| 1 | C71×#3482 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | Q8×#41×C71 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C71×#3395 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | Q8×SD16×C71 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C71×#3363 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C71×#3359 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C71×#3356 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | C71×#3331 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | C71×#3328 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | C71×#3276 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C71×#3185 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | C71×#3116 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | C71×#3113 | C2 | 1 | 3 | yes | maximal, complemented |
| 14 | C71×#2971 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C4×#137×C71 | C2 | 1 | 3 | yes | maximal, complemented |
| 16 | C2×#137×C71 | C22 | 1 | 3 | yes | — |
| 17 | Q82×C71 | C22 | 1 | 1 | yes | characteristic |
| 18 | #557×C71 | — | 2 | 1 | no | — |
| 19 | #557×C71 | C22 | 1 | 1 | yes | characteristic |
| 20 | #557×C71 | C22 | 1 | 1 | yes | characteristic |
| 21 | #556×C71 | C22 | 1 | 3 | yes | — |
| 22 | #554×C71 | — | 2 | 3 | no | — |
| 23 | #554×C71 | C22 | 1 | 3 | yes | — |
| 24 | #552×C71 | — | 2 | 3 | no | — |
| 25 | D4×Q8×C71 | C22 | 1 | 3 | yes | — |
| 26 | D4×Q8×C71 | C22 | 1 | 1 | yes | characteristic |
| 27 | #548×C71 | — | 2 | 1 | no | — |
| 28 | #547×C71 | C22 | 1 | 3 | yes | — |
| 29 | #533×C71 | — | 2 | 3 | no | — |
| 30 | #533×C71 | C22 | 1 | 3 | yes | — |
| 31 | #533×C71 | C22 | 1 | 3 | yes | — |
| 32 | #529×C71 | — | 2 | 3 | no | — |
| 33 | C4×#41×C71 | — | 2 | 1 | no | — |
| 34 | C4×#41×C71 | C22 | 1 | 3 | yes | — |
| 35 | C4×#41×C71 | C22 | 1 | 1 | yes | characteristic |
| 36 | C2×C4×Q8×C71 | — | 2 | 1 | no | — |
| 37 | C2×C4×Q8×C71 | C22 | 1 | 3 | yes | — |
| 38 | #498×C71 | C22 | 1 | 3 | yes | — |
| 39 | #494×C71 | C22 | 1 | 3 | yes | — |
| 40 | #487×C71 | C22 | 1 | 3 | yes | — |
| 41 | #487×C71 | C22 | 1 | 3 | yes | — |
| 42 | #485×C71 | C22 | 1 | 6 | yes | — |
| 43 | #483×C71 | C22 | 1 | 6 | yes | — |
| 44 | #477×C71 | C22 | 1 | 3 | yes | — |
| 45 | #476×C71 | C22 | 1 | 3 | yes | — |
| 46 | #475×C71 | C22 | 1 | 3 | yes | — |
| 47 | #475×C71 | C22 | 1 | 3 | yes | — |
| 48 | #470×C71 | C22 | 1 | 6 | yes | — |
| 49 | #470×C71 | C22 | 1 | 6 | yes | — |
| 50 | #462×C71 | C22 | 1 | 3 | yes | — |
| 51 | #462×C71 | C22 | 1 | 3 | yes | — |
| 52 | #462×C71 | C22 | 1 | 3 | yes | — |
| 53 | #461×C71 | C22 | 1 | 3 | yes | — |
| 54 | #452×C71 | C22 | 1 | 6 | yes | — |
| 55 | #451×C71 | C22 | 1 | 6 | yes | — |
| 56 | C8×Q8×C71 | C22 | 1 | 1 | yes | characteristic |
| 57 | C8×Q8×C71 | C22 | 1 | 1 | yes | characteristic |
| 58 | #441×C71 | C22 | 1 | 3 | yes | — |
| 59 | #441×C71 | C22 | 1 | 6 | yes | — |
| 60 | #441×C71 | C22 | 1 | 3 | yes | — |
| 61 | #440×C71 | C22 | 1 | 3 | yes | — |
| 62 | #440×C71 | C22 | 1 | 1 | yes | characteristic |
| 63 | C4×Q16×C71 | C22 | 1 | 3 | yes | — |
| 64 | C4×Q16×C71 | C22 | 1 | 3 | yes | — |
| 65 | C4×SD16×C71 | C22 | 1 | 3 | yes | — |
| 66 | C4×SD16×C71 | C22 | 1 | 3 | yes | — |
| 67 | #436×C71 | C22 | 1 | 3 | yes | — |
| 68 | #436×C71 | C22 | 1 | 3 | yes | — |
| 69 | #432×C71 | C22 | 1 | 3 | yes | — |
| 70 | #428×C71 | C22 | 1 | 3 | yes | — |
| 71 | #419×C71 | C22 | 1 | 3 | yes | — |
| 72 | #417×C71 | C22 | 1 | 3 | yes | — |
| 73 | C4×M16×C71 | C22 | 1 | 3 | yes | — |
| 74 | C2×#41×C71 | D4 | 1 | 1 | yes | characteristic |
| 75 | C2×#41×C71 | C23 | 1 | 3 | yes | — |
| 76 | C22×Q8×C71 | — | 2 | 1 | no | — |
| 77 | C22×Q8×C71 | C23 | 1 | 3 | yes | — |
| 78 | #137×C71 | — | 2 | 12 | no | — |
| 79 | C2×Q16×C71 | C23 | 1 | 3 | yes | — |
| 80 | C2×Q16×C71 | C23 | 1 | 3 | yes | — |
| 81 | C2×Q16×C71 | C23 | 1 | 6 | yes | — |
| 82 | C2×SD16×C71 | C23 | 1 | 3 | yes | — |
| 83 | C2×SD16×C71 | C23 | 1 | 1 | yes | characteristic |
| 84 | C2×M16×C71 | C23 | 1 | 3 | yes | — |
| 85 | C2×M16×C71 | C23 | 1 | 3 | yes | — |
| 86 | C4⋊Q8×C71 | — | 2 | 3 | no | — |
| 87 | C4⋊Q8×C71 | — | 2 | 3 | no | — |
| 88 | C4⋊Q8×C71 | C23 | 1 | 3 | yes | — |
| 89 | C4⋊Q8×C71 | C23 | 1 | 3 | yes | — |
| 90 | C4⋊Q8×C71 | C23 | 1 | 3 | yes | — |
| 91 | C4⋊Q8×C71 | C23 | 1 | 3 | yes | — |
| 92 | #126×C71 | — | 2 | 6 | no | — |
| 93 | #125×C71 | — | 2 | 3 | no | — |
| 94 | #125×C71 | — | 2 | 3 | no | — |
| 95 | #125×C71 | — | 2 | 3 | no | — |
| 96 | #125×C71 | — | 2 | 3 | no | — |
| 97 | #125×C71 | — | 2 | 3 | no | — |
| 98 | #124×C71 | — | 2 | 3 | no | — |
| 99 | #123×C71 | — | 2 | 6 | no | — |
| 100 | C22⋊Q8×C71 | — | 2 | 3 | no | — |
| 101 | C22⋊Q8×C71 | — | 2 | 3 | no | — |
| 102 | C22⋊Q8×C71 | — | 2 | 3 | no | — |
| 103 | C22⋊Q8×C71 | — | 2 | 6 | no | — |
| 104 | C22⋊Q8×C71 | — | 2 | 6 | no | — |
| 105 | C22⋊Q8×C71 | C23 | 1 | 6 | yes | — |
| 106 | C22⋊Q8×C71 | C23 | 1 | 6 | yes | — |
| 107 | #121×C71 | — | 2 | 3 | no | — |
| 108 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 109 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 110 | C4×Q8×C71 | — | 2 | 1 | no | — |
| 111 | C4×Q8×C71 | — | 2 | 3 | no | — |
| 112 | C4×Q8×C71 | — | 2 | 3 | no | — |
| 113 | C4×Q8×C71 | — | 2 | 3 | no | — |
| 114 | C4×Q8×C71 | — | 2 | 3 | no | — |
| 115 | C4×Q8×C71 | — | 2 | 3 | no | — |
| 116 | C4×Q8×C71 | D4 | 1 | 1 | yes | characteristic |
| 117 | C4×Q8×C71 | C23 | 1 | 3 | yes | — |
| 118 | C4×Q8×C71 | C23 | 1 | 3 | yes | — |
| 119 | C4×Q8×C71 | C23 | 1 | 3 | yes | — |
| 120 | C4×Q8×C71 | C23 | 1 | 1 | yes | characteristic |
| 121 | C4×Q8×C71 | C23 | 1 | 3 | yes | — |
| 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 | D4 | 1 | 3 | yes | — |
| 129 | C4×D4×C71 | C23 | 1 | 3 | yes | — |
| 130 | C4×D4×C71 | C23 | 1 | 1 | yes | characteristic |
| 131 | C4×D4×C71 | C23 | 1 | 3 | yes | — |
| 132 | #117×C71 | — | 2 | 3 | no | — |
| 133 | #117×C71 | — | 2 | 3 | no | — |
| 134 | #117×C71 | — | 2 | 3 | no | — |
| 135 | #117×C71 | D4 | 1 | 3 | yes | — |
| 136 | #117×C71 | C23 | 1 | 3 | yes | — |
| 137 | C2×C4⋊C4×C71 | — | 2 | 3 | no | — |
| 138 | C2×C4⋊C4×C71 | — | 2 | 3 | no | — |
| 139 | C2×C4⋊C4×C71 | C23 | 1 | 3 | yes | — |
| 140 | C2×C42×C71 | — | 2 | 3 | no | — |
| 141 | C2×C42×C71 | — | 2 | 3 | no | — |
| 142 | C2×C42×C71 | C23 | 1 | 3 | yes | — |
| 143 | #107×C71 | C23 | 1 | 1 | yes | characteristic |
| 144 | #107×C71 | C23 | 1 | 3 | yes | — |
| 145 | #106×C71 | C23 | 1 | 3 | yes | — |
| 146 | #106×C71 | C23 | 1 | 3 | yes | — |
| 147 | #106×C71 | C23 | 1 | 6 | yes | — |
| 148 | C4⋊C8×C71 | C23 | 1 | 3 | yes | — |
| 149 | C4⋊C8×C71 | C23 | 1 | 3 | yes | — |
| 150 | #103×C71 | C23 | 1 | 3 | yes | — |
| 151 | #103×C71 | C23 | 1 | 3 | yes | — |
| 152 | #103×C71 | C23 | 1 | 1 | yes | characteristic |
| 153 | #103×C71 | C23 | 1 | 3 | yes | — |
| 154 | #103×C71 | C23 | 1 | 3 | yes | — |
| 155 | #103×C71 | C23 | 1 | 3 | yes | — |
| 156 | #103×C71 | C23 | 1 | 6 | yes | — |
| 157 | #103×C71 | C23 | 1 | 6 | yes | — |
| 158 | #102×C71 | C23 | 1 | 1 | yes | characteristic |
| 159 | #102×C71 | C23 | 1 | 3 | yes | — |
| 160 | C22⋊C8×C71 | C23 | 1 | 6 | yes | — |
| 161 | #97×C71 | C23 | 1 | 3 | yes | — |
| 162 | #97×C71 | C23 | 1 | 1 | yes | characteristic |
| 163 | C4×C8×C71 | C23 | 1 | 3 | yes | — |
| 164 | C4×C8×C71 | C23 | 1 | 3 | yes | — |
| 165 | #41×C71 | — | 2 | 4 | no | — |
| 166 | #41×C71 | — | 2 | 6 | no | — |
| 167 | #41×C71 | — | 4 | 3 | no | — |
| 168 | C2×Q8×C71 | — | 2 | 3 | no | — |
| 169 | C2×Q8×C71 | — | 2 | 3 | no | — |
| 170 | C2×Q8×C71 | — | 2 | 3 | no | — |
| 171 | C2×Q8×C71 | — | 2 | 6 | no | — |
| 172 | C2×Q8×C71 | — | 4 | 3 | no | — |
| 173 | C2×Q8×C71 | — | 4 | 4 | no | — |
| 174 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C2×Q8×C71 | C24 | 1 | 3 | yes | — |
| 176 | C2×Q8×C71 | C24 | 1 | 3 | yes | — |
| 177 | C2×Q8×C71 | C24 | 1 | 1 | yes | characteristic |
| 178 | C2×D4×C71 | — | 2 | 3 | no | — |
| 179 | C2×D4×C71 | C2×D4 | 1 | 3 | yes | — |
| 180 | C2×D4×C71 | C24 | 1 | 1 | yes | characteristic |
| 181 | C22×C4×C71 | — | 2 | 3 | no | — |
| 182 | C22×C4×C71 | — | 2 | 3 | no | — |
| 183 | C22×C4×C71 | — | 2 | 1 | no | — |
| 184 | C22×C4×C71 | — | 2 | 3 | no | — |
| 185 | C22×C4×C71 | — | 2 | 3 | no | — |
| 186 | C22×C4×C71 | C2×D4 | 1 | 3 | yes | — |
| 187 | C22×C4×C71 | C2×D4 | 1 | 3 | yes | — |
| 188 | C22×C4×C71 | C24 | 1 | 3 | yes | — |
| 189 | Q16×C71 | — | 2 | 6 | no | — |
| 190 | Q16×C71 | — | 2 | 6 | no | — |
| 191 | Q16×C71 | — | 4 | 6 | no | — |
| 192 | SD16×C71 | — | 2 | 6 | no | — |
| 193 | SD16×C71 | #41 | 1 | 4 | yes | complemented |
| 194 | M16×C71 | — | 2 | 6 | no | — |
| 195 | M16×C71 | — | 4 | 3 | no | — |
| 196 | C2×C8×C71 | C24 | 1 | 1 | yes | characteristic |
| 197 | C2×C8×C71 | C24 | 1 | 3 | yes | — |
| 198 | C2×C8×C71 | C24 | 1 | 3 | yes | — |
| 199 | C2×C8×C71 | C24 | 1 | 1 | yes | characteristic |
| 200 | C4⋊C4×C71 | — | 2 | 1 | no | — |
| 201 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 202 | C4⋊C4×C71 | — | 2 | 6 | no | — |
| 203 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 204 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 205 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 206 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 207 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 208 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 209 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 210 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 211 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 212 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 213 | C4⋊C4×C71 | — | 2 | 3 | no | — |
| 214 | C4⋊C4×C71 | — | 2 | 6 | no | — |
| 215 | C4⋊C4×C71 | C2×D4 | 1 | 3 | yes | — |
| 216 | C4⋊C4×C71 | C2×D4 | 1 | 3 | yes | — |
| 217 | C4⋊C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 218 | C4⋊C4×C71 | C24 | 1 | 3 | yes | — |
| 219 | C4⋊C4×C71 | C24 | 1 | 3 | yes | — |
| 220 | C4⋊C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 221 | C22⋊C4×C71 | — | 2 | 6 | no | — |
| 222 | C22⋊C4×C71 | — | 2 | 6 | no | — |
| 223 | C22⋊C4×C71 | — | 2 | 3 | no | — |
| 224 | C22⋊C4×C71 | — | 2 | 1 | no | — |
| 225 | C22⋊C4×C71 | — | 2 | 3 | no | — |
| 226 | C22⋊C4×C71 | C2×D4 | 1 | 6 | yes | — |
| 227 | C42×C71 | — | 2 | 1 | no | — |
| 228 | C42×C71 | — | 2 | 3 | no | — |
| 229 | C42×C71 | — | 2 | 3 | no | — |
| 230 | C42×C71 | — | 2 | 3 | no | — |
| 231 | C42×C71 | — | 2 | 3 | no | — |
| 232 | C42×C71 | — | 2 | 3 | no | — |
| 233 | C42×C71 | — | 2 | 3 | no | — |
| 234 | C42×C71 | C2×D4 | 1 | 3 | yes | — |
| 235 | C42×C71 | C2×D4 | 1 | 3 | yes | — |
| 236 | C42×C71 | C24 | 1 | 3 | yes | — |
| 237 | C42×C71 | C24 | 1 | 1 | yes | characteristic |
| 238 | C23×C71 | — | 2 | 1 | no | — |
| 239 | C23×C71 | C22×D4 | 1 | 3 | yes | — |
| 240 | Q8×C71 | — | 2 | 1 | no | — |
| 241 | Q8×C71 | — | 2 | 3 | no | — |
| 242 | Q8×C71 | — | 2 | 3 | no | — |
| 243 | Q8×C71 | — | 2 | 3 | no | — |
| 244 | Q8×C71 | — | 2 | 3 | no | — |
| 245 | Q8×C71 | — | 4 | 6 | no | — |
| 246 | Q8×C71 | — | 4 | 6 | no | — |
| 247 | Q8×C71 | — | 8 | 3 | no | — |
| 248 | Q8×C71 | #137 | 1 | 4 | yes | complemented |
| 249 | Q8×C71 | C2×#41 | 1 | 2 | yes | — |
| 250 | D4×C71 | — | 2 | 6 | no | — |
| 251 | D4×C71 | — | 2 | 1 | no | — |
| 252 | D4×C71 | — | 4 | 6 | no | — |
| 253 | D4×C71 | C2×#41 | 1 | 2 | yes | — |
| 254 | C2×C4×C71 | — | 2 | 1 | no | — |
| 255 | C2×C4×C71 | — | 2 | 6 | no | — |
| 256 | C2×C4×C71 | — | 2 | 3 | no | — |
| 257 | C2×C4×C71 | — | 2 | 3 | no | — |
| 258 | C2×C4×C71 | — | 2 | 1 | no | — |
| 259 | C2×C4×C71 | — | 2 | 1 | no | — |
| 260 | C2×C4×C71 | — | 2 | 3 | no | — |
| 261 | C2×C4×C71 | — | 2 | 3 | no | — |
| 262 | C2×C4×C71 | — | 2 | 3 | no | — |
| 263 | C2×C4×C71 | — | 2 | 3 | no | — |
| 264 | C2×C4×C71 | — | 4 | 3 | no | — |
| 265 | C2×C4×C71 | — | 4 | 6 | no | — |
| 266 | C2×C4×C71 | — | 4 | 6 | no | — |
| 267 | C2×C4×C71 | — | 4 | 2 | no | — |
| 268 | C2×C4×C71 | — | 4 | 6 | no | — |
| 269 | C2×C4×C71 | — | 8 | 3 | no | — |
| 270 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 271 | C2×C4×C71 | C22×D4 | 1 | 1 | yes | characteristic |
| 272 | C2×C4×C71 | C22×D4 | 1 | 3 | yes | — |
| 273 | C2×C4×C71 | C22×D4 | 1 | 3 | yes | — |
| 274 | C2×C4×C71 | C22×D4 | 1 | 3 | yes | — |
| 275 | C2×C4×C71 | C25 | 1 | 1 | yes | characteristic |
| 276 | C8×C71 | — | 2 | 3 | no | — |
| 277 | C8×C71 | — | 2 | 1 | no | — |
| 278 | C8×C71 | — | 2 | 3 | no | — |
| 279 | C8×C71 | C2×#41 | 1 | 2 | yes | — |
| 280 | C22×C71 | — | 2 | 3 | no | — |
| 281 | C22×C71 | — | 2 | 3 | no | — |
| 282 | C22×C71 | — | 2 | 2 | no | — |
| 283 | C22×C71 | — | 2 | 3 | no | — |
| 284 | C22×C71 | — | 4 | 1 | no | — |
| 285 | C22×C71 | — | 4 | 1 | no | — |
| 286 | C22×C71 | C23×D4 | 1 | 1 | yes | characteristic |
| 287 | C4×C71 | — | 2 | 1 | no | — |
| 288 | C4×C71 | — | 2 | 3 | no | — |
| 289 | C4×C71 | — | 2 | 3 | no | — |
| 290 | C4×C71 | — | 2 | 2 | no | — |
| 291 | C4×C71 | — | 2 | 1 | no | — |
| 292 | C4×C71 | — | 4 | 1 | no | — |
| 293 | C4×C71 | — | 4 | 1 | no | — |
| 294 | C4×C71 | — | 4 | 3 | no | — |
| 295 | C4×C71 | — | 4 | 3 | no | — |
| 296 | C4×C71 | — | 4 | 3 | no | — |
| 297 | C4×C71 | — | 4 | 3 | no | — |
| 298 | C4×C71 | C2×#137 | 1 | 6 | yes | — |
| 299 | C4×C71 | C22×#41 | 1 | 1 | yes | characteristic |
| 300 | C4×C71 | #585 | 1 | 1 | yes | characteristic |
| 301 | #61470 | C71 | 1 | 1 | yes | maximal, characteristic, direct product factor, Sylow |
| 302 | C2×C71 | — | 4 | 3 | no | — |
| 303 | C2×C71 | — | 4 | 2 | no | — |
| 304 | C2×C71 | D4×#41 | 1 | 1 | yes | characteristic |
| 305 | C2×C71 | C22×#137 | 1 | 1 | yes | characteristic |
| 306 | C2×C71 | #3586 | 1 | 1 | yes | characteristic |
| 307 | #3482 | C2×C71 | 1 | 1 | yes | characteristic |
| 308 | Q8×#41 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 309 | #3395 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 310 | Q8×SD16 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 311 | #3363 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 312 | #3359 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 313 | #3356 | C2×C71 | 1 | 3 | yes | complemented |
| 314 | #3331 | C2×C71 | 1 | 3 | yes | complemented |
| 315 | #3328 | C2×C71 | 1 | 3 | yes | complemented |
| 316 | #3276 | C2×C71 | 1 | 3 | yes | complemented |
| 317 | #3185 | C2×C71 | 1 | 3 | yes | complemented |
| 318 | #3116 | C2×C71 | 1 | 3 | yes | complemented |
| 319 | #3113 | C2×C71 | 1 | 3 | yes | complemented |
| 320 | #2971 | C2×C71 | 1 | 1 | yes | characteristic, complemented |
| 321 | C4×#137 | C2×C71 | 1 | 3 | yes | complemented |
| 322 | C71 | #61470 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 323 | C2×#137 | C22×C71 | 1 | 3 | yes | — |
| 324 | Q82 | C22×C71 | 1 | 1 | yes | characteristic |
| 325 | #557 | — | 2 | 1 | no | — |
| 326 | #557 | C22×C71 | 1 | 1 | yes | characteristic |
| 327 | #557 | C22×C71 | 1 | 1 | yes | characteristic |
| 328 | #556 | C22×C71 | 1 | 3 | yes | — |
| 329 | #554 | — | 2 | 3 | no | — |
| 330 | #554 | C22×C71 | 1 | 3 | yes | — |
| 331 | #552 | — | 2 | 3 | no | — |
| 332 | D4×Q8 | C22×C71 | 1 | 3 | yes | — |
| 333 | D4×Q8 | C22×C71 | 1 | 1 | yes | characteristic |
| 334 | #548 | — | 2 | 1 | no | — |
| 335 | #547 | C22×C71 | 1 | 3 | yes | — |
| 336 | #533 | — | 2 | 3 | no | — |
| 337 | #533 | C22×C71 | 1 | 3 | yes | — |
| 338 | #533 | C22×C71 | 1 | 3 | yes | — |
| 339 | #529 | — | 2 | 3 | no | — |
| 340 | C4×#41 | — | 2 | 1 | no | — |
| 341 | C4×#41 | C22×C71 | 1 | 3 | yes | — |
| 342 | C4×#41 | C22×C71 | 1 | 1 | yes | characteristic |
| 343 | C2×C4×Q8 | — | 2 | 1 | no | — |
| 344 | C2×C4×Q8 | C22×C71 | 1 | 3 | yes | — |
| 345 | #498 | C22×C71 | 1 | 3 | yes | — |
| 346 | #494 | C22×C71 | 1 | 3 | yes | — |
| 347 | #487 | C22×C71 | 1 | 3 | yes | — |
| 348 | #487 | C22×C71 | 1 | 3 | yes | — |
| 349 | #485 | C22×C71 | 1 | 6 | yes | — |
| 350 | #483 | C22×C71 | 1 | 6 | yes | — |
| 351 | #477 | C22×C71 | 1 | 3 | yes | — |
| 352 | #476 | C22×C71 | 1 | 3 | yes | — |
| 353 | #475 | C22×C71 | 1 | 3 | yes | — |
| 354 | #475 | C22×C71 | 1 | 3 | yes | — |
| 355 | #470 | C22×C71 | 1 | 6 | yes | — |
| 356 | #470 | C22×C71 | 1 | 6 | yes | — |
| 357 | #462 | C22×C71 | 1 | 3 | yes | — |
| 358 | #462 | C22×C71 | 1 | 3 | yes | — |
| 359 | #462 | C22×C71 | 1 | 3 | yes | — |
| 360 | #461 | C22×C71 | 1 | 3 | yes | — |
| 361 | #452 | C22×C71 | 1 | 6 | yes | — |
| 362 | #451 | C22×C71 | 1 | 6 | yes | — |
| 363 | C8×Q8 | C22×C71 | 1 | 1 | yes | characteristic |
| 364 | C8×Q8 | C22×C71 | 1 | 1 | yes | characteristic |
| 365 | #441 | C22×C71 | 1 | 3 | yes | — |
| 366 | #441 | C22×C71 | 1 | 6 | yes | — |
| 367 | #441 | C22×C71 | 1 | 3 | yes | — |
| 368 | #440 | C22×C71 | 1 | 3 | yes | — |
| 369 | #440 | C22×C71 | 1 | 1 | yes | characteristic |
| 370 | C4×Q16 | C22×C71 | 1 | 3 | yes | — |
| 371 | C4×Q16 | C22×C71 | 1 | 3 | yes | — |
| 372 | C4×SD16 | C22×C71 | 1 | 3 | yes | — |
| 373 | C4×SD16 | C22×C71 | 1 | 3 | yes | — |
| 374 | #436 | C22×C71 | 1 | 3 | yes | — |
| 375 | #436 | C22×C71 | 1 | 3 | yes | — |
| 376 | #432 | C22×C71 | 1 | 3 | yes | — |
| 377 | #428 | C22×C71 | 1 | 3 | yes | — |
| 378 | #419 | C22×C71 | 1 | 3 | yes | — |
| 379 | #417 | C22×C71 | 1 | 3 | yes | — |
| 380 | C4×M16 | C22×C71 | 1 | 3 | yes | — |
| 381 | C2×#41 | D4×C71 | 1 | 1 | yes | characteristic |
| 382 | C2×#41 | C23×C71 | 1 | 3 | yes | — |
| 383 | C22×Q8 | — | 2 | 1 | no | — |
| 384 | C22×Q8 | C23×C71 | 1 | 3 | yes | — |
| 385 | #137 | — | 2 | 12 | no | — |
| 386 | C2×Q16 | C23×C71 | 1 | 3 | yes | — |
| 387 | C2×Q16 | C23×C71 | 1 | 3 | yes | — |
| 388 | C2×Q16 | C23×C71 | 1 | 6 | yes | — |
| 389 | C2×SD16 | C23×C71 | 1 | 3 | yes | — |
| 390 | C2×SD16 | C23×C71 | 1 | 1 | yes | characteristic |
| 391 | C2×M16 | C23×C71 | 1 | 3 | yes | — |
| 392 | C2×M16 | C23×C71 | 1 | 3 | yes | — |
| 393 | C4⋊Q8 | — | 2 | 3 | no | — |
| 394 | C4⋊Q8 | — | 2 | 3 | no | — |
| 395 | C4⋊Q8 | C23×C71 | 1 | 3 | yes | — |
| 396 | C4⋊Q8 | C23×C71 | 1 | 3 | yes | — |
| 397 | C4⋊Q8 | C23×C71 | 1 | 3 | yes | — |
| 398 | C4⋊Q8 | C23×C71 | 1 | 3 | yes | — |
| 399 | #126 | — | 2 | 6 | no | — |
| 400 | #125 | — | 2 | 3 | no | — |
| 401 | #125 | — | 2 | 3 | no | — |
| 402 | #125 | — | 2 | 3 | no | — |
| 403 | #125 | — | 2 | 3 | no | — |
| 404 | #125 | — | 2 | 3 | no | — |
| 405 | #124 | — | 2 | 3 | no | — |
| 406 | #123 | — | 2 | 6 | no | — |
| 407 | C22⋊Q8 | — | 2 | 3 | no | — |
| 408 | C22⋊Q8 | — | 2 | 3 | no | — |
| 409 | C22⋊Q8 | — | 2 | 3 | no | — |
| 410 | C22⋊Q8 | — | 2 | 6 | no | — |
| 411 | C22⋊Q8 | — | 2 | 6 | no | — |
| 412 | C22⋊Q8 | C23×C71 | 1 | 6 | yes | — |
| 413 | C22⋊Q8 | C23×C71 | 1 | 6 | yes | — |
| 414 | #121 | — | 2 | 3 | no | — |
| 415 | C4×Q8 | — | 2 | 1 | no | — |
| 416 | C4×Q8 | — | 2 | 1 | no | — |
| 417 | C4×Q8 | — | 2 | 1 | no | — |
| 418 | C4×Q8 | — | 2 | 3 | no | — |
| 419 | C4×Q8 | — | 2 | 3 | no | — |
| 420 | C4×Q8 | — | 2 | 3 | no | — |
| 421 | C4×Q8 | — | 2 | 3 | no | — |
| 422 | C4×Q8 | — | 2 | 3 | no | — |
| 423 | C4×Q8 | D4×C71 | 1 | 1 | yes | characteristic |
| 424 | C4×Q8 | C23×C71 | 1 | 1 | yes | characteristic |
| 425 | C4×Q8 | C23×C71 | 1 | 3 | yes | — |
| 426 | C4×Q8 | C23×C71 | 1 | 3 | yes | — |
| 427 | C4×Q8 | C23×C71 | 1 | 3 | yes | — |
| 428 | C4×Q8 | C23×C71 | 1 | 3 | yes | — |
| 429 | C4×Q8 | C23×C71 | 1 | 3 | yes | — |
| 430 | C4×Q8 | C23×C71 | 1 | 1 | yes | characteristic |
| 431 | C4×D4 | — | 2 | 3 | no | — |
| 432 | C4×D4 | — | 2 | 3 | no | — |
| 433 | C4×D4 | — | 2 | 3 | no | — |
| 434 | C4×D4 | — | 2 | 3 | no | — |
| 435 | C4×D4 | D4×C71 | 1 | 3 | yes | — |
| 436 | C4×D4 | C23×C71 | 1 | 1 | yes | characteristic |
| 437 | C4×D4 | C23×C71 | 1 | 3 | yes | — |
| 438 | C4×D4 | C23×C71 | 1 | 3 | yes | — |
| 439 | #117 | — | 2 | 3 | no | — |
| 440 | #117 | — | 2 | 3 | no | — |
| 441 | #117 | — | 2 | 3 | no | — |
| 442 | #117 | D4×C71 | 1 | 3 | yes | — |
| 443 | #117 | C23×C71 | 1 | 3 | yes | — |
| 444 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 445 | C2×C4⋊C4 | — | 2 | 3 | no | — |
| 446 | C2×C4⋊C4 | C23×C71 | 1 | 3 | yes | — |
| 447 | C2×C42 | — | 2 | 3 | no | — |
| 448 | C2×C42 | — | 2 | 3 | no | — |
| 449 | C2×C42 | C23×C71 | 1 | 3 | yes | — |
| 450 | #107 | C23×C71 | 1 | 1 | yes | characteristic |
| 451 | #107 | C23×C71 | 1 | 3 | yes | — |
| 452 | #106 | C23×C71 | 1 | 3 | yes | — |
| 453 | #106 | C23×C71 | 1 | 3 | yes | — |
| 454 | #106 | C23×C71 | 1 | 6 | yes | — |
| 455 | C4⋊C8 | C23×C71 | 1 | 3 | yes | — |
| 456 | C4⋊C8 | C23×C71 | 1 | 3 | yes | — |
| 457 | #103 | C23×C71 | 1 | 3 | yes | — |
| 458 | #103 | C23×C71 | 1 | 3 | yes | — |
| 459 | #103 | C23×C71 | 1 | 1 | yes | characteristic |
| 460 | #103 | C23×C71 | 1 | 3 | yes | — |
| 461 | #103 | C23×C71 | 1 | 3 | yes | — |
| 462 | #103 | C23×C71 | 1 | 3 | yes | — |
| 463 | #103 | C23×C71 | 1 | 6 | yes | — |
| 464 | #103 | C23×C71 | 1 | 6 | yes | — |
| 465 | #102 | C23×C71 | 1 | 1 | yes | characteristic |
| 466 | #102 | C23×C71 | 1 | 3 | yes | — |
| 467 | C22⋊C8 | C23×C71 | 1 | 6 | yes | — |
| 468 | #97 | C23×C71 | 1 | 1 | yes | characteristic |
| 469 | #97 | C23×C71 | 1 | 3 | yes | — |
| 470 | C4×C8 | C23×C71 | 1 | 3 | yes | — |
| 471 | C4×C8 | C23×C71 | 1 | 3 | yes | — |
| 472 | #41 | — | 2 | 4 | no | — |
| 473 | #41 | — | 2 | 6 | no | — |
| 474 | #41 | — | 4 | 3 | no | — |
| 475 | C2×Q8 | — | 2 | 3 | no | — |
| 476 | C2×Q8 | — | 2 | 3 | no | — |
| 477 | C2×Q8 | — | 2 | 3 | no | — |
| 478 | C2×Q8 | — | 2 | 6 | no | — |
| 479 | C2×Q8 | — | 4 | 3 | no | — |
| 480 | C2×Q8 | — | 4 | 4 | no | — |
| 481 | C2×Q8 | C2×D4×C71 | 1 | 1 | yes | characteristic |
| 482 | C2×Q8 | C24×C71 | 1 | 3 | yes | — |
| 483 | C2×Q8 | C24×C71 | 1 | 3 | yes | — |
| 484 | C2×Q8 | C24×C71 | 1 | 1 | yes | characteristic |
| 485 | C2×D4 | — | 2 | 3 | no | — |
| 486 | C2×D4 | C2×D4×C71 | 1 | 3 | yes | — |
| 487 | C2×D4 | C24×C71 | 1 | 1 | yes | characteristic |
| 488 | C22×C4 | — | 2 | 3 | no | — |
| 489 | C22×C4 | — | 2 | 3 | no | — |
| 490 | C22×C4 | — | 2 | 1 | no | — |
| 491 | C22×C4 | — | 2 | 3 | no | — |
| 492 | C22×C4 | — | 2 | 3 | no | — |
| 493 | C22×C4 | C2×D4×C71 | 1 | 3 | yes | — |
| 494 | C22×C4 | C2×D4×C71 | 1 | 3 | yes | — |
| 495 | C22×C4 | C24×C71 | 1 | 3 | yes | — |
| 496 | Q16 | — | 2 | 6 | no | — |
| 497 | Q16 | — | 2 | 6 | no | — |
| 498 | Q16 | — | 4 | 6 | no | — |
| 499 | SD16 | — | 2 | 6 | no | — |
| 500 | SD16 | #41×C71 | 1 | 4 | yes | complemented |
| 501 | M16 | — | 2 | 6 | no | — |
| 502 | M16 | — | 4 | 3 | no | — |
| 503 | C2×C8 | C24×C71 | 1 | 1 | yes | characteristic |
| 504 | C2×C8 | C24×C71 | 1 | 3 | yes | — |
| 505 | C2×C8 | C24×C71 | 1 | 3 | yes | — |
| 506 | C2×C8 | C24×C71 | 1 | 1 | yes | characteristic |
| 507 | C4⋊C4 | — | 2 | 1 | no | — |
| 508 | C4⋊C4 | — | 2 | 3 | no | — |
| 509 | C4⋊C4 | — | 2 | 6 | no | — |
| 510 | C4⋊C4 | — | 2 | 3 | no | — |
| 511 | C4⋊C4 | — | 2 | 3 | no | — |
| 512 | C4⋊C4 | — | 2 | 3 | no | — |
| 513 | C4⋊C4 | — | 2 | 3 | no | — |
| 514 | C4⋊C4 | — | 2 | 3 | no | — |
| 515 | C4⋊C4 | — | 2 | 3 | no | — |
| 516 | C4⋊C4 | — | 2 | 3 | no | — |
| 517 | C4⋊C4 | — | 2 | 3 | no | — |
| 518 | C4⋊C4 | — | 2 | 3 | no | — |
| 519 | C4⋊C4 | — | 2 | 3 | no | — |
| 520 | C4⋊C4 | — | 2 | 3 | no | — |
| 521 | C4⋊C4 | — | 2 | 6 | no | — |
| 522 | C4⋊C4 | C2×D4×C71 | 1 | 3 | yes | — |
| 523 | C4⋊C4 | C2×D4×C71 | 1 | 3 | yes | — |
| 524 | C4⋊C4 | C24×C71 | 1 | 1 | yes | characteristic |
| 525 | C4⋊C4 | C24×C71 | 1 | 3 | yes | — |
| 526 | C4⋊C4 | C24×C71 | 1 | 3 | yes | — |
| 527 | C4⋊C4 | C24×C71 | 1 | 1 | yes | characteristic |
| 528 | C22⋊C4 | — | 2 | 6 | no | — |
| 529 | C22⋊C4 | — | 2 | 6 | no | — |
| 530 | C22⋊C4 | — | 2 | 3 | no | — |
| 531 | C22⋊C4 | — | 2 | 1 | no | — |
| 532 | C22⋊C4 | — | 2 | 3 | no | — |
| 533 | C22⋊C4 | C2×D4×C71 | 1 | 6 | yes | — |
| 534 | C42 | — | 2 | 1 | no | — |
| 535 | C42 | — | 2 | 3 | no | — |
| 536 | C42 | — | 2 | 3 | no | — |
| 537 | C42 | — | 2 | 3 | no | — |
| 538 | C42 | — | 2 | 3 | no | — |
| 539 | C42 | — | 2 | 3 | no | — |
| 540 | C42 | — | 2 | 3 | no | — |
| 541 | C42 | C2×D4×C71 | 1 | 3 | yes | — |
| 542 | C42 | C2×D4×C71 | 1 | 3 | yes | — |
| 543 | C42 | C24×C71 | 1 | 3 | yes | — |
| 544 | C42 | C24×C71 | 1 | 1 | yes | characteristic |
| 545 | C23 | — | 2 | 1 | no | — |
| 546 | C23 | C22×D4×C71 | 1 | 3 | yes | — |
| 547 | Q8 | — | 2 | 1 | no | — |
| 548 | Q8 | — | 2 | 3 | no | — |
| 549 | Q8 | — | 2 | 3 | no | — |
| 550 | Q8 | — | 2 | 3 | no | — |
| 551 | Q8 | — | 2 | 3 | no | — |
| 552 | Q8 | — | 4 | 6 | no | — |
| 553 | Q8 | — | 4 | 6 | no | — |
| 554 | Q8 | — | 8 | 3 | no | — |
| 555 | Q8 | #137×C71 | 1 | 4 | yes | complemented |
| 556 | Q8 | C2×#41×C71 | 1 | 2 | yes | — |
| 557 | D4 | — | 2 | 6 | no | — |
| 558 | D4 | — | 2 | 1 | no | — |
| 559 | D4 | — | 4 | 6 | no | — |
| 560 | D4 | C2×#41×C71 | 1 | 2 | yes | — |
| 561 | C2×C4 | — | 2 | 1 | no | — |
| 562 | C2×C4 | — | 2 | 6 | no | — |
| 563 | C2×C4 | — | 2 | 3 | no | — |
| 564 | C2×C4 | — | 2 | 3 | no | — |
| 565 | C2×C4 | — | 2 | 1 | no | — |
| 566 | C2×C4 | — | 2 | 1 | no | — |
| 567 | C2×C4 | — | 2 | 3 | no | — |
| 568 | C2×C4 | — | 2 | 3 | no | — |
| 569 | C2×C4 | — | 2 | 3 | no | — |
| 570 | C2×C4 | — | 2 | 3 | no | — |
| 571 | C2×C4 | — | 4 | 3 | no | — |
| 572 | C2×C4 | — | 4 | 6 | no | — |
| 573 | C2×C4 | — | 4 | 6 | no | — |
| 574 | C2×C4 | — | 4 | 2 | no | — |
| 575 | C2×C4 | — | 4 | 6 | no | — |
| 576 | C2×C4 | — | 8 | 3 | no | — |
| 577 | C2×C4 | C22×D4×C71 | 1 | 1 | yes | characteristic |
| 578 | C2×C4 | C22×D4×C71 | 1 | 1 | yes | characteristic |
| 579 | C2×C4 | C22×D4×C71 | 1 | 3 | yes | — |
| 580 | C2×C4 | C22×D4×C71 | 1 | 3 | yes | — |
| 581 | C2×C4 | C22×D4×C71 | 1 | 3 | yes | — |
| 582 | C2×C4 | C25×C71 | 1 | 1 | yes | characteristic |
| 583 | C8 | — | 2 | 3 | no | — |
| 584 | C8 | — | 2 | 1 | no | — |
| 585 | C8 | — | 2 | 3 | no | — |
| 586 | C8 | C2×#41×C71 | 1 | 2 | yes | — |
| 587 | C22 | — | 2 | 3 | no | — |
| 588 | C22 | — | 2 | 3 | no | — |
| 589 | C22 | — | 2 | 3 | no | — |
| 590 | C22 | — | 2 | 2 | no | — |
| 591 | C22 | — | 4 | 1 | no | — |
| 592 | C22 | — | 4 | 1 | no | — |
| 593 | C22 | C23×D4×C71 | 1 | 1 | yes | characteristic |
| 594 | C4 | — | 2 | 1 | no | — |
| 595 | C4 | — | 2 | 1 | no | — |
| 596 | C4 | — | 2 | 3 | no | — |
| 597 | C4 | — | 2 | 3 | no | — |
| 598 | C4 | — | 2 | 2 | no | — |
| 599 | C4 | — | 4 | 3 | no | — |
| 600 | C4 | — | 4 | 1 | no | — |
| 601 | C4 | — | 4 | 1 | no | — |
| 602 | C4 | — | 4 | 3 | no | — |
| 603 | C4 | — | 4 | 3 | no | — |
| 604 | C4 | — | 4 | 3 | no | — |
| 605 | C4 | C2×#137×C71 | 1 | 6 | yes | — |
| 606 | C4 | C22×#41×C71 | 1 | 1 | yes | characteristic |
| 607 | C4 | #585×C71 | 1 | 1 | yes | characteristic |
| 608 | C2 | — | 4 | 3 | no | — |
| 609 | C2 | — | 4 | 2 | no | — |
| 610 | C2 | D4×#41×C71 | 1 | 1 | yes | characteristic |
| 611 | C2 | C22×#137×C71 | 1 | 1 | yes | characteristic |
| 612 | C2 | C71×#3586 | 1 | 1 | yes | characteristic |
Finite Group Databasebeta