| 1 | #3097×C131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #3042×C131 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #2949×C131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #2947×C131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #2064×C131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #2019×C131 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #2013×C131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #2005×C131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #1977×C131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #1930×C131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #1929×C131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #1922×C131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #1886×C131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #1883×C131 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | #1856×C131 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×#137×C131 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×AGL(1,ℤ/8)×C131 | C22 | 1 | 1 | yes | characteristic |
| 18 | C22×SD16×C131 | C22 | 1 | 1 | yes | characteristic |
| 19 | C22×SD16×C131 | C22 | 1 | 1 | yes | characteristic |
| 20 | #536×C131 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×C4⋊Q8×C131 | C22 | 1 | 1 | yes | characteristic |
| 22 | #520×C131 | C22 | 1 | 1 | yes | characteristic |
| 23 | #519×C131 | C22 | 1 | 1 | yes | characteristic |
| 24 | #518×C131 | C22 | 1 | 1 | yes | characteristic |
| 25 | #485×C131 | — | 2 | 1 | no | — |
| 26 | #485×C131 | — | 2 | 1 | no | — |
| 27 | #484×C131 | — | 2 | 1 | no | — |
| 28 | #483×C131 | — | 2 | 1 | no | — |
| 29 | #463×C131 | — | 2 | 1 | no | — |
| 30 | #463×C131 | — | 2 | 1 | no | — |
| 31 | #461×C131 | — | 2 | 1 | no | — |
| 32 | #461×C131 | — | 2 | 1 | no | — |
| 33 | #441×C131 | — | 2 | 1 | no | — |
| 34 | #440×C131 | — | 2 | 1 | no | — |
| 35 | #440×C131 | — | 2 | 1 | no | — |
| 36 | #440×C131 | — | 2 | 1 | no | — |
| 37 | C4×Q16×C131 | — | 2 | 1 | no | — |
| 38 | C4×SD16×C131 | — | 2 | 1 | no | — |
| 39 | C4×SD16×C131 | — | 2 | 1 | no | — |
| 40 | C4×SD16×C131 | — | 2 | 1 | no | — |
| 41 | C2×#108×C131 | C22 | 1 | 1 | yes | characteristic |
| 42 | #428×C131 | C22 | 1 | 1 | yes | characteristic |
| 43 | #428×C131 | C22 | 1 | 1 | yes | characteristic |
| 44 | #427×C131 | C22 | 1 | 1 | yes | characteristic |
| 45 | #424×C131 | C22 | 1 | 1 | yes | characteristic |
| 46 | C2×#104×C131 | C22 | 1 | 1 | yes | characteristic |
| 47 | #419×C131 | C22 | 1 | 1 | yes | characteristic |
| 48 | #419×C131 | C22 | 1 | 1 | yes | characteristic |
| 49 | #419×C131 | C22 | 1 | 1 | yes | characteristic |
| 50 | #418×C131 | C22 | 1 | 1 | yes | characteristic |
| 51 | #416×C131 | C22 | 1 | 1 | yes | characteristic |
| 52 | C2×#103×C131 | C22 | 1 | 1 | yes | characteristic |
| 53 | C2×#103×C131 | C22 | 1 | 1 | yes | characteristic |
| 54 | C2×#101×C131 | C22 | 1 | 1 | yes | characteristic |
| 55 | C2×#101×C131 | C22 | 1 | 1 | yes | characteristic |
| 56 | C2×#100×C131 | C22 | 1 | 1 | yes | characteristic |
| 57 | #408×C131 | C22 | 1 | 1 | yes | characteristic |
| 58 | #405×C131 | C22 | 1 | 1 | yes | characteristic |
| 59 | #405×C131 | C22 | 1 | 1 | yes | characteristic |
| 60 | #390×C131 | C22 | 1 | 1 | yes | characteristic |
| 61 | #343×C131 | C22 | 1 | 1 | yes | characteristic |
| 62 | #341×C131 | C22 | 1 | 1 | yes | characteristic |
| 63 | #339×C131 | C22 | 1 | 1 | yes | characteristic |
| 64 | #339×C131 | C22 | 1 | 1 | yes | characteristic |
| 65 | #339×C131 | C22 | 1 | 1 | yes | characteristic |
| 66 | #336×C131 | C22 | 1 | 1 | yes | characteristic |
| 67 | C2×#41×C131 | C23 | 1 | 1 | yes | characteristic |
| 68 | C22×Q8×C131 | C23 | 1 | 1 | yes | characteristic |
| 69 | C22×Q8×C131 | C23 | 1 | 1 | yes | characteristic |
| 70 | C22×D4×C131 | C23 | 1 | 1 | yes | characteristic |
| 71 | #137×C131 | — | 2 | 2 | no | — |
| 72 | #137×C131 | — | 2 | 2 | no | — |
| 73 | AGL(1,ℤ/8)×C131 | — | 2 | 2 | no | — |
| 74 | AGL(1,ℤ/8)×C131 | — | 4 | 1 | no | — |
| 75 | C2×Q16×C131 | — | 2 | 1 | no | — |
| 76 | C2×SD16×C131 | — | 2 | 2 | no | — |
| 77 | C2×SD16×C131 | — | 2 | 1 | no | — |
| 78 | C2×SD16×C131 | — | 2 | 2 | no | — |
| 79 | C2×SD16×C131 | — | 2 | 1 | no | — |
| 80 | C2×SD16×C131 | — | 2 | 2 | no | — |
| 81 | C2×SD16×C131 | — | 2 | 1 | no | — |
| 82 | C2×SD16×C131 | — | 2 | 1 | no | — |
| 83 | C2×SD16×C131 | — | 2 | 1 | no | — |
| 84 | C2×SD16×C131 | — | 2 | 1 | no | — |
| 85 | C2×SD16×C131 | — | 4 | 1 | no | — |
| 86 | C2×D8×C131 | — | 2 | 1 | no | — |
| 87 | C2×M16×C131 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×M16×C131 | C23 | 1 | 1 | yes | characteristic |
| 89 | C2×M16×C131 | C23 | 1 | 1 | yes | characteristic |
| 90 | C2×M16×C131 | C23 | 1 | 1 | yes | characteristic |
| 91 | C22×C8×C131 | C23 | 1 | 1 | yes | characteristic |
| 92 | C22×C8×C131 | C23 | 1 | 1 | yes | characteristic |
| 93 | C4⋊Q8×C131 | — | 2 | 1 | no | — |
| 94 | C4⋊Q8×C131 | — | 2 | 2 | no | — |
| 95 | C4⋊Q8×C131 | — | 4 | 1 | no | — |
| 96 | #124×C131 | — | 2 | 1 | no | — |
| 97 | #123×C131 | — | 4 | 1 | no | — |
| 98 | C22⋊Q8×C131 | — | 2 | 1 | no | — |
| 99 | C22⋊Q8×C131 | — | 2 | 1 | no | — |
| 100 | C4×Q8×C131 | — | 2 | 1 | no | — |
| 101 | C4×Q8×C131 | — | 2 | 1 | no | — |
| 102 | C4×Q8×C131 | — | 2 | 1 | no | — |
| 103 | C4×Q8×C131 | — | 2 | 1 | no | — |
| 104 | C4×Q8×C131 | — | 2 | 1 | no | — |
| 105 | C4×D4×C131 | — | 2 | 1 | no | — |
| 106 | C4×D4×C131 | — | 2 | 1 | no | — |
| 107 | C4×D4×C131 | — | 2 | 1 | no | — |
| 108 | C4×D4×C131 | — | 2 | 1 | no | — |
| 109 | C4×D4×C131 | — | 2 | 1 | no | — |
| 110 | C4×D4×C131 | — | 4 | 1 | no | — |
| 111 | #117×C131 | — | 2 | 1 | no | — |
| 112 | #117×C131 | — | 4 | 1 | no | — |
| 113 | #117×C131 | C23 | 1 | 1 | yes | characteristic |
| 114 | #117×C131 | C23 | 1 | 1 | yes | characteristic |
| 115 | #117×C131 | C23 | 1 | 1 | yes | characteristic |
| 116 | C2×C4⋊C4×C131 | — | 2 | 1 | no | — |
| 117 | C2×C4⋊C4×C131 | — | 4 | 1 | no | — |
| 118 | C2×C4⋊C4×C131 | C23 | 1 | 1 | yes | characteristic |
| 119 | C2×C22⋊C4×C131 | — | 4 | 1 | no | — |
| 120 | C2×C22⋊C4×C131 | — | 4 | 1 | no | — |
| 121 | C2×C42×C131 | C23 | 1 | 1 | yes | characteristic |
| 122 | #108×C131 | — | 4 | 1 | no | — |
| 123 | #107×C131 | — | 2 | 1 | no | — |
| 124 | #107×C131 | — | 2 | 1 | no | — |
| 125 | #107×C131 | D4 | 1 | 1 | yes | characteristic |
| 126 | #107×C131 | D4 | 1 | 1 | yes | characteristic |
| 127 | #106×C131 | — | 2 | 1 | no | — |
| 128 | #106×C131 | — | 2 | 1 | no | — |
| 129 | #106×C131 | D4 | 1 | 1 | yes | characteristic |
| 130 | #106×C131 | D4 | 1 | 1 | yes | characteristic |
| 131 | C4⋊C8×C131 | — | 2 | 1 | no | — |
| 132 | C4⋊C8×C131 | — | 2 | 1 | no | — |
| 133 | #104×C131 | — | 4 | 1 | no | — |
| 134 | #103×C131 | — | 2 | 1 | no | — |
| 135 | #103×C131 | — | 2 | 1 | no | — |
| 136 | #103×C131 | — | 2 | 1 | no | — |
| 137 | #103×C131 | — | 2 | 1 | no | — |
| 138 | #103×C131 | — | 2 | 1 | no | — |
| 139 | #103×C131 | — | 2 | 1 | no | — |
| 140 | #103×C131 | — | 2 | 1 | no | — |
| 141 | #103×C131 | — | 2 | 1 | no | — |
| 142 | #103×C131 | — | 2 | 1 | no | — |
| 143 | #103×C131 | — | 2 | 1 | no | — |
| 144 | #103×C131 | D4 | 1 | 1 | yes | characteristic |
| 145 | #103×C131 | D4 | 1 | 1 | yes | characteristic |
| 146 | #102×C131 | — | 2 | 1 | no | — |
| 147 | #102×C131 | — | 2 | 1 | no | — |
| 148 | #102×C131 | D4 | 1 | 1 | yes | characteristic |
| 149 | #102×C131 | D4 | 1 | 1 | yes | characteristic |
| 150 | #101×C131 | — | 2 | 2 | no | — |
| 151 | #101×C131 | — | 4 | 1 | no | — |
| 152 | #100×C131 | — | 2 | 2 | no | — |
| 153 | C22⋊C8×C131 | — | 2 | 1 | no | — |
| 154 | C22⋊C8×C131 | — | 2 | 1 | no | — |
| 155 | #97×C131 | — | 2 | 1 | no | — |
| 156 | #97×C131 | — | 2 | 1 | no | — |
| 157 | C4×C8×C131 | — | 2 | 1 | no | — |
| 158 | C4×C8×C131 | — | 2 | 1 | no | — |
| 159 | C24×C131 | — | 2 | 1 | no | — |
| 160 | #41×C131 | — | 2 | 1 | no | — |
| 161 | #41×C131 | — | 2 | 1 | no | — |
| 162 | #41×C131 | — | 2 | 1 | no | — |
| 163 | #41×C131 | — | 2 | 1 | no | — |
| 164 | C2×Q8×C131 | — | 2 | 1 | no | — |
| 165 | C2×Q8×C131 | — | 2 | 1 | no | — |
| 166 | C2×Q8×C131 | — | 2 | 1 | no | — |
| 167 | C2×Q8×C131 | — | 2 | 1 | no | — |
| 168 | C2×Q8×C131 | — | 2 | 1 | no | — |
| 169 | C2×Q8×C131 | — | 2 | 1 | no | — |
| 170 | C2×Q8×C131 | — | 2 | 1 | no | — |
| 171 | C2×Q8×C131 | — | 2 | 1 | no | — |
| 172 | C2×Q8×C131 | — | 2 | 1 | no | — |
| 173 | C2×Q8×C131 | — | 2 | 1 | no | — |
| 174 | C2×Q8×C131 | — | 2 | 1 | no | — |
| 175 | C2×Q8×C131 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C2×Q8×C131 | #41 | 1 | 2 | yes | — |
| 177 | C2×D4×C131 | — | 2 | 1 | no | — |
| 178 | C2×D4×C131 | — | 2 | 1 | no | — |
| 179 | C2×D4×C131 | — | 2 | 1 | no | — |
| 180 | C2×D4×C131 | — | 2 | 1 | no | — |
| 181 | C2×D4×C131 | — | 2 | 1 | no | — |
| 182 | C2×D4×C131 | — | 2 | 1 | no | — |
| 183 | C2×D4×C131 | C2×D4 | 1 | 1 | yes | characteristic |
| 184 | C2×D4×C131 | #41 | 1 | 2 | yes | — |
| 185 | C22×C4×C131 | — | 2 | 1 | no | — |
| 186 | C22×C4×C131 | — | 2 | 1 | no | — |
| 187 | C22×C4×C131 | — | 2 | 1 | no | — |
| 188 | C22×C4×C131 | — | 2 | 1 | no | — |
| 189 | C22×C4×C131 | — | 2 | 1 | no | — |
| 190 | C22×C4×C131 | — | 4 | 1 | no | — |
| 191 | C22×C4×C131 | — | 4 | 1 | no | — |
| 192 | C22×C4×C131 | — | 4 | 1 | no | — |
| 193 | C22×C4×C131 | C24 | 1 | 1 | yes | characteristic |
| 194 | Q16×C131 | — | 2 | 4 | no | — |
| 195 | SD16×C131 | — | 2 | 4 | no | — |
| 196 | SD16×C131 | — | 2 | 4 | no | — |
| 197 | SD16×C131 | — | 2 | 4 | no | — |
| 198 | SD16×C131 | — | 4 | 2 | no | — |
| 199 | SD16×C131 | — | 4 | 2 | no | — |
| 200 | SD16×C131 | — | 4 | 2 | no | — |
| 201 | D8×C131 | — | 4 | 2 | no | — |
| 202 | M16×C131 | — | 2 | 1 | no | — |
| 203 | M16×C131 | — | 2 | 1 | no | — |
| 204 | M16×C131 | — | 2 | 1 | no | — |
| 205 | M16×C131 | — | 2 | 1 | no | — |
| 206 | M16×C131 | — | 2 | 1 | no | — |
| 207 | M16×C131 | — | 2 | 1 | no | — |
| 208 | M16×C131 | — | 2 | 1 | no | — |
| 209 | M16×C131 | #41 | 1 | 2 | yes | — |
| 210 | C2×C8×C131 | — | 2 | 1 | no | — |
| 211 | C2×C8×C131 | — | 2 | 1 | no | — |
| 212 | C2×C8×C131 | — | 2 | 1 | no | — |
| 213 | C2×C8×C131 | — | 2 | 1 | no | — |
| 214 | C2×C8×C131 | — | 2 | 1 | no | — |
| 215 | C2×C8×C131 | — | 2 | 1 | no | — |
| 216 | C2×C8×C131 | — | 2 | 1 | no | — |
| 217 | C2×C8×C131 | — | 2 | 1 | no | — |
| 218 | C2×C8×C131 | C2×D4 | 1 | 1 | yes | characteristic |
| 219 | C2×C8×C131 | C2×D4 | 1 | 1 | yes | characteristic |
| 220 | C2×C8×C131 | C2×D4 | 1 | 1 | yes | characteristic |
| 221 | C2×C8×C131 | C2×D4 | 1 | 1 | yes | characteristic |
| 222 | C4⋊C4×C131 | — | 2 | 1 | no | — |
| 223 | C4⋊C4×C131 | — | 2 | 1 | no | — |
| 224 | C4⋊C4×C131 | — | 4 | 1 | no | — |
| 225 | C4⋊C4×C131 | — | 4 | 1 | no | — |
| 226 | C4⋊C4×C131 | — | 4 | 1 | no | — |
| 227 | C4⋊C4×C131 | — | 4 | 1 | no | — |
| 228 | C4⋊C4×C131 | — | 4 | 1 | no | — |
| 229 | C4⋊C4×C131 | — | 4 | 4 | no | — |
| 230 | C4⋊C4×C131 | C2×D4 | 1 | 1 | yes | characteristic |
| 231 | C4⋊C4×C131 | C2×D4 | 1 | 1 | yes | characteristic |
| 232 | C4⋊C4×C131 | C2×D4 | 1 | 1 | yes | characteristic |
| 233 | C4⋊C4×C131 | C2×D4 | 1 | 1 | yes | characteristic |
| 234 | C4⋊C4×C131 | C2×D4 | 1 | 1 | yes | characteristic |
| 235 | C4⋊C4×C131 | C2×D4 | 1 | 1 | yes | characteristic |
| 236 | C22⋊C4×C131 | — | 2 | 1 | no | — |
| 237 | C22⋊C4×C131 | — | 2 | 1 | no | — |
| 238 | C22⋊C4×C131 | — | 2 | 1 | no | — |
| 239 | C22⋊C4×C131 | — | 4 | 1 | no | — |
| 240 | C22⋊C4×C131 | — | 4 | 1 | no | — |
| 241 | C22⋊C4×C131 | — | 4 | 1 | no | — |
| 242 | C22⋊C4×C131 | — | 4 | 1 | no | — |
| 243 | C22⋊C4×C131 | — | 4 | 1 | no | — |
| 244 | C22⋊C4×C131 | — | 8 | 2 | no | — |
| 245 | C42×C131 | — | 2 | 1 | no | — |
| 246 | C42×C131 | — | 2 | 1 | no | — |
| 247 | C42×C131 | — | 2 | 1 | no | — |
| 248 | C42×C131 | — | 2 | 1 | no | — |
| 249 | C42×C131 | — | 2 | 1 | no | — |
| 250 | C42×C131 | — | 4 | 1 | no | — |
| 251 | C42×C131 | — | 4 | 1 | no | — |
| 252 | C42×C131 | — | 4 | 1 | no | — |
| 253 | C23×C131 | — | 2 | 1 | no | — |
| 254 | C23×C131 | — | 2 | 2 | no | — |
| 255 | C23×C131 | — | 4 | 1 | no | — |
| 256 | C23×C131 | — | 4 | 1 | no | — |
| 257 | C23×C131 | — | 8 | 1 | no | — |
| 258 | C23×C131 | — | 8 | 1 | no | — |
| 259 | C23×C131 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 260 | Q8×C131 | — | 2 | 2 | no | — |
| 261 | Q8×C131 | — | 2 | 2 | no | — |
| 262 | Q8×C131 | — | 2 | 1 | no | — |
| 263 | Q8×C131 | — | 2 | 1 | no | — |
| 264 | Q8×C131 | — | 4 | 1 | no | — |
| 265 | Q8×C131 | — | 4 | 1 | no | — |
| 266 | Q8×C131 | — | 4 | 1 | no | — |
| 267 | Q8×C131 | — | 4 | 1 | no | — |
| 268 | Q8×C131 | — | 4 | 1 | no | — |
| 269 | Q8×C131 | — | 4 | 1 | no | — |
| 270 | D4×C131 | — | 2 | 2 | no | — |
| 271 | D4×C131 | — | 2 | 1 | no | — |
| 272 | D4×C131 | — | 2 | 1 | no | — |
| 273 | D4×C131 | — | 2 | 2 | no | — |
| 274 | D4×C131 | — | 4 | 1 | no | — |
| 275 | D4×C131 | — | 4 | 1 | no | — |
| 276 | D4×C131 | — | 4 | 1 | no | — |
| 277 | D4×C131 | — | 4 | 1 | no | — |
| 278 | C2×C4×C131 | — | 2 | 2 | no | — |
| 279 | C2×C4×C131 | — | 2 | 2 | no | — |
| 280 | C2×C4×C131 | — | 2 | 1 | no | — |
| 281 | C2×C4×C131 | — | 2 | 1 | no | — |
| 282 | C2×C4×C131 | — | 2 | 1 | no | — |
| 283 | C2×C4×C131 | — | 2 | 1 | no | — |
| 284 | C2×C4×C131 | — | 2 | 1 | no | — |
| 285 | C2×C4×C131 | — | 2 | 1 | no | — |
| 286 | C2×C4×C131 | — | 2 | 1 | no | — |
| 287 | C2×C4×C131 | — | 4 | 1 | no | — |
| 288 | C2×C4×C131 | — | 4 | 1 | no | — |
| 289 | C2×C4×C131 | — | 4 | 1 | no | — |
| 290 | C2×C4×C131 | — | 4 | 1 | no | — |
| 291 | C2×C4×C131 | — | 4 | 1 | no | — |
| 292 | C2×C4×C131 | — | 4 | 1 | no | — |
| 293 | C2×C4×C131 | — | 4 | 1 | no | — |
| 294 | C2×C4×C131 | — | 4 | 1 | no | — |
| 295 | C2×C4×C131 | — | 4 | 1 | no | — |
| 296 | C2×C4×C131 | — | 4 | 1 | no | — |
| 297 | C2×C4×C131 | — | 8 | 1 | no | — |
| 298 | C2×C4×C131 | — | 16 | 1 | no | — |
| 299 | C2×C4×C131 | — | 16 | 1 | no | — |
| 300 | C2×C4×C131 | — | 16 | 1 | no | — |
| 301 | C2×C4×C131 | C22×D4 | 1 | 1 | yes | characteristic |
| 302 | C2×C4×C131 | C22×D4 | 1 | 1 | yes | characteristic |
| 303 | C2×C4×C131 | C2×#41 | 1 | 1 | yes | characteristic |
| 304 | C2×C4×C131 | C2×#41 | 1 | 1 | yes | characteristic |
| 305 | C2×C4×C131 | C2×#41 | 1 | 1 | yes | characteristic |
| 306 | C2×C4×C131 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 307 | C8×C131 | — | 2 | 1 | no | — |
| 308 | C8×C131 | — | 2 | 1 | no | — |
| 309 | C8×C131 | — | 2 | 2 | no | — |
| 310 | C8×C131 | — | 2 | 1 | no | — |
| 311 | C8×C131 | — | 2 | 1 | no | — |
| 312 | C8×C131 | — | 4 | 1 | no | — |
| 313 | C8×C131 | — | 4 | 1 | no | — |
| 314 | C8×C131 | — | 4 | 1 | no | — |
| 315 | C22×C131 | — | 2 | 1 | no | — |
| 316 | C22×C131 | — | 2 | 1 | no | — |
| 317 | C22×C131 | — | 4 | 1 | no | — |
| 318 | C22×C131 | — | 4 | 2 | no | — |
| 319 | C22×C131 | — | 4 | 1 | no | — |
| 320 | C22×C131 | — | 4 | 1 | no | — |
| 321 | C22×C131 | — | 8 | 2 | no | — |
| 322 | C22×C131 | — | 8 | 1 | no | — |
| 323 | C22×C131 | — | 8 | 1 | no | — |
| 324 | C22×C131 | — | 16 | 1 | no | — |
| 325 | C22×C131 | #538 | 1 | 1 | yes | characteristic |
| 326 | C22×C131 | D42 | 1 | 1 | yes | characteristic |
| 327 | C22×C131 | #553 | 1 | 1 | yes | characteristic |
| 328 | C4×C131 | — | 4 | 2 | no | — |
| 329 | C4×C131 | — | 4 | 1 | no | — |
| 330 | C4×C131 | — | 4 | 2 | no | — |
| 331 | C4×C131 | — | 4 | 1 | no | — |
| 332 | C4×C131 | — | 4 | 1 | no | — |
| 333 | C4×C131 | — | 4 | 1 | no | — |
| 334 | C4×C131 | — | 4 | 1 | no | — |
| 335 | C4×C131 | — | 4 | 1 | no | — |
| 336 | C4×C131 | — | 4 | 1 | no | — |
| 337 | C4×C131 | — | 8 | 1 | no | — |
| 338 | C4×C131 | — | 8 | 1 | no | — |
| 339 | C4×C131 | #525 | 1 | 1 | yes | characteristic |
| 340 | C4×C131 | #525 | 1 | 1 | yes | characteristic |
| 341 | C4×C131 | #546 | 1 | 1 | yes | characteristic |
| 342 | C4×C131 | #550 | 1 | 1 | yes | characteristic |
| 343 | C2×C131 | — | 2 | 1 | no | — |
| 344 | C2×C131 | — | 2 | 1 | no | — |
| 345 | C2×C131 | — | 8 | 1 | no | — |
| 346 | C2×C131 | — | 8 | 2 | no | — |
| 347 | C2×C131 | #2456 | 1 | 1 | yes | characteristic |
| 348 | C2×C131 | #3289 | 1 | 1 | yes | characteristic |
| 349 | C2×C131 | #3291 | 1 | 1 | yes | characteristic |
| 350 | #26654 | C131 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 351 | C131 | #26654 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 352 | #3097 | C2×C131 | 1 | 1 | yes | characteristic, complemented |
| 353 | #3042 | C2×C131 | 1 | 1 | yes | characteristic |
| 354 | #2949 | C2×C131 | 1 | 1 | yes | characteristic, complemented |
| 355 | #2947 | C2×C131 | 1 | 1 | yes | characteristic, complemented |
| 356 | #2064 | C2×C131 | 1 | 1 | yes | characteristic, complemented |
| 357 | #2019 | C2×C131 | 1 | 1 | yes | characteristic |
| 358 | #2013 | C2×C131 | 1 | 1 | yes | characteristic, complemented |
| 359 | #2005 | C2×C131 | 1 | 1 | yes | characteristic, complemented |
| 360 | #1977 | C2×C131 | 1 | 1 | yes | characteristic, complemented |
| 361 | #1930 | C2×C131 | 1 | 1 | yes | characteristic, complemented |
| 362 | #1929 | C2×C131 | 1 | 1 | yes | characteristic, complemented |
| 363 | #1922 | C2×C131 | 1 | 1 | yes | characteristic, complemented |
| 364 | #1886 | C2×C131 | 1 | 1 | yes | characteristic, complemented |
| 365 | #1883 | C2×C131 | 1 | 1 | yes | characteristic |
| 366 | #1856 | C2×C131 | 1 | 1 | yes | characteristic, complemented |
| 367 | C2×#137 | C22×C131 | 1 | 1 | yes | characteristic |
| 368 | C2×AGL(1,ℤ/8) | C22×C131 | 1 | 1 | yes | characteristic |
| 369 | C22×SD16 | C22×C131 | 1 | 1 | yes | characteristic |
| 370 | C22×SD16 | C22×C131 | 1 | 1 | yes | characteristic |
| 371 | #536 | C22×C131 | 1 | 1 | yes | characteristic |
| 372 | C2×C4⋊Q8 | C22×C131 | 1 | 1 | yes | characteristic |
| 373 | #520 | C22×C131 | 1 | 1 | yes | characteristic |
| 374 | #519 | C22×C131 | 1 | 1 | yes | characteristic |
| 375 | #518 | C22×C131 | 1 | 1 | yes | characteristic |
| 376 | #485 | — | 2 | 1 | no | — |
| 377 | #485 | — | 2 | 1 | no | — |
| 378 | #484 | — | 2 | 1 | no | — |
| 379 | #483 | — | 2 | 1 | no | — |
| 380 | #463 | — | 2 | 1 | no | — |
| 381 | #463 | — | 2 | 1 | no | — |
| 382 | #461 | — | 2 | 1 | no | — |
| 383 | #461 | — | 2 | 1 | no | — |
| 384 | #441 | — | 2 | 1 | no | — |
| 385 | #440 | — | 2 | 1 | no | — |
| 386 | #440 | — | 2 | 1 | no | — |
| 387 | #440 | — | 2 | 1 | no | — |
| 388 | C4×Q16 | — | 2 | 1 | no | — |
| 389 | C4×SD16 | — | 2 | 1 | no | — |
| 390 | C4×SD16 | — | 2 | 1 | no | — |
| 391 | C4×SD16 | — | 2 | 1 | no | — |
| 392 | C2×#108 | C22×C131 | 1 | 1 | yes | characteristic |
| 393 | #428 | C22×C131 | 1 | 1 | yes | characteristic |
| 394 | #428 | C22×C131 | 1 | 1 | yes | characteristic |
| 395 | #427 | C22×C131 | 1 | 1 | yes | characteristic |
| 396 | #424 | C22×C131 | 1 | 1 | yes | characteristic |
| 397 | C2×#104 | C22×C131 | 1 | 1 | yes | characteristic |
| 398 | #419 | C22×C131 | 1 | 1 | yes | characteristic |
| 399 | #419 | C22×C131 | 1 | 1 | yes | characteristic |
| 400 | #419 | C22×C131 | 1 | 1 | yes | characteristic |
| 401 | #418 | C22×C131 | 1 | 1 | yes | characteristic |
| 402 | #416 | C22×C131 | 1 | 1 | yes | characteristic |
| 403 | C2×#103 | C22×C131 | 1 | 1 | yes | characteristic |
| 404 | C2×#103 | C22×C131 | 1 | 1 | yes | characteristic |
| 405 | C2×#101 | C22×C131 | 1 | 1 | yes | characteristic |
| 406 | C2×#101 | C22×C131 | 1 | 1 | yes | characteristic |
| 407 | C2×#100 | C22×C131 | 1 | 1 | yes | characteristic |
| 408 | #408 | C22×C131 | 1 | 1 | yes | characteristic |
| 409 | #405 | C22×C131 | 1 | 1 | yes | characteristic |
| 410 | #405 | C22×C131 | 1 | 1 | yes | characteristic |
| 411 | #390 | C22×C131 | 1 | 1 | yes | characteristic |
| 412 | #343 | C22×C131 | 1 | 1 | yes | characteristic |
| 413 | #341 | C22×C131 | 1 | 1 | yes | characteristic |
| 414 | #339 | C22×C131 | 1 | 1 | yes | characteristic |
| 415 | #339 | C22×C131 | 1 | 1 | yes | characteristic |
| 416 | #339 | C22×C131 | 1 | 1 | yes | characteristic |
| 417 | #336 | C22×C131 | 1 | 1 | yes | characteristic |
| 418 | C2×#41 | C23×C131 | 1 | 1 | yes | characteristic |
| 419 | C22×Q8 | C23×C131 | 1 | 1 | yes | characteristic |
| 420 | C22×Q8 | C23×C131 | 1 | 1 | yes | characteristic |
| 421 | C22×D4 | C23×C131 | 1 | 1 | yes | characteristic |
| 422 | #137 | — | 2 | 2 | no | — |
| 423 | #137 | — | 2 | 2 | no | — |
| 424 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 425 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 426 | C2×Q16 | — | 2 | 1 | no | — |
| 427 | C2×SD16 | — | 2 | 2 | no | — |
| 428 | C2×SD16 | — | 2 | 1 | no | — |
| 429 | C2×SD16 | — | 2 | 2 | no | — |
| 430 | C2×SD16 | — | 2 | 1 | no | — |
| 431 | C2×SD16 | — | 2 | 2 | no | — |
| 432 | C2×SD16 | — | 2 | 1 | no | — |
| 433 | C2×SD16 | — | 2 | 1 | no | — |
| 434 | C2×SD16 | — | 2 | 1 | no | — |
| 435 | C2×SD16 | — | 2 | 1 | no | — |
| 436 | C2×SD16 | — | 4 | 1 | no | — |
| 437 | C2×D8 | — | 2 | 1 | no | — |
| 438 | C2×M16 | C23×C131 | 1 | 1 | yes | characteristic |
| 439 | C2×M16 | C23×C131 | 1 | 1 | yes | characteristic |
| 440 | C2×M16 | C23×C131 | 1 | 1 | yes | characteristic |
| 441 | C2×M16 | C23×C131 | 1 | 1 | yes | characteristic |
| 442 | C22×C8 | C23×C131 | 1 | 1 | yes | characteristic |
| 443 | C22×C8 | C23×C131 | 1 | 1 | yes | characteristic |
| 444 | C4⋊Q8 | — | 2 | 1 | no | — |
| 445 | C4⋊Q8 | — | 2 | 2 | no | — |
| 446 | C4⋊Q8 | — | 4 | 1 | no | — |
| 447 | #124 | — | 2 | 1 | no | — |
| 448 | #123 | — | 4 | 1 | no | — |
| 449 | C22⋊Q8 | — | 2 | 1 | no | — |
| 450 | C22⋊Q8 | — | 2 | 1 | no | — |
| 451 | C4×Q8 | — | 2 | 1 | no | — |
| 452 | C4×Q8 | — | 2 | 1 | no | — |
| 453 | C4×Q8 | — | 2 | 1 | no | — |
| 454 | C4×Q8 | — | 2 | 1 | no | — |
| 455 | C4×Q8 | — | 2 | 1 | no | — |
| 456 | C4×D4 | — | 2 | 1 | no | — |
| 457 | C4×D4 | — | 2 | 1 | no | — |
| 458 | C4×D4 | — | 2 | 1 | no | — |
| 459 | C4×D4 | — | 2 | 1 | no | — |
| 460 | C4×D4 | — | 2 | 1 | no | — |
| 461 | C4×D4 | — | 4 | 1 | no | — |
| 462 | #117 | — | 2 | 1 | no | — |
| 463 | #117 | — | 4 | 1 | no | — |
| 464 | #117 | C23×C131 | 1 | 1 | yes | characteristic |
| 465 | #117 | C23×C131 | 1 | 1 | yes | characteristic |
| 466 | #117 | C23×C131 | 1 | 1 | yes | characteristic |
| 467 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 468 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 469 | C2×C4⋊C4 | C23×C131 | 1 | 1 | yes | characteristic |
| 470 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 471 | C2×C22⋊C4 | — | 4 | 1 | no | — |
| 472 | C2×C42 | C23×C131 | 1 | 1 | yes | characteristic |
| 473 | #108 | — | 4 | 1 | no | — |
| 474 | #107 | — | 2 | 1 | no | — |
| 475 | #107 | — | 2 | 1 | no | — |
| 476 | #107 | D4×C131 | 1 | 1 | yes | characteristic |
| 477 | #107 | D4×C131 | 1 | 1 | yes | characteristic |
| 478 | #106 | — | 2 | 1 | no | — |
| 479 | #106 | — | 2 | 1 | no | — |
| 480 | #106 | D4×C131 | 1 | 1 | yes | characteristic |
| 481 | #106 | D4×C131 | 1 | 1 | yes | characteristic |
| 482 | C4⋊C8 | — | 2 | 1 | no | — |
| 483 | C4⋊C8 | — | 2 | 1 | no | — |
| 484 | #104 | — | 4 | 1 | no | — |
| 485 | #103 | — | 2 | 1 | no | — |
| 486 | #103 | — | 2 | 1 | no | — |
| 487 | #103 | — | 2 | 1 | no | — |
| 488 | #103 | — | 2 | 1 | no | — |
| 489 | #103 | — | 2 | 1 | no | — |
| 490 | #103 | — | 2 | 1 | no | — |
| 491 | #103 | — | 2 | 1 | no | — |
| 492 | #103 | — | 2 | 1 | no | — |
| 493 | #103 | — | 2 | 1 | no | — |
| 494 | #103 | — | 2 | 1 | no | — |
| 495 | #103 | D4×C131 | 1 | 1 | yes | characteristic |
| 496 | #103 | D4×C131 | 1 | 1 | yes | characteristic |
| 497 | #102 | — | 2 | 1 | no | — |
| 498 | #102 | — | 2 | 1 | no | — |
| 499 | #102 | D4×C131 | 1 | 1 | yes | characteristic |
| 500 | #102 | D4×C131 | 1 | 1 | yes | characteristic |
| 501 | #101 | — | 2 | 2 | no | — |
| 502 | #101 | — | 4 | 1 | no | — |
| 503 | #100 | — | 2 | 2 | no | — |
| 504 | C22⋊C8 | — | 2 | 1 | no | — |
| 505 | C22⋊C8 | — | 2 | 1 | no | — |
| 506 | #97 | — | 2 | 1 | no | — |
| 507 | #97 | — | 2 | 1 | no | — |
| 508 | C4×C8 | — | 2 | 1 | no | — |
| 509 | C4×C8 | — | 2 | 1 | no | — |
| 510 | C24 | — | 2 | 1 | no | — |
| 511 | #41 | — | 2 | 1 | no | — |
| 512 | #41 | — | 2 | 1 | no | — |
| 513 | #41 | — | 2 | 1 | no | — |
| 514 | #41 | — | 2 | 1 | no | — |
| 515 | C2×Q8 | — | 2 | 1 | no | — |
| 516 | C2×Q8 | — | 2 | 1 | no | — |
| 517 | C2×Q8 | — | 2 | 1 | no | — |
| 518 | C2×Q8 | — | 2 | 1 | no | — |
| 519 | C2×Q8 | — | 2 | 1 | no | — |
| 520 | C2×Q8 | — | 2 | 1 | no | — |
| 521 | C2×Q8 | — | 2 | 1 | no | — |
| 522 | C2×Q8 | — | 2 | 1 | no | — |
| 523 | C2×Q8 | — | 2 | 1 | no | — |
| 524 | C2×Q8 | — | 2 | 1 | no | — |
| 525 | C2×Q8 | — | 2 | 1 | no | — |
| 526 | C2×Q8 | C2×D4×C131 | 1 | 1 | yes | characteristic |
| 527 | C2×Q8 | #41×C131 | 1 | 2 | yes | — |
| 528 | C2×D4 | — | 2 | 1 | no | — |
| 529 | C2×D4 | — | 2 | 1 | no | — |
| 530 | C2×D4 | — | 2 | 1 | no | — |
| 531 | C2×D4 | — | 2 | 1 | no | — |
| 532 | C2×D4 | — | 2 | 1 | no | — |
| 533 | C2×D4 | — | 2 | 1 | no | — |
| 534 | C2×D4 | C2×D4×C131 | 1 | 1 | yes | characteristic |
| 535 | C2×D4 | #41×C131 | 1 | 2 | yes | — |
| 536 | C22×C4 | — | 2 | 1 | no | — |
| 537 | C22×C4 | — | 2 | 1 | no | — |
| 538 | C22×C4 | — | 2 | 1 | no | — |
| 539 | C22×C4 | — | 2 | 1 | no | — |
| 540 | C22×C4 | — | 2 | 1 | no | — |
| 541 | C22×C4 | — | 4 | 1 | no | — |
| 542 | C22×C4 | — | 4 | 1 | no | — |
| 543 | C22×C4 | — | 4 | 1 | no | — |
| 544 | C22×C4 | C24×C131 | 1 | 1 | yes | characteristic |
| 545 | Q16 | — | 2 | 4 | no | — |
| 546 | SD16 | — | 2 | 4 | no | — |
| 547 | SD16 | — | 2 | 4 | no | — |
| 548 | SD16 | — | 2 | 4 | no | — |
| 549 | SD16 | — | 4 | 2 | no | — |
| 550 | SD16 | — | 4 | 2 | no | — |
| 551 | SD16 | — | 4 | 2 | no | — |
| 552 | D8 | — | 4 | 2 | no | — |
| 553 | M16 | — | 2 | 1 | no | — |
| 554 | M16 | — | 2 | 1 | no | — |
| 555 | M16 | — | 2 | 1 | no | — |
| 556 | M16 | — | 2 | 1 | no | — |
| 557 | M16 | — | 2 | 1 | no | — |
| 558 | M16 | — | 2 | 1 | no | — |
| 559 | M16 | — | 2 | 1 | no | — |
| 560 | M16 | #41×C131 | 1 | 2 | yes | — |
| 561 | C2×C8 | — | 2 | 1 | no | — |
| 562 | C2×C8 | — | 2 | 1 | no | — |
| 563 | C2×C8 | — | 2 | 1 | no | — |
| 564 | C2×C8 | — | 2 | 1 | no | — |
| 565 | C2×C8 | — | 2 | 1 | no | — |
| 566 | C2×C8 | — | 2 | 1 | no | — |
| 567 | C2×C8 | — | 2 | 1 | no | — |
| 568 | C2×C8 | — | 2 | 1 | no | — |
| 569 | C2×C8 | C2×D4×C131 | 1 | 1 | yes | characteristic |
| 570 | C2×C8 | C2×D4×C131 | 1 | 1 | yes | characteristic |
| 571 | C2×C8 | C2×D4×C131 | 1 | 1 | yes | characteristic |
| 572 | C2×C8 | C2×D4×C131 | 1 | 1 | yes | characteristic |
| 573 | C4⋊C4 | — | 2 | 1 | no | — |
| 574 | C4⋊C4 | — | 2 | 1 | no | — |
| 575 | C4⋊C4 | — | 4 | 1 | no | — |
| 576 | C4⋊C4 | — | 4 | 1 | no | — |
| 577 | C4⋊C4 | — | 4 | 1 | no | — |
| 578 | C4⋊C4 | — | 4 | 1 | no | — |
| 579 | C4⋊C4 | — | 4 | 1 | no | — |
| 580 | C4⋊C4 | — | 4 | 4 | no | — |
| 581 | C4⋊C4 | C2×D4×C131 | 1 | 1 | yes | characteristic |
| 582 | C4⋊C4 | C2×D4×C131 | 1 | 1 | yes | characteristic |
| 583 | C4⋊C4 | C2×D4×C131 | 1 | 1 | yes | characteristic |
| 584 | C4⋊C4 | C2×D4×C131 | 1 | 1 | yes | characteristic |
| 585 | C4⋊C4 | C2×D4×C131 | 1 | 1 | yes | characteristic |
| 586 | C4⋊C4 | C2×D4×C131 | 1 | 1 | yes | characteristic |
| 587 | C22⋊C4 | — | 2 | 1 | no | — |
| 588 | C22⋊C4 | — | 2 | 1 | no | — |
| 589 | C22⋊C4 | — | 2 | 1 | no | — |
| 590 | C22⋊C4 | — | 4 | 1 | no | — |
| 591 | C22⋊C4 | — | 4 | 1 | no | — |
| 592 | C22⋊C4 | — | 4 | 1 | no | — |
| 593 | C22⋊C4 | — | 4 | 1 | no | — |
| 594 | C22⋊C4 | — | 4 | 1 | no | — |
| 595 | C22⋊C4 | — | 8 | 2 | no | — |
| 596 | C42 | — | 2 | 1 | no | — |
| 597 | C42 | — | 2 | 1 | no | — |
| 598 | C42 | — | 2 | 1 | no | — |
| 599 | C42 | — | 2 | 1 | no | — |
| 600 | C42 | — | 2 | 1 | no | — |
| 601 | C42 | — | 4 | 1 | no | — |
| 602 | C42 | — | 4 | 1 | no | — |
| 603 | C42 | — | 4 | 1 | no | — |
| 604 | C23 | — | 2 | 1 | no | — |
| 605 | C23 | — | 2 | 2 | no | — |
| 606 | C23 | — | 4 | 1 | no | — |
| 607 | C23 | — | 4 | 1 | no | — |
| 608 | C23 | — | 8 | 1 | no | — |
| 609 | C23 | — | 8 | 1 | no | — |
| 610 | C23 | H(5,𝔽2)×C131 | 1 | 1 | yes | characteristic |
| 611 | Q8 | — | 2 | 2 | no | — |
| 612 | Q8 | — | 2 | 2 | no | — |
| 613 | Q8 | — | 2 | 1 | no | — |
| 614 | Q8 | — | 2 | 1 | no | — |
| 615 | Q8 | — | 4 | 1 | no | — |
| 616 | Q8 | — | 4 | 1 | no | — |
| 617 | Q8 | — | 4 | 1 | no | — |
| 618 | Q8 | — | 4 | 1 | no | — |
| 619 | Q8 | — | 4 | 1 | no | — |
| 620 | Q8 | — | 4 | 1 | no | — |
| 621 | D4 | — | 2 | 2 | no | — |
| 622 | D4 | — | 2 | 1 | no | — |
| 623 | D4 | — | 2 | 1 | no | — |
| 624 | D4 | — | 2 | 2 | no | — |
| 625 | D4 | — | 4 | 1 | no | — |
| 626 | D4 | — | 4 | 1 | no | — |
| 627 | D4 | — | 4 | 1 | no | — |
| 628 | D4 | — | 4 | 1 | no | — |
| 629 | C2×C4 | — | 2 | 2 | no | — |
| 630 | C2×C4 | — | 2 | 2 | no | — |
| 631 | C2×C4 | — | 2 | 1 | no | — |
| 632 | C2×C4 | — | 2 | 1 | no | — |
| 633 | C2×C4 | — | 2 | 1 | no | — |
| 634 | C2×C4 | — | 2 | 1 | no | — |
| 635 | C2×C4 | — | 2 | 1 | no | — |
| 636 | C2×C4 | — | 2 | 1 | no | — |
| 637 | C2×C4 | — | 2 | 1 | no | — |
| 638 | C2×C4 | — | 4 | 1 | no | — |
| 639 | C2×C4 | — | 4 | 1 | no | — |
| 640 | C2×C4 | — | 4 | 1 | no | — |
| 641 | C2×C4 | — | 4 | 1 | no | — |
| 642 | C2×C4 | — | 4 | 1 | no | — |
| 643 | C2×C4 | — | 4 | 1 | no | — |
| 644 | C2×C4 | — | 4 | 1 | no | — |
| 645 | C2×C4 | — | 4 | 1 | no | — |
| 646 | C2×C4 | — | 4 | 1 | no | — |
| 647 | C2×C4 | — | 4 | 1 | no | — |
| 648 | C2×C4 | — | 8 | 1 | no | — |
| 649 | C2×C4 | — | 16 | 1 | no | — |
| 650 | C2×C4 | — | 16 | 1 | no | — |
| 651 | C2×C4 | — | 16 | 1 | no | — |
| 652 | C2×C4 | C22×D4×C131 | 1 | 1 | yes | characteristic |
| 653 | C2×C4 | C22×D4×C131 | 1 | 1 | yes | characteristic |
| 654 | C2×C4 | C2×#41×C131 | 1 | 1 | yes | characteristic |
| 655 | C2×C4 | C2×#41×C131 | 1 | 1 | yes | characteristic |
| 656 | C2×C4 | C2×#41×C131 | 1 | 1 | yes | characteristic |
| 657 | C2×C4 | H(5,𝔽2)×C131 | 1 | 1 | yes | characteristic |
| 658 | C8 | — | 2 | 1 | no | — |
| 659 | C8 | — | 2 | 1 | no | — |
| 660 | C8 | — | 2 | 2 | no | — |
| 661 | C8 | — | 2 | 1 | no | — |
| 662 | C8 | — | 2 | 1 | no | — |
| 663 | C8 | — | 4 | 1 | no | — |
| 664 | C8 | — | 4 | 1 | no | — |
| 665 | C8 | — | 4 | 1 | no | — |
| 666 | C22 | — | 2 | 1 | no | — |
| 667 | C22 | — | 2 | 1 | no | — |
| 668 | C22 | — | 4 | 1 | no | — |
| 669 | C22 | — | 4 | 1 | no | — |
| 670 | C22 | — | 4 | 1 | no | — |
| 671 | C22 | — | 4 | 2 | no | — |
| 672 | C22 | — | 8 | 2 | no | — |
| 673 | C22 | — | 8 | 1 | no | — |
| 674 | C22 | — | 8 | 1 | no | — |
| 675 | C22 | — | 16 | 1 | no | — |
| 676 | C22 | #538×C131 | 1 | 1 | yes | characteristic |
| 677 | C22 | D42×C131 | 1 | 1 | yes | characteristic |
| 678 | C22 | #553×C131 | 1 | 1 | yes | characteristic |
| 679 | C4 | — | 4 | 2 | no | — |
| 680 | C4 | — | 4 | 1 | no | — |
| 681 | C4 | — | 4 | 1 | no | — |
| 682 | C4 | — | 4 | 1 | no | — |
| 683 | C4 | — | 4 | 1 | no | — |
| 684 | C4 | — | 4 | 1 | no | — |
| 685 | C4 | — | 4 | 1 | no | — |
| 686 | C4 | — | 4 | 1 | no | — |
| 687 | C4 | — | 4 | 2 | no | — |
| 688 | C4 | — | 8 | 1 | no | — |
| 689 | C4 | — | 8 | 1 | no | — |
| 690 | C4 | #525×C131 | 1 | 1 | yes | characteristic |
| 691 | C4 | #525×C131 | 1 | 1 | yes | characteristic |
| 692 | C4 | #546×C131 | 1 | 1 | yes | characteristic |
| 693 | C4 | #550×C131 | 1 | 1 | yes | characteristic |
| 694 | C2 | — | 2 | 1 | no | — |
| 695 | C2 | — | 2 | 1 | no | — |
| 696 | C2 | — | 8 | 1 | no | — |
| 697 | C2 | — | 8 | 2 | no | — |
| 698 | C2 | #2456×C131 | 1 | 1 | yes | characteristic |
| 699 | C2 | #3289×C131 | 1 | 1 | yes | characteristic |
| 700 | C2 | #3291×C131 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta