| 1 | #22598389 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22597338 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22597075 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22587253 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22587229 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22587217 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #22587203 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #22587175 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #22587168 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #22587151 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #22587134 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #22586803 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #22586730 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #22586635 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C71×#1574 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×M16×D71 | — | 2 | 1 | no | — |
| 17 | #17986533 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×C4×D284 | C22 | 1 | 1 | yes | characteristic |
| 19 | #17986335 | C4 | 1 | 1 | yes | characteristic |
| 20 | #17986318 | C4 | 1 | 1 | yes | characteristic |
| 21 | #17986300 | C4 | 1 | 1 | yes | characteristic |
| 22 | #17986300 | C4 | 1 | 1 | yes | characteristic |
| 23 | #17986215 | C4 | 1 | 1 | yes | characteristic |
| 24 | #17986215 | C4 | 1 | 1 | yes | characteristic |
| 25 | #17986152 | C4 | 1 | 1 | yes | characteristic |
| 26 | #17986135 | C4 | 1 | 1 | yes | characteristic |
| 27 | #17986126 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #17986123 | C22 | 1 | 1 | yes | characteristic, complemented |
| 29 | C4×#11765854 | C22 | 1 | 1 | yes | characteristic |
| 30 | C4×#11765854 | C22 | 1 | 1 | yes | characteristic |
| 31 | C4×D568 | C22 | 1 | 1 | yes | characteristic |
| 32 | C4×D568 | C22 | 1 | 1 | yes | characteristic |
| 33 | #17986076 | C22 | 1 | 1 | yes | characteristic |
| 34 | #17986076 | C22 | 1 | 1 | yes | characteristic |
| 35 | #17986076 | C22 | 1 | 1 | yes | characteristic, complemented |
| 36 | #17986074 | — | 2 | 1 | no | — |
| 37 | #17986073 | — | 2 | 1 | no | — |
| 38 | #17986069 | — | 2 | 1 | no | — |
| 39 | #17986069 | — | 2 | 1 | no | — |
| 40 | #17986064 | C22 | 1 | 1 | yes | characteristic |
| 41 | #17986064 | C22 | 1 | 1 | yes | characteristic |
| 42 | #17986064 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | #17986058 | — | 2 | 1 | no | — |
| 44 | #17986052 | C22 | 1 | 1 | yes | characteristic |
| 45 | #17985962 | — | 2 | 1 | no | — |
| 46 | #17985953 | — | 2 | 1 | no | — |
| 47 | C4×#11765849 | C22 | 1 | 1 | yes | characteristic |
| 48 | #17985729 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | #17985729 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #17985726 | C22 | 1 | 1 | yes | characteristic |
| 51 | #17985726 | C22 | 1 | 1 | yes | characteristic |
| 52 | #17985726 | C22 | 1 | 1 | yes | characteristic |
| 53 | #17985726 | C22 | 1 | 1 | yes | characteristic |
| 54 | #17985726 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | #17985726 | C22 | 1 | 1 | yes | characteristic, complemented |
| 56 | #17985721 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | #17985721 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | #17985720 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | C8×C71⋊C8 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | #431×C71 | C22 | 1 | 1 | yes | characteristic |
| 61 | #431×C71 | C22 | 1 | 1 | yes | characteristic |
| 62 | #423×C71 | C22 | 1 | 1 | yes | characteristic |
| 63 | #335×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | #335×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | #334×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 66 | #334×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 67 | C22×D284 | C2×C4 | 1 | 1 | yes | characteristic |
| 68 | C22×C4×D71 | — | 2 | 1 | no | — |
| 69 | C2×#11765854 | C2×C4 | 1 | 1 | yes | characteristic |
| 70 | C2×#11765854 | C2×C4 | 1 | 1 | yes | characteristic |
| 71 | C2×D568 | C2×C4 | 1 | 1 | yes | characteristic |
| 72 | C2×D568 | C2×C4 | 1 | 1 | yes | characteristic |
| 73 | C2×#11765849 | D4 | 1 | 1 | yes | characteristic |
| 74 | C2×#11765849 | D4 | 1 | 1 | yes | characteristic |
| 75 | C2×#11765848 | — | 2 | 1 | no | — |
| 76 | C2×#11765848 | — | 2 | 1 | no | — |
| 77 | C2×#11765848 | — | 2 | 1 | no | — |
| 78 | M16×D71 | — | 4 | 4 | no | — |
| 79 | C2×C8×D71 | — | 2 | 1 | no | — |
| 80 | C2×C8×D71 | — | 2 | 1 | no | — |
| 81 | C2×C8×D71 | — | 2 | 1 | no | — |
| 82 | #14556122 | — | 2 | 1 | no | — |
| 83 | #14556120 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | #14556116 | C2×C4 | 1 | 1 | yes | characteristic |
| 85 | #14556111 | — | 2 | 1 | no | — |
| 86 | #14556107 | C2×C4 | 1 | 1 | yes | characteristic |
| 87 | #14556102 | C2×C4 | 1 | 1 | yes | characteristic |
| 88 | C4×Dic142 | C23 | 1 | 1 | yes | characteristic |
| 89 | C4×D284 | — | 2 | 1 | no | — |
| 90 | C4×D284 | — | 2 | 1 | no | — |
| 91 | C4×D284 | C2×C4 | 1 | 1 | yes | characteristic |
| 92 | C4×D284 | C2×C4 | 1 | 1 | yes | characteristic |
| 93 | C4×D284 | C23 | 1 | 1 | yes | characteristic |
| 94 | C4×D284 | C23 | 1 | 1 | yes | characteristic |
| 95 | C4×D284 | C23 | 1 | 1 | yes | characteristic |
| 96 | C4×C22⋊D71 | — | 2 | 1 | no | — |
| 97 | #14556085 | — | 2 | 1 | no | — |
| 98 | C2×C4⋊Dic71 | C2×C4 | 1 | 1 | yes | characteristic |
| 99 | C2×(C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 100 | #14556062 | C2×C4 | 1 | 1 | yes | characteristic |
| 101 | #14556062 | C2×C4 | 1 | 1 | yes | characteristic |
| 102 | #14556060 | C2×C4 | 1 | 1 | yes | characteristic |
| 103 | #14556060 | C2×C4 | 1 | 1 | yes | characteristic |
| 104 | C4⋊(C71⋊C8) | — | 2 | 1 | no | — |
| 105 | Dic71⋊C8 | — | 2 | 1 | no | — |
| 106 | Dic71⋊C8 | — | 2 | 1 | no | — |
| 107 | #14556053 | C2×C4 | 1 | 1 | yes | characteristic |
| 108 | #14556053 | C2×C4 | 1 | 1 | yes | characteristic |
| 109 | #14556050 | C2×C4 | 1 | 1 | yes | characteristic |
| 110 | #14556050 | C2×C4 | 1 | 1 | yes | characteristic |
| 111 | #14556050 | C2×C4 | 1 | 1 | yes | characteristic |
| 112 | #14556050 | C2×C4 | 1 | 1 | yes | characteristic |
| 113 | #14556050 | C2×C4 | 1 | 1 | yes | characteristic |
| 114 | #14556050 | C2×C4 | 1 | 1 | yes | characteristic |
| 115 | C22⋊(C71⋊C8) | — | 2 | 1 | no | — |
| 116 | (C2×D71)⋊C8 | — | 2 | 1 | no | — |
| 117 | (C2×D71)⋊C8 | — | 2 | 1 | no | — |
| 118 | (C2×D71)⋊C8 | — | 2 | 1 | no | — |
| 119 | (C2×D71)⋊C8 | — | 2 | 1 | no | — |
| 120 | (C2×D71)⋊C8 | — | 2 | 1 | no | — |
| 121 | (C2×D71)⋊C8 | — | 2 | 1 | no | — |
| 122 | #14556039 | D4 | 1 | 1 | yes | characteristic |
| 123 | #14556039 | D4 | 1 | 1 | yes | characteristic |
| 124 | #14556038 | — | 2 | 1 | no | — |
| 125 | C4×C71⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 126 | C4×C71⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 127 | C4×C71⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 128 | C4×C71⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 129 | C8×Dic71 | — | 2 | 1 | no | — |
| 130 | C2×M16×C71 | — | 2 | 1 | no | — |
| 131 | C2×C42×C71 | C23 | 1 | 1 | yes | characteristic |
| 132 | C4⋊C8×C71 | — | 2 | 1 | no | — |
| 133 | C4⋊C8×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 134 | C4⋊C8×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 135 | C4⋊C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 136 | C4⋊C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 137 | C4⋊C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 138 | C4⋊C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 139 | C22⋊C8×C71 | — | 2 | 1 | no | — |
| 140 | C22⋊C8×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 141 | C22⋊C8×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 142 | C4×C8×C71 | — | 2 | 1 | no | — |
| 143 | C4×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 144 | C4×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 145 | C23×D71 | — | 2 | 1 | no | — |
| 146 | C2×Dic142 | C22×C4 | 1 | 1 | yes | characteristic |
| 147 | C2×D284 | — | 2 | 2 | no | — |
| 148 | C2×D284 | — | 2 | 1 | no | — |
| 149 | C2×D284 | — | 4 | 1 | no | — |
| 150 | C2×D284 | C22×C4 | 1 | 1 | yes | characteristic |
| 151 | C2×D284 | C22×C4 | 1 | 1 | yes | characteristic |
| 152 | C2×D284 | C22×C4 | 1 | 1 | yes | characteristic |
| 153 | C2×C22⋊D71 | — | 2 | 1 | no | — |
| 154 | C22×Dic71 | — | 2 | 1 | no | — |
| 155 | C2×C4×D71 | — | 2 | 1 | no | — |
| 156 | C2×C4×D71 | — | 2 | 1 | no | — |
| 157 | C2×C4×D71 | — | 2 | 1 | no | — |
| 158 | C2×C4×D71 | — | 2 | 1 | no | — |
| 159 | C2×C4×D71 | — | 2 | 1 | no | — |
| 160 | C2×C4×D71 | — | 4 | 2 | no | — |
| 161 | C2×C4×D71 | — | 4 | 2 | no | — |
| 162 | #11765854 | — | 2 | 2 | no | — |
| 163 | #11765854 | — | 4 | 1 | no | — |
| 164 | D568 | — | 2 | 2 | no | — |
| 165 | D568 | — | 4 | 1 | no | — |
| 166 | #11765849 | — | 2 | 2 | no | — |
| 167 | #11765849 | — | 4 | 1 | no | — |
| 168 | #11765848 | — | 4 | 2 | no | — |
| 169 | #11765848 | — | 4 | 2 | no | — |
| 170 | #11765848 | — | 4 | 2 | no | — |
| 171 | C2×C71⋊C8 | — | 2 | 1 | no | — |
| 172 | C2×C71⋊C8 | — | 2 | 1 | no | — |
| 173 | C2×C71⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C2×C71⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C2×C71⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C2×C71⋊C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | C8×D71 | — | 4 | 2 | no | — |
| 178 | C8×D71 | — | 4 | 2 | no | — |
| 179 | C8×D71 | — | 4 | 2 | no | — |
| 180 | C4⋊Dic71 | — | 2 | 1 | no | — |
| 181 | C4⋊Dic71 | C22×C4 | 1 | 1 | yes | characteristic |
| 182 | C4⋊Dic71 | C22×C4 | 1 | 1 | yes | characteristic |
| 183 | C4⋊Dic71 | C22×C4 | 1 | 1 | yes | characteristic |
| 184 | C4⋊Dic71 | C22×C4 | 1 | 1 | yes | characteristic |
| 185 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 186 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 187 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 188 | Dic71⋊C4 | — | 2 | 1 | no | — |
| 189 | C22⋊Dic71 | — | 2 | 1 | no | — |
| 190 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 191 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 192 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 193 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 194 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 195 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 196 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 197 | (C2×D71)⋊C4 | — | 2 | 1 | no | — |
| 198 | C4×Dic71 | — | 2 | 1 | no | — |
| 199 | C22×C4×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 200 | C22×C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 201 | C22×C4×C71 | #41 | 1 | 1 | yes | characteristic |
| 202 | M16×C71 | — | 4 | 2 | no | — |
| 203 | C2×C8×C71 | — | 2 | 1 | no | — |
| 204 | C2×C8×C71 | — | 2 | 1 | no | — |
| 205 | C2×C8×C71 | — | 2 | 1 | no | — |
| 206 | C2×C8×C71 | — | 2 | 1 | no | — |
| 207 | C2×C8×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 208 | C2×C8×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 209 | C2×C8×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 210 | C2×C8×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 211 | C42×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 212 | C42×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 213 | C42×C71 | #41 | 1 | 1 | yes | characteristic |
| 214 | C42×C71 | C24 | 1 | 1 | yes | characteristic |
| 215 | C23×C71 | C4×D4 | 1 | 1 | yes | characteristic |
| 216 | C22×D71 | — | 2 | 1 | no | — |
| 217 | C22×D71 | — | 2 | 1 | no | — |
| 218 | C22×D71 | — | 2 | 1 | no | — |
| 219 | C22×D71 | — | 4 | 2 | no | — |
| 220 | C22×D71 | — | 4 | 2 | no | — |
| 221 | C22×D71 | — | 8 | 1 | no | — |
| 222 | C2×C4×C71 | — | 2 | 1 | no | — |
| 223 | C2×C4×C71 | — | 2 | 1 | no | — |
| 224 | C2×C4×C71 | — | 2 | 1 | no | — |
| 225 | C2×C4×C71 | — | 2 | 1 | no | — |
| 226 | C2×C4×C71 | — | 4 | 1 | no | — |
| 227 | C2×C4×C71 | C4×D4 | 1 | 1 | yes | characteristic |
| 228 | C2×C4×C71 | C4×D4 | 1 | 1 | yes | characteristic |
| 229 | C2×C4×C71 | C4×D4 | 1 | 1 | yes | characteristic |
| 230 | C2×C4×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 231 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 232 | C2×C4×C71 | C2×#41 | 1 | 1 | yes | characteristic |
| 233 | C22⋊D71 | — | 8 | 1 | no | — |
| 234 | C2×Dic71 | — | 2 | 1 | no | — |
| 235 | C2×Dic71 | — | 2 | 1 | no | — |
| 236 | C2×Dic71 | — | 2 | 1 | no | — |
| 237 | C2×Dic71 | — | 2 | 1 | no | — |
| 238 | C2×Dic71 | — | 2 | 1 | no | — |
| 239 | C2×Dic71 | — | 4 | 2 | no | — |
| 240 | D284 | — | 2 | 1 | no | — |
| 241 | D284 | — | 2 | 1 | no | — |
| 242 | D284 | — | 2 | 1 | no | — |
| 243 | D284 | — | 2 | 1 | no | — |
| 244 | D284 | — | 2 | 1 | no | — |
| 245 | D284 | — | 4 | 2 | no | — |
| 246 | D284 | #131 | 1 | 2 | yes | — |
| 247 | C4×D71 | — | 4 | 2 | no | — |
| 248 | C4×D71 | — | 4 | 2 | no | — |
| 249 | C4×D71 | — | 4 | 1 | no | — |
| 250 | C4×D71 | — | 4 | 1 | no | — |
| 251 | C4×D71 | — | 4 | 1 | no | — |
| 252 | C4×D71 | — | 4 | 1 | no | — |
| 253 | C4×D71 | — | 4 | 1 | no | — |
| 254 | C4×D71 | — | 4 | 1 | no | — |
| 255 | Dic142 | — | 2 | 1 | no | — |
| 256 | Dic142 | — | 2 | 1 | no | — |
| 257 | C8×C71 | — | 2 | 1 | no | — |
| 258 | C8×C71 | — | 2 | 1 | no | — |
| 259 | C8×C71 | — | 2 | 1 | no | — |
| 260 | C8×C71 | — | 2 | 1 | no | — |
| 261 | C8×C71 | — | 4 | 1 | no | — |
| 262 | C8×C71 | — | 4 | 1 | no | — |
| 263 | C8×C71 | — | 4 | 1 | no | — |
| 264 | C8×C71 | — | 4 | 1 | no | — |
| 265 | C71⋊C8 | — | 2 | 1 | no | — |
| 266 | C71⋊C8 | — | 2 | 1 | no | — |
| 267 | C71⋊C8 | — | 2 | 1 | no | — |
| 268 | C71⋊C8 | — | 4 | 1 | no | — |
| 269 | C71⋊C8 | — | 4 | 1 | no | — |
| 270 | C71⋊C8 | AGL(1,ℤ/8) | 1 | 2 | yes | — |
| 271 | C22×C71 | — | 2 | 1 | no | — |
| 272 | C22×C71 | — | 2 | 1 | no | — |
| 273 | C22×C71 | — | 2 | 1 | no | — |
| 274 | C22×C71 | C2×C4×D4 | 1 | 1 | yes | characteristic |
| 275 | C2×D71 | — | 2 | 2 | no | — |
| 276 | C2×D71 | — | 4 | 1 | no | — |
| 277 | C2×D71 | — | 4 | 1 | no | — |
| 278 | C2×D71 | — | 4 | 1 | no | — |
| 279 | C2×D71 | — | 4 | 1 | no | — |
| 280 | C2×D71 | — | 4 | 1 | no | — |
| 281 | C2×D71 | — | 4 | 1 | no | — |
| 282 | C2×D71 | — | 4 | 1 | no | — |
| 283 | C2×D71 | — | 4 | 1 | no | — |
| 284 | C2×D71 | — | 8 | 4 | no | — |
| 285 | C4×C71 | — | 2 | 1 | no | — |
| 286 | C4×C71 | — | 2 | 1 | no | — |
| 287 | C4×C71 | — | 2 | 1 | no | — |
| 288 | C4×C71 | — | 2 | 1 | no | — |
| 289 | C4×C71 | C2×#131 | 1 | 1 | yes | characteristic |
| 290 | C4×C71 | #568 | 1 | 1 | yes | characteristic |
| 291 | C4×C71 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 292 | C4×C71 | #575 | 1 | 1 | yes | characteristic |
| 293 | Dic71 | — | 4 | 1 | no | — |
| 294 | Dic71 | — | 4 | 1 | no | — |
| 295 | Dic71 | — | 4 | 1 | no | — |
| 296 | Dic71 | — | 4 | 1 | no | — |
| 297 | Dic71 | — | 4 | 1 | no | — |
| 298 | #18006 | — | 71 | 1 | no | maximal, Sylow |
| 299 | C2×C71 | — | 4 | 1 | no | — |
| 300 | C2×C71 | #2933 | 1 | 1 | yes | characteristic |
| 301 | C2×C71 | C4×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 302 | C2×C71 | #2957 | 1 | 1 | yes | characteristic |
| 303 | D71 | — | 4 | 2 | no | — |
| 304 | D71 | — | 8 | 1 | no | — |
| 305 | D71 | — | 8 | 1 | no | — |
| 306 | #3105 | — | 71 | 1 | no | — |
| 307 | #2969 | — | 71 | 1 | no | — |
| 308 | D4×M16 | — | 71 | 1 | no | — |
| 309 | #1594 | — | 71 | 1 | no | — |
| 310 | #1590 | — | 71 | 1 | no | — |
| 311 | #1588 | — | 71 | 1 | no | — |
| 312 | #1586 | — | 71 | 1 | no | — |
| 313 | #1582 | — | 71 | 1 | no | — |
| 314 | #1581 | — | 71 | 1 | no | — |
| 315 | SD16⋊C8 | — | 71 | 1 | no | — |
| 316 | C8×D8 | — | 71 | 1 | no | — |
| 317 | #1574 | D71 | 1 | 1 | yes | characteristic, complemented |
| 318 | #1495 | — | 71 | 1 | no | — |
| 319 | #1478 | — | 71 | 1 | no | — |
| 320 | #1453 | — | 71 | 1 | no | — |
| 321 | C71 | #18006 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 322 | C22×M16 | — | 142 | 1 | no | — |
| 323 | #529 | — | 71 | 1 | no | — |
| 324 | C2×C4×D4 | — | 71 | 1 | no | — |
| 325 | #484 | — | 71 | 1 | no | — |
| 326 | #481 | — | 71 | 1 | no | — |
| 327 | #478 | — | 71 | 1 | no | — |
| 328 | #478 | — | 71 | 1 | no | — |
| 329 | #463 | — | 71 | 1 | no | — |
| 330 | #463 | — | 71 | 1 | no | — |
| 331 | #450 | — | 71 | 1 | no | — |
| 332 | #447 | — | 71 | 1 | no | — |
| 333 | #446 | — | 71 | 1 | no | — |
| 334 | C8×Q8 | — | 71 | 1 | no | — |
| 335 | C4×SD16 | — | 71 | 1 | no | — |
| 336 | C4×SD16 | — | 71 | 1 | no | — |
| 337 | C4×D8 | — | 71 | 1 | no | — |
| 338 | C4×D8 | — | 71 | 1 | no | — |
| 339 | #436 | — | 71 | 1 | no | — |
| 340 | #436 | — | 71 | 1 | no | — |
| 341 | #436 | — | 71 | 1 | no | — |
| 342 | #436 | — | 142 | 1 | no | — |
| 343 | #435 | — | 142 | 1 | no | — |
| 344 | #435 | — | 142 | 1 | no | — |
| 345 | #435 | — | 142 | 1 | no | — |
| 346 | C8×D4 | — | 71 | 1 | no | — |
| 347 | C8×D4 | — | 71 | 1 | no | — |
| 348 | C8×D4 | — | 71 | 1 | no | — |
| 349 | #433 | — | 142 | 1 | no | — |
| 350 | #431 | — | 71 | 1 | no | — |
| 351 | #431 | C2×D71 | 1 | 1 | yes | characteristic |
| 352 | #431 | C2×D71 | 1 | 1 | yes | characteristic |
| 353 | #423 | C2×D71 | 1 | 1 | yes | characteristic |
| 354 | #407 | — | 142 | 1 | no | — |
| 355 | #405 | — | 142 | 1 | no | — |
| 356 | C4×M16 | — | 71 | 1 | no | — |
| 357 | #335 | C2×D71 | 1 | 1 | yes | characteristic, complemented |
| 358 | #335 | C2×D71 | 1 | 1 | yes | characteristic, complemented |
| 359 | #334 | C2×D71 | 1 | 1 | yes | characteristic, complemented |
| 360 | #334 | C2×D71 | 1 | 1 | yes | characteristic, complemented |
| 361 | Q8⋊C8 | — | 71 | 1 | no | — |
| 362 | Q8⋊C8 | — | 71 | 1 | no | — |
| 363 | D4⋊C8 | — | 71 | 1 | no | — |
| 364 | D4⋊C8 | — | 71 | 1 | no | — |
| 365 | D4⋊C8 | — | 71 | 1 | no | — |
| 366 | D4⋊C8 | — | 71 | 1 | no | — |
| 367 | D4⋊C8 | — | 71 | 1 | no | — |
| 368 | D4⋊C8 | — | 71 | 1 | no | — |
| 369 | #322 | — | 71 | 1 | no | — |
| 370 | #322 | — | 71 | 1 | no | — |
| 371 | #322 | — | 71 | 1 | no | — |
| 372 | C82 | — | 71 | 1 | no | — |
| 373 | C22×D4 | — | 71 | 1 | no | — |
| 374 | C23×C4 | — | 142 | 1 | no | — |
| 375 | C2×SD16 | — | 71 | 1 | no | — |
| 376 | C2×SD16 | — | 71 | 1 | no | — |
| 377 | C2×D8 | — | 71 | 1 | no | — |
| 378 | C2×D8 | — | 71 | 1 | no | — |
| 379 | C2×M16 | — | 2 | 1 | no | — |
| 380 | C2×M16 | — | 284 | 4 | no | — |
| 381 | C2×M16 | — | 71 | 1 | no | — |
| 382 | C2×M16 | — | 71 | 1 | no | — |
| 383 | C2×M16 | — | 142 | 1 | no | — |
| 384 | C2×M16 | — | 142 | 1 | no | — |
| 385 | C2×M16 | — | 142 | 1 | no | — |
| 386 | C22×C8 | — | 142 | 1 | no | — |
| 387 | C22×C8 | — | 142 | 1 | no | — |
| 388 | C22×C8 | — | 142 | 1 | no | — |
| 389 | #126 | — | 142 | 1 | no | — |
| 390 | #125 | — | 71 | 1 | no | — |
| 391 | #124 | — | 71 | 1 | no | — |
| 392 | #123 | — | 142 | 1 | no | — |
| 393 | C22⋊Q8 | — | 71 | 1 | no | — |
| 394 | #121 | — | 71 | 1 | no | — |
| 395 | C4×Q8 | — | 71 | 1 | no | — |
| 396 | C4×D4 | — | 71 | 1 | no | — |
| 397 | C4×D4 | — | 71 | 1 | no | — |
| 398 | C4×D4 | — | 71 | 1 | no | — |
| 399 | C4×D4 | — | 71 | 1 | no | — |
| 400 | C4×D4 | — | 71 | 1 | no | — |
| 401 | C4×D4 | — | 142 | 1 | no | — |
| 402 | C4×D4 | — | 142 | 1 | no | — |
| 403 | C4×D4 | — | 142 | 1 | no | — |
| 404 | #117 | — | 142 | 1 | no | — |
| 405 | C2×C4⋊C4 | — | 71 | 1 | no | — |
| 406 | C2×C22⋊C4 | — | 142 | 1 | no | — |
| 407 | C2×C42 | C22×D71 | 1 | 1 | yes | characteristic |
| 408 | #107 | — | 71 | 1 | no | — |
| 409 | #107 | — | 71 | 1 | no | — |
| 410 | #106 | — | 71 | 1 | no | — |
| 411 | #106 | — | 71 | 1 | no | — |
| 412 | C4⋊C8 | — | 2 | 1 | no | — |
| 413 | C4⋊C8 | — | 142 | 1 | no | — |
| 414 | C4⋊C8 | — | 142 | 1 | no | — |
| 415 | C4⋊C8 | — | 142 | 1 | no | — |
| 416 | C4⋊C8 | C4×D71 | 1 | 1 | yes | characteristic |
| 417 | C4⋊C8 | C4×D71 | 1 | 1 | yes | characteristic |
| 418 | C4⋊C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 419 | C4⋊C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 420 | C4⋊C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 421 | C4⋊C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 422 | #103 | — | 71 | 1 | no | — |
| 423 | #103 | — | 71 | 1 | no | — |
| 424 | #102 | — | 71 | 1 | no | — |
| 425 | #102 | — | 71 | 1 | no | — |
| 426 | #102 | — | 71 | 1 | no | — |
| 427 | #102 | — | 71 | 1 | no | — |
| 428 | #102 | — | 71 | 1 | no | — |
| 429 | #102 | — | 71 | 1 | no | — |
| 430 | C22⋊C8 | — | 2 | 1 | no | — |
| 431 | C22⋊C8 | — | 142 | 1 | no | — |
| 432 | C22⋊C8 | — | 142 | 1 | no | — |
| 433 | C22⋊C8 | — | 142 | 1 | no | — |
| 434 | C22⋊C8 | — | 142 | 1 | no | — |
| 435 | C22⋊C8 | — | 142 | 1 | no | — |
| 436 | C22⋊C8 | — | 142 | 1 | no | — |
| 437 | C22⋊C8 | — | 142 | 1 | no | — |
| 438 | C22⋊C8 | C4×D71 | 1 | 1 | yes | characteristic |
| 439 | C22⋊C8 | C4×D71 | 1 | 1 | yes | characteristic |
| 440 | #97 | — | 71 | 1 | no | — |
| 441 | #97 | — | 71 | 1 | no | — |
| 442 | #97 | — | 142 | 1 | no | — |
| 443 | C4×C8 | — | 2 | 1 | no | — |
| 444 | C4×C8 | — | 71 | 1 | no | — |
| 445 | C4×C8 | — | 71 | 1 | no | — |
| 446 | C4×C8 | — | 71 | 1 | no | — |
| 447 | C4×C8 | — | 71 | 1 | no | — |
| 448 | C4×C8 | — | 142 | 1 | no | — |
| 449 | C4×C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 450 | C4×C8 | C22×D71 | 1 | 1 | yes | characteristic |
| 451 | C24 | — | 142 | 1 | no | — |
| 452 | C2×Q8 | — | 71 | 1 | no | — |
| 453 | C2×D4 | — | 284 | 1 | no | — |
| 454 | C2×D4 | — | 71 | 1 | no | — |
| 455 | C2×D4 | — | 71 | 1 | no | — |
| 456 | C2×D4 | — | 71 | 1 | no | — |
| 457 | C2×D4 | — | 142 | 2 | no | — |
| 458 | C2×D4 | — | 142 | 1 | no | — |
| 459 | C2×D4 | — | 142 | 1 | no | — |
| 460 | C22×C4 | — | 284 | 2 | no | — |
| 461 | C22×C4 | — | 284 | 2 | no | — |
| 462 | C22×C4 | — | 142 | 1 | no | — |
| 463 | C22×C4 | — | 142 | 1 | no | — |
| 464 | C22×C4 | — | 142 | 1 | no | — |
| 465 | C22×C4 | — | 142 | 1 | no | — |
| 466 | C22×C4 | — | 142 | 1 | no | — |
| 467 | C22×C4 | — | 142 | 1 | no | — |
| 468 | C22×C4 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 469 | C22×C4 | D4×D71 | 1 | 1 | yes | characteristic |
| 470 | C22×C4 | #11765866 | 1 | 1 | yes | characteristic |
| 471 | SD16 | — | 284 | 1 | no | — |
| 472 | SD16 | — | 142 | 2 | no | — |
| 473 | D8 | — | 284 | 1 | no | — |
| 474 | D8 | — | 142 | 2 | no | — |
| 475 | M16 | — | 4 | 2 | no | — |
| 476 | M16 | — | 284 | 2 | no | — |
| 477 | M16 | — | 284 | 2 | no | — |
| 478 | M16 | — | 284 | 2 | no | — |
| 479 | M16 | — | 284 | 1 | no | — |
| 480 | M16 | — | 142 | 2 | no | — |
| 481 | C2×C8 | — | 2 | 1 | no | — |
| 482 | C2×C8 | — | 2 | 1 | no | — |
| 483 | C2×C8 | — | 2 | 1 | no | — |
| 484 | C2×C8 | — | 2 | 1 | no | — |
| 485 | C2×C8 | — | 284 | 2 | no | — |
| 486 | C2×C8 | — | 284 | 2 | no | — |
| 487 | C2×C8 | — | 284 | 2 | no | — |
| 488 | C2×C8 | — | 71 | 1 | no | — |
| 489 | C2×C8 | — | 71 | 1 | no | — |
| 490 | C2×C8 | — | 71 | 1 | no | — |
| 491 | C2×C8 | — | 71 | 1 | no | — |
| 492 | C2×C8 | — | 142 | 1 | no | — |
| 493 | C2×C8 | — | 142 | 1 | no | — |
| 494 | C2×C8 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 495 | C2×C8 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 496 | C2×C8 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 497 | C2×C8 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 498 | C4⋊C4 | — | 71 | 1 | no | — |
| 499 | C4⋊C4 | — | 71 | 1 | no | — |
| 500 | C4⋊C4 | — | 71 | 1 | no | — |
| 501 | C4⋊C4 | — | 71 | 1 | no | — |
| 502 | C4⋊C4 | — | 142 | 1 | no | — |
| 503 | C4⋊C4 | — | 142 | 1 | no | — |
| 504 | C4⋊C4 | — | 142 | 1 | no | — |
| 505 | C4⋊C4 | — | 142 | 1 | no | — |
| 506 | C4⋊C4 | — | 142 | 1 | no | — |
| 507 | C22⋊C4 | — | 142 | 1 | no | — |
| 508 | C22⋊C4 | — | 142 | 1 | no | — |
| 509 | C22⋊C4 | — | 142 | 1 | no | — |
| 510 | C22⋊C4 | — | 142 | 1 | no | — |
| 511 | C22⋊C4 | — | 142 | 1 | no | — |
| 512 | C22⋊C4 | — | 142 | 1 | no | — |
| 513 | C22⋊C4 | — | 142 | 1 | no | — |
| 514 | C22⋊C4 | — | 142 | 1 | no | — |
| 515 | C22⋊C4 | — | 142 | 1 | no | — |
| 516 | C42 | — | 142 | 1 | no | — |
| 517 | C42 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 518 | C42 | D4×D71 | 1 | 1 | yes | characteristic |
| 519 | C42 | #11765866 | 1 | 1 | yes | characteristic |
| 520 | C42 | C23×D71 | 1 | 1 | yes | characteristic |
| 521 | C23 | — | 284 | 2 | no | — |
| 522 | C23 | — | 284 | 2 | no | — |
| 523 | C23 | — | 568 | 1 | no | — |
| 524 | C23 | — | 142 | 1 | no | — |
| 525 | C23 | — | 142 | 1 | no | — |
| 526 | C23 | — | 142 | 1 | no | — |
| 527 | C23 | #14556090 | 1 | 1 | yes | characteristic |
| 528 | Q8 | — | 142 | 1 | no | — |
| 529 | Q8 | — | 142 | 1 | no | — |
| 530 | D4 | — | 284 | 2 | no | — |
| 531 | D4 | — | 568 | 1 | no | — |
| 532 | D4 | — | 71 | 2 | no | — |
| 533 | D4 | — | 142 | 1 | no | — |
| 534 | D4 | — | 142 | 1 | no | — |
| 535 | D4 | — | 142 | 1 | no | — |
| 536 | D4 | — | 142 | 1 | no | — |
| 537 | D4 | — | 142 | 1 | no | — |
| 538 | C2×C4 | — | 2 | 1 | no | — |
| 539 | C2×C4 | — | 2 | 1 | no | — |
| 540 | C2×C4 | — | 2 | 1 | no | — |
| 541 | C2×C4 | — | 2 | 1 | no | — |
| 542 | C2×C4 | — | 4 | 1 | no | — |
| 543 | C2×C4 | — | 284 | 2 | no | — |
| 544 | C2×C4 | — | 284 | 2 | no | — |
| 545 | C2×C4 | — | 284 | 2 | no | — |
| 546 | C2×C4 | — | 284 | 1 | no | — |
| 547 | C2×C4 | — | 284 | 1 | no | — |
| 548 | C2×C4 | — | 284 | 1 | no | — |
| 549 | C2×C4 | — | 284 | 1 | no | — |
| 550 | C2×C4 | — | 284 | 1 | no | — |
| 551 | C2×C4 | — | 284 | 1 | no | — |
| 552 | C2×C4 | — | 142 | 1 | no | — |
| 553 | C2×C4 | — | 142 | 1 | no | — |
| 554 | C2×C4 | — | 142 | 1 | no | — |
| 555 | C2×C4 | — | 142 | 1 | no | — |
| 556 | C2×C4 | — | 142 | 1 | no | — |
| 557 | C2×C4 | #14556090 | 1 | 1 | yes | characteristic |
| 558 | C2×C4 | #14556090 | 1 | 1 | yes | characteristic |
| 559 | C2×C4 | #14556090 | 1 | 1 | yes | characteristic |
| 560 | C2×C4 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 561 | C2×C4 | C2×D4×D71 | 1 | 1 | yes | characteristic |
| 562 | C2×C4 | C2×#11765866 | 1 | 1 | yes | characteristic |
| 563 | C8 | — | 2 | 1 | no | — |
| 564 | C8 | — | 2 | 1 | no | — |
| 565 | C8 | — | 2 | 1 | no | — |
| 566 | C8 | — | 2 | 1 | no | — |
| 567 | C8 | — | 4 | 1 | no | — |
| 568 | C8 | — | 4 | 1 | no | — |
| 569 | C8 | — | 4 | 1 | no | — |
| 570 | C8 | — | 4 | 1 | no | — |
| 571 | C8 | — | 284 | 1 | no | — |
| 572 | C8 | — | 284 | 1 | no | — |
| 573 | C8 | — | 71 | 2 | no | — |
| 574 | C8 | — | 142 | 1 | no | — |
| 575 | C8 | — | 142 | 1 | no | — |
| 576 | C8 | — | 142 | 1 | no | — |
| 577 | C22 | — | 2 | 1 | no | — |
| 578 | C22 | — | 2 | 1 | no | — |
| 579 | C22 | — | 2 | 1 | no | — |
| 580 | C22 | — | 284 | 1 | no | — |
| 581 | C22 | — | 284 | 1 | no | — |
| 582 | C22 | — | 284 | 1 | no | — |
| 583 | C22 | — | 284 | 1 | no | — |
| 584 | C22 | — | 284 | 1 | no | — |
| 585 | C22 | — | 284 | 1 | no | — |
| 586 | C22 | — | 284 | 1 | no | — |
| 587 | C22 | — | 284 | 1 | no | — |
| 588 | C22 | — | 568 | 4 | no | — |
| 589 | C22 | — | 142 | 2 | no | — |
| 590 | C22 | C2×#14556090 | 1 | 1 | yes | characteristic |
| 591 | C4 | — | 2 | 1 | no | — |
| 592 | C4 | — | 2 | 1 | no | — |
| 593 | C4 | — | 2 | 1 | no | — |
| 594 | C4 | — | 2 | 1 | no | — |
| 595 | C4 | — | 284 | 1 | no | — |
| 596 | C4 | — | 284 | 1 | no | — |
| 597 | C4 | — | 284 | 1 | no | — |
| 598 | C4 | — | 284 | 1 | no | — |
| 599 | C4 | — | 284 | 1 | no | — |
| 600 | C4 | #131×D71 | 1 | 1 | yes | characteristic |
| 601 | C4 | #17986764 | 1 | 1 | yes | characteristic |
| 602 | C4 | AGL(1,ℤ/8)×D71 | 1 | 1 | yes | characteristic |
| 603 | C4 | #17986798 | 1 | 1 | yes | characteristic |
| 604 | C2 | — | 4 | 1 | no | — |
| 605 | C2 | — | 284 | 2 | no | — |
| 606 | C2 | — | 568 | 1 | no | — |
| 607 | C2 | — | 568 | 1 | no | — |
| 608 | C2 | #22597064 | 1 | 1 | yes | characteristic |
| 609 | C2 | #22597147 | 1 | 1 | yes | characteristic |
| 610 | C2 | #22597256 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta