| 1 | #3093×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#482×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #3055×C137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #2933×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #2090×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #2078×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #2063×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #2051×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #1952×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #1931×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #1907×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #1900×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #1855×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #1815×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | #1742×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×AGL(1,ℤ/8)×C137 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#131×C137 | C22 | 1 | 1 | yes | characteristic |
| 18 | C22×M16×C137 | C22 | 1 | 1 | yes | characteristic |
| 19 | C22×M16×C137 | C22 | 1 | 1 | yes | characteristic |
| 20 | #525×C137 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#121×C137 | C22 | 1 | 1 | yes | characteristic |
| 22 | C2×#117×C137 | C22 | 1 | 1 | yes | characteristic |
| 23 | #485×C137 | — | 2 | 1 | no | — |
| 24 | #485×C137 | — | 2 | 1 | no | — |
| 25 | #482×C137 | — | 2 | 1 | no | — |
| 26 | #482×C137 | — | 2 | 1 | no | — |
| 27 | #482×C137 | — | 2 | 1 | no | — |
| 28 | #482×C137 | — | 2 | 1 | no | — |
| 29 | #482×C137 | — | 2 | 1 | no | — |
| 30 | #482×C137 | — | 2 | 1 | no | — |
| 31 | #469×C137 | — | 2 | 1 | no | — |
| 32 | #468×C137 | — | 2 | 1 | no | — |
| 33 | #466×C137 | — | 2 | 1 | no | — |
| 34 | #465×C137 | — | 2 | 1 | no | — |
| 35 | #436×C137 | — | 2 | 1 | no | — |
| 36 | #435×C137 | — | 2 | 1 | no | — |
| 37 | #435×C137 | — | 2 | 1 | no | — |
| 38 | C8×D4×C137 | — | 2 | 1 | no | — |
| 39 | C2×#108×C137 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#108×C137 | C22 | 1 | 1 | yes | characteristic |
| 41 | #428×C137 | C22 | 1 | 1 | yes | characteristic |
| 42 | #428×C137 | C22 | 1 | 1 | yes | characteristic |
| 43 | #428×C137 | C22 | 1 | 1 | yes | characteristic |
| 44 | C2×#107×C137 | C22 | 1 | 1 | yes | characteristic |
| 45 | C2×#106×C137 | C22 | 1 | 1 | yes | characteristic |
| 46 | #424×C137 | C22 | 1 | 1 | yes | characteristic |
| 47 | #418×C137 | C22 | 1 | 1 | yes | characteristic |
| 48 | #417×C137 | C22 | 1 | 1 | yes | characteristic |
| 49 | #417×C137 | C22 | 1 | 1 | yes | characteristic |
| 50 | #417×C137 | C22 | 1 | 1 | yes | characteristic |
| 51 | C2×#102×C137 | C22 | 1 | 1 | yes | characteristic |
| 52 | C2×#102×C137 | C22 | 1 | 1 | yes | characteristic |
| 53 | C2×#100×C137 | C22 | 1 | 1 | yes | characteristic |
| 54 | C2×#100×C137 | C22 | 1 | 1 | yes | characteristic |
| 55 | #408×C137 | C22 | 1 | 1 | yes | characteristic |
| 56 | #407×C137 | C22 | 1 | 1 | yes | characteristic |
| 57 | C2×C22⋊C8×C137 | C22 | 1 | 1 | yes | characteristic |
| 58 | #405×C137 | C22 | 1 | 1 | yes | characteristic |
| 59 | #343×C137 | C22 | 1 | 1 | yes | characteristic |
| 60 | #343×C137 | C22 | 1 | 1 | yes | characteristic |
| 61 | #343×C137 | C22 | 1 | 1 | yes | characteristic |
| 62 | #343×C137 | C22 | 1 | 1 | yes | characteristic |
| 63 | #343×C137 | C22 | 1 | 1 | yes | characteristic |
| 64 | #343×C137 | C22 | 1 | 1 | yes | characteristic |
| 65 | #341×C137 | C22 | 1 | 1 | yes | characteristic |
| 66 | #341×C137 | C22 | 1 | 1 | yes | characteristic |
| 67 | C2×#41×C137 | C23 | 1 | 1 | yes | characteristic |
| 68 | C22×D4×C137 | — | 2 | 1 | no | — |
| 69 | C22×D4×C137 | C23 | 1 | 1 | yes | characteristic |
| 70 | C23×C4×C137 | C23 | 1 | 1 | yes | characteristic |
| 71 | AGL(1,ℤ/8)×C137 | — | 2 | 2 | no | — |
| 72 | AGL(1,ℤ/8)×C137 | — | 4 | 1 | no | — |
| 73 | C2×SD16×C137 | — | 2 | 1 | no | — |
| 74 | C2×D8×C137 | — | 2 | 1 | no | — |
| 75 | #131×C137 | — | 2 | 2 | no | — |
| 76 | #131×C137 | — | 4 | 1 | no | — |
| 77 | C2×M16×C137 | — | 2 | 1 | no | — |
| 78 | C2×M16×C137 | — | 2 | 1 | no | — |
| 79 | C2×M16×C137 | — | 2 | 1 | no | — |
| 80 | C2×M16×C137 | — | 2 | 2 | no | — |
| 81 | C2×M16×C137 | — | 2 | 2 | no | — |
| 82 | C2×M16×C137 | — | 4 | 1 | no | — |
| 83 | C2×M16×C137 | — | 4 | 1 | no | — |
| 84 | C2×M16×C137 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×M16×C137 | C23 | 1 | 1 | yes | characteristic |
| 86 | C2×M16×C137 | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×M16×C137 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×M16×C137 | C23 | 1 | 1 | yes | characteristic |
| 89 | C2×M16×C137 | C23 | 1 | 1 | yes | characteristic |
| 90 | C22×C8×C137 | — | 2 | 1 | no | — |
| 91 | C22×C8×C137 | — | 2 | 1 | no | — |
| 92 | C22×C8×C137 | — | 2 | 1 | no | — |
| 93 | C22×C8×C137 | C23 | 1 | 1 | yes | characteristic |
| 94 | C22×C8×C137 | C23 | 1 | 1 | yes | characteristic |
| 95 | #123×C137 | — | 2 | 1 | no | — |
| 96 | C22⋊Q8×C137 | D4 | 1 | 1 | yes | characteristic |
| 97 | C22⋊Q8×C137 | D4 | 1 | 1 | yes | characteristic |
| 98 | #121×C137 | — | 2 | 1 | no | — |
| 99 | #121×C137 | — | 2 | 1 | no | — |
| 100 | #121×C137 | — | 2 | 1 | no | — |
| 101 | #121×C137 | — | 2 | 1 | no | — |
| 102 | #121×C137 | D4 | 1 | 1 | yes | characteristic |
| 103 | #121×C137 | D4 | 1 | 1 | yes | characteristic |
| 104 | #120×C137 | — | 2 | 1 | no | — |
| 105 | C4×D4×C137 | — | 2 | 1 | no | — |
| 106 | C4×D4×C137 | — | 2 | 1 | no | — |
| 107 | #117×C137 | — | 2 | 1 | no | — |
| 108 | #117×C137 | — | 2 | 1 | no | — |
| 109 | #117×C137 | — | 2 | 1 | no | — |
| 110 | #117×C137 | — | 2 | 1 | no | — |
| 111 | #117×C137 | C23 | 1 | 1 | yes | characteristic |
| 112 | C2×C4⋊C4×C137 | C23 | 1 | 1 | yes | characteristic |
| 113 | C2×C4⋊C4×C137 | C23 | 1 | 1 | yes | characteristic |
| 114 | C2×C4⋊C4×C137 | C23 | 1 | 1 | yes | characteristic |
| 115 | C2×C22⋊C4×C137 | — | 2 | 1 | no | — |
| 116 | C2×C22⋊C4×C137 | — | 2 | 1 | no | — |
| 117 | C2×C42×C137 | — | 2 | 1 | no | — |
| 118 | #108×C137 | — | 2 | 2 | no | — |
| 119 | #108×C137 | — | 4 | 1 | no | — |
| 120 | #107×C137 | — | 2 | 1 | no | — |
| 121 | #107×C137 | — | 2 | 1 | no | — |
| 122 | #107×C137 | — | 2 | 1 | no | — |
| 123 | #107×C137 | — | 2 | 1 | no | — |
| 124 | #107×C137 | — | 2 | 1 | no | — |
| 125 | #106×C137 | — | 2 | 1 | no | — |
| 126 | #106×C137 | — | 2 | 1 | no | — |
| 127 | #106×C137 | — | 2 | 1 | no | — |
| 128 | #106×C137 | — | 2 | 1 | no | — |
| 129 | #106×C137 | — | 2 | 1 | no | — |
| 130 | C4⋊C8×C137 | — | 2 | 1 | no | — |
| 131 | C4⋊C8×C137 | — | 2 | 1 | no | — |
| 132 | #103×C137 | — | 2 | 1 | no | — |
| 133 | #103×C137 | — | 2 | 1 | no | — |
| 134 | #103×C137 | — | 2 | 1 | no | — |
| 135 | #102×C137 | — | 2 | 1 | no | — |
| 136 | #102×C137 | — | 2 | 1 | no | — |
| 137 | #102×C137 | — | 2 | 1 | no | — |
| 138 | #102×C137 | — | 2 | 1 | no | — |
| 139 | #102×C137 | — | 2 | 1 | no | — |
| 140 | #102×C137 | — | 2 | 1 | no | — |
| 141 | #102×C137 | — | 2 | 1 | no | — |
| 142 | #102×C137 | — | 2 | 1 | no | — |
| 143 | #102×C137 | — | 2 | 1 | no | — |
| 144 | #100×C137 | — | 2 | 2 | no | — |
| 145 | #100×C137 | — | 4 | 1 | no | — |
| 146 | C22⋊C8×C137 | — | 2 | 1 | no | — |
| 147 | C22⋊C8×C137 | — | 2 | 1 | no | — |
| 148 | C22⋊C8×C137 | — | 2 | 1 | no | — |
| 149 | C22⋊C8×C137 | — | 2 | 1 | no | — |
| 150 | C22⋊C8×C137 | D4 | 1 | 1 | yes | characteristic |
| 151 | C22⋊C8×C137 | D4 | 1 | 1 | yes | characteristic |
| 152 | C22⋊C8×C137 | D4 | 1 | 1 | yes | characteristic |
| 153 | C22⋊C8×C137 | D4 | 1 | 1 | yes | characteristic |
| 154 | #97×C137 | — | 2 | 1 | no | — |
| 155 | C4×C8×C137 | — | 2 | 1 | no | — |
| 156 | C24×C137 | — | 2 | 1 | no | — |
| 157 | C24×C137 | #41 | 1 | 1 | yes | characteristic |
| 158 | #41×C137 | — | 2 | 1 | no | — |
| 159 | #41×C137 | — | 2 | 1 | no | — |
| 160 | #41×C137 | — | 2 | 1 | no | — |
| 161 | #41×C137 | — | 2 | 1 | no | — |
| 162 | C2×Q8×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 163 | C2×D4×C137 | — | 2 | 1 | no | — |
| 164 | C2×D4×C137 | — | 2 | 1 | no | — |
| 165 | C2×D4×C137 | — | 2 | 1 | no | — |
| 166 | C2×D4×C137 | — | 2 | 1 | no | — |
| 167 | C2×D4×C137 | — | 2 | 1 | no | — |
| 168 | C2×D4×C137 | — | 2 | 1 | no | — |
| 169 | C2×D4×C137 | — | 2 | 1 | no | — |
| 170 | C2×D4×C137 | — | 2 | 1 | no | — |
| 171 | C2×D4×C137 | — | 2 | 1 | no | — |
| 172 | C2×D4×C137 | — | 4 | 1 | no | — |
| 173 | C2×D4×C137 | — | 4 | 1 | no | — |
| 174 | C2×D4×C137 | — | 8 | 2 | no | — |
| 175 | C2×D4×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C22×C4×C137 | — | 2 | 1 | no | — |
| 177 | C22×C4×C137 | — | 2 | 1 | no | — |
| 178 | C22×C4×C137 | — | 2 | 1 | no | — |
| 179 | C22×C4×C137 | — | 2 | 1 | no | — |
| 180 | C22×C4×C137 | — | 2 | 1 | no | — |
| 181 | C22×C4×C137 | — | 2 | 1 | no | — |
| 182 | C22×C4×C137 | — | 2 | 1 | no | — |
| 183 | C22×C4×C137 | — | 2 | 1 | no | — |
| 184 | C22×C4×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 185 | C22×C4×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 186 | C22×C4×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 187 | C22×C4×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 188 | C22×C4×C137 | #41 | 1 | 1 | yes | characteristic |
| 189 | C22×C4×C137 | C24 | 1 | 1 | yes | characteristic |
| 190 | SD16×C137 | — | 4 | 2 | no | — |
| 191 | D8×C137 | — | 4 | 2 | no | — |
| 192 | M16×C137 | — | 2 | 1 | no | — |
| 193 | M16×C137 | — | 2 | 1 | no | — |
| 194 | M16×C137 | — | 2 | 1 | no | — |
| 195 | M16×C137 | — | 2 | 1 | no | — |
| 196 | M16×C137 | — | 2 | 1 | no | — |
| 197 | M16×C137 | — | 2 | 1 | no | — |
| 198 | M16×C137 | — | 2 | 1 | no | — |
| 199 | M16×C137 | — | 2 | 1 | no | — |
| 200 | M16×C137 | — | 2 | 1 | no | — |
| 201 | M16×C137 | — | 2 | 1 | no | — |
| 202 | M16×C137 | — | 4 | 2 | no | — |
| 203 | M16×C137 | — | 4 | 2 | no | — |
| 204 | M16×C137 | — | 4 | 2 | no | — |
| 205 | M16×C137 | #41 | 1 | 2 | yes | — |
| 206 | M16×C137 | #41 | 1 | 2 | yes | — |
| 207 | C2×C8×C137 | — | 2 | 1 | no | — |
| 208 | C2×C8×C137 | — | 2 | 1 | no | — |
| 209 | C2×C8×C137 | — | 2 | 1 | no | — |
| 210 | C2×C8×C137 | — | 2 | 1 | no | — |
| 211 | C2×C8×C137 | — | 2 | 1 | no | — |
| 212 | C2×C8×C137 | — | 2 | 1 | no | — |
| 213 | C2×C8×C137 | — | 2 | 1 | no | — |
| 214 | C2×C8×C137 | — | 2 | 1 | no | — |
| 215 | C2×C8×C137 | — | 2 | 1 | no | — |
| 216 | C2×C8×C137 | — | 2 | 1 | no | — |
| 217 | C2×C8×C137 | — | 4 | 2 | no | — |
| 218 | C2×C8×C137 | — | 4 | 2 | no | — |
| 219 | C2×C8×C137 | — | 4 | 2 | no | — |
| 220 | C2×C8×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 221 | C2×C8×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 222 | C2×C8×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 223 | C2×C8×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 224 | C4⋊C4×C137 | — | 2 | 1 | no | — |
| 225 | C4⋊C4×C137 | — | 2 | 1 | no | — |
| 226 | C4⋊C4×C137 | — | 2 | 1 | no | — |
| 227 | C4⋊C4×C137 | — | 2 | 1 | no | — |
| 228 | C4⋊C4×C137 | — | 2 | 1 | no | — |
| 229 | C4⋊C4×C137 | — | 2 | 1 | no | — |
| 230 | C4⋊C4×C137 | — | 2 | 1 | no | — |
| 231 | C4⋊C4×C137 | — | 2 | 1 | no | — |
| 232 | C4⋊C4×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 233 | C4⋊C4×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 234 | C22⋊C4×C137 | — | 2 | 1 | no | — |
| 235 | C22⋊C4×C137 | — | 2 | 1 | no | — |
| 236 | C22⋊C4×C137 | — | 2 | 1 | no | — |
| 237 | C22⋊C4×C137 | — | 2 | 1 | no | — |
| 238 | C22⋊C4×C137 | — | 2 | 1 | no | — |
| 239 | C22⋊C4×C137 | — | 4 | 1 | no | — |
| 240 | C22⋊C4×C137 | — | 4 | 1 | no | — |
| 241 | C22⋊C4×C137 | — | 4 | 1 | no | — |
| 242 | C22⋊C4×C137 | — | 4 | 1 | no | — |
| 243 | C42×C137 | — | 2 | 1 | no | — |
| 244 | C42×C137 | — | 4 | 1 | no | — |
| 245 | C42×C137 | — | 4 | 1 | no | — |
| 246 | C23×C137 | — | 2 | 1 | no | — |
| 247 | C23×C137 | — | 2 | 1 | no | — |
| 248 | C23×C137 | — | 2 | 1 | no | — |
| 249 | C23×C137 | — | 4 | 1 | no | — |
| 250 | C23×C137 | — | 4 | 1 | no | — |
| 251 | C23×C137 | — | 4 | 1 | no | — |
| 252 | C23×C137 | — | 4 | 1 | no | — |
| 253 | C23×C137 | — | 4 | 1 | no | — |
| 254 | C23×C137 | — | 8 | 1 | no | — |
| 255 | C23×C137 | — | 8 | 1 | no | — |
| 256 | C23×C137 | #121 | 1 | 1 | yes | characteristic |
| 257 | C23×C137 | #121 | 1 | 1 | yes | characteristic |
| 258 | C23×C137 | C2×#41 | 1 | 1 | yes | characteristic |
| 259 | Q8×C137 | — | 2 | 1 | no | — |
| 260 | Q8×C137 | — | 2 | 1 | no | — |
| 261 | D4×C137 | — | 2 | 1 | no | — |
| 262 | D4×C137 | — | 2 | 1 | no | — |
| 263 | D4×C137 | — | 4 | 2 | no | — |
| 264 | D4×C137 | — | 4 | 1 | no | — |
| 265 | D4×C137 | — | 4 | 1 | no | — |
| 266 | D4×C137 | — | 4 | 1 | no | — |
| 267 | D4×C137 | — | 4 | 1 | no | — |
| 268 | D4×C137 | — | 4 | 1 | no | — |
| 269 | D4×C137 | — | 4 | 1 | no | — |
| 270 | D4×C137 | — | 8 | 1 | no | — |
| 271 | D4×C137 | — | 8 | 2 | no | — |
| 272 | D4×C137 | — | 8 | 2 | no | — |
| 273 | C2×C4×C137 | — | 2 | 1 | no | — |
| 274 | C2×C4×C137 | — | 2 | 1 | no | — |
| 275 | C2×C4×C137 | — | 2 | 1 | no | — |
| 276 | C2×C4×C137 | — | 2 | 1 | no | — |
| 277 | C2×C4×C137 | — | 2 | 1 | no | — |
| 278 | C2×C4×C137 | — | 2 | 1 | no | — |
| 279 | C2×C4×C137 | — | 2 | 1 | no | — |
| 280 | C2×C4×C137 | — | 2 | 1 | no | — |
| 281 | C2×C4×C137 | — | 2 | 1 | no | — |
| 282 | C2×C4×C137 | — | 2 | 1 | no | — |
| 283 | C2×C4×C137 | — | 2 | 1 | no | — |
| 284 | C2×C4×C137 | — | 2 | 1 | no | — |
| 285 | C2×C4×C137 | — | 2 | 1 | no | — |
| 286 | C2×C4×C137 | — | 4 | 1 | no | — |
| 287 | C2×C4×C137 | — | 4 | 1 | no | — |
| 288 | C2×C4×C137 | — | 4 | 1 | no | — |
| 289 | C2×C4×C137 | — | 4 | 1 | no | — |
| 290 | C2×C4×C137 | — | 4 | 1 | no | — |
| 291 | C2×C4×C137 | — | 8 | 1 | no | — |
| 292 | C2×C4×C137 | — | 8 | 1 | no | — |
| 293 | C2×C4×C137 | — | 8 | 1 | no | — |
| 294 | C2×C4×C137 | #121 | 1 | 1 | yes | characteristic |
| 295 | C2×C4×C137 | #121 | 1 | 1 | yes | characteristic |
| 296 | C2×C4×C137 | C22×D4 | 1 | 1 | yes | characteristic |
| 297 | C2×C4×C137 | C22×D4 | 1 | 1 | yes | characteristic |
| 298 | C2×C4×C137 | C2×#41 | 1 | 1 | yes | characteristic |
| 299 | C2×C4×C137 | C2×#41 | 1 | 1 | yes | characteristic |
| 300 | C2×C4×C137 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 301 | C2×C4×C137 | 2−1+4 | 1 | 1 | yes | characteristic |
| 302 | C8×C137 | — | 2 | 1 | no | — |
| 303 | C8×C137 | — | 2 | 1 | no | — |
| 304 | C8×C137 | — | 2 | 2 | no | — |
| 305 | C8×C137 | — | 2 | 2 | no | — |
| 306 | C8×C137 | — | 2 | 1 | no | — |
| 307 | C8×C137 | — | 2 | 1 | no | — |
| 308 | C8×C137 | — | 4 | 1 | no | — |
| 309 | C8×C137 | — | 4 | 1 | no | — |
| 310 | C8×C137 | — | 4 | 1 | no | — |
| 311 | C8×C137 | — | 4 | 1 | no | — |
| 312 | C22×C137 | — | 2 | 1 | no | — |
| 313 | C22×C137 | — | 2 | 1 | no | — |
| 314 | C22×C137 | — | 2 | 1 | no | — |
| 315 | C22×C137 | — | 2 | 1 | no | — |
| 316 | C22×C137 | — | 2 | 1 | no | — |
| 317 | C22×C137 | — | 2 | 1 | no | — |
| 318 | C22×C137 | — | 2 | 1 | no | — |
| 319 | C22×C137 | — | 2 | 1 | no | — |
| 320 | C22×C137 | — | 4 | 1 | no | — |
| 321 | C22×C137 | — | 4 | 1 | no | — |
| 322 | C22×C137 | — | 4 | 1 | no | — |
| 323 | C22×C137 | — | 8 | 1 | no | — |
| 324 | C22×C137 | — | 8 | 1 | no | — |
| 325 | C22×C137 | — | 8 | 1 | no | — |
| 326 | C22×C137 | — | 8 | 1 | no | — |
| 327 | C22×C137 | — | 8 | 1 | no | — |
| 328 | C22×C137 | — | 16 | 1 | no | — |
| 329 | C22×C137 | — | 16 | 1 | no | — |
| 330 | C22×C137 | C2×#121 | 1 | 1 | yes | characteristic |
| 331 | C22×C137 | #529 | 1 | 1 | yes | characteristic |
| 332 | C22×C137 | #539 | 1 | 1 | yes | characteristic |
| 333 | C4×C137 | — | 2 | 1 | no | — |
| 334 | C4×C137 | — | 2 | 1 | no | — |
| 335 | C4×C137 | — | 4 | 1 | no | — |
| 336 | C4×C137 | — | 4 | 1 | no | — |
| 337 | C4×C137 | — | 4 | 1 | no | — |
| 338 | C4×C137 | — | 8 | 1 | no | — |
| 339 | C4×C137 | — | 8 | 1 | no | — |
| 340 | C4×C137 | — | 8 | 1 | no | — |
| 341 | C4×C137 | #546 | 1 | 1 | yes | characteristic |
| 342 | C4×C137 | #546 | 1 | 1 | yes | characteristic |
| 343 | C4×C137 | #547 | 1 | 1 | yes | characteristic |
| 344 | C4×C137 | #547 | 1 | 1 | yes | characteristic |
| 345 | C2×C137 | — | 2 | 1 | no | — |
| 346 | C2×C137 | — | 2 | 1 | no | — |
| 347 | C2×C137 | — | 4 | 1 | no | — |
| 348 | C2×C137 | — | 4 | 1 | no | — |
| 349 | C2×C137 | — | 8 | 1 | no | — |
| 350 | C2×C137 | — | 16 | 1 | no | — |
| 351 | C2×C137 | #2425 | 1 | 1 | yes | characteristic |
| 352 | C2×C137 | #3067 | 1 | 1 | yes | characteristic |
| 353 | C2×C137 | #3068 | 1 | 1 | yes | characteristic |
| 354 | #25269 | C137 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 355 | C137 | #25269 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 356 | #3093 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 357 | C2×#482 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 358 | #3055 | C2×C137 | 1 | 1 | yes | characteristic |
| 359 | #2933 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 360 | #2090 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 361 | #2078 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 362 | #2063 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 363 | #2051 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 364 | #1952 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 365 | #1931 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 366 | #1907 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 367 | #1900 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 368 | #1855 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 369 | #1815 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 370 | #1742 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 371 | C2×AGL(1,ℤ/8) | C22×C137 | 1 | 1 | yes | characteristic |
| 372 | C2×#131 | C22×C137 | 1 | 1 | yes | characteristic |
| 373 | C22×M16 | C22×C137 | 1 | 1 | yes | characteristic |
| 374 | C22×M16 | C22×C137 | 1 | 1 | yes | characteristic |
| 375 | #525 | C22×C137 | 1 | 1 | yes | characteristic |
| 376 | C2×#121 | C22×C137 | 1 | 1 | yes | characteristic |
| 377 | C2×#117 | C22×C137 | 1 | 1 | yes | characteristic |
| 378 | #485 | — | 2 | 1 | no | — |
| 379 | #485 | — | 2 | 1 | no | — |
| 380 | #482 | — | 2 | 1 | no | — |
| 381 | #482 | — | 2 | 1 | no | — |
| 382 | #482 | — | 2 | 1 | no | — |
| 383 | #482 | — | 2 | 1 | no | — |
| 384 | #482 | — | 2 | 1 | no | — |
| 385 | #482 | — | 2 | 1 | no | — |
| 386 | #469 | — | 2 | 1 | no | — |
| 387 | #468 | — | 2 | 1 | no | — |
| 388 | #466 | — | 2 | 1 | no | — |
| 389 | #465 | — | 2 | 1 | no | — |
| 390 | #436 | — | 2 | 1 | no | — |
| 391 | #435 | — | 2 | 1 | no | — |
| 392 | #435 | — | 2 | 1 | no | — |
| 393 | C8×D4 | — | 2 | 1 | no | — |
| 394 | C2×#108 | C22×C137 | 1 | 1 | yes | characteristic |
| 395 | C2×#108 | C22×C137 | 1 | 1 | yes | characteristic |
| 396 | #428 | C22×C137 | 1 | 1 | yes | characteristic |
| 397 | #428 | C22×C137 | 1 | 1 | yes | characteristic |
| 398 | #428 | C22×C137 | 1 | 1 | yes | characteristic |
| 399 | C2×#107 | C22×C137 | 1 | 1 | yes | characteristic |
| 400 | C2×#106 | C22×C137 | 1 | 1 | yes | characteristic |
| 401 | #424 | C22×C137 | 1 | 1 | yes | characteristic |
| 402 | #418 | C22×C137 | 1 | 1 | yes | characteristic |
| 403 | #417 | C22×C137 | 1 | 1 | yes | characteristic |
| 404 | #417 | C22×C137 | 1 | 1 | yes | characteristic |
| 405 | #417 | C22×C137 | 1 | 1 | yes | characteristic |
| 406 | C2×#102 | C22×C137 | 1 | 1 | yes | characteristic |
| 407 | C2×#102 | C22×C137 | 1 | 1 | yes | characteristic |
| 408 | C2×#100 | C22×C137 | 1 | 1 | yes | characteristic |
| 409 | C2×#100 | C22×C137 | 1 | 1 | yes | characteristic |
| 410 | #408 | C22×C137 | 1 | 1 | yes | characteristic |
| 411 | #407 | C22×C137 | 1 | 1 | yes | characteristic |
| 412 | C2×C22⋊C8 | C22×C137 | 1 | 1 | yes | characteristic |
| 413 | #405 | C22×C137 | 1 | 1 | yes | characteristic |
| 414 | #343 | C22×C137 | 1 | 1 | yes | characteristic |
| 415 | #343 | C22×C137 | 1 | 1 | yes | characteristic |
| 416 | #343 | C22×C137 | 1 | 1 | yes | characteristic |
| 417 | #343 | C22×C137 | 1 | 1 | yes | characteristic |
| 418 | #343 | C22×C137 | 1 | 1 | yes | characteristic |
| 419 | #343 | C22×C137 | 1 | 1 | yes | characteristic |
| 420 | #341 | C22×C137 | 1 | 1 | yes | characteristic |
| 421 | #341 | C22×C137 | 1 | 1 | yes | characteristic |
| 422 | C2×#41 | C23×C137 | 1 | 1 | yes | characteristic |
| 423 | C22×D4 | — | 2 | 1 | no | — |
| 424 | C22×D4 | C23×C137 | 1 | 1 | yes | characteristic |
| 425 | C23×C4 | C23×C137 | 1 | 1 | yes | characteristic |
| 426 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 427 | AGL(1,ℤ/8) | — | 4 | 1 | no | — |
| 428 | C2×SD16 | — | 2 | 1 | no | — |
| 429 | C2×D8 | — | 2 | 1 | no | — |
| 430 | #131 | — | 2 | 2 | no | — |
| 431 | #131 | — | 4 | 1 | no | — |
| 432 | C2×M16 | — | 2 | 1 | no | — |
| 433 | C2×M16 | — | 2 | 1 | no | — |
| 434 | C2×M16 | — | 2 | 1 | no | — |
| 435 | C2×M16 | — | 2 | 2 | no | — |
| 436 | C2×M16 | — | 2 | 2 | no | — |
| 437 | C2×M16 | — | 4 | 1 | no | — |
| 438 | C2×M16 | — | 4 | 1 | no | — |
| 439 | C2×M16 | C23×C137 | 1 | 1 | yes | characteristic |
| 440 | C2×M16 | C23×C137 | 1 | 1 | yes | characteristic |
| 441 | C2×M16 | C23×C137 | 1 | 1 | yes | characteristic |
| 442 | C2×M16 | C23×C137 | 1 | 1 | yes | characteristic |
| 443 | C2×M16 | C23×C137 | 1 | 1 | yes | characteristic |
| 444 | C2×M16 | C23×C137 | 1 | 1 | yes | characteristic |
| 445 | C22×C8 | — | 2 | 1 | no | — |
| 446 | C22×C8 | — | 2 | 1 | no | — |
| 447 | C22×C8 | — | 2 | 1 | no | — |
| 448 | C22×C8 | C23×C137 | 1 | 1 | yes | characteristic |
| 449 | C22×C8 | C23×C137 | 1 | 1 | yes | characteristic |
| 450 | #123 | — | 2 | 1 | no | — |
| 451 | C22⋊Q8 | D4×C137 | 1 | 1 | yes | characteristic |
| 452 | C22⋊Q8 | D4×C137 | 1 | 1 | yes | characteristic |
| 453 | #121 | — | 2 | 1 | no | — |
| 454 | #121 | — | 2 | 1 | no | — |
| 455 | #121 | — | 2 | 1 | no | — |
| 456 | #121 | — | 2 | 1 | no | — |
| 457 | #121 | D4×C137 | 1 | 1 | yes | characteristic |
| 458 | #121 | D4×C137 | 1 | 1 | yes | characteristic |
| 459 | #120 | — | 2 | 1 | no | — |
| 460 | C4×D4 | — | 2 | 1 | no | — |
| 461 | C4×D4 | — | 2 | 1 | no | — |
| 462 | #117 | — | 2 | 1 | no | — |
| 463 | #117 | — | 2 | 1 | no | — |
| 464 | #117 | — | 2 | 1 | no | — |
| 465 | #117 | — | 2 | 1 | no | — |
| 466 | #117 | C23×C137 | 1 | 1 | yes | characteristic |
| 467 | C2×C4⋊C4 | C23×C137 | 1 | 1 | yes | characteristic |
| 468 | C2×C4⋊C4 | C23×C137 | 1 | 1 | yes | characteristic |
| 469 | C2×C4⋊C4 | C23×C137 | 1 | 1 | yes | characteristic |
| 470 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 471 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 472 | C2×C42 | — | 2 | 1 | no | — |
| 473 | #108 | — | 2 | 2 | no | — |
| 474 | #108 | — | 4 | 1 | no | — |
| 475 | #107 | — | 2 | 1 | no | — |
| 476 | #107 | — | 2 | 1 | no | — |
| 477 | #107 | — | 2 | 1 | no | — |
| 478 | #107 | — | 2 | 1 | no | — |
| 479 | #107 | — | 2 | 1 | no | — |
| 480 | #106 | — | 2 | 1 | no | — |
| 481 | #106 | — | 2 | 1 | no | — |
| 482 | #106 | — | 2 | 1 | no | — |
| 483 | #106 | — | 2 | 1 | no | — |
| 484 | #106 | — | 2 | 1 | no | — |
| 485 | C4⋊C8 | — | 2 | 1 | no | — |
| 486 | C4⋊C8 | — | 2 | 1 | no | — |
| 487 | #103 | — | 2 | 1 | no | — |
| 488 | #103 | — | 2 | 1 | no | — |
| 489 | #103 | — | 2 | 1 | no | — |
| 490 | #102 | — | 2 | 1 | no | — |
| 491 | #102 | — | 2 | 1 | no | — |
| 492 | #102 | — | 2 | 1 | no | — |
| 493 | #102 | — | 2 | 1 | no | — |
| 494 | #102 | — | 2 | 1 | no | — |
| 495 | #102 | — | 2 | 1 | no | — |
| 496 | #102 | — | 2 | 1 | no | — |
| 497 | #102 | — | 2 | 1 | no | — |
| 498 | #102 | — | 2 | 1 | no | — |
| 499 | #100 | — | 2 | 2 | no | — |
| 500 | #100 | — | 4 | 1 | no | — |
| 501 | C22⋊C8 | — | 2 | 1 | no | — |
| 502 | C22⋊C8 | — | 2 | 1 | no | — |
| 503 | C22⋊C8 | — | 2 | 1 | no | — |
| 504 | C22⋊C8 | — | 2 | 1 | no | — |
| 505 | C22⋊C8 | D4×C137 | 1 | 1 | yes | characteristic |
| 506 | C22⋊C8 | D4×C137 | 1 | 1 | yes | characteristic |
| 507 | C22⋊C8 | D4×C137 | 1 | 1 | yes | characteristic |
| 508 | C22⋊C8 | D4×C137 | 1 | 1 | yes | characteristic |
| 509 | #97 | — | 2 | 1 | no | — |
| 510 | C4×C8 | — | 2 | 1 | no | — |
| 511 | C24 | — | 2 | 1 | no | — |
| 512 | C24 | #41×C137 | 1 | 1 | yes | characteristic |
| 513 | #41 | — | 2 | 1 | no | — |
| 514 | #41 | — | 2 | 1 | no | — |
| 515 | #41 | — | 2 | 1 | no | — |
| 516 | #41 | — | 2 | 1 | no | — |
| 517 | C2×Q8 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 518 | C2×D4 | — | 2 | 1 | no | — |
| 519 | C2×D4 | — | 2 | 1 | no | — |
| 520 | C2×D4 | — | 2 | 1 | no | — |
| 521 | C2×D4 | — | 2 | 1 | no | — |
| 522 | C2×D4 | — | 2 | 1 | no | — |
| 523 | C2×D4 | — | 2 | 1 | no | — |
| 524 | C2×D4 | — | 2 | 1 | no | — |
| 525 | C2×D4 | — | 2 | 1 | no | — |
| 526 | C2×D4 | — | 2 | 1 | no | — |
| 527 | C2×D4 | — | 4 | 1 | no | — |
| 528 | C2×D4 | — | 4 | 1 | no | — |
| 529 | C2×D4 | — | 8 | 2 | no | — |
| 530 | C2×D4 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 531 | C22×C4 | — | 2 | 1 | no | — |
| 532 | C22×C4 | — | 2 | 1 | no | — |
| 533 | C22×C4 | — | 2 | 1 | no | — |
| 534 | C22×C4 | — | 2 | 1 | no | — |
| 535 | C22×C4 | — | 2 | 1 | no | — |
| 536 | C22×C4 | — | 2 | 1 | no | — |
| 537 | C22×C4 | — | 2 | 1 | no | — |
| 538 | C22×C4 | — | 2 | 1 | no | — |
| 539 | C22×C4 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 540 | C22×C4 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 541 | C22×C4 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 542 | C22×C4 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 543 | C22×C4 | #41×C137 | 1 | 1 | yes | characteristic |
| 544 | C22×C4 | C24×C137 | 1 | 1 | yes | characteristic |
| 545 | SD16 | — | 4 | 2 | no | — |
| 546 | D8 | — | 4 | 2 | no | — |
| 547 | M16 | — | 2 | 1 | no | — |
| 548 | M16 | — | 2 | 1 | no | — |
| 549 | M16 | — | 2 | 1 | no | — |
| 550 | M16 | — | 2 | 1 | no | — |
| 551 | M16 | — | 2 | 1 | no | — |
| 552 | M16 | — | 2 | 1 | no | — |
| 553 | M16 | — | 2 | 1 | no | — |
| 554 | M16 | — | 2 | 1 | no | — |
| 555 | M16 | — | 2 | 1 | no | — |
| 556 | M16 | — | 2 | 1 | no | — |
| 557 | M16 | — | 4 | 2 | no | — |
| 558 | M16 | — | 4 | 2 | no | — |
| 559 | M16 | — | 4 | 2 | no | — |
| 560 | M16 | #41×C137 | 1 | 2 | yes | — |
| 561 | M16 | #41×C137 | 1 | 2 | yes | — |
| 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 | — | 2 | 1 | no | — |
| 570 | C2×C8 | — | 2 | 1 | no | — |
| 571 | C2×C8 | — | 2 | 1 | no | — |
| 572 | C2×C8 | — | 4 | 2 | no | — |
| 573 | C2×C8 | — | 4 | 2 | no | — |
| 574 | C2×C8 | — | 4 | 2 | no | — |
| 575 | C2×C8 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 576 | C2×C8 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 577 | C2×C8 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 578 | C2×C8 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 579 | C4⋊C4 | — | 2 | 1 | no | — |
| 580 | C4⋊C4 | — | 2 | 1 | no | — |
| 581 | C4⋊C4 | — | 2 | 1 | no | — |
| 582 | C4⋊C4 | — | 2 | 1 | no | — |
| 583 | C4⋊C4 | — | 2 | 1 | no | — |
| 584 | C4⋊C4 | — | 2 | 1 | no | — |
| 585 | C4⋊C4 | — | 2 | 1 | no | — |
| 586 | C4⋊C4 | — | 2 | 1 | no | — |
| 587 | C4⋊C4 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 588 | C4⋊C4 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 589 | C22⋊C4 | — | 2 | 1 | no | — |
| 590 | C22⋊C4 | — | 2 | 1 | no | — |
| 591 | C22⋊C4 | — | 2 | 1 | no | — |
| 592 | C22⋊C4 | — | 2 | 1 | no | — |
| 593 | C22⋊C4 | — | 2 | 1 | no | — |
| 594 | C22⋊C4 | — | 4 | 1 | no | — |
| 595 | C22⋊C4 | — | 4 | 1 | no | — |
| 596 | C22⋊C4 | — | 4 | 1 | no | — |
| 597 | C22⋊C4 | — | 4 | 1 | no | — |
| 598 | C42 | — | 2 | 1 | no | — |
| 599 | C42 | — | 4 | 1 | no | — |
| 600 | C42 | — | 4 | 1 | no | — |
| 601 | C23 | — | 2 | 1 | no | — |
| 602 | C23 | — | 2 | 1 | no | — |
| 603 | C23 | — | 2 | 1 | no | — |
| 604 | C23 | — | 4 | 1 | no | — |
| 605 | C23 | — | 4 | 1 | no | — |
| 606 | C23 | — | 4 | 1 | no | — |
| 607 | C23 | — | 4 | 1 | no | — |
| 608 | C23 | — | 4 | 1 | no | — |
| 609 | C23 | — | 8 | 1 | no | — |
| 610 | C23 | — | 8 | 1 | no | — |
| 611 | C23 | #121×C137 | 1 | 1 | yes | characteristic |
| 612 | C23 | #121×C137 | 1 | 1 | yes | characteristic |
| 613 | C23 | C2×#41×C137 | 1 | 1 | yes | characteristic |
| 614 | Q8 | — | 2 | 1 | no | — |
| 615 | Q8 | — | 2 | 1 | no | — |
| 616 | D4 | — | 2 | 1 | no | — |
| 617 | D4 | — | 2 | 1 | no | — |
| 618 | D4 | — | 4 | 2 | no | — |
| 619 | D4 | — | 4 | 1 | no | — |
| 620 | D4 | — | 4 | 1 | no | — |
| 621 | D4 | — | 4 | 1 | no | — |
| 622 | D4 | — | 4 | 1 | no | — |
| 623 | D4 | — | 4 | 1 | no | — |
| 624 | D4 | — | 4 | 1 | no | — |
| 625 | D4 | — | 8 | 1 | no | — |
| 626 | D4 | — | 8 | 2 | no | — |
| 627 | D4 | — | 8 | 2 | no | — |
| 628 | C2×C4 | — | 2 | 1 | no | — |
| 629 | C2×C4 | — | 2 | 1 | no | — |
| 630 | C2×C4 | — | 2 | 1 | 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 | — | 2 | 1 | no | — |
| 639 | C2×C4 | — | 2 | 1 | no | — |
| 640 | C2×C4 | — | 2 | 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 | — | 8 | 1 | no | — |
| 647 | C2×C4 | — | 8 | 1 | no | — |
| 648 | C2×C4 | — | 8 | 1 | no | — |
| 649 | C2×C4 | #121×C137 | 1 | 1 | yes | characteristic |
| 650 | C2×C4 | #121×C137 | 1 | 1 | yes | characteristic |
| 651 | C2×C4 | C22×D4×C137 | 1 | 1 | yes | characteristic |
| 652 | C2×C4 | C22×D4×C137 | 1 | 1 | yes | characteristic |
| 653 | C2×C4 | C2×#41×C137 | 1 | 1 | yes | characteristic |
| 654 | C2×C4 | C2×#41×C137 | 1 | 1 | yes | characteristic |
| 655 | C2×C4 | H(5,𝔽2)×C137 | 1 | 1 | yes | characteristic |
| 656 | C2×C4 | 2−1+4×C137 | 1 | 1 | yes | characteristic |
| 657 | C8 | — | 2 | 1 | no | — |
| 658 | C8 | — | 2 | 1 | no | — |
| 659 | C8 | — | 2 | 2 | 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 | C8 | — | 4 | 1 | no | — |
| 667 | C22 | — | 2 | 1 | no | — |
| 668 | C22 | — | 2 | 1 | no | — |
| 669 | C22 | — | 2 | 1 | no | — |
| 670 | C22 | — | 2 | 1 | no | — |
| 671 | C22 | — | 2 | 1 | no | — |
| 672 | C22 | — | 2 | 1 | no | — |
| 673 | C22 | — | 2 | 1 | no | — |
| 674 | C22 | — | 2 | 1 | no | — |
| 675 | C22 | — | 4 | 1 | no | — |
| 676 | C22 | — | 4 | 1 | no | — |
| 677 | C22 | — | 4 | 1 | no | — |
| 678 | C22 | — | 8 | 1 | no | — |
| 679 | C22 | — | 8 | 1 | no | — |
| 680 | C22 | — | 8 | 1 | no | — |
| 681 | C22 | — | 8 | 1 | no | — |
| 682 | C22 | — | 8 | 1 | no | — |
| 683 | C22 | — | 16 | 1 | no | — |
| 684 | C22 | — | 16 | 1 | no | — |
| 685 | C22 | C2×#121×C137 | 1 | 1 | yes | characteristic |
| 686 | C22 | #529×C137 | 1 | 1 | yes | characteristic |
| 687 | C22 | #539×C137 | 1 | 1 | yes | characteristic |
| 688 | C4 | — | 2 | 1 | no | — |
| 689 | C4 | — | 2 | 1 | no | — |
| 690 | C4 | — | 4 | 1 | no | — |
| 691 | C4 | — | 4 | 1 | no | — |
| 692 | C4 | — | 4 | 1 | no | — |
| 693 | C4 | — | 8 | 1 | no | — |
| 694 | C4 | — | 8 | 1 | no | — |
| 695 | C4 | — | 8 | 1 | no | — |
| 696 | C4 | #546×C137 | 1 | 1 | yes | characteristic |
| 697 | C4 | #546×C137 | 1 | 1 | yes | characteristic |
| 698 | C4 | #547×C137 | 1 | 1 | yes | characteristic |
| 699 | C4 | #547×C137 | 1 | 1 | yes | characteristic |
| 700 | C2 | — | 2 | 1 | no | — |
| 701 | C2 | — | 2 | 1 | no | — |
| 702 | C2 | — | 4 | 1 | no | — |
| 703 | C2 | — | 4 | 1 | no | — |
| 704 | C2 | — | 8 | 1 | no | — |
| 705 | C2 | — | 16 | 1 | no | — |
| 706 | C2 | #2425×C137 | 1 | 1 | yes | characteristic |
| 707 | C2 | #3067×C137 | 1 | 1 | yes | characteristic |
| 708 | C2 | #3068×C137 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta