| 1 | C2×#510×C137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#444×C137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C2×#362×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#360×C137 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #1971×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #1383×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #1375×C137 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#135×C137 | C22 | 1 | 1 | yes | characteristic |
| 9 | C22×Q16×C137 | C22 | 1 | 1 | yes | characteristic |
| 10 | C2×#131×C137 | — | 2 | 1 | no | — |
| 11 | #510×C137 | — | 2 | 2 | no | — |
| 12 | #510×C137 | — | 2 | 2 | no | — |
| 13 | C2×Q32×C137 | C4 | 1 | 2 | yes | complemented |
| 14 | C2×SD32×C137 | C4 | 1 | 2 | yes | complemented |
| 15 | C2×M32×C137 | C22 | 1 | 1 | yes | characteristic |
| 16 | C2×M32×C137 | C22 | 1 | 1 | yes | characteristic |
| 17 | #444×C137 | — | 2 | 2 | no | — |
| 18 | #444×C137 | — | 2 | 2 | no | — |
| 19 | C2×#108×C137 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×#106×C137 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#104×C137 | — | 2 | 1 | no | — |
| 22 | C2×#103×C137 | — | 2 | 1 | no | — |
| 23 | C2×#97×C137 | C22 | 1 | 1 | yes | characteristic |
| 24 | #391×C137 | — | 2 | 1 | no | — |
| 25 | #362×C137 | — | 2 | 2 | no | — |
| 26 | #360×C137 | — | 2 | 2 | no | — |
| 27 | C2×#41×C137 | — | 2 | 1 | no | — |
| 28 | C22×Q8×C137 | — | 2 | 1 | no | — |
| 29 | #135×C137 | — | 2 | 1 | no | — |
| 30 | #135×C137 | — | 2 | 1 | no | — |
| 31 | #135×C137 | D4 | 1 | 2 | yes | — |
| 32 | #135×C137 | D4 | 1 | 2 | yes | — |
| 33 | C2×Q16×C137 | — | 2 | 1 | no | — |
| 34 | C2×Q16×C137 | — | 2 | 1 | no | — |
| 35 | C2×Q16×C137 | — | 2 | 1 | no | — |
| 36 | C2×Q16×C137 | — | 2 | 1 | no | — |
| 37 | C2×Q16×C137 | — | 2 | 1 | no | — |
| 38 | C2×Q16×C137 | C2×C4 | 1 | 2 | yes | — |
| 39 | C2×Q16×C137 | C2×C4 | 1 | 1 | yes | characteristic |
| 40 | C2×SD16×C137 | — | 2 | 1 | no | — |
| 41 | C2×D8×C137 | C2×C4 | 1 | 1 | yes | characteristic |
| 42 | #131×C137 | — | 2 | 4 | no | — |
| 43 | #131×C137 | — | 4 | 2 | no | — |
| 44 | C2×M16×C137 | — | 2 | 1 | no | — |
| 45 | C2×M16×C137 | — | 4 | 1 | no | — |
| 46 | C22×C8×C137 | — | 4 | 1 | no | — |
| 47 | C22×C8×C137 | D4 | 1 | 1 | yes | characteristic |
| 48 | C22×C8×C137 | C23 | 1 | 1 | yes | characteristic |
| 49 | C2×C4⋊C4×C137 | — | 2 | 1 | no | — |
| 50 | C2×C42×C137 | D4 | 1 | 1 | yes | characteristic |
| 51 | Q32×C137 | — | 2 | 4 | no | — |
| 52 | SD32×C137 | — | 2 | 4 | no | — |
| 53 | M32×C137 | — | 2 | 1 | no | — |
| 54 | M32×C137 | — | 2 | 1 | no | — |
| 55 | M32×C137 | — | 2 | 1 | no | — |
| 56 | M32×C137 | — | 2 | 1 | no | — |
| 57 | C2×C16×C137 | — | 2 | 1 | no | — |
| 58 | C2×C16×C137 | C2×C4 | 1 | 2 | yes | — |
| 59 | #108×C137 | — | 2 | 1 | no | — |
| 60 | #108×C137 | D4 | 1 | 2 | yes | — |
| 61 | #106×C137 | — | 2 | 1 | no | — |
| 62 | #106×C137 | — | 2 | 1 | no | — |
| 63 | #104×C137 | — | 2 | 4 | no | — |
| 64 | #103×C137 | — | 4 | 2 | no | — |
| 65 | #97×C137 | — | 2 | 1 | no | — |
| 66 | #97×C137 | — | 2 | 1 | no | — |
| 67 | #95×C137 | — | 4 | 2 | no | — |
| 68 | #41×C137 | — | 2 | 2 | no | — |
| 69 | #41×C137 | — | 2 | 2 | no | — |
| 70 | #41×C137 | — | 4 | 1 | no | — |
| 71 | #41×C137 | — | 4 | 1 | no | — |
| 72 | C2×Q8×C137 | — | 2 | 1 | no | — |
| 73 | C2×Q8×C137 | — | 2 | 2 | no | — |
| 74 | C2×Q8×C137 | — | 4 | 1 | no | — |
| 75 | C2×Q8×C137 | — | 4 | 1 | no | — |
| 76 | C2×Q8×C137 | — | 4 | 1 | no | — |
| 77 | C2×Q8×C137 | — | 4 | 1 | no | — |
| 78 | C2×Q8×C137 | — | 4 | 1 | no | — |
| 79 | C2×D4×C137 | — | 2 | 1 | no | — |
| 80 | C2×D4×C137 | — | 4 | 1 | no | — |
| 81 | C22×C4×C137 | — | 2 | 1 | no | — |
| 82 | C22×C4×C137 | — | 4 | 1 | no | — |
| 83 | C22×C4×C137 | — | 4 | 1 | no | — |
| 84 | C22×C4×C137 | — | 4 | 1 | no | — |
| 85 | C22×C4×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 86 | Q16×C137 | — | 2 | 2 | no | — |
| 87 | Q16×C137 | — | 2 | 1 | no | — |
| 88 | Q16×C137 | — | 2 | 2 | no | — |
| 89 | Q16×C137 | — | 4 | 1 | no | — |
| 90 | Q16×C137 | — | 4 | 1 | no | — |
| 91 | Q16×C137 | C22⋊C4 | 1 | 2 | yes | — |
| 92 | SD16×C137 | — | 2 | 2 | no | — |
| 93 | SD16×C137 | — | 2 | 2 | no | — |
| 94 | D8×C137 | — | 2 | 1 | no | — |
| 95 | D8×C137 | C22⋊C4 | 1 | 2 | yes | — |
| 96 | M16×C137 | — | 2 | 2 | no | — |
| 97 | M16×C137 | — | 4 | 4 | no | — |
| 98 | M16×C137 | — | 4 | 1 | no | — |
| 99 | C2×C8×C137 | — | 2 | 1 | no | — |
| 100 | C2×C8×C137 | — | 2 | 1 | no | — |
| 101 | C2×C8×C137 | — | 4 | 4 | no | — |
| 102 | C2×C8×C137 | — | 4 | 1 | no | — |
| 103 | C2×C8×C137 | D8 | 1 | 2 | yes | — |
| 104 | C2×C8×C137 | C22×C4 | 1 | 1 | yes | characteristic |
| 105 | C2×C8×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 106 | C2×C8×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 107 | C2×C8×C137 | C2×D4 | 1 | 1 | yes | characteristic |
| 108 | C2×C8×C137 | #41 | 1 | 1 | yes | characteristic |
| 109 | C2×C8×C137 | #41 | 1 | 1 | yes | characteristic |
| 110 | C4⋊C4×C137 | — | 4 | 1 | no | — |
| 111 | C4⋊C4×C137 | — | 4 | 1 | no | — |
| 112 | C42×C137 | — | 2 | 1 | no | — |
| 113 | C42×C137 | — | 2 | 1 | no | — |
| 114 | C16×C137 | — | 2 | 2 | no | — |
| 115 | C16×C137 | — | 4 | 1 | no | — |
| 116 | C23×C137 | — | 4 | 1 | no | — |
| 117 | C23×C137 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 118 | Q8×C137 | — | 2 | 2 | no | — |
| 119 | Q8×C137 | — | 4 | 1 | no | — |
| 120 | Q8×C137 | — | 4 | 2 | no | — |
| 121 | Q8×C137 | — | 4 | 2 | no | — |
| 122 | Q8×C137 | — | 8 | 1 | no | — |
| 123 | Q8×C137 | — | 8 | 1 | no | — |
| 124 | D4×C137 | — | 2 | 2 | no | — |
| 125 | D4×C137 | — | 4 | 2 | no | — |
| 126 | D4×C137 | — | 4 | 2 | no | — |
| 127 | D4×C137 | — | 4 | 1 | no | — |
| 128 | C2×C4×C137 | — | 4 | 1 | no | — |
| 129 | C2×C4×C137 | — | 4 | 2 | no | — |
| 130 | C2×C4×C137 | — | 4 | 2 | no | — |
| 131 | C2×C4×C137 | — | 4 | 2 | no | — |
| 132 | C2×C4×C137 | — | 4 | 2 | no | — |
| 133 | C2×C4×C137 | — | 4 | 1 | no | — |
| 134 | C2×C4×C137 | — | 8 | 1 | no | — |
| 135 | C2×C4×C137 | — | 8 | 1 | no | — |
| 136 | C2×C4×C137 | — | 8 | 2 | no | — |
| 137 | C2×C4×C137 | — | 8 | 1 | no | — |
| 138 | C2×C4×C137 | C4×D4 | 1 | 1 | yes | characteristic |
| 139 | C2×C4×C137 | #120 | 1 | 1 | yes | characteristic |
| 140 | C2×C4×C137 | #121 | 1 | 1 | yes | characteristic |
| 141 | C2×C4×C137 | C2×D8 | 1 | 1 | yes | characteristic |
| 142 | C2×C4×C137 | #135 | 1 | 1 | yes | characteristic |
| 143 | C2×C4×C137 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 144 | C8×C137 | — | 2 | 2 | no | — |
| 145 | C8×C137 | — | 4 | 2 | no | — |
| 146 | C8×C137 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 147 | C8×C137 | C4×D4 | 1 | 1 | yes | characteristic |
| 148 | C8×C137 | #121 | 1 | 1 | yes | characteristic |
| 149 | C8×C137 | #123 | 1 | 1 | yes | characteristic |
| 150 | C22×C137 | — | 2 | 2 | no | — |
| 151 | C22×C137 | — | 4 | 2 | no | — |
| 152 | C22×C137 | — | 8 | 2 | no | — |
| 153 | C22×C137 | #442 | 1 | 1 | yes | characteristic |
| 154 | C22×C137 | #449 | 1 | 1 | yes | characteristic |
| 155 | C22×C137 | #459 | 1 | 1 | yes | characteristic |
| 156 | C4×C137 | — | 4 | 2 | no | — |
| 157 | C4×C137 | — | 8 | 1 | no | — |
| 158 | C4×C137 | — | 8 | 2 | no | — |
| 159 | C4×C137 | — | 16 | 1 | no | — |
| 160 | C4×C137 | #386 | 1 | 1 | yes | characteristic |
| 161 | C4×C137 | C4×D8 | 1 | 1 | yes | characteristic |
| 162 | C4×C137 | #447 | 1 | 1 | yes | characteristic |
| 163 | C4×C137 | #463 | 1 | 1 | yes | characteristic |
| 164 | C2×C137 | — | 2 | 1 | no | — |
| 165 | C2×C137 | — | 2 | 1 | no | — |
| 166 | C2×C137 | — | 8 | 2 | no | — |
| 167 | C2×C137 | #1879 | 1 | 1 | yes | characteristic |
| 168 | C2×C137 | #2180 | 1 | 2 | yes | — |
| 169 | #13039 | C137 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 170 | C137 | #13039 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 171 | C2×#510 | C2×C137 | 1 | 1 | yes | characteristic |
| 172 | C2×#444 | C2×C137 | 1 | 1 | yes | characteristic |
| 173 | C2×#362 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 174 | C2×#360 | C2×C137 | 1 | 1 | yes | characteristic |
| 175 | #1971 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 176 | #1383 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 177 | #1375 | C2×C137 | 1 | 1 | yes | characteristic, complemented |
| 178 | C2×#135 | C22×C137 | 1 | 1 | yes | characteristic |
| 179 | C22×Q16 | C22×C137 | 1 | 1 | yes | characteristic |
| 180 | C2×#131 | — | 2 | 1 | no | — |
| 181 | #510 | — | 2 | 2 | no | — |
| 182 | #510 | — | 2 | 2 | no | — |
| 183 | C2×Q32 | C4×C137 | 1 | 2 | yes | complemented |
| 184 | C2×SD32 | C4×C137 | 1 | 2 | yes | complemented |
| 185 | C2×M32 | C22×C137 | 1 | 1 | yes | characteristic |
| 186 | C2×M32 | C22×C137 | 1 | 1 | yes | characteristic |
| 187 | #444 | — | 2 | 2 | no | — |
| 188 | #444 | — | 2 | 2 | no | — |
| 189 | C2×#108 | C22×C137 | 1 | 1 | yes | characteristic |
| 190 | C2×#106 | C22×C137 | 1 | 1 | yes | characteristic |
| 191 | C2×#104 | — | 2 | 1 | no | — |
| 192 | C2×#103 | — | 2 | 1 | no | — |
| 193 | C2×#97 | C22×C137 | 1 | 1 | yes | characteristic |
| 194 | #391 | — | 2 | 1 | no | — |
| 195 | #362 | — | 2 | 2 | no | — |
| 196 | #360 | — | 2 | 2 | no | — |
| 197 | C2×#41 | — | 2 | 1 | no | — |
| 198 | C22×Q8 | — | 2 | 1 | no | — |
| 199 | #135 | — | 2 | 1 | no | — |
| 200 | #135 | — | 2 | 1 | no | — |
| 201 | #135 | D4×C137 | 1 | 2 | yes | — |
| 202 | #135 | D4×C137 | 1 | 2 | yes | — |
| 203 | C2×Q16 | — | 2 | 1 | no | — |
| 204 | C2×Q16 | — | 2 | 1 | no | — |
| 205 | C2×Q16 | — | 2 | 1 | no | — |
| 206 | C2×Q16 | — | 2 | 1 | no | — |
| 207 | C2×Q16 | — | 2 | 1 | no | — |
| 208 | C2×Q16 | C2×C4×C137 | 1 | 2 | yes | — |
| 209 | C2×Q16 | C2×C4×C137 | 1 | 1 | yes | characteristic |
| 210 | C2×SD16 | — | 2 | 1 | no | — |
| 211 | C2×D8 | C2×C4×C137 | 1 | 1 | yes | characteristic |
| 212 | #131 | — | 2 | 4 | no | — |
| 213 | #131 | — | 4 | 2 | no | — |
| 214 | C2×M16 | — | 2 | 1 | no | — |
| 215 | C2×M16 | — | 4 | 1 | no | — |
| 216 | C22×C8 | — | 4 | 1 | no | — |
| 217 | C22×C8 | D4×C137 | 1 | 1 | yes | characteristic |
| 218 | C22×C8 | C23×C137 | 1 | 1 | yes | characteristic |
| 219 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 220 | C2×C42 | D4×C137 | 1 | 1 | yes | characteristic |
| 221 | Q32 | — | 2 | 4 | no | — |
| 222 | SD32 | — | 2 | 4 | no | — |
| 223 | M32 | — | 2 | 1 | no | — |
| 224 | M32 | — | 2 | 1 | no | — |
| 225 | M32 | — | 2 | 1 | no | — |
| 226 | M32 | — | 2 | 1 | no | — |
| 227 | C2×C16 | — | 2 | 1 | no | — |
| 228 | C2×C16 | C2×C4×C137 | 1 | 2 | yes | — |
| 229 | #108 | — | 2 | 1 | no | — |
| 230 | #108 | D4×C137 | 1 | 2 | yes | — |
| 231 | #106 | — | 2 | 1 | no | — |
| 232 | #106 | — | 2 | 1 | no | — |
| 233 | #104 | — | 2 | 4 | no | — |
| 234 | #103 | — | 4 | 2 | no | — |
| 235 | #97 | — | 2 | 1 | no | — |
| 236 | #97 | — | 2 | 1 | no | — |
| 237 | #95 | — | 4 | 2 | no | — |
| 238 | #41 | — | 2 | 2 | no | — |
| 239 | #41 | — | 2 | 2 | no | — |
| 240 | #41 | — | 4 | 1 | no | — |
| 241 | #41 | — | 4 | 1 | no | — |
| 242 | C2×Q8 | — | 2 | 1 | no | — |
| 243 | C2×Q8 | — | 2 | 2 | no | — |
| 244 | C2×Q8 | — | 4 | 1 | no | — |
| 245 | C2×Q8 | — | 4 | 1 | no | — |
| 246 | C2×Q8 | — | 4 | 1 | no | — |
| 247 | C2×Q8 | — | 4 | 1 | no | — |
| 248 | C2×Q8 | — | 4 | 1 | no | — |
| 249 | C2×D4 | — | 2 | 1 | no | — |
| 250 | C2×D4 | — | 4 | 1 | no | — |
| 251 | C22×C4 | — | 2 | 1 | no | — |
| 252 | C22×C4 | — | 4 | 1 | no | — |
| 253 | C22×C4 | — | 4 | 1 | no | — |
| 254 | C22×C4 | — | 4 | 1 | no | — |
| 255 | C22×C4 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 256 | Q16 | — | 2 | 2 | no | — |
| 257 | Q16 | — | 2 | 1 | no | — |
| 258 | Q16 | — | 2 | 2 | no | — |
| 259 | Q16 | — | 4 | 1 | no | — |
| 260 | Q16 | — | 4 | 1 | no | — |
| 261 | Q16 | C22⋊C4×C137 | 1 | 2 | yes | — |
| 262 | SD16 | — | 2 | 2 | no | — |
| 263 | SD16 | — | 2 | 2 | no | — |
| 264 | D8 | — | 2 | 1 | no | — |
| 265 | D8 | C22⋊C4×C137 | 1 | 2 | yes | — |
| 266 | M16 | — | 2 | 2 | no | — |
| 267 | M16 | — | 4 | 4 | no | — |
| 268 | M16 | — | 4 | 1 | no | — |
| 269 | C2×C8 | — | 2 | 1 | no | — |
| 270 | C2×C8 | — | 2 | 1 | no | — |
| 271 | C2×C8 | — | 4 | 4 | no | — |
| 272 | C2×C8 | — | 4 | 1 | no | — |
| 273 | C2×C8 | D8×C137 | 1 | 2 | yes | — |
| 274 | C2×C8 | C22×C4×C137 | 1 | 1 | yes | characteristic |
| 275 | C2×C8 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 276 | C2×C8 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 277 | C2×C8 | C2×D4×C137 | 1 | 1 | yes | characteristic |
| 278 | C2×C8 | #41×C137 | 1 | 1 | yes | characteristic |
| 279 | C2×C8 | #41×C137 | 1 | 1 | yes | characteristic |
| 280 | C4⋊C4 | — | 4 | 1 | no | — |
| 281 | C4⋊C4 | — | 4 | 1 | no | — |
| 282 | C42 | — | 2 | 1 | no | — |
| 283 | C42 | — | 2 | 1 | no | — |
| 284 | C16 | — | 2 | 2 | no | — |
| 285 | C16 | — | 4 | 1 | no | — |
| 286 | C23 | — | 4 | 1 | no | — |
| 287 | C23 | AGL(1,ℤ/8)×C137 | 1 | 1 | yes | characteristic |
| 288 | Q8 | — | 2 | 2 | no | — |
| 289 | Q8 | — | 4 | 1 | no | — |
| 290 | Q8 | — | 4 | 2 | no | — |
| 291 | Q8 | — | 4 | 2 | no | — |
| 292 | Q8 | — | 8 | 1 | no | — |
| 293 | Q8 | — | 8 | 1 | no | — |
| 294 | D4 | — | 2 | 2 | no | — |
| 295 | D4 | — | 4 | 2 | no | — |
| 296 | D4 | — | 4 | 2 | no | — |
| 297 | D4 | — | 4 | 1 | no | — |
| 298 | C2×C4 | — | 4 | 1 | no | — |
| 299 | C2×C4 | — | 4 | 2 | no | — |
| 300 | C2×C4 | — | 4 | 2 | no | — |
| 301 | C2×C4 | — | 4 | 2 | no | — |
| 302 | C2×C4 | — | 4 | 2 | no | — |
| 303 | C2×C4 | — | 4 | 1 | no | — |
| 304 | C2×C4 | — | 8 | 1 | no | — |
| 305 | C2×C4 | — | 8 | 1 | no | — |
| 306 | C2×C4 | — | 8 | 2 | no | — |
| 307 | C2×C4 | — | 8 | 1 | no | — |
| 308 | C2×C4 | C4×D4×C137 | 1 | 1 | yes | characteristic |
| 309 | C2×C4 | #120×C137 | 1 | 1 | yes | characteristic |
| 310 | C2×C4 | #121×C137 | 1 | 1 | yes | characteristic |
| 311 | C2×C4 | C2×D8×C137 | 1 | 1 | yes | characteristic |
| 312 | C2×C4 | #135×C137 | 1 | 1 | yes | characteristic |
| 313 | C2×C4 | AGL(1,ℤ/8)×C137 | 1 | 1 | yes | characteristic |
| 314 | C8 | — | 2 | 2 | no | — |
| 315 | C8 | — | 4 | 2 | no | — |
| 316 | C8 | C2×C22⋊C4×C137 | 1 | 1 | yes | characteristic |
| 317 | C8 | C4×D4×C137 | 1 | 1 | yes | characteristic |
| 318 | C8 | #121×C137 | 1 | 1 | yes | characteristic |
| 319 | C8 | #123×C137 | 1 | 1 | yes | characteristic |
| 320 | C22 | — | 2 | 2 | no | — |
| 321 | C22 | — | 4 | 2 | no | — |
| 322 | C22 | — | 8 | 2 | no | — |
| 323 | C22 | #442×C137 | 1 | 1 | yes | characteristic |
| 324 | C22 | #449×C137 | 1 | 1 | yes | characteristic |
| 325 | C22 | #459×C137 | 1 | 1 | yes | characteristic |
| 326 | C4 | — | 4 | 2 | no | — |
| 327 | C4 | — | 8 | 1 | no | — |
| 328 | C4 | — | 8 | 2 | no | — |
| 329 | C4 | — | 16 | 1 | no | — |
| 330 | C4 | #386×C137 | 1 | 1 | yes | characteristic |
| 331 | C4 | C4×D8×C137 | 1 | 1 | yes | characteristic |
| 332 | C4 | #447×C137 | 1 | 1 | yes | characteristic |
| 333 | C4 | #463×C137 | 1 | 1 | yes | characteristic |
| 334 | C2 | — | 2 | 1 | no | — |
| 335 | C2 | — | 2 | 1 | no | — |
| 336 | C2 | — | 8 | 2 | no | — |
| 337 | C2 | #1879×C137 | 1 | 1 | yes | characteristic |
| 338 | C2 | #2180×C137 | 1 | 2 | yes | — |
Finite Group Databasebeta