 4 | 1 | no | — |
| 704 | C2×C4 | — | 4 | 1 | no | — |
| 705 | C2×C4 | — | 4 | 1 | no | — |
| 706 | C2×C4 | C22×D4×C53 | 1 | 1 | yes | characteristic |
| 707 | C2×C4 | C22×D4×C53 | 1 | 1 | yes | characteristic |
| 708 | C2×C4 | C22×D4×C53 | 1 | 1 | yes | characteristic |
| 709 | C2×C4 | C2×#41×C53 | 1 | 1 | yes | characteristic |
| 710 | C2×C4 | H(5,𝔽2)×C53 | 1 | 1 | yes | characteristic |
| 711 | C2×C4 | H(5,𝔽2)×C53 | 1 | 1 | yes | characteristic |
| 712 | C8 | — | 2 | 2 | no | — |
| 713 | C8 | — | 2 | 2 | no | — |
| 714 | C8 | — | 2 | 2 | no | — |
| 715 | C8 | — | 2 | 2 | no | — |
| 716 | C8 | — | 4 | 1 | no | — |
| 717 | C8 | — | 4 | 1 | no | — |
| 718 | C8 | — | 4 | 1 | no | — |
| 719 | C8 | #121×C53 | 1 | 1 | yes | characteristic |
| 720 | C8 | #121×C53 | 1 | 1 | yes | characteristic |
| 721 | C8 | #121×C53 | 1 | 1 | yes | characteristic |
| 722 | C8 | #121×C53 | 1 | 1 | yes | characteristic |
| 723 | C22 | — | 4 | 1 | no | — |
| 724 | C22 | — | 4 | 1 | no | — |
| 725 | C22 | — | 4 | 1 | no | — |
| 726 | C22 | — | 4 | 1 | no | — |
| 727 | C22 | — | 8 | 1 | no | — |
| 728 | C22 | — | 8 | 1 | no | — |
| 729 | C22 | — | 8 | 1 | no | — |
| 730 | C22 | — | 8 | 2 | no | — |
| 731 | C22 | — | 8 | 1 | no | — |
| 732 | C22 | — | 16 | 1 | no | — |
| 733 | C22 | — | 16 | 1 | no | — |
| 734 | C22 | C53×#532 | 1 | 1 | yes | characteristic |
| 735 | C22 | C53×#546 | 1 | 1 | yes | characteristic |
| 736 | C22 | C53×#550 | 1 | 1 | yes | characteristic |
| 737 | C4 | — | 4 | 2 | no | — |
| 738 | C4 | — | 4 | 1 | no | — |
| 739 | C4 | — | 4 | 1 | no | — |
| 740 | C4 | — | 4 | 1 | no | — |
| 741 | C4 | — | 8 | 1 | no | — |
| 742 | C4 | — | 8 | 1 | no | — |
| 743 | C4 | C2×#121×C53 | 1 | 1 | yes | characteristic |
| 744 | C4 | C53×#540 | 1 | 1 | yes | characteristic |
| 745 | C4 | D42×C53 | 1 | 1 | yes | characteristic |
| 746 | C4 | D42×C53 | 1 | 1 | yes | characteristic |
| 747 | C2 | — | 2 | 1 | no | — |
| 748 | C2 | — | 2 | 1 | no | — |
| 749 | C2 | — | 2 | 1 | no | — |
| 750 | C2 | — | 8 | 1 | no | — |
| 751 | C2 | — | 8 | 1 | no | — |
| 752 | C2 | — | 8 | 1 | no | — |
| 753 | C2 | — | 16 | 1 | no | — |
| 754 | C2 | C53×#2428 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta