| 1 | C71×#3517 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D4×#41×C71 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C71×#3392 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C71×#3391 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C71×#3359 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C71×#3358 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C71×#3332 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C71×#3330 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | C71×#3274 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | C71×#3272 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C71×#3251 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | C71×#3207 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | C71×#3105 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | C71×#3036 | C2 | 1 | 3 | yes | maximal, complemented |
| 15 | C71×#2991 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C22×#41×C71 | — | 2 | 1 | no | — |
| 17 | C2×AGL(1,ℤ/8)×C71 | C22 | 1 | 6 | yes | — |
| 18 | #557×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 19 | #553×C71 | — | 2 | 3 | no | — |
| 20 | #550×C71 | — | 2 | 1 | no | — |
| 21 | #550×C71 | C22 | 1 | 1 | yes | characteristic |
| 22 | #550×C71 | C22 | 1 | 3 | yes | complemented |
| 23 | #550×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | D4×Q8×C71 | C22 | 1 | 1 | yes | characteristic |
| 25 | #548×C71 | — | 2 | 1 | no | — |
| 26 | #547×C71 | C22 | 1 | 3 | yes | — |
| 27 | #547×C71 | C22 | 1 | 3 | yes | complemented |
| 28 | #546×C71 | — | 2 | 3 | no | — |
| 29 | D42×C71 | C22 | 1 | 3 | yes | — |
| 30 | #540×C71 | — | 2 | 3 | no | — |
| 31 | #532×C71 | C22 | 1 | 3 | yes | — |
| 32 | #532×C71 | C22 | 1 | 3 | yes | complemented |
| 33 | #529×C71 | C22 | 1 | 3 | yes | complemented |
| 34 | #525×C71 | — | 2 | 3 | no | — |
| 35 | #520×C71 | — | 2 | 1 | no | — |
| 36 | C4×#41×C71 | C22 | 1 | 1 | yes | characteristic |
| 37 | C2×C4×D4×C71 | C22 | 1 | 3 | yes | — |
| 38 | #493×C71 | C22 | 1 | 3 | yes | complemented |
| 39 | #492×C71 | C22 | 1 | 3 | yes | complemented |
| 40 | #487×C71 | C22 | 1 | 3 | yes | complemented |
| 41 | #486×C71 | C22 | 1 | 3 | yes | complemented |
| 42 | #484×C71 | C22 | 1 | 3 | yes | complemented |
| 43 | #481×C71 | C22 | 1 | 3 | yes | complemented |
| 44 | #478×C71 | C22 | 1 | 1 | yes | characteristic |
| 45 | #478×C71 | C22 | 1 | 3 | yes | complemented |
| 46 | #475×C71 | C22 | 1 | 3 | yes | complemented |
| 47 | #474×C71 | C22 | 1 | 3 | yes | complemented |
| 48 | #469×C71 | C22 | 1 | 6 | yes | complemented |
| 49 | #468×C71 | C22 | 1 | 6 | yes | complemented |
| 50 | #463×C71 | C22 | 1 | 3 | yes | — |
| 51 | #463×C71 | C22 | 1 | 3 | yes | complemented |
| 52 | #463×C71 | C22 | 1 | 6 | yes | complemented |
| 53 | #461×C71 | C22 | 1 | 3 | yes | — |
| 54 | #461×C71 | C22 | 1 | 3 | yes | complemented |
| 55 | #460×C71 | C22 | 1 | 3 | yes | complemented |
| 56 | #459×C71 | C22 | 1 | 3 | yes | — |
| 57 | #459×C71 | C22 | 1 | 3 | yes | complemented |
| 58 | #459×C71 | C22 | 1 | 3 | yes | complemented |
| 59 | #450×C71 | C22 | 1 | 3 | yes | — |
| 60 | #449×C71 | C22 | 1 | 6 | yes | complemented |
| 61 | #449×C71 | C22 | 1 | 6 | yes | complemented |
| 62 | #447×C71 | C22 | 1 | 3 | yes | — |
| 63 | C8×Q8×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | C8×Q8×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | C4×SD16×C71 | C22 | 1 | 3 | yes | — |
| 66 | C4×SD16×C71 | C22 | 1 | 3 | yes | complemented |
| 67 | C4×D8×C71 | C22 | 1 | 3 | yes | — |
| 68 | C4×D8×C71 | C22 | 1 | 3 | yes | complemented |
| 69 | #436×C71 | C22 | 1 | 3 | yes | complemented |
| 70 | #436×C71 | C22 | 1 | 3 | yes | complemented |
| 71 | #431×C71 | C22 | 1 | 3 | yes | complemented |
| 72 | #423×C71 | C22 | 1 | 3 | yes | complemented |
| 73 | #417×C71 | C22 | 1 | 6 | yes | complemented |
| 74 | C2×#41×C71 | — | 2 | 1 | no | — |
| 75 | C2×#41×C71 | — | 2 | 1 | no | — |
| 76 | C2×#41×C71 | — | 2 | 3 | no | — |
| 77 | C2×#41×C71 | — | 2 | 3 | no | — |
| 78 | C2×#41×C71 | — | 4 | 8 | no | — |
| 79 | C2×#41×C71 | D4 | 1 | 1 | yes | characteristic |
| 80 | C2×#41×C71 | C23 | 1 | 6 | yes | — |
| 81 | C22×Q8×C71 | — | 2 | 1 | no | — |
| 82 | C22×D4×C71 | — | 2 | 3 | no | — |
| 83 | C22×D4×C71 | C23 | 1 | 3 | yes | — |
| 84 | C23×C4×C71 | — | 2 | 3 | no | — |
| 85 | AGL(1,ℤ/8)×C71 | — | 4 | 12 | no | — |
| 86 | C2×SD16×C71 | C23 | 1 | 3 | yes | — |
| 87 | C2×SD16×C71 | C23 | 1 | 3 | yes | — |
| 88 | C2×SD16×C71 | C23 | 1 | 6 | yes | — |
| 89 | C2×D8×C71 | C23 | 1 | 3 | yes | — |
| 90 | C2×D8×C71 | C23 | 1 | 3 | yes | — |
| 91 | C2×D8×C71 | C23 | 1 | 6 | yes | — |
| 92 | C2×M16×C71 | C23 | 1 | 6 | yes | — |
| 93 | C4⋊Q8×C71 | C23 | 1 | 3 | yes | — |
| 94 | C4⋊Q8×C71 | C23 | 1 | 3 | yes | — |
| 95 | #127×C71 | — | 2 | 3 | no | — |
| 96 | #127×C71 | C23 | 1 | 3 | yes | — |
| 97 | #127×C71 | C23 | 1 | 3 | yes | — |
| 98 | #126×C71 | — | 2 | 3 | no | — |
| 99 | #125×C71 | — | 2 | 3 | no | — |
| 100 | #125×C71 | C23 | 1 | 1 | yes | characteristic |
| 101 | #124×C71 | — | 2 | 3 | no | — |
| 102 | #124×C71 | C23 | 1 | 3 | yes | — |
| 103 | #123×C71 | — | 2 | 3 | no | — |
| 104 | #123×C71 | — | 2 | 6 | no | — |
| 105 | #123×C71 | — | 2 | 6 | no | — |
| 106 | C22⋊Q8×C71 | — | 2 | 3 | no | — |
| 107 | C22⋊Q8×C71 | — | 2 | 3 | no | — |
| 108 | C22⋊Q8×C71 | C23 | 1 | 3 | yes | — |
| 109 | #121×C71 | — | 2 | 3 | no | — |
| 110 | #121×C71 | — | 2 | 3 | no | — |
| 111 | #121×C71 | — | 2 | 3 | no | — |
| 112 | #121×C71 | — | 2 | 3 | no | — |
| 113 | #121×C71 | — | 2 | 3 | no | — |
| 114 | #121×C71 | — | 2 | 3 | no | — |
| 115 | #121×C71 | — | 2 | 3 | no | — |
| 116 | #121×C71 | — | 2 | 6 | no | — |
| 117 | #121×C71 | C23 | 1 | 3 | yes | — |
| 118 | #121×C71 | C23 | 1 | 6 | yes | — |
| 119 | #120×C71 | — | 2 | 6 | no | — |
| 120 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 121 | C4×Q8×C71 | D4 | 1 | 1 | yes | characteristic |
| 122 | C4×Q8×C71 | C23 | 1 | 3 | yes | — |
| 123 | C4×Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 124 | C4×D4×C71 | — | 2 | 3 | no | — |
| 125 | C4×D4×C71 | — | 2 | 3 | no | — |
| 126 | C4×D4×C71 | — | 2 | 3 | no | — |
| 127 | C4×D4×C71 | — | 2 | 3 | no | — |
| 128 | C4×D4×C71 | — | 2 | 3 | no | — |
| 129 | C4×D4×C71 | — | 2 | 3 | no | — |
| 130 | C4×D4×C71 | — | 2 | 3 | no | — |
| 131 | C4×D4×C71 | D4 | 1 | 3 | yes | — |
| 132 | C4×D4×C71 | C23 | 1 | 3 | yes | — |
| 133 | C4×D4×C71 | C23 | 1 | 3 | yes | — |
| 134 | C4×D4×C71 | C23 | 1 | 3 | yes | — |
| 135 | C4×D4×C71 | C23 | 1 | 1 | yes | characteristic |
| 136 | C4×D4×C71 | C23 | 1 | 3 | yes | — |
| 137 | C4×D4×C71 | C23 | 1 | 3 | yes | — |
| 138 | #117×C71 | — | 2 | 3 | no | — |
| 139 | #117×C71 | D4 | 1 | 3 | yes | — |
| 140 | C2×C4⋊C4×C71 | — | 2 | 3 | no | — |
| 141 | C2×C4⋊C4×C71 | C23 | 1 | 3 | yes | — |
| 142 | C2×C22⋊C4×C71 | — | 2 | 3 | no | — |
| 143 | C2×C42×C71 | C23 | 1 | 3 | yes | — |
| 144 | #107×C71 | C23 | 1 | 3 | yes | — |
| 145 | #107×C71 | C23 | 1 | 1 | yes | characteristic |
| 146 | #106×C71 | C23 | 1 | 3 | yes | — |
| 147 | #106×C71 | C23 | 1 | 1 | yes | characteristic |
| 148 | C4⋊C8×C71 | C23 | 1 | 3 | yes | — |
| 149 | C4⋊C8×C71 | C23 | 1 | 3 | yes | — |
| 150 | C4⋊C8×C71 | C23 | 1 | 3 | yes | — |
| 151 | C4⋊C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 152 | #103×C71 | C23 | 1 | 3 | yes | — |
| 153 | #103×C71 | C23 | 1 | 6 | yes | — |
| 154 | #103×C71 | C23 | 1 | 3 | yes | — |
| 155 | #102×C71 | C23 | 1 | 3 | yes | — |
| 156 | #102×C71 | C23 | 1 | 6 | yes | — |
| 157 | #102×C71 | C23 | 1 | 1 | yes | characteristic |
| 158 | #102×C71 | C23 | 1 | 3 | yes | — |
| 159 | #102×C71 | C23 | 1 | 3 | yes | — |
| 160 | #102×C71 | C23 | 1 | 1 | yes | characteristic |
| 161 | #102×C71 | C23 | 1 | 3 | yes | — |
| 162 | C22⋊C8×C71 | C23 | 1 | 3 | yes | — |
| 163 | C22⋊C8×C71 | C23 | 1 | 3 | yes | — |
| 164 | C4×C8×C71 | C23 | 1 | 3 | yes | — |
| 165 | C4×C8×C71 | C23 | 1 | 3 | yes | — |
| 166 | C24×C71 | — | 2 | 3 | no | — |
| 167 | #41×C71 | — | 2 | 4 | no | — |
| 168 | #41×C71 | — | 4 | 12 | no | — |
| 169 | #41×C71 | — | 4 | 6 | no | — |
| 170 | #41×C71 | — | 4 | 6 | no | — |
| 171 | #41×C71 | — | 4 | 12 | no | — |
| 172 | #41×C71 | — | 4 | 4 | no | — |
| 173 | #41×C71 | — | 4 | 4 | no | — |
| 174 | C2×Q8×C71 | — | 2 | 3 | no | — |
| 175 | C2×Q8×C71 | — | 4 | 4 | no | — |
| 176 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | C2×Q8×C71 | C24 | 1 | 3 | yes | — |
| 178 | C2×D4×C71 | — | 2 | 6 | no | — |
| 179 | C2×D4×C71 | — | 2 | 6 | no | — |
| 180 | C2×D4×C71 | — | 2 | 3 | no | — |
| 181 | C2×D4×C71 | — | 2 | 6 | no | — |
| 182 | C2×D4×C71 | — | 2 | 3 | no | — |
| 183 | C2×D4×C71 | — | 2 | 3 | no | — |
| 184 | C2×D4×C71 | — | 2 | 3 | no | — |
| 185 | C2×D4×C71 | — | 2 | 3 | no | — |
| 186 | C2×D4×C71 | — | 2 | 3 | no | — |
| 187 | C2×D4×C71 | — | 4 | 3 | no | — |
| 188 | C2×D4×C71 | — | 4 | 12 | no | — |
| 189 | C2×D4×C71 | C2×D4 | 1 | 3 | yes | — |
| 190 | C2×D4×C71 | C24 | 1 | 3 | yes | — |
| 191 | C2×D4×C71 | C24 | 1 | 3 | yes | — |
| 192 | C2×D4×C71 | C24 | 1 | 1 | yes | characteristic |
| 193 | C22×C4×C71 | — | 2 | 3 | no | — |
| 194 | C22×C4×C71 | — | 2 | 3 | no | — |
| 195 | C22×C4×C71 | — | 2 | 1 | no | — |
| 196 | C22×C4×C71 | — | 2 | 3 | no | — |
| 197 | C22×C4×C71 | — | 2 | 3 | no | — |
| 198 | C22×C4×C71 | — | 2 | 3 | no | — |
| 199 | C22×C4×C71 | — | 2 | 6 | no | — |
| 200 | C22×C4×C71 | — | 4 | 12 | no | — |
| 201 | C22×C4×C71 | C2×D4 | 1 | 3 | yes | — |
| 202 | C22×C4×C71 | C2×D4 | 1 | 3 | yes | — |
| 203 | C22×C4×C71 | C24 | 1 | 3 | yes | — |
| 204 | SD16×C71 | — | 2 | 6 | no | — |
| 205 | SD16×C71 | — | 4 | 3 | no | — |
| 206 | SD16×C71 | — | 4 | 6 | no | — |
| 207 | D8×C71 | — | 2 | 6 | no | — |
| 208 | D8×C71 | — | 4 | 3 | no | — |
| 209 | D8×C71 | — | 4 | 6 | no | — |
| 210 | M16×C71 | — | 4 | 6 | no | — |
| 211 | C2×C8×C71 | C24 | 1 | 1 | yes | characteristic |
| 212 | C2×C8×C71 | C24 | 1 | 1 | yes | characteristic |
| 213 | C2×C8×C71 | C24 | 1 | 3 | yes | — |
| 214 | C2×C8×C71 | C24 | 1 | 3 | yes | — |
| 215 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 216 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 217 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 218 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 219 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 220 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 221 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 222 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 223 | C4⋊C4×C71 | C2×D4 | 1 | 3 | yes | — |
| 224 | C4⋊C4×C71 | C2×D4 | 1 | 3 | yes | — |
| 225 | C4⋊C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 226 | C4⋊C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 227 | C4⋊C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 228 | C4⋊C4×C71 | C24 | 1 | 3 | yes | — |
| 229 | C22⋊C4×C71 | — | 2 | 3 | no | — |
| 230 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 231 | C22⋊C4×C71 | — | 2 | 3 | no | — |
| 232 | C22⋊C4×C71 | — | 2 | 3 | no | — |
| 233 | C22⋊C4×C71 | — | 2 | 3 | no | — |
| 234 | C22⋊C4×C71 | — | 2 | 3 | no | — |
| 235 | C22⋊C4×C71 | — | 2 | 3 | no | — |
| 236 | C22⋊C4×C71 | — | 2 | 3 | no | — |
| 237 | C22⋊C4×C71 | — | 2 | 6 | no | — |
| 238 | C22⋊C4×C71 | — | 2 | 3 | no | — |
| 239 | C22⋊C4×C71 | C2×D4 | 1 | 6 | yes | — |
| 240 | C42×C71 | — | 2 | 3 | no | — |
| 241 | C42×C71 | C2×D4 | 1 | 3 | yes | — |
| 242 | C42×C71 | C2×D4 | 1 | 3 | yes | — |
| 243 | C42×C71 | C24 | 1 | 3 | yes | — |
| 244 | C42×C71 | C24 | 1 | 1 | yes | characteristic |
| 245 | C23×C71 | — | 2 | 1 | no | — |
| 246 | C23×C71 | — | 2 | 3 | no | — |
| 247 | C23×C71 | — | 2 | 3 | no | — |
| 248 | C23×C71 | — | 4 | 6 | no | — |
| 249 | C23×C71 | — | 4 | 6 | no | — |
| 250 | C23×C71 | — | 8 | 3 | no | — |
| 251 | C23×C71 | C22×D4 | 1 | 3 | yes | — |
| 252 | Q8×C71 | — | 2 | 3 | no | — |
| 253 | Q8×C71 | — | 2 | 3 | no | — |
| 254 | Q8×C71 | — | 4 | 6 | no | — |
| 255 | Q8×C71 | AGL(1,ℤ/8) | 1 | 4 | yes | complemented |
| 256 | D4×C71 | — | 2 | 6 | no | — |
| 257 | D4×C71 | — | 2 | 3 | no | — |
| 258 | D4×C71 | — | 2 | 3 | no | — |
| 259 | D4×C71 | — | 2 | 1 | no | — |
| 260 | D4×C71 | — | 2 | 3 | no | — |
| 261 | D4×C71 | — | 2 | 3 | no | — |
| 262 | D4×C71 | — | 4 | 6 | no | — |
| 263 | D4×C71 | — | 4 | 12 | no | — |
| 264 | D4×C71 | — | 4 | 6 | no | — |
| 265 | D4×C71 | — | 4 | 6 | no | — |
| 266 | D4×C71 | — | 8 | 3 | no | — |
| 267 | D4×C71 | — | 8 | 3 | no | — |
| 268 | D4×C71 | — | 8 | 3 | no | — |
| 269 | D4×C71 | — | 8 | 6 | no | — |
| 270 | D4×C71 | H(5,𝔽2) | 1 | 2 | yes | — |
| 271 | C2×C4×C71 | — | 2 | 6 | no | — |
| 272 | C2×C4×C71 | — | 2 | 3 | no | — |
| 273 | C2×C4×C71 | — | 2 | 3 | no | — |
| 274 | C2×C4×C71 | — | 2 | 1 | no | — |
| 275 | C2×C4×C71 | — | 2 | 3 | no | — |
| 276 | C2×C4×C71 | — | 2 | 1 | no | — |
| 277 | C2×C4×C71 | — | 2 | 1 | no | — |
| 278 | C2×C4×C71 | — | 2 | 3 | no | — |
| 279 | C2×C4×C71 | — | 4 | 3 | no | — |
| 280 | C2×C4×C71 | — | 4 | 2 | no | — |
| 281 | C2×C4×C71 | — | 4 | 6 | no | — |
| 282 | C2×C4×C71 | — | 4 | 6 | no | — |
| 283 | C2×C4×C71 | — | 4 | 6 | no | — |
| 284 | C2×C4×C71 | — | 4 | 6 | no | — |
| 285 | C2×C4×C71 | — | 4 | 6 | no | — |
| 286 | C2×C4×C71 | — | 8 | 6 | no | — |
| 287 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 288 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 289 | C2×C4×C71 | C22×D4 | 1 | 3 | yes | — |
| 290 | C2×C4×C71 | C22×D4 | 1 | 3 | yes | — |
| 291 | C2×C4×C71 | C22×D4 | 1 | 3 | yes | — |
| 292 | C2×C4×C71 | C25 | 1 | 1 | yes | characteristic |
| 293 | C8×C71 | — | 2 | 3 | no | — |
| 294 | C8×C71 | — | 2 | 3 | no | — |
| 295 | C8×C71 | — | 2 | 1 | no | — |
| 296 | C8×C71 | — | 2 | 1 | no | — |
| 297 | C22×C71 | — | 2 | 3 | no | — |
| 298 | C22×C71 | — | 2 | 3 | no | — |
| 299 | C22×C71 | — | 2 | 2 | no | — |
| 300 | C22×C71 | — | 2 | 3 | no | — |
| 301 | C22×C71 | — | 4 | 1 | no | — |
| 302 | C22×C71 | — | 4 | 1 | no | — |
| 303 | C22×C71 | — | 4 | 3 | no | — |
| 304 | C22×C71 | — | 4 | 3 | no | — |
| 305 | C22×C71 | — | 4 | 3 | no | — |
| 306 | C22×C71 | — | 4 | 3 | no | — |
| 307 | C22×C71 | — | 4 | 3 | no | — |
| 308 | C22×C71 | — | 4 | 3 | no | — |
| 309 | C22×C71 | — | 8 | 12 | no | — |
| 310 | C22×C71 | C23×D4 | 1 | 1 | yes | characteristic |
| 311 | C4×C71 | — | 2 | 1 | no | — |
| 312 | C4×C71 | — | 2 | 3 | no | — |
| 313 | C4×C71 | — | 2 | 3 | no | — |
| 314 | C4×C71 | — | 2 | 1 | no | — |
| 315 | C4×C71 | — | 4 | 1 | no | — |
| 316 | C4×C71 | — | 4 | 3 | no | — |
| 317 | C4×C71 | — | 4 | 1 | no | — |
| 318 | C4×C71 | — | 4 | 1 | no | — |
| 319 | C4×C71 | — | 4 | 3 | no | — |
| 320 | C4×C71 | C2×AGL(1,ℤ/8) | 1 | 6 | yes | — |
| 321 | C4×C71 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 322 | C4×C71 | #585 | 1 | 1 | yes | characteristic |
| 323 | #62003 | C71 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 324 | C2×C71 | — | 4 | 3 | no | — |
| 325 | C2×C71 | — | 4 | 2 | no | — |
| 326 | C2×C71 | — | 8 | 3 | no | — |
| 327 | C2×C71 | — | 8 | 3 | no | — |
| 328 | C2×C71 | #3488 | 1 | 1 | yes | characteristic |
| 329 | C2×C71 | C22×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 330 | C2×C71 | #3584 | 1 | 1 | yes | characteristic |
| 331 | #3517 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 332 | D4×#41 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 333 | #3392 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 334 | #3391 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 335 | #3359 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 336 | #3358 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 337 | #3332 | C2×C71 | 1 | 3 | yes | complemented |
| 338 | #3330 | C2×C71 | 1 | 3 | yes | complemented |
| 339 | #3274 | C2×C71 | 1 | 3 | yes | complemented |
| 340 | #3272 | C2×C71 | 1 | 3 | yes | complemented |
| 341 | #3251 | C2×C71 | 1 | 3 | yes | complemented |
| 342 | #3207 | C2×C71 | 1 | 3 | yes | complemented |
| 343 | #3105 | C2×C71 | 1 | 3 | yes | complemented |
| 344 | #3036 | C2×C71 | 1 | 3 | yes | complemented |
| 345 | #2991 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 346 | C71 | #62003 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 347 | C22×#41 | — | 2 | 1 | no | — |
| 348 | C2×AGL(1,ℤ/8) | C22×C71 | 1 | 6 | yes | — |
| 349 | #557 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 350 | #553 | — | 2 | 3 | no | — |
| 351 | #550 | — | 2 | 1 | no | — |
| 352 | #550 | C22×C71 | 1 | 1 | yes | characteristic |
| 353 | #550 | C22×C71 | 1 | 3 | yes | complemented |
| 354 | #550 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 355 | D4×Q8 | C22×C71 | 1 | 1 | yes | characteristic |
| 356 | #548 | — | 2 | 1 | no | — |
| 357 | #547 | C22×C71 | 1 | 3 | yes | — |
| 358 | #547 | C22×C71 | 1 | 3 | yes | complemented |
| 359 | #546 | — | 2 | 3 | no | — |
| 360 | D42 | C22×C71 | 1 | 3 | yes | — |
| 361 | #540 | — | 2 | 3 | no | — |
| 362 | #532 | C22×C71 | 1 | 3 | yes | — |
| 363 | #532 | C22×C71 | 1 | 3 | yes | complemented |
| 364 | #529 | C22×C71 | 1 | 3 | yes | complemented |
| 365 | #525 | — | 2 | 3 | no | — |
| 366 | #520 | — | 2 | 1 | no | — |
| 367 | C4×#41 | C22×C71 | 1 | 1 | yes | characteristic |
| 368 | C2×C4×D4 | C22×C71 | 1 | 3 | yes | — |
| 369 | #493 | C22×C71 | 1 | 3 | yes | complemented |
| 370 | #492 | C22×C71 | 1 | 3 | yes | complemented |
| 371 | #487 | C22×C71 | 1 | 3 | yes | complemented |
| 372 | #486 | C22×C71 | 1 | 3 | yes | complemented |
| 373 | #484 | C22×C71 | 1 | 3 | yes | complemented |
| 374 | #481 | C22×C71 | 1 | 3 | yes | complemented |
| 375 | #478 | C22×C71 | 1 | 1 | yes | characteristic |
| 376 | #478 | C22×C71 | 1 | 3 | yes | complemented |
| 377 | #475 | C22×C71 | 1 | 3 | yes | complemented |
| 378 | #474 | C22×C71 | 1 | 3 | yes | complemented |
| 379 | #469 | C22×C71 | 1 | 6 | yes | complemented |
| 380 | #468 | C22×C71 | 1 | 6 | yes | complemented |
| 381 | #463 | C22×C71 | 1 | 3 | yes | — |
| 382 | #463 | C22×C71 | 1 | 3 | yes | complemented |
| 383 | #463 | C22×C71 | 1 | 6 | yes | complemented |
| 384 | #461 | C22×C71 | 1 | 3 | yes | — |
| 385 | #461 | C22×C71 | 1 | 3 | yes | complemented |
| 386 | #460 | C22×C71 | 1 | 3 | yes | complemented |
| 387 | #459 | C22×C71 | 1 | 3 | yes | — |
| 388 | #459 | C22×C71 | 1 | 3 | yes | complemented |
| 389 | #459 | C22×C71 | 1 | 3 | yes | complemented |
| 390 | #450 | C22×C71 | 1 | 3 | yes | — |
| 391 | #449 | C22×C71 | 1 | 6 | yes | complemented |
| 392 | #449 | C22×C71 | 1 | 6 | yes | complemented |
| 393 | #447 | C22×C71 | 1 | 3 | yes | — |
| 394 | C8×Q8 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 395 | C8×Q8 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 396 | C4×SD16 | C22×C71 | 1 | 3 | yes | — |
| 397 | C4×SD16 | C22×C71 | 1 | 3 | yes | complemented |
| 398 | C4×D8 | C22×C71 | 1 | 3 | yes | — |
| 399 | C4×D8 | C22×C71 | 1 | 3 | yes | complemented |
| 400 | #436 | C22×C71 | 1 | 3 | yes | complemented |
| 401 | #436 | C22×C71 | 1 | 3 | yes | complemented |
| 402 | #431 | C22×C71 | 1 | 3 | yes | complemented |
| 403 | #423 | C22×C71 | 1 | 3 | yes | complemented |
| 404 | #417 | C22×C71 | 1 | 6 | yes | complemented |
| 405 | C2×#41 | — | 2 | 1 | no | — |
| 406 | C2×#41 | — | 2 | 1 | no | — |
| 407 | C2×#41 | — | 2 | 3 | no | — |
| 408 | C2×#41 | — | 2 | 3 | no | — |
| 409 | C2×#41 | — | 4 | 8 | no | — |
| 410 | C2×#41 | D4×C71 | 1 | 1 | yes | characteristic |
| 411 | C2×#41 | C23×C71 | 1 | 6 | yes | — |
| 412 | C22×Q8 | — | 2 | 1 | no | — |
| 413 | C22×D4 | — | 2 | 3 | no | — |
| 414 | C22×D4 | C23×C71 | 1 | 3 | yes | — |
| 415 | C23×C4 | — | 2 | 3 | no | — |
| 416 | AGL(1,ℤ/8) | — | 4 | 12 | no | — |
| 417 | C2×SD16 | C23×C71 | 1 | 3 | yes | — |
| 418 | C2×SD16 | C23×C71 | 1 | 6 | yes | — |
| 419 | C2×SD16 | C23×C71 | 1 | 3 | yes | — |
| 420 | C2×D8 | C23×C71 | 1 | 3 | yes | — |
| 421 | C2×D8 | C23×C71 | 1 | 6 | yes | — |
| 422 | C2×D8 | C23×C71 | 1 | 3 | yes | — |
| 423 | C2×M16 | C23×C71 | 1 | 6 | yes | — |
| 424 | C4⋊Q8 | C23×C71 | 1 | 3 | yes | — |
| 425 | C4⋊Q8 | C23×C71 | 1 | 3 | yes | — |
| 426 | #127 | — | 2 | 3 | no | — |
| 427 | #127 | C23×C71 | 1 | 3 | yes | — |
| 428 | #127 | C23×C71 | 1 | 3 | yes | — |
| 429 | #126 | — | 2 | 3 | no | — |
| 430 | #125 | — | 2 | 3 | no | — |
| 431 | #125 | C23×C71 | 1 | 1 | yes | characteristic |
| 432 | #124 | — | 2 | 3 | no | — |
| 433 | #124 | C23×C71 | 1 | 3 | yes | — |
| 434 | #123 | — | 2 | 3 | no | — |
| 435 | #123 | — | 2 | 6 | no | — |
| 436 | #123 | — | 2 | 6 | no | — |
| 437 | C22⋊Q8 | — | 2 | 3 | no | — |
| 438 | C22⋊Q8 | — | 2 | 3 | no | — |
| 439 | C22⋊Q8 | C23×C71 | 1 | 3 | yes | — |
| 440 | #121 | — | 2 | 3 | no | — |
| 441 | #121 | — | 2 | 3 | no | — |
| 442 | #121 | — | 2 | 3 | no | — |
| 443 | #121 | — | 2 | 3 | no | — |
| 444 | #121 | — | 2 | 3 | no | — |
| 445 | #121 | — | 2 | 3 | no | — |
| 446 | #121 | — | 2 | 3 | no | — |
| 447 | #121 | — | 2 | 6 | no | — |
| 448 | #121 | C23×C71 | 1 | 3 | yes | — |
| 449 | #121 | C23×C71 | 1 | 6 | yes | — |
| 450 | #120 | — | 2 | 6 | no | — |
| 451 | C4×Q8 | — | 2 | 1 | no | — |
| 452 | C4×Q8 | D4×C71 | 1 | 1 | yes | characteristic |
| 453 | C4×Q8 | C23×C71 | 1 | 3 | yes | — |
| 454 | C4×Q8 | C23×C71 | 1 | 1 | yes | characteristic |
| 455 | C4×D4 | — | 2 | 3 | no | — |
| 456 | C4×D4 | — | 2 | 3 | no | — |
| 457 | C4×D4 | — | 2 | 3 | no | — |
| 458 | C4×D4 | — | 2 | 3 | no | — |
| 459 | C4×D4 | — | 2 | 3 | no | — |
| 460 | C4×D4 | — | 2 | 3 | no | — |
| 461 | C4×D4 | — | 2 | 3 | no | — |
| 462 | C4×D4 | D4×C71 | 1 | 3 | yes | — |
| 463 | C4×D4 | C23×C71 | 1 | 1 | yes | characteristic |
| 464 | C4×D4 | C23×C71 | 1 | 3 | yes | — |
| 465 | C4×D4 | C23×C71 | 1 | 3 | yes | — |
| 466 | C4×D4 | C23×C71 | 1 | 3 | yes | — |
| 467 | C4×D4 | C23×C71 | 1 | 3 | yes | — |
| 468 | C4×D4 | C23×C71 | 1 | 3 | yes | — |
| 469 | #117 | — | 2 | 3 | no | — |
| 470 | #117 | D4×C71 | 1 | 3 | yes | — |
| 471 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 472 | C2×C4⋊C4 | C23×C71 | 1 | 3 | yes | — |
| 473 | C2×C22⋊C4 | — | 2 | 3 | no | — |
| 474 | C2×C42 | C23×C71 | 1 | 3 | yes | — |
| 475 | #107 | C23×C71 | 1 | 3 | yes | — |
| 476 | #107 | C23×C71 | 1 | 1 | yes | characteristic |
| 477 | #106 | C23×C71 | 1 | 3 | yes | — |
| 478 | #106 | C23×C71 | 1 | 1 | yes | characteristic |
| 479 | C4⋊C8 | C23×C71 | 1 | 3 | yes | — |
| 480 | C4⋊C8 | C23×C71 | 1 | 3 | yes | — |
| 481 | C4⋊C8 | C23×C71 | 1 | 3 | yes | — |
| 482 | C4⋊C8 | C23×C71 | 1 | 1 | yes | characteristic |
| 483 | #103 | C23×C71 | 1 | 3 | yes | — |
| 484 | #103 | C23×C71 | 1 | 6 | yes | — |
| 485 | #103 | C23×C71 | 1 | 3 | yes | — |
| 486 | #102 | C23×C71 | 1 | 3 | yes | — |
| 487 | #102 | C23×C71 | 1 | 6 | yes | — |
| 488 | #102 | C23×C71 | 1 | 1 | yes | characteristic |
| 489 | #102 | C23×C71 | 1 | 3 | yes | — |
| 490 | #102 | C23×C71 | 1 | 3 | yes | — |
| 491 | #102 | C23×C71 | 1 | 1 | yes | characteristic |
| 492 | #102 | C23×C71 | 1 | 3 | yes | — |
| 493 | C22⋊C8 | C23×C71 | 1 | 3 | yes | — |
| 494 | C22⋊C8 | C23×C71 | 1 | 3 | yes | — |
| 495 | C4×C8 | C23×C71 | 1 | 3 | yes | — |
| 496 | C4×C8 | C23×C71 | 1 | 3 | yes | — |
| 497 | C24 | — | 2 | 3 | no | — |
| 498 | #41 | — | 2 | 4 | no | — |
| 499 | #41 | — | 4 | 12 | no | — |
| 500 | #41 | — | 4 | 6 | no | — |
| 501 | #41 | — | 4 | 6 | no | — |
| 502 | #41 | — | 4 | 12 | no | — |
| 503 | #41 | — | 4 | 4 | no | — |
| 504 | #41 | — | 4 | 4 | no | — |
| 505 | C2×Q8 | — | 2 | 3 | no | — |
| 506 | C2×Q8 | — | 4 | 4 | no | — |
| 507 | C2×Q8 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 508 | C2×Q8 | C24×C71 | 1 | 3 | yes | — |
| 509 | C2×D4 | — | 2 | 6 | no | — |
| 510 | C2×D4 | — | 2 | 6 | no | — |
| 511 | C2×D4 | — | 2 | 3 | no | — |
| 512 | C2×D4 | — | 2 | 6 | no | — |
| 513 | C2×D4 | — | 2 | 3 | no | — |
| 514 | C2×D4 | — | 2 | 3 | no | — |
| 515 | C2×D4 | — | 2 | 3 | no | — |
| 516 | C2×D4 | — | 2 | 3 | no | — |
| 517 | C2×D4 | — | 2 | 3 | no | — |
| 518 | C2×D4 | — | 4 | 3 | no | — |
| 519 | C2×D4 | — | 4 | 12 | no | — |
| 520 | C2×D4 | C2×D4×C71 | 1 | 3 | yes | — |
| 521 | C2×D4 | C24×C71 | 1 | 3 | yes | — |
| 522 | C2×D4 | C24×C71 | 1 | 3 | yes | — |
| 523 | C2×D4 | C24×C71 | 1 | 1 | yes | characteristic |
| 524 | C22×C4 | — | 2 | 3 | no | — |
| 525 | C22×C4 | — | 2 | 3 | no | — |
| 526 | C22×C4 | — | 2 | 1 | no | — |
| 527 | C22×C4 | — | 2 | 3 | no | — |
| 528 | C22×C4 | — | 2 | 3 | no | — |
| 529 | C22×C4 | — | 2 | 3 | no | — |
| 530 | C22×C4 | — | 2 | 6 | no | — |
| 531 | C22×C4 | — | 4 | 12 | no | — |
| 532 | C22×C4 | C2×D4×C71 | 1 | 3 | yes | — |
| 533 | C22×C4 | C2×D4×C71 | 1 | 3 | yes | — |
| 534 | C22×C4 | C24×C71 | 1 | 3 | yes | — |
| 535 | SD16 | — | 2 | 6 | no | — |
| 536 | SD16 | — | 4 | 3 | no | — |
| 537 | SD16 | — | 4 | 6 | no | — |
| 538 | D8 | — | 2 | 6 | no | — |
| 539 | D8 | — | 4 | 3 | no | — |
| 540 | D8 | — | 4 | 6 | no | — |
| 541 | M16 | — | 4 | 6 | no | — |
| 542 | C2×C8 | C24×C71 | 1 | 1 | yes | characteristic |
| 543 | C2×C8 | C24×C71 | 1 | 1 | yes | characteristic |
| 544 | C2×C8 | C24×C71 | 1 | 3 | yes | — |
| 545 | C2×C8 | C24×C71 | 1 | 3 | yes | — |
| 546 | C4⋊C4 | — | 2 | 3 | no | — |
| 547 | C4⋊C4 | — | 2 | 3 | no | — |
| 548 | C4⋊C4 | — | 2 | 3 | no | — |
| 549 | C4⋊C4 | — | 2 | 1 | no | — |
| 550 | C4⋊C4 | — | 2 | 1 | no | — |
| 551 | C4⋊C4 | — | 2 | 3 | no | — |
| 552 | C4⋊C4 | — | 2 | 3 | no | — |
| 553 | C4⋊C4 | — | 2 | 3 | no | — |
| 554 | C4⋊C4 | C2×D4×C71 | 1 | 3 | yes | — |
| 555 | C4⋊C4 | C2×D4×C71 | 1 | 3 | yes | — |
| 556 | C4⋊C4 | C24×C71 | 1 | 1 | yes | characteristic |
| 557 | C4⋊C4 | C24×C71 | 1 | 1 | yes | characteristic |
| 558 | C4⋊C4 | C24×C71 | 1 | 1 | yes | characteristic |
| 559 | C4⋊C4 | C24×C71 | 1 | 3 | yes | — |
| 560 | C22⋊C4 | — | 2 | 3 | no | — |
| 561 | C22⋊C4 | — | 2 | 1 | no | — |
| 562 | C22⋊C4 | — | 2 | 3 | no | — |
| 563 | C22⋊C4 | — | 2 | 3 | no | — |
| 564 | C22⋊C4 | — | 2 | 3 | no | — |
| 565 | C22⋊C4 | — | 2 | 3 | no | — |
| 566 | C22⋊C4 | — | 2 | 3 | no | — |
| 567 | C22⋊C4 | — | 2 | 3 | no | — |
| 568 | C22⋊C4 | — | 2 | 6 | no | — |
| 569 | C22⋊C4 | — | 2 | 3 | no | — |
| 570 | C22⋊C4 | C2×D4×C71 | 1 | 6 | yes | — |
| 571 | C42 | — | 2 | 3 | no | — |
| 572 | C42 | C2×D4×C71 | 1 | 3 | yes | — |
| 573 | C42 | C2×D4×C71 | 1 | 3 | yes | — |
| 574 | C42 | C24×C71 | 1 | 3 | yes | — |
| 575 | C42 | C24×C71 | 1 | 1 | yes | characteristic |
| 576 | C23 | — | 2 | 1 | no | — |
| 577 | C23 | — | 2 | 3 | no | — |
| 578 | C23 | — | 2 | 3 | no | — |
| 579 | C23 | — | 4 | 6 | no | — |
| 580 | C23 | — | 4 | 6 | no | — |
| 581 | C23 | — | 8 | 3 | no | — |
| 582 | C23 | C22×D4×C71 | 1 | 3 | yes | — |
| 583 | Q8 | — | 2 | 3 | no | — |
| 584 | Q8 | — | 2 | 3 | no | — |
| 585 | Q8 | — | 4 | 6 | no | — |
| 586 | Q8 | AGL(1,ℤ/8)×C71 | 1 | 4 | yes | complemented |
| 587 | D4 | — | 2 | 6 | no | — |
| 588 | D4 | — | 2 | 3 | no | — |
| 589 | D4 | — | 2 | 3 | no | — |
| 590 | D4 | — | 2 | 1 | no | — |
| 591 | D4 | — | 2 | 3 | no | — |
| 592 | D4 | — | 2 | 3 | no | — |
| 593 | D4 | — | 4 | 6 | no | — |
| 594 | D4 | — | 4 | 12 | no | — |
| 595 | D4 | — | 4 | 6 | no | — |
| 596 | D4 | — | 4 | 6 | no | — |
| 597 | D4 | — | 8 | 3 | no | — |
| 598 | D4 | — | 8 | 3 | no | — |
| 599 | D4 | — | 8 | 6 | no | — |
| 600 | D4 | — | 8 | 3 | no | — |
| 601 | D4 | H(5,𝔽2)×C71 | 1 | 2 | yes | — |
| 602 | C2×C4 | — | 2 | 6 | no | — |
| 603 | C2×C4 | — | 2 | 3 | no | — |
| 604 | C2×C4 | — | 2 | 3 | no | — |
| 605 | C2×C4 | — | 2 | 1 | no | — |
| 606 | C2×C4 | — | 2 | 3 | no | — |
| 607 | C2×C4 | — | 2 | 1 | no | — |
| 608 | C2×C4 | — | 2 | 1 | no | — |
| 609 | C2×C4 | — | 2 | 3 | no | — |
| 610 | C2×C4 | — | 4 | 3 | no | — |
| 611 | C2×C4 | — | 4 | 2 | no | — |
| 612 | C2×C4 | — | 4 | 6 | no | — |
| 613 | C2×C4 | — | 4 | 6 | no | — |
| 614 | C2×C4 | — | 4 | 6 | no | — |
| 615 | C2×C4 | — | 4 | 6 | no | — |
| 616 | C2×C4 | — | 4 | 6 | no | — |
| 617 | C2×C4 | — | 8 | 6 | no | — |
| 618 | C2×C4 | C22×D4×C71 | 1 | 1 | yes | characteristic |
| 619 | C2×C4 | C22×D4×C71 | 1 | 1 | yes | characteristic |
| 620 | C2×C4 | C22×D4×C71 | 1 | 3 | yes | — |
| 621 | C2×C4 | C22×D4×C71 | 1 | 3 | yes | — |
| 622 | C2×C4 | C22×D4×C71 | 1 | 3 | yes | — |
| 623 | C2×C4 | C25×C71 | 1 | 1 | yes | characteristic |
| 624 | C8 | — | 2 | 3 | no | — |
| 625 | C8 | — | 2 | 3 | no | — |
| 626 | C8 | — | 2 | 1 | no | — |
| 627 | C8 | — | 2 | 1 | no | — |
| 628 | C22 | — | 2 | 3 | no | — |
| 629 | C22 | — | 2 | 3 | no | — |
| 630 | C22 | — | 2 | 3 | no | — |
| 631 | C22 | — | 2 | 2 | no | — |
| 632 | C22 | — | 4 | 1 | no | — |
| 633 | C22 | — | 4 | 1 | no | — |
| 634 | C22 | — | 4 | 3 | no | — |
| 635 | C22 | — | 4 | 3 | no | — |
| 636 | C22 | — | 4 | 3 | no | — |
| 637 | C22 | — | 4 | 3 | no | — |
| 638 | C22 | — | 4 | 3 | no | — |
| 639 | C22 | — | 4 | 3 | no | — |
| 640 | C22 | — | 8 | 12 | no | — |
| 641 | C22 | C23×D4×C71 | 1 | 1 | yes | characteristic |
| 642 | C4 | — | 2 | 1 | no | — |
| 643 | C4 | — | 2 | 1 | no | — |
| 644 | C4 | — | 2 | 3 | no | — |
| 645 | C4 | — | 2 | 3 | no | — |
| 646 | C4 | — | 4 | 1 | no | — |
| 647 | C4 | — | 4 | 3 | no | — |
| 648 | C4 | — | 4 | 1 | no | — |
| 649 | C4 | — | 4 | 1 | no | — |
| 650 | C4 | — | 4 | 3 | no | — |
| 651 | C4 | C2×AGL(1,ℤ/8)×C71 | 1 | 6 | yes | — |
| 652 | C4 | C2×H(5,𝔽2)×C71 | 1 | 1 | yes | characteristic |
| 653 | C4 | #585×C71 | 1 | 1 | yes | characteristic |
| 654 | C2 | — | 4 | 3 | no | — |
| 655 | C2 | — | 4 | 2 | no | — |
| 656 | C2 | — | 8 | 3 | no | — |
| 657 | C2 | — | 8 | 3 | no | — |
| 658 | C2 | C71×#3488 | 1 | 1 | yes | characteristic |
| 659 | C2 | C22×AGL(1,ℤ/8)×C71 | 1 | 1 | yes | characteristic |
| 660 | C2 | C71×#3584 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta