| 1 | Q8×D8×C71 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C71×#3298 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | D4×SD16×C71 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C71×#3272 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C71×#1714 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C71×#1693 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C71×#1679 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C71×#1666 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C71×#1665 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | C71×#1654 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C71×#1651 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C71×#1639 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | C71×#1627 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | C71×#1583 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C71×#1580 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | C2×AGL(1,ℤ/8)×C71 | — | 2 | 1 | no | — |
| 17 | C22×SD16×C71 | — | 2 | 1 | no | — |
| 18 | D4×Q8×C71 | C22 | 1 | 1 | yes | characteristic |
| 19 | D4×Q8×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | #547×C71 | C22 | 1 | 1 | yes | characteristic |
| 21 | D42×C71 | C22 | 1 | 1 | yes | characteristic |
| 22 | #500×C71 | — | 2 | 1 | no | — |
| 23 | #500×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | #498×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 25 | #492×C71 | C22 | 1 | 1 | yes | characteristic |
| 26 | #492×C71 | C22 | 1 | 1 | yes | characteristic |
| 27 | #487×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 28 | #486×C71 | C22 | 1 | 1 | yes | characteristic |
| 29 | #483×C71 | — | 2 | 1 | no | — |
| 30 | #475×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 31 | #474×C71 | — | 2 | 1 | no | — |
| 32 | #474×C71 | — | 2 | 1 | no | — |
| 33 | #474×C71 | C22 | 1 | 1 | yes | characteristic |
| 34 | #474×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 35 | #468×C71 | — | 2 | 1 | no | — |
| 36 | #465×C71 | — | 2 | 1 | no | — |
| 37 | #465×C71 | — | 2 | 1 | no | — |
| 38 | #461×C71 | C22 | 1 | 1 | yes | characteristic |
| 39 | #461×C71 | C22 | 1 | 1 | yes | characteristic |
| 40 | #461×C71 | C22 | 1 | 1 | yes | characteristic |
| 41 | #460×C71 | C22 | 1 | 1 | yes | characteristic |
| 42 | #459×C71 | C22 | 1 | 1 | yes | characteristic |
| 43 | #450×C71 | — | 2 | 1 | no | — |
| 44 | #450×C71 | — | 2 | 1 | no | — |
| 45 | #449×C71 | — | 2 | 1 | no | — |
| 46 | #448×C71 | — | 2 | 1 | no | — |
| 47 | #448×C71 | — | 2 | 1 | no | — |
| 48 | C8×Q8×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 49 | C4×SD16×C71 | C22 | 1 | 1 | yes | characteristic |
| 50 | C4×D8×C71 | — | 2 | 1 | no | — |
| 51 | C4×D8×C71 | C22 | 1 | 1 | yes | characteristic |
| 52 | #436×C71 | C22 | 1 | 1 | yes | characteristic |
| 53 | C8×D4×C71 | C22 | 1 | 1 | yes | characteristic |
| 54 | C8×D4×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | C2×#103×C71 | — | 2 | 1 | no | — |
| 56 | #334×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | #334×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 58 | #332×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 59 | #332×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 60 | #332×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | #331×C71 | C22 | 1 | 1 | yes | characteristic |
| 62 | Q8⋊C8×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | D4⋊C8×C71 | C22 | 1 | 1 | yes | characteristic |
| 64 | D4⋊C8×C71 | C22 | 1 | 1 | yes | characteristic |
| 65 | D4⋊C8×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 66 | #322×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 67 | C2×#41×C71 | — | 2 | 1 | no | — |
| 68 | C22×Q8×C71 | — | 2 | 1 | no | — |
| 69 | C22×Q8×C71 | — | 2 | 1 | no | — |
| 70 | C22×D4×C71 | — | 2 | 1 | no | — |
| 71 | C22×D4×C71 | — | 2 | 1 | no | — |
| 72 | AGL(1,ℤ/8)×C71 | — | 4 | 4 | no | — |
| 73 | C2×SD16×C71 | — | 2 | 1 | no | — |
| 74 | C2×SD16×C71 | — | 2 | 1 | no | — |
| 75 | C2×SD16×C71 | — | 2 | 1 | no | — |
| 76 | C2×SD16×C71 | — | 2 | 1 | no | — |
| 77 | C2×SD16×C71 | — | 2 | 1 | no | — |
| 78 | C2×SD16×C71 | — | 2 | 1 | no | — |
| 79 | C2×SD16×C71 | — | 2 | 1 | no | — |
| 80 | C2×SD16×C71 | — | 2 | 1 | no | — |
| 81 | C2×SD16×C71 | — | 4 | 4 | no | — |
| 82 | C2×SD16×C71 | D4 | 1 | 1 | yes | characteristic |
| 83 | C2×D8×C71 | — | 2 | 1 | no | — |
| 84 | C2×D8×C71 | D4 | 1 | 1 | yes | characteristic |
| 85 | C2×M16×C71 | — | 2 | 1 | no | — |
| 86 | C22×C8×C71 | — | 2 | 1 | no | — |
| 87 | C22×C8×C71 | — | 2 | 1 | no | — |
| 88 | C4⋊Q8×C71 | — | 2 | 1 | no | — |
| 89 | C4⋊Q8×C71 | — | 2 | 1 | no | — |
| 90 | C4⋊Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 91 | C4⋊Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 92 | C4⋊Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 93 | #127×C71 | C23 | 1 | 1 | yes | characteristic |
| 94 | #123×C71 | — | 4 | 1 | no | — |
| 95 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 96 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 97 | C22⋊Q8×C71 | — | 2 | 1 | no | — |
| 98 | C22⋊Q8×C71 | — | 4 | 1 | no | — |
| 99 | C22⋊Q8×C71 | — | 4 | 1 | no | — |
| 100 | #121×C71 | — | 2 | 1 | no | — |
| 101 | #121×C71 | — | 2 | 1 | no | — |
| 102 | #121×C71 | — | 2 | 1 | no | — |
| 103 | #120×C71 | — | 4 | 1 | no | — |
| 104 | C4×Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 105 | C4×D4×C71 | — | 2 | 1 | no | — |
| 106 | C4×D4×C71 | — | 2 | 1 | no | — |
| 107 | C4×D4×C71 | C23 | 1 | 1 | yes | characteristic |
| 108 | C4×D4×C71 | C23 | 1 | 1 | yes | characteristic |
| 109 | C4×D4×C71 | C23 | 1 | 1 | yes | characteristic |
| 110 | C2×C4⋊C4×C71 | — | 2 | 1 | no | — |
| 111 | #107×C71 | — | 2 | 1 | no | — |
| 112 | #107×C71 | — | 2 | 1 | no | — |
| 113 | #107×C71 | — | 2 | 1 | no | — |
| 114 | #107×C71 | — | 2 | 1 | no | — |
| 115 | #107×C71 | D4 | 1 | 1 | yes | characteristic |
| 116 | #106×C71 | — | 2 | 1 | no | — |
| 117 | #106×C71 | — | 4 | 1 | no | — |
| 118 | #106×C71 | D4 | 1 | 1 | yes | characteristic |
| 119 | C4⋊C8×C71 | — | 2 | 1 | no | — |
| 120 | C4⋊C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 121 | C4⋊C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 122 | C4⋊C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 123 | C4⋊C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 124 | #103×C71 | — | 2 | 1 | no | — |
| 125 | #103×C71 | — | 2 | 1 | no | — |
| 126 | #103×C71 | — | 2 | 1 | no | — |
| 127 | #103×C71 | — | 2 | 1 | no | — |
| 128 | #103×C71 | — | 2 | 1 | no | — |
| 129 | #103×C71 | — | 2 | 1 | no | — |
| 130 | #103×C71 | D4 | 1 | 1 | yes | characteristic |
| 131 | #102×C71 | — | 2 | 1 | no | — |
| 132 | #102×C71 | — | 2 | 1 | no | — |
| 133 | #102×C71 | — | 2 | 1 | no | — |
| 134 | #102×C71 | — | 2 | 1 | no | — |
| 135 | #102×C71 | — | 4 | 1 | no | — |
| 136 | #102×C71 | D4 | 1 | 1 | yes | characteristic |
| 137 | #102×C71 | D4 | 1 | 1 | yes | characteristic |
| 138 | #102×C71 | D4 | 1 | 1 | yes | characteristic |
| 139 | C22⋊C8×C71 | — | 2 | 1 | no | — |
| 140 | C22⋊C8×C71 | — | 2 | 1 | no | — |
| 141 | C22⋊C8×C71 | — | 2 | 1 | no | — |
| 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 | C4×C8×C71 | C23 | 1 | 1 | yes | characteristic |
| 146 | C24×C71 | — | 4 | 1 | no | — |
| 147 | #41×C71 | — | 4 | 2 | no | — |
| 148 | #41×C71 | — | 8 | 1 | no | — |
| 149 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 150 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 151 | C2×Q8×C71 | — | 2 | 1 | no | — |
| 152 | C2×Q8×C71 | — | 4 | 1 | no | — |
| 153 | C2×Q8×C71 | — | 4 | 1 | no | — |
| 154 | C2×Q8×C71 | — | 4 | 2 | no | — |
| 155 | C2×Q8×C71 | — | 4 | 2 | no | — |
| 156 | C2×Q8×C71 | — | 8 | 1 | no | — |
| 157 | C2×Q8×C71 | — | 8 | 1 | no | — |
| 158 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 159 | C2×D4×C71 | — | 2 | 1 | no | — |
| 160 | C2×D4×C71 | — | 2 | 1 | no | — |
| 161 | C2×D4×C71 | — | 2 | 1 | no | — |
| 162 | C2×D4×C71 | — | 4 | 1 | no | — |
| 163 | C2×D4×C71 | — | 4 | 1 | no | — |
| 164 | C2×D4×C71 | — | 4 | 2 | no | — |
| 165 | C2×D4×C71 | — | 4 | 2 | no | — |
| 166 | C2×D4×C71 | — | 4 | 1 | no | — |
| 167 | C2×D4×C71 | — | 8 | 1 | no | — |
| 168 | C2×D4×C71 | — | 8 | 1 | no | — |
| 169 | C2×D4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 170 | C2×D4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 171 | C2×D4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | C22×C4×C71 | — | 2 | 1 | no | — |
| 173 | C22×C4×C71 | — | 2 | 1 | no | — |
| 174 | C22×C4×C71 | — | 2 | 1 | no | — |
| 175 | C22×C4×C71 | — | 4 | 1 | no | — |
| 176 | C22×C4×C71 | — | 4 | 1 | no | — |
| 177 | C22×C4×C71 | — | 4 | 1 | no | — |
| 178 | SD16×C71 | — | 2 | 2 | no | — |
| 179 | SD16×C71 | — | 4 | 2 | no | — |
| 180 | SD16×C71 | — | 4 | 2 | no | — |
| 181 | SD16×C71 | — | 4 | 2 | no | — |
| 182 | SD16×C71 | — | 4 | 2 | no | — |
| 183 | SD16×C71 | — | 4 | 2 | no | — |
| 184 | SD16×C71 | — | 8 | 1 | no | — |
| 185 | SD16×C71 | — | 8 | 1 | no | — |
| 186 | SD16×C71 | — | 8 | 1 | no | — |
| 187 | D8×C71 | — | 4 | 2 | no | — |
| 188 | D8×C71 | SD16 | 1 | 4 | yes | complemented |
| 189 | M16×C71 | — | 4 | 2 | no | — |
| 190 | C2×C8×C71 | — | 2 | 1 | no | — |
| 191 | C2×C8×C71 | — | 2 | 1 | no | — |
| 192 | C2×C8×C71 | — | 2 | 1 | no | — |
| 193 | C2×C8×C71 | — | 2 | 1 | no | — |
| 194 | C2×C8×C71 | — | 2 | 1 | no | — |
| 195 | C2×C8×C71 | — | 4 | 2 | no | — |
| 196 | C2×C8×C71 | — | 8 | 1 | no | — |
| 197 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 198 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 199 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 200 | C2×C8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 201 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 202 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 203 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 204 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 205 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 206 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 207 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 208 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 209 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 210 | C4⋊C4×C71 | — | 4 | 1 | no | — |
| 211 | C4⋊C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 212 | C4⋊C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 213 | C4⋊C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 214 | C4⋊C4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 215 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 216 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 217 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 218 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 219 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 220 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 221 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 222 | C42×C71 | — | 2 | 1 | no | — |
| 223 | C42×C71 | C24 | 1 | 1 | yes | characteristic |
| 224 | C23×C71 | — | 2 | 1 | no | — |
| 225 | C23×C71 | — | 2 | 1 | no | — |
| 226 | C23×C71 | — | 2 | 1 | no | — |
| 227 | C23×C71 | — | 4 | 1 | no | — |
| 228 | C23×C71 | — | 8 | 2 | no | — |
| 229 | C23×C71 | — | 8 | 2 | no | — |
| 230 | C23×C71 | — | 16 | 1 | no | — |
| 231 | Q8×C71 | — | 2 | 1 | no | — |
| 232 | Q8×C71 | — | 4 | 1 | no | — |
| 233 | Q8×C71 | — | 4 | 1 | no | — |
| 234 | Q8×C71 | — | 4 | 1 | no | — |
| 235 | Q8×C71 | — | 4 | 1 | no | — |
| 236 | Q8×C71 | — | 4 | 1 | no | — |
| 237 | Q8×C71 | — | 4 | 1 | no | — |
| 238 | Q8×C71 | — | 8 | 2 | no | — |
| 239 | Q8×C71 | — | 8 | 2 | no | — |
| 240 | Q8×C71 | AGL(1,ℤ/8) | 1 | 2 | yes | complemented |
| 241 | D4×C71 | — | 2 | 1 | no | — |
| 242 | D4×C71 | — | 2 | 1 | no | — |
| 243 | D4×C71 | — | 2 | 1 | no | — |
| 244 | D4×C71 | — | 2 | 1 | no | — |
| 245 | D4×C71 | — | 4 | 1 | no | — |
| 246 | D4×C71 | — | 4 | 1 | no | — |
| 247 | D4×C71 | — | 4 | 1 | no | — |
| 248 | D4×C71 | — | 4 | 1 | no | — |
| 249 | D4×C71 | — | 8 | 1 | no | — |
| 250 | D4×C71 | — | 8 | 2 | no | — |
| 251 | D4×C71 | — | 8 | 2 | no | — |
| 252 | D4×C71 | — | 8 | 2 | no | — |
| 253 | D4×C71 | C2×SD16 | 1 | 2 | yes | — |
| 254 | D4×C71 | C2×SD16 | 1 | 2 | yes | complemented |
| 255 | C2×C4×C71 | — | 2 | 1 | no | — |
| 256 | C2×C4×C71 | — | 2 | 1 | no | — |
| 257 | C2×C4×C71 | — | 2 | 1 | no | — |
| 258 | C2×C4×C71 | — | 2 | 1 | no | — |
| 259 | C2×C4×C71 | — | 2 | 1 | no | — |
| 260 | C2×C4×C71 | — | 4 | 1 | no | — |
| 261 | C2×C4×C71 | — | 4 | 1 | no | — |
| 262 | C2×C4×C71 | — | 4 | 1 | no | — |
| 263 | C2×C4×C71 | — | 4 | 1 | no | — |
| 264 | C2×C4×C71 | — | 4 | 1 | no | — |
| 265 | C2×C4×C71 | — | 4 | 1 | no | — |
| 266 | C2×C4×C71 | — | 4 | 1 | no | — |
| 267 | C2×C4×C71 | — | 4 | 1 | no | — |
| 268 | C2×C4×C71 | — | 4 | 1 | no | — |
| 269 | C2×C4×C71 | — | 8 | 2 | no | — |
| 270 | C2×C4×C71 | — | 8 | 2 | no | — |
| 271 | C2×C4×C71 | — | 8 | 2 | no | — |
| 272 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 273 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 274 | C2×C4×C71 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 275 | C8×C71 | — | 2 | 1 | no | — |
| 276 | C8×C71 | — | 2 | 1 | no | — |
| 277 | C8×C71 | — | 2 | 1 | no | — |
| 278 | C8×C71 | — | 4 | 1 | no | — |
| 279 | C8×C71 | — | 4 | 1 | no | — |
| 280 | C8×C71 | — | 4 | 1 | no | — |
| 281 | C8×C71 | — | 4 | 1 | no | — |
| 282 | C8×C71 | — | 4 | 1 | no | — |
| 283 | C8×C71 | C2×SD16 | 1 | 2 | yes | complemented |
| 284 | C22×C71 | — | 2 | 2 | no | — |
| 285 | C22×C71 | — | 2 | 2 | no | — |
| 286 | C22×C71 | — | 4 | 1 | no | — |
| 287 | C22×C71 | — | 4 | 1 | no | — |
| 288 | C22×C71 | — | 4 | 1 | no | — |
| 289 | C22×C71 | — | 4 | 1 | no | — |
| 290 | C22×C71 | — | 4 | 1 | no | — |
| 291 | C22×C71 | — | 4 | 1 | no | — |
| 292 | C22×C71 | — | 4 | 1 | no | — |
| 293 | C22×C71 | — | 8 | 1 | no | — |
| 294 | C22×C71 | — | 8 | 1 | no | — |
| 295 | C22×C71 | — | 8 | 1 | no | — |
| 296 | C22×C71 | — | 16 | 4 | no | — |
| 297 | C22×C71 | D42 | 1 | 1 | yes | characteristic |
| 298 | C4×C71 | — | 2 | 2 | no | — |
| 299 | C4×C71 | — | 2 | 1 | no | — |
| 300 | C4×C71 | — | 4 | 1 | no | — |
| 301 | C4×C71 | — | 4 | 1 | no | — |
| 302 | C4×C71 | — | 4 | 1 | no | — |
| 303 | C4×C71 | — | 4 | 1 | no | — |
| 304 | C4×C71 | — | 8 | 1 | no | — |
| 305 | C4×C71 | — | 8 | 1 | no | — |
| 306 | C4×C71 | — | 8 | 1 | no | — |
| 307 | C4×C71 | C22×SD16 | 1 | 1 | yes | characteristic |
| 308 | C4×C71 | C2×AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 309 | C4×C71 | #576 | 1 | 1 | yes | characteristic |
| 310 | C4×C71 | #577 | 1 | 1 | yes | characteristic |
| 311 | #19803 | C71 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 312 | C2×C71 | — | 4 | 2 | no | — |
| 313 | C2×C71 | — | 4 | 2 | no | — |
| 314 | C2×C71 | — | 8 | 1 | no | — |
| 315 | C2×C71 | — | 16 | 1 | no | — |
| 316 | C2×C71 | #3264 | 1 | 1 | yes | characteristic |
| 317 | C2×C71 | D4×SD16 | 1 | 1 | yes | characteristic |
| 318 | C2×C71 | #3289 | 1 | 1 | yes | characteristic |
| 319 | Q8×D8 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 320 | #3298 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 321 | D4×SD16 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 322 | #3272 | C2×C71 | 1 | 1 | yes | characteristic |
| 323 | #1714 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 324 | #1693 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 325 | #1679 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 326 | #1666 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 327 | #1665 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 328 | #1654 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 329 | #1651 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 330 | #1639 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 331 | #1627 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 332 | #1583 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 333 | #1580 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 334 | C71 | #19803 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 335 | C2×AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 336 | C22×SD16 | — | 2 | 1 | no | — |
| 337 | D4×Q8 | C22×C71 | 1 | 1 | yes | characteristic |
| 338 | D4×Q8 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 339 | #547 | C22×C71 | 1 | 1 | yes | characteristic |
| 340 | D42 | C22×C71 | 1 | 1 | yes | characteristic |
| 341 | #500 | — | 2 | 1 | no | — |
| 342 | #500 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 343 | #498 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 344 | #492 | C22×C71 | 1 | 1 | yes | characteristic |
| 345 | #492 | C22×C71 | 1 | 1 | yes | characteristic |
| 346 | #487 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 347 | #486 | C22×C71 | 1 | 1 | yes | characteristic |
| 348 | #483 | — | 2 | 1 | no | — |
| 349 | #475 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 350 | #474 | — | 2 | 1 | no | — |
| 351 | #474 | — | 2 | 1 | no | — |
| 352 | #474 | C22×C71 | 1 | 1 | yes | characteristic |
| 353 | #474 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 354 | #468 | — | 2 | 1 | no | — |
| 355 | #465 | — | 2 | 1 | no | — |
| 356 | #465 | — | 2 | 1 | no | — |
| 357 | #461 | C22×C71 | 1 | 1 | yes | characteristic |
| 358 | #461 | C22×C71 | 1 | 1 | yes | characteristic |
| 359 | #461 | C22×C71 | 1 | 1 | yes | characteristic |
| 360 | #460 | C22×C71 | 1 | 1 | yes | characteristic |
| 361 | #459 | C22×C71 | 1 | 1 | yes | characteristic |
| 362 | #450 | — | 2 | 1 | no | — |
| 363 | #450 | — | 2 | 1 | no | — |
| 364 | #449 | — | 2 | 1 | no | — |
| 365 | #448 | — | 2 | 1 | no | — |
| 366 | #448 | — | 2 | 1 | no | — |
| 367 | C8×Q8 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 368 | C4×SD16 | C22×C71 | 1 | 1 | yes | characteristic |
| 369 | C4×D8 | — | 2 | 1 | no | — |
| 370 | C4×D8 | C22×C71 | 1 | 1 | yes | characteristic |
| 371 | #436 | C22×C71 | 1 | 1 | yes | characteristic |
| 372 | C8×D4 | C22×C71 | 1 | 1 | yes | characteristic |
| 373 | C8×D4 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 374 | C2×#103 | — | 2 | 1 | no | — |
| 375 | #334 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 376 | #334 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 377 | #332 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 378 | #332 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 379 | #332 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 380 | #331 | C22×C71 | 1 | 1 | yes | characteristic |
| 381 | Q8⋊C8 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 382 | D4⋊C8 | C22×C71 | 1 | 1 | yes | characteristic |
| 383 | D4⋊C8 | C22×C71 | 1 | 1 | yes | characteristic |
| 384 | D4⋊C8 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 385 | #322 | C22×C71 | 1 | 1 | yes | characteristic, complemented |
| 386 | C2×#41 | — | 2 | 1 | no | — |
| 387 | C22×Q8 | — | 2 | 1 | no | — |
| 388 | C22×Q8 | — | 2 | 1 | no | — |
| 389 | C22×D4 | — | 2 | 1 | no | — |
| 390 | C22×D4 | — | 2 | 1 | no | — |
| 391 | AGL(1,ℤ/8) | — | 4 | 4 | no | — |
| 392 | C2×SD16 | — | 2 | 1 | no | — |
| 393 | C2×SD16 | — | 2 | 1 | no | — |
| 394 | C2×SD16 | — | 2 | 1 | no | — |
| 395 | C2×SD16 | — | 2 | 1 | no | — |
| 396 | C2×SD16 | — | 2 | 1 | no | — |
| 397 | C2×SD16 | — | 2 | 1 | no | — |
| 398 | C2×SD16 | — | 2 | 1 | no | — |
| 399 | C2×SD16 | — | 2 | 1 | no | — |
| 400 | C2×SD16 | — | 4 | 4 | no | — |
| 401 | C2×SD16 | D4×C71 | 1 | 1 | yes | characteristic |
| 402 | C2×D8 | — | 2 | 1 | no | — |
| 403 | C2×D8 | D4×C71 | 1 | 1 | yes | characteristic |
| 404 | C2×M16 | — | 2 | 1 | no | — |
| 405 | C22×C8 | — | 2 | 1 | no | — |
| 406 | C22×C8 | — | 2 | 1 | no | — |
| 407 | C4⋊Q8 | — | 2 | 1 | no | — |
| 408 | C4⋊Q8 | — | 2 | 1 | no | — |
| 409 | C4⋊Q8 | C23×C71 | 1 | 1 | yes | characteristic |
| 410 | C4⋊Q8 | C23×C71 | 1 | 1 | yes | characteristic |
| 411 | C4⋊Q8 | C23×C71 | 1 | 1 | yes | characteristic |
| 412 | #127 | C23×C71 | 1 | 1 | yes | characteristic |
| 413 | #123 | — | 4 | 1 | no | — |
| 414 | C22⋊Q8 | — | 2 | 1 | no | — |
| 415 | C22⋊Q8 | — | 2 | 1 | no | — |
| 416 | C22⋊Q8 | — | 2 | 1 | no | — |
| 417 | C22⋊Q8 | — | 4 | 1 | no | — |
| 418 | C22⋊Q8 | — | 4 | 1 | no | — |
| 419 | #121 | — | 2 | 1 | no | — |
| 420 | #121 | — | 2 | 1 | no | — |
| 421 | #121 | — | 2 | 1 | no | — |
| 422 | #120 | — | 4 | 1 | no | — |
| 423 | C4×Q8 | C23×C71 | 1 | 1 | yes | characteristic |
| 424 | C4×D4 | — | 2 | 1 | no | — |
| 425 | C4×D4 | — | 2 | 1 | no | — |
| 426 | C4×D4 | C23×C71 | 1 | 1 | yes | characteristic |
| 427 | C4×D4 | C23×C71 | 1 | 1 | yes | characteristic |
| 428 | C4×D4 | C23×C71 | 1 | 1 | yes | characteristic |
| 429 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 430 | #107 | — | 2 | 1 | no | — |
| 431 | #107 | — | 2 | 1 | no | — |
| 432 | #107 | — | 2 | 1 | no | — |
| 433 | #107 | — | 2 | 1 | no | — |
| 434 | #107 | D4×C71 | 1 | 1 | yes | characteristic |
| 435 | #106 | — | 2 | 1 | no | — |
| 436 | #106 | — | 4 | 1 | no | — |
| 437 | #106 | D4×C71 | 1 | 1 | yes | characteristic |
| 438 | C4⋊C8 | — | 2 | 1 | no | — |
| 439 | C4⋊C8 | C23×C71 | 1 | 1 | yes | characteristic |
| 440 | C4⋊C8 | C23×C71 | 1 | 1 | yes | characteristic |
| 441 | C4⋊C8 | C23×C71 | 1 | 1 | yes | characteristic |
| 442 | C4⋊C8 | C23×C71 | 1 | 1 | yes | characteristic |
| 443 | #103 | — | 2 | 1 | no | — |
| 444 | #103 | — | 2 | 1 | no | — |
| 445 | #103 | — | 2 | 1 | no | — |
| 446 | #103 | — | 2 | 1 | no | — |
| 447 | #103 | — | 2 | 1 | no | — |
| 448 | #103 | — | 2 | 1 | no | — |
| 449 | #103 | D4×C71 | 1 | 1 | yes | characteristic |
| 450 | #102 | — | 2 | 1 | no | — |
| 451 | #102 | — | 2 | 1 | no | — |
| 452 | #102 | — | 2 | 1 | no | — |
| 453 | #102 | — | 2 | 1 | no | — |
| 454 | #102 | — | 4 | 1 | no | — |
| 455 | #102 | D4×C71 | 1 | 1 | yes | characteristic |
| 456 | #102 | D4×C71 | 1 | 1 | yes | characteristic |
| 457 | #102 | D4×C71 | 1 | 1 | yes | characteristic |
| 458 | C22⋊C8 | — | 2 | 1 | no | — |
| 459 | C22⋊C8 | — | 2 | 1 | no | — |
| 460 | C22⋊C8 | — | 2 | 1 | no | — |
| 461 | C4×C8 | — | 2 | 1 | no | — |
| 462 | C4×C8 | C23×C71 | 1 | 1 | yes | characteristic |
| 463 | C4×C8 | C23×C71 | 1 | 1 | yes | characteristic |
| 464 | C4×C8 | C23×C71 | 1 | 1 | yes | characteristic |
| 465 | C24 | — | 4 | 1 | no | — |
| 466 | #41 | — | 4 | 2 | no | — |
| 467 | #41 | — | 8 | 1 | no | — |
| 468 | C2×Q8 | — | 2 | 1 | no | — |
| 469 | C2×Q8 | — | 2 | 1 | no | — |
| 470 | C2×Q8 | — | 2 | 1 | no | — |
| 471 | C2×Q8 | — | 4 | 1 | no | — |
| 472 | C2×Q8 | — | 4 | 1 | no | — |
| 473 | C2×Q8 | — | 4 | 2 | no | — |
| 474 | C2×Q8 | — | 4 | 2 | no | — |
| 475 | C2×Q8 | — | 8 | 1 | no | — |
| 476 | C2×Q8 | — | 8 | 1 | no | — |
| 477 | C2×Q8 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 478 | C2×D4 | — | 2 | 1 | no | — |
| 479 | C2×D4 | — | 2 | 1 | no | — |
| 480 | C2×D4 | — | 2 | 1 | no | — |
| 481 | C2×D4 | — | 4 | 1 | no | — |
| 482 | C2×D4 | — | 4 | 1 | no | — |
| 483 | C2×D4 | — | 4 | 2 | no | — |
| 484 | C2×D4 | — | 4 | 2 | no | — |
| 485 | C2×D4 | — | 4 | 1 | no | — |
| 486 | C2×D4 | — | 8 | 1 | no | — |
| 487 | C2×D4 | — | 8 | 1 | no | — |
| 488 | C2×D4 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 489 | C2×D4 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 490 | C2×D4 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 491 | C22×C4 | — | 2 | 1 | no | — |
| 492 | C22×C4 | — | 2 | 1 | no | — |
| 493 | C22×C4 | — | 2 | 1 | no | — |
| 494 | C22×C4 | — | 4 | 1 | no | — |
| 495 | C22×C4 | — | 4 | 1 | no | — |
| 496 | C22×C4 | — | 4 | 1 | no | — |
| 497 | SD16 | — | 2 | 2 | no | — |
| 498 | SD16 | — | 4 | 2 | no | — |
| 499 | SD16 | — | 4 | 2 | no | — |
| 500 | SD16 | — | 4 | 2 | no | — |
| 501 | SD16 | — | 4 | 2 | no | — |
| 502 | SD16 | — | 4 | 2 | no | — |
| 503 | SD16 | — | 8 | 1 | no | — |
| 504 | SD16 | — | 8 | 1 | no | — |
| 505 | SD16 | — | 8 | 1 | no | — |
| 506 | D8 | — | 4 | 2 | no | — |
| 507 | D8 | SD16×C71 | 1 | 4 | yes | complemented |
| 508 | M16 | — | 4 | 2 | no | — |
| 509 | C2×C8 | — | 2 | 1 | no | — |
| 510 | C2×C8 | — | 2 | 1 | no | — |
| 511 | C2×C8 | — | 2 | 1 | no | — |
| 512 | C2×C8 | — | 2 | 1 | no | — |
| 513 | C2×C8 | — | 2 | 1 | no | — |
| 514 | C2×C8 | — | 4 | 2 | no | — |
| 515 | C2×C8 | — | 8 | 1 | no | — |
| 516 | C2×C8 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 517 | C2×C8 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 518 | C2×C8 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 519 | C2×C8 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 520 | C4⋊C4 | — | 2 | 1 | no | — |
| 521 | C4⋊C4 | — | 2 | 1 | no | — |
| 522 | C4⋊C4 | — | 2 | 1 | no | — |
| 523 | C4⋊C4 | — | 2 | 1 | no | — |
| 524 | C4⋊C4 | — | 2 | 1 | no | — |
| 525 | C4⋊C4 | — | 2 | 1 | no | — |
| 526 | C4⋊C4 | — | 2 | 1 | no | — |
| 527 | C4⋊C4 | — | 4 | 1 | no | — |
| 528 | C4⋊C4 | — | 4 | 1 | no | — |
| 529 | C4⋊C4 | — | 4 | 1 | no | — |
| 530 | C4⋊C4 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 531 | C4⋊C4 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 532 | C4⋊C4 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 533 | C4⋊C4 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 534 | C22⋊C4 | — | 2 | 1 | no | — |
| 535 | C22⋊C4 | — | 2 | 1 | no | — |
| 536 | C22⋊C4 | — | 2 | 1 | no | — |
| 537 | C22⋊C4 | — | 4 | 1 | no | — |
| 538 | C22⋊C4 | — | 4 | 1 | no | — |
| 539 | C22⋊C4 | — | 4 | 1 | no | — |
| 540 | C22⋊C4 | — | 4 | 1 | no | — |
| 541 | C42 | — | 2 | 1 | no | — |
| 542 | C42 | C24×C71 | 1 | 1 | yes | characteristic |
| 543 | C23 | — | 2 | 1 | no | — |
| 544 | C23 | — | 2 | 1 | no | — |
| 545 | C23 | — | 2 | 1 | no | — |
| 546 | C23 | — | 4 | 1 | no | — |
| 547 | C23 | — | 8 | 2 | no | — |
| 548 | C23 | — | 8 | 2 | no | — |
| 549 | C23 | — | 16 | 1 | no | — |
| 550 | Q8 | — | 2 | 1 | no | — |
| 551 | Q8 | — | 4 | 1 | no | — |
| 552 | Q8 | — | 4 | 1 | no | — |
| 553 | Q8 | — | 4 | 1 | no | — |
| 554 | Q8 | — | 4 | 1 | no | — |
| 555 | Q8 | — | 4 | 1 | no | — |
| 556 | Q8 | — | 4 | 1 | no | — |
| 557 | Q8 | — | 8 | 2 | no | — |
| 558 | Q8 | — | 8 | 2 | no | — |
| 559 | Q8 | AGL(1,ℤ/8)×C71 | 1 | 2 | yes | complemented |
| 560 | D4 | — | 2 | 1 | no | — |
| 561 | D4 | — | 2 | 1 | no | — |
| 562 | D4 | — | 2 | 1 | no | — |
| 563 | D4 | — | 2 | 1 | no | — |
| 564 | D4 | — | 4 | 1 | no | — |
| 565 | D4 | — | 4 | 1 | no | — |
| 566 | D4 | — | 4 | 1 | no | — |
| 567 | D4 | — | 4 | 1 | no | — |
| 568 | D4 | — | 8 | 1 | no | — |
| 569 | D4 | — | 8 | 2 | no | — |
| 570 | D4 | — | 8 | 2 | no | — |
| 571 | D4 | — | 8 | 2 | no | — |
| 572 | D4 | C2×SD16×C71 | 1 | 2 | yes | — |
| 573 | D4 | C2×SD16×C71 | 1 | 2 | yes | complemented |
| 574 | C2×C4 | — | 2 | 1 | no | — |
| 575 | C2×C4 | — | 2 | 1 | no | — |
| 576 | C2×C4 | — | 2 | 1 | no | — |
| 577 | C2×C4 | — | 2 | 1 | no | — |
| 578 | C2×C4 | — | 2 | 1 | no | — |
| 579 | C2×C4 | — | 4 | 1 | no | — |
| 580 | C2×C4 | — | 4 | 1 | no | — |
| 581 | C2×C4 | — | 4 | 1 | no | — |
| 582 | C2×C4 | — | 4 | 1 | no | — |
| 583 | C2×C4 | — | 4 | 1 | no | — |
| 584 | C2×C4 | — | 4 | 1 | no | — |
| 585 | C2×C4 | — | 4 | 1 | no | — |
| 586 | C2×C4 | — | 4 | 1 | no | — |
| 587 | C2×C4 | — | 4 | 1 | no | — |
| 588 | C2×C4 | — | 8 | 2 | no | — |
| 589 | C2×C4 | — | 8 | 2 | no | — |
| 590 | C2×C4 | — | 8 | 2 | no | — |
| 591 | C2×C4 | C22×D4×C71 | 1 | 1 | yes | characteristic |
| 592 | C2×C4 | C22×D4×C71 | 1 | 1 | yes | characteristic |
| 593 | C2×C4 | H(5,𝔽2)×C71 | 1 | 1 | yes | characteristic |
| 594 | C8 | — | 2 | 1 | no | — |
| 595 | C8 | — | 2 | 1 | no | — |
| 596 | C8 | — | 2 | 1 | no | — |
| 597 | C8 | — | 4 | 1 | no | — |
| 598 | C8 | — | 4 | 1 | no | — |
| 599 | C8 | — | 4 | 1 | no | — |
| 600 | C8 | — | 4 | 1 | no | — |
| 601 | C8 | — | 4 | 1 | no | — |
| 602 | C8 | C2×SD16×C71 | 1 | 2 | yes | complemented |
| 603 | C22 | — | 2 | 2 | no | — |
| 604 | C22 | — | 2 | 2 | no | — |
| 605 | C22 | — | 4 | 1 | no | — |
| 606 | C22 | — | 4 | 1 | no | — |
| 607 | C22 | — | 4 | 1 | no | — |
| 608 | C22 | — | 4 | 1 | no | — |
| 609 | C22 | — | 4 | 1 | no | — |
| 610 | C22 | — | 4 | 1 | no | — |
| 611 | C22 | — | 4 | 1 | no | — |
| 612 | C22 | — | 8 | 1 | no | — |
| 613 | C22 | — | 8 | 1 | no | — |
| 614 | C22 | — | 8 | 1 | no | — |
| 615 | C22 | — | 16 | 4 | no | — |
| 616 | C22 | D42×C71 | 1 | 1 | yes | characteristic |
| 617 | C4 | — | 2 | 2 | no | — |
| 618 | C4 | — | 2 | 1 | no | — |
| 619 | C4 | — | 4 | 1 | no | — |
| 620 | C4 | — | 4 | 1 | no | — |
| 621 | C4 | — | 4 | 1 | no | — |
| 622 | C4 | — | 4 | 1 | no | — |
| 623 | C4 | — | 8 | 1 | no | — |
| 624 | C4 | — | 8 | 1 | no | — |
| 625 | C4 | — | 8 | 1 | no | — |
| 626 | C4 | C22×SD16×C71 | 1 | 1 | yes | characteristic |
| 627 | C4 | C2×AGL(1,ℤ/8)×C71 | 1 | 1 | yes | characteristic |
| 628 | C4 | #576×C71 | 1 | 1 | yes | characteristic |
| 629 | C4 | #577×C71 | 1 | 1 | yes | characteristic |
| 630 | C2 | — | 4 | 2 | no | — |
| 631 | C2 | — | 4 | 2 | no | — |
| 632 | C2 | — | 8 | 1 | no | — |
| 633 | C2 | — | 16 | 1 | no | — |
| 634 | C2 | C71×#3264 | 1 | 1 | yes | characteristic |
| 635 | C2 | D4×SD16×C71 | 1 | 1 | yes | characteristic |
| 636 | C2 | C71×#3289 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta