Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
4756 conjugacy classes of subgroups.
The subgroup lattice has 886 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#16811460 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C2×#16811438 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#16811435 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20288396 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20284035 | C2 | 1 | 3 | yes | maximal, complemented |
| 6 | #20284021 | C2 | 1 | 3 | yes | maximal, complemented |
| 7 | #20284011 | C2 | 1 | 3 | yes | maximal, complemented |
| 8 | #20283995 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #20283976 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #20283961 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | #20283935 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | C2×#16810788 | C2 | 1 | 3 | yes | maximal, complemented |
| 13 | #20283238 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #20283162 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C53×#2898 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #16811460 | — | 2 | 8 | no | — |
| 17 | #16811460 | — | 2 | 8 | no | — |
| 18 | C2×#13133265 | — | 2 | 1 | no | — |
| 19 | C2×#13133265 | C22 | 1 | 3 | yes | — |
| 20 | C2×#13133264 | C22 | 1 | 1 | yes | characteristic, complemented |
| 21 | C2×#13133263 | — | 2 | 3 | no | — |
| 22 | C2×#13133263 | C22 | 1 | 1 | yes | characteristic |
| 23 | C2×#13133263 | C22 | 1 | 3 | yes | — |
| 24 | C22×#11719949 | — | 2 | 1 | no | — |
| 25 | C22×#11719949 | C22 | 1 | 3 | yes | — |
| 26 | C2×#41×D53 | — | 2 | 3 | no | — |
| 27 | C2×#41×D53 | C22 | 1 | 3 | yes | — |
| 28 | C2×#41×D53 | C22 | 1 | 1 | yes | characteristic |
| 29 | #16811438 | — | 2 | 8 | no | — |
| 30 | #16811435 | — | 2 | 8 | no | — |
| 31 | C2×#13133250 | C22 | 1 | 3 | yes | complemented |
| 32 | C2×#13133248 | C22 | 1 | 3 | yes | complemented |
| 33 | C2×#13133247 | C22 | 1 | 3 | yes | complemented |
| 34 | C2×#13133245 | C22 | 1 | 3 | yes | complemented |
| 35 | C2×#13133239 | C22 | 1 | 3 | yes | complemented |
| 36 | C2×#13133237 | C22 | 1 | 3 | yes | complemented |
| 37 | C22×#11719925 | C22 | 1 | 3 | yes | complemented |
| 38 | C22×#11719913 | C22 | 1 | 3 | yes | complemented |
| 39 | C2×#13133224 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | Q8×D212 | — | 2 | 1 | no | — |
| 41 | #16811285 | — | 2 | 1 | no | — |
| 42 | #16811277 | — | 2 | 3 | no | — |
| 43 | #16811268 | — | 2 | 3 | no | — |
| 44 | #16811204 | C22 | 1 | 3 | yes | complemented |
| 45 | #16811199 | C22 | 1 | 3 | yes | complemented |
| 46 | #16811135 | C22 | 1 | 3 | yes | complemented |
| 47 | C2×#13133197 | C22 | 1 | 3 | yes | complemented |
| 48 | #16810788 | C22 | 1 | 3 | yes | complemented |
| 49 | #16810788 | C22 | 1 | 6 | yes | complemented |
| 50 | #16810788 | C22 | 1 | 6 | yes | complemented |
| 51 | #16810788 | C22 | 1 | 6 | yes | complemented |
| 52 | #16810788 | C22 | 1 | 6 | yes | complemented |
| 53 | #16810786 | C22 | 1 | 3 | yes | complemented |
| 54 | #16810780 | C22 | 1 | 3 | yes | complemented |
| 55 | #16810780 | C22 | 1 | 6 | yes | complemented |
| 56 | #16810775 | C22 | 1 | 3 | yes | complemented |
| 57 | #16810775 | C22 | 1 | 6 | yes | complemented |
| 58 | #16810771 | C22 | 1 | 3 | yes | complemented |
| 59 | #16810771 | C22 | 1 | 6 | yes | complemented |
| 60 | #16810769 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | #16810763 | C22 | 1 | 3 | yes | complemented |
| 62 | #16810758 | C22 | 1 | 3 | yes | complemented |
| 63 | #16810627 | C22 | 1 | 3 | yes | complemented |
| 64 | #16810622 | C22 | 1 | 3 | yes | complemented |
| 65 | #16810617 | C22 | 1 | 3 | yes | complemented |
| 66 | C2×#13133137 | C22 | 1 | 3 | yes | complemented |
| 67 | #16810591 | C22 | 1 | 3 | yes | complemented |
| 68 | #16810589 | C22 | 1 | 3 | yes | complemented |
| 69 | #16810586 | C22 | 1 | 3 | yes | complemented |
| 70 | C2×#13133129 | C22 | 1 | 3 | yes | complemented |
| 71 | C2×2−1+4×C53 | C22 | 1 | 1 | yes | characteristic |
| 72 | C2×#131×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 73 | C53×#520 | C22 | 1 | 1 | yes | characteristic, complemented |
| 74 | C53×#419 | C22 | 1 | 3 | yes | complemented |
| 75 | C53×#417 | C22 | 1 | 3 | yes | complemented |
| 76 | C53×#416 | C22 | 1 | 3 | yes | complemented |
| 77 | C2×#103×C53 | C22 | 1 | 3 | yes | complemented |
| 78 | #13133265 | — | 2 | 16 | no | — |
| 79 | #13133265 | — | 2 | 12 | no | — |
| 80 | #13133265 | — | 2 | 12 | no | — |
| 81 | #13133264 | — | 2 | 4 | no | — |
| 82 | #13133264 | — | 2 | 4 | no | — |
| 83 | #13133263 | — | 2 | 48 | no | — |
| 84 | #13133263 | — | 2 | 12 | no | — |
| 85 | #13133263 | — | 2 | 4 | no | — |
| 86 | #13133263 | — | 2 | 12 | no | — |
| 87 | #13133263 | D4 | 1 | 8 | yes | complemented |
| 88 | C2×#11719949 | — | 2 | 16 | no | — |
| 89 | C2×#11719949 | — | 2 | 1 | no | — |
| 90 | C2×#11719949 | — | 2 | 12 | no | — |
| 91 | C2×#11719949 | — | 2 | 3 | no | — |
| 92 | C2×#11719949 | — | 2 | 12 | no | — |
| 93 | C2×#11719949 | — | 2 | 3 | no | — |
| 94 | C2×#11719949 | — | 2 | 3 | no | — |
| 95 | C2×#11719949 | D4 | 1 | 1 | yes | characteristic |
| 96 | C2×#11719949 | C23 | 1 | 3 | yes | — |
| 97 | C2×#11719949 | C23 | 1 | 6 | yes | — |
| 98 | C2×#11719945 | — | 2 | 6 | no | — |
| 99 | C2×#11719945 | — | 2 | 3 | no | — |
| 100 | C2×#11719945 | — | 2 | 3 | no | — |
| 101 | C2×#11719945 | C23 | 1 | 3 | yes | — |
| 102 | C2×#11719945 | C23 | 1 | 3 | yes | — |
| 103 | C2×#11719945 | C23 | 1 | 3 | yes | — |
| 104 | C2×#11719947 | — | 2 | 3 | no | — |
| 105 | C2×#11719947 | — | 2 | 3 | no | — |
| 106 | C2×#11719947 | D4 | 1 | 3 | yes | — |
| 107 | C2×#11719947 | C23 | 1 | 1 | yes | characteristic |
| 108 | #41×D53 | — | 2 | 48 | no | — |
| 109 | #41×D53 | — | 2 | 12 | no | — |
| 110 | #41×D53 | — | 2 | 4 | no | — |
| 111 | #41×D53 | — | 2 | 4 | no | — |
| 112 | #41×D53 | — | 2 | 12 | no | — |
| 113 | C22×Dic106 | C23 | 1 | 3 | yes | — |
| 114 | C2×Q8×D53 | — | 2 | 1 | no | — |
| 115 | C2×Q8×D53 | — | 2 | 3 | no | — |
| 116 | C2×Q8×D53 | D4 | 1 | 1 | yes | characteristic |
| 117 | C2×Q8×D53 | C23 | 1 | 3 | yes | — |
| 118 | C22×D212 | — | 2 | 3 | no | — |
| 119 | C22×D212 | — | 2 | 3 | no | — |
| 120 | C22×D212 | C23 | 1 | 3 | yes | — |
| 121 | C2×D4×D53 | — | 2 | 3 | no | — |
| 122 | C2×D4×D53 | — | 2 | 3 | no | — |
| 123 | C2×D4×D53 | — | 2 | 6 | no | — |
| 124 | C2×D4×D53 | D4 | 1 | 3 | yes | — |
| 125 | C2×D4×D53 | C23 | 1 | 3 | yes | — |
| 126 | C22×C4×D53 | — | 2 | 3 | no | — |
| 127 | C22×C4×D53 | — | 2 | 3 | no | — |
| 128 | C22×C4×D53 | C23 | 1 | 3 | yes | — |
| 129 | #13133250 | — | 2 | 12 | no | — |
| 130 | #13133248 | — | 2 | 12 | no | — |
| 131 | #13133247 | — | 2 | 12 | no | — |
| 132 | #13133245 | — | 2 | 12 | no | — |
| 133 | #13133239 | — | 2 | 12 | no | — |
| 134 | #13133237 | — | 2 | 12 | no | — |
| 135 | C2×Dic212 | C23 | 1 | 3 | yes | — |
| 136 | C2×#11719925 | — | 2 | 12 | no | — |
| 137 | C2×#11719925 | C23 | 1 | 3 | yes | — |
| 138 | C2×#11719925 | C23 | 1 | 6 | yes | — |
| 139 | C2×#11719913 | — | 2 | 12 | no | — |
| 140 | C2×#11719913 | C23 | 1 | 1 | yes | characteristic |
| 141 | C2×#11719913 | C23 | 1 | 3 | yes | — |
| 142 | C2×#11719913 | C23 | 1 | 6 | yes | — |
| 143 | C2×#11719923 | C23 | 1 | 3 | yes | — |
| 144 | C2×#11719924 | C23 | 1 | 3 | yes | — |
| 145 | C2×D424 | C23 | 1 | 3 | yes | — |
| 146 | C2×#11719922 | C23 | 1 | 1 | yes | characteristic |
| 147 | #13133224 | — | 2 | 4 | no | — |
| 148 | C2×#11719917 | C23 | 1 | 3 | yes | — |
| 149 | C22×#88322 | C23 | 1 | 3 | yes | — |
| 150 | #13133217 | — | 2 | 3 | no | — |
| 151 | #13133205 | — | 2 | 3 | no | — |
| 152 | #13133201 | — | 2 | 6 | no | — |
| 153 | #13133201 | — | 2 | 3 | no | — |
| 154 | #13133197 | — | 2 | 3 | no | — |
| 155 | #13133197 | — | 2 | 3 | no | — |
| 156 | #13133197 | — | 2 | 3 | no | — |
| 157 | #13133197 | C23 | 1 | 6 | yes | — |
| 158 | #13133197 | C23 | 1 | 3 | yes | — |
| 159 | #13133197 | C23 | 1 | 3 | yes | — |
| 160 | #13133192 | — | 2 | 3 | no | — |
| 161 | #13133192 | C23 | 1 | 3 | yes | — |
| 162 | #13133192 | C23 | 1 | 1 | yes | characteristic |
| 163 | #13133191 | — | 2 | 6 | no | — |
| 164 | #13133187 | — | 2 | 3 | no | — |
| 165 | C4×D212 | — | 2 | 3 | no | — |
| 166 | C4×D212 | — | 2 | 3 | no | — |
| 167 | C2×C4⋊Dic53 | — | 2 | 3 | no | — |
| 168 | C2×#11719921 | — | 2 | 3 | no | — |
| 169 | #13133140 | C23 | 1 | 3 | yes | — |
| 170 | #13133140 | C23 | 1 | 1 | yes | characteristic |
| 171 | #13133137 | C23 | 1 | 3 | yes | — |
| 172 | #13133137 | C23 | 1 | 6 | yes | — |
| 173 | #13133137 | C23 | 1 | 3 | yes | — |
| 174 | #13133129 | C23 | 1 | 3 | yes | — |
| 175 | #13133129 | C23 | 1 | 3 | yes | — |
| 176 | #13133129 | C23 | 1 | 1 | yes | characteristic |
| 177 | #13133129 | C23 | 1 | 6 | yes | — |
| 178 | #13133129 | C23 | 1 | 3 | yes | — |
| 179 | 2−1+4×C53 | — | 2 | 4 | no | — |
| 180 | 2−1+4×C53 | D4 | 1 | 8 | yes | complemented |
| 181 | C2×#41×C53 | — | 2 | 3 | no | — |
| 182 | C2×#41×C53 | C23 | 1 | 3 | yes | — |
| 183 | C2×#41×C53 | C23 | 1 | 1 | yes | characteristic |
| 184 | C22×Q8×C53 | — | 2 | 1 | no | — |
| 185 | C22×Q8×C53 | C23 | 1 | 3 | yes | — |
| 186 | #131×C53 | — | 2 | 4 | no | — |
| 187 | C2×M16×C53 | C23 | 1 | 3 | yes | — |
| 188 | C22×C8×C53 | C23 | 1 | 3 | yes | — |
| 189 | C4×Q8×C53 | — | 2 | 1 | no | — |
| 190 | C4×D4×C53 | — | 2 | 3 | no | — |
| 191 | #117×C53 | C23 | 1 | 3 | yes | — |
| 192 | C2×C4⋊C4×C53 | C23 | 1 | 3 | yes | — |
| 193 | #103×C53 | C23 | 1 | 3 | yes | — |
| 194 | #103×C53 | C23 | 1 | 6 | yes | — |
| 195 | #103×C53 | C23 | 1 | 3 | yes | — |
| 196 | #102×C53 | C23 | 1 | 3 | yes | — |
| 197 | #102×C53 | C23 | 1 | 1 | yes | characteristic |
| 198 | C23×D53 | — | 2 | 3 | no | — |
| 199 | C23×D53 | — | 2 | 3 | no | — |
| 200 | C23×D53 | C2×D4 | 1 | 3 | yes | — |
| 201 | #41×C53 | — | 2 | 24 | no | — |
| 202 | #41×C53 | — | 2 | 6 | no | — |
| 203 | #41×C53 | C2×D4 | 1 | 12 | yes | — |
| 204 | #41×C53 | C2×D4 | 1 | 4 | yes | — |
| 205 | #41×C53 | C2×D4 | 1 | 4 | yes | — |
| 206 | C2×Q8×C53 | — | 2 | 8 | no | — |
| 207 | C2×Q8×C53 | — | 2 | 3 | no | — |
| 208 | C2×Q8×C53 | — | 2 | 6 | no | — |
| 209 | C2×Q8×C53 | C2×D4 | 1 | 12 | yes | — |
| 210 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 211 | C2×Q8×C53 | C24 | 1 | 3 | yes | — |
| 212 | C2×D4×C53 | — | 2 | 3 | no | — |
| 213 | C2×D4×C53 | C2×D4 | 1 | 3 | yes | — |
| 214 | C2×D4×C53 | C24 | 1 | 1 | yes | characteristic |
| 215 | C22×C4×C53 | — | 2 | 3 | no | — |
| 216 | C22×C4×C53 | — | 2 | 3 | no | — |
| 217 | C22×C4×C53 | — | 2 | 3 | no | — |
| 218 | C22×C4×C53 | C24 | 1 | 3 | yes | — |
| 219 | C2×C22⋊D53 | — | 2 | 3 | no | — |
| 220 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 221 | C2×C22⋊D53 | — | 2 | 3 | no | — |
| 222 | C2×C22⋊D53 | — | 2 | 3 | no | — |
| 223 | C2×C22⋊D53 | C2×D4 | 1 | 6 | yes | — |
| 224 | C22×Dic53 | — | 2 | 1 | no | — |
| 225 | C22×Dic53 | — | 2 | 3 | no | — |
| 226 | C22×Dic53 | C2×D4 | 1 | 3 | yes | — |
| 227 | #11719949 | — | 2 | 24 | no | — |
| 228 | #11719949 | — | 2 | 24 | no | — |
| 229 | #11719949 | — | 2 | 24 | no | — |
| 230 | #11719949 | — | 2 | 4 | no | — |
| 231 | #11719949 | — | 2 | 8 | no | — |
| 232 | #11719949 | — | 2 | 6 | no | — |
| 233 | #11719949 | — | 2 | 12 | no | — |
| 234 | #11719949 | — | 2 | 6 | no | — |
| 235 | #11719949 | — | 2 | 12 | no | — |
| 236 | Q8×D53 | — | 2 | 24 | no | — |
| 237 | Q8×D53 | — | 2 | 4 | no | — |
| 238 | Q8×D53 | — | 2 | 6 | no | — |
| 239 | Q8×D53 | — | 2 | 6 | no | — |
| 240 | Q8×D53 | — | 4 | 4 | no | — |
| 241 | #11719947 | — | 2 | 24 | no | — |
| 242 | #11719947 | — | 2 | 12 | no | — |
| 243 | #11719947 | — | 2 | 2 | no | — |
| 244 | #11719947 | — | 2 | 2 | no | — |
| 245 | #11719947 | — | 4 | 12 | no | — |
| 246 | D4×D53 | — | 2 | 48 | no | — |
| 247 | D4×D53 | — | 2 | 24 | no | — |
| 248 | D4×D53 | — | 2 | 24 | no | — |
| 249 | D4×D53 | — | 2 | 12 | no | — |
| 250 | D4×D53 | — | 2 | 6 | no | — |
| 251 | D4×D53 | — | 2 | 6 | no | — |
| 252 | #11719945 | — | 2 | 48 | no | — |
| 253 | #11719945 | — | 2 | 24 | no | — |
| 254 | #11719945 | — | 2 | 24 | no | — |
| 255 | #11719945 | — | 2 | 6 | no | — |
| 256 | #11719945 | — | 2 | 6 | no | — |
| 257 | #11719945 | — | 2 | 6 | no | — |
| 258 | #11719945 | — | 2 | 6 | no | — |
| 259 | #11719945 | — | 2 | 6 | no | — |
| 260 | #11719945 | C2×D4 | 1 | 12 | yes | — |
| 261 | C2×D212 | — | 2 | 24 | no | — |
| 262 | C2×D212 | — | 2 | 24 | no | — |
| 263 | C2×D212 | — | 2 | 6 | no | — |
| 264 | C2×D212 | — | 2 | 3 | no | — |
| 265 | C2×D212 | — | 2 | 3 | no | — |
| 266 | C2×D212 | — | 2 | 6 | no | — |
| 267 | C2×D212 | — | 2 | 1 | no | — |
| 268 | C2×D212 | — | 2 | 3 | no | — |
| 269 | C2×D212 | C2×D4 | 1 | 3 | yes | — |
| 270 | C2×D212 | C2×D4 | 1 | 12 | yes | — |
| 271 | C2×D212 | C24 | 1 | 1 | yes | characteristic |
| 272 | C2×D212 | C24 | 1 | 3 | yes | — |
| 273 | C2×C4×D53 | — | 2 | 24 | no | — |
| 274 | C2×C4×D53 | — | 2 | 24 | no | — |
| 275 | C2×C4×D53 | — | 2 | 3 | no | — |
| 276 | C2×C4×D53 | — | 2 | 3 | no | — |
| 277 | C2×C4×D53 | — | 2 | 6 | no | — |
| 278 | C2×C4×D53 | — | 2 | 6 | no | — |
| 279 | C2×C4×D53 | — | 2 | 3 | no | — |
| 280 | C2×C4×D53 | — | 2 | 6 | no | — |
| 281 | C2×C4×D53 | — | 2 | 3 | no | — |
| 282 | C2×C4×D53 | C2×D4 | 1 | 3 | yes | — |
| 283 | C2×C4×D53 | C2×D4 | 1 | 3 | yes | — |
| 284 | C2×C4×D53 | C24 | 1 | 1 | yes | characteristic |
| 285 | C2×C4×D53 | C24 | 1 | 3 | yes | — |
| 286 | C2×Dic106 | — | 2 | 3 | no | — |
| 287 | C2×Dic106 | — | 2 | 6 | no | — |
| 288 | C2×Dic106 | — | 2 | 6 | no | — |
| 289 | C2×Dic106 | — | 2 | 3 | no | — |
| 290 | C2×Dic106 | C2×D4 | 1 | 3 | yes | — |
| 291 | C2×Dic106 | C24 | 1 | 3 | yes | — |
| 292 | C2×Dic106 | C24 | 1 | 1 | yes | characteristic |
| 293 | M16×C53 | — | 2 | 6 | no | — |
| 294 | C2×C8×C53 | — | 2 | 6 | no | — |
| 295 | C2×C8×C53 | C24 | 1 | 1 | yes | characteristic |
| 296 | C2×C8×C53 | C24 | 1 | 3 | yes | — |
| 297 | C4⋊C4×C53 | — | 2 | 3 | no | — |
| 298 | C4⋊C4×C53 | C24 | 1 | 3 | yes | — |
| 299 | C4⋊C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 300 | C22⋊C4×C53 | — | 2 | 3 | no | — |
| 301 | C42×C53 | — | 2 | 3 | no | — |
| 302 | #11719925 | — | 2 | 6 | no | — |
| 303 | #11719925 | — | 2 | 12 | no | — |
| 304 | #11719924 | — | 2 | 6 | no | — |
| 305 | #11719923 | — | 2 | 6 | no | — |
| 306 | #11719922 | — | 2 | 2 | no | — |
| 307 | #11719921 | — | 2 | 3 | no | — |
| 308 | #11719921 | — | 2 | 6 | no | — |
| 309 | #11719921 | — | 2 | 3 | no | — |
| 310 | #11719921 | — | 2 | 1 | no | — |
| 311 | #11719921 | — | 2 | 3 | no | — |
| 312 | C4⋊Dic53 | — | 2 | 3 | no | — |
| 313 | C4⋊Dic53 | — | 2 | 6 | no | — |
| 314 | C4⋊Dic53 | — | 2 | 3 | no | — |
| 315 | #11719917 | — | 2 | 6 | no | — |
| 316 | C2×#88322 | — | 2 | 6 | no | — |
| 317 | C2×#88322 | C24 | 1 | 1 | yes | characteristic |
| 318 | C2×#88322 | C24 | 1 | 3 | yes | — |
| 319 | Dic212 | — | 2 | 6 | no | — |
| 320 | D424 | — | 2 | 6 | no | — |
| 321 | #11719913 | — | 2 | 6 | no | — |
| 322 | #11719913 | — | 2 | 12 | no | — |
| 323 | #11719913 | — | 2 | 2 | no | — |
| 324 | C23×C53 | — | 2 | 1 | no | — |
| 325 | C23×C53 | C22×D4 | 1 | 3 | yes | — |
| 326 | C22×D53 | — | 2 | 3 | no | — |
| 327 | C22×D53 | — | 2 | 12 | no | — |
| 328 | C22×D53 | — | 2 | 6 | no | — |
| 329 | C22×D53 | — | 2 | 12 | no | — |
| 330 | C22×D53 | — | 2 | 1 | no | — |
| 331 | C22×D53 | — | 4 | 3 | no | — |
| 332 | C22×D53 | — | 4 | 3 | no | — |
| 333 | C22×D53 | — | 8 | 3 | no | — |
| 334 | C22×D53 | — | 8 | 3 | no | — |
| 335 | C22×D53 | — | 8 | 3 | no | — |
| 336 | C22×D53 | — | 8 | 3 | no | — |
| 337 | C22×D53 | C22×D4 | 1 | 3 | yes | — |
| 338 | C22×D53 | C22×D4 | 1 | 1 | yes | characteristic |
| 339 | Q8×C53 | — | 2 | 12 | no | — |
| 340 | Q8×C53 | — | 2 | 3 | no | — |
| 341 | Q8×C53 | #120 | 1 | 4 | yes | — |
| 342 | Q8×C53 | C22×D4 | 1 | 6 | yes | — |
| 343 | D4×C53 | — | 2 | 12 | no | — |
| 344 | D4×C53 | — | 2 | 1 | no | — |
| 345 | D4×C53 | #120 | 1 | 12 | yes | — |
| 346 | D4×C53 | C22×D4 | 1 | 2 | yes | — |
| 347 | C2×C4×C53 | — | 2 | 12 | no | — |
| 348 | C2×C4×C53 | — | 2 | 3 | no | — |
| 349 | C2×C4×C53 | — | 2 | 12 | no | — |
| 350 | C2×C4×C53 | — | 2 | 3 | no | — |
| 351 | C2×C4×C53 | — | 2 | 1 | no | — |
| 352 | C2×C4×C53 | — | 8 | 3 | no | — |
| 353 | C2×C4×C53 | C22×D4 | 1 | 3 | yes | — |
| 354 | C2×C4×C53 | C22×D4 | 1 | 6 | yes | — |
| 355 | C2×C4×C53 | C22×D4 | 1 | 6 | yes | — |
| 356 | C2×C4×C53 | C25 | 1 | 1 | yes | characteristic |
| 357 | C22⋊D53 | — | 2 | 12 | no | — |
| 358 | C22⋊D53 | — | 2 | 4 | no | — |
| 359 | C22⋊D53 | — | 2 | 12 | no | — |
| 360 | C22⋊D53 | — | 2 | 12 | no | — |
| 361 | C22⋊D53 | — | 4 | 6 | no | — |
| 362 | C2×Dic53 | — | 2 | 4 | no | — |
| 363 | C2×Dic53 | — | 2 | 6 | no | — |
| 364 | C2×Dic53 | — | 2 | 1 | no | — |
| 365 | C2×Dic53 | — | 2 | 3 | no | — |
| 366 | C2×Dic53 | — | 4 | 6 | no | — |
| 367 | C2×Dic53 | C22×D4 | 1 | 3 | yes | — |
| 368 | C2×Dic53 | C22×D4 | 1 | 1 | yes | characteristic |
| 369 | D212 | — | 2 | 24 | no | — |
| 370 | D212 | — | 2 | 12 | no | — |
| 371 | D212 | — | 2 | 6 | no | — |
| 372 | D212 | — | 2 | 12 | no | — |
| 373 | D212 | — | 2 | 3 | no | — |
| 374 | D212 | — | 2 | 1 | no | — |
| 375 | D212 | — | 2 | 1 | no | — |
| 376 | D212 | — | 4 | 2 | no | — |
| 377 | D212 | — | 8 | 3 | no | — |
| 378 | D212 | C22×D4 | 1 | 6 | yes | — |
| 379 | C4×D53 | — | 2 | 12 | no | — |
| 380 | C4×D53 | — | 2 | 24 | no | — |
| 381 | C4×D53 | — | 2 | 12 | no | — |
| 382 | C4×D53 | — | 2 | 6 | no | — |
| 383 | C4×D53 | — | 2 | 12 | no | — |
| 384 | C4×D53 | — | 2 | 6 | no | — |
| 385 | C4×D53 | — | 2 | 1 | no | — |
| 386 | C4×D53 | — | 2 | 1 | no | — |
| 387 | C4×D53 | — | 2 | 3 | no | — |
| 388 | C4×D53 | — | 2 | 3 | no | — |
| 389 | C4×D53 | — | 4 | 6 | no | — |
| 390 | Dic106 | — | 2 | 12 | no | — |
| 391 | Dic106 | — | 2 | 6 | no | — |
| 392 | Dic106 | — | 2 | 1 | no | — |
| 393 | Dic106 | — | 2 | 3 | no | — |
| 394 | Dic106 | — | 2 | 3 | no | — |
| 395 | Dic106 | — | 4 | 6 | no | — |
| 396 | Dic106 | C22×D4 | 1 | 2 | yes | — |
| 397 | C8×C53 | — | 2 | 1 | no | — |
| 398 | C8×C53 | — | 2 | 3 | no | — |
| 399 | #88322 | — | 2 | 1 | no | — |
| 400 | #88322 | — | 2 | 3 | no | — |
| 401 | #60377 | — | 53 | 1 | no | maximal, Sylow |
| 402 | C22×C53 | — | 2 | 3 | no | — |
| 403 | C22×C53 | — | 2 | 3 | no | — |
| 404 | C22×C53 | — | 2 | 2 | no | — |
| 405 | C22×C53 | — | 4 | 1 | no | — |
| 406 | C22×C53 | — | 4 | 1 | no | — |
| 407 | C22×C53 | C2×#120 | 1 | 6 | yes | — |
| 408 | C22×C53 | C23×D4 | 1 | 1 | yes | characteristic |
| 409 | C2×D53 | — | 2 | 3 | no | — |
| 410 | C2×D53 | — | 2 | 1 | no | — |
| 411 | C2×D53 | — | 2 | 1 | no | — |
| 412 | C2×D53 | — | 2 | 3 | no | — |
| 413 | C2×D53 | — | 2 | 3 | no | — |
| 414 | C2×D53 | — | 2 | 1 | no | — |
| 415 | C2×D53 | — | 2 | 6 | no | — |
| 416 | C2×D53 | — | 4 | 3 | no | — |
| 417 | C2×D53 | — | 4 | 3 | no | — |
| 418 | C2×D53 | — | 4 | 1 | no | — |
| 419 | C2×D53 | — | 4 | 1 | no | — |
| 420 | C2×D53 | — | 4 | 1 | no | — |
| 421 | C2×D53 | — | 8 | 6 | no | — |
| 422 | C2×D53 | — | 8 | 12 | no | — |
| 423 | C2×D53 | — | 8 | 12 | no | — |
| 424 | C4×C53 | — | 2 | 6 | no | — |
| 425 | C4×C53 | — | 4 | 3 | no | — |
| 426 | C4×C53 | — | 4 | 1 | no | — |
| 427 | C4×C53 | C2×#120 | 1 | 6 | yes | — |
| 428 | C4×C53 | C23×D4 | 1 | 1 | yes | characteristic |
| 429 | C4×C53 | C23×D4 | 1 | 1 | yes | characteristic |
| 430 | Dic53 | — | 2 | 3 | no | — |
| 431 | Dic53 | — | 2 | 2 | no | — |
| 432 | Dic53 | — | 2 | 1 | no | — |
| 433 | Dic53 | — | 4 | 3 | no | — |
| 434 | C2×#585 | — | 53 | 1 | no | — |
| 435 | C2×#578 | — | 53 | 1 | no | — |
| 436 | C2×#577 | — | 53 | 1 | no | — |
| 437 | #3489 | — | 53 | 1 | no | — |
| 438 | #3013 | — | 53 | 3 | no | — |
| 439 | #3012 | — | 53 | 3 | no | — |
| 440 | #3011 | — | 53 | 3 | no | — |
| 441 | #3009 | — | 53 | 3 | no | — |
| 442 | #3007 | — | 53 | 3 | no | — |
| 443 | #3005 | — | 53 | 3 | no | — |
| 444 | #3002 | — | 53 | 3 | no | — |
| 445 | C2×#452 | — | 53 | 3 | no | — |
| 446 | #2898 | D53 | 1 | 1 | yes | characteristic, complemented |
| 447 | #2897 | — | 53 | 1 | no | — |
| 448 | #2880 | — | 53 | 1 | no | — |
| 449 | C2×C53 | — | 2 | 6 | no | — |
| 450 | C2×C53 | — | 4 | 2 | no | — |
| 451 | C2×C53 | C22×#120 | 1 | 1 | yes | characteristic |
| 452 | C2×C53 | #3584 | 1 | 1 | yes | characteristic |
| 453 | C2×C53 | #3586 | 1 | 1 | yes | characteristic |
| 454 | D53 | — | 4 | 3 | no | — |
| 455 | D53 | — | 4 | 1 | no | — |
| 456 | D53 | — | 4 | 6 | no | — |
| 457 | D53 | — | 8 | 1 | no | — |
| 458 | #585 | — | 106 | 8 | no | — |
| 459 | #585 | — | 106 | 8 | no | — |
| 460 | C2×2−1+4 | — | 53 | 1 | no | — |
| 461 | C2×2−1+4 | — | 53 | 3 | no | — |
| 462 | C2×2−1+4 | — | 106 | 1 | no | — |
| 463 | C2×2−1+4 | C2×D53 | 1 | 1 | yes | characteristic |
| 464 | C2×H(5,𝔽2) | — | 53 | 3 | no | — |
| 465 | C2×H(5,𝔽2) | — | 53 | 1 | no | — |
| 466 | C2×H(5,𝔽2) | — | 106 | 3 | no | — |
| 467 | C22×#41 | — | 53 | 1 | no | — |
| 468 | C22×#41 | — | 53 | 3 | no | — |
| 469 | C22×#41 | — | 53 | 3 | no | — |
| 470 | C22×#41 | — | 106 | 1 | no | — |
| 471 | C22×#41 | — | 106 | 3 | no | — |
| 472 | #578 | — | 106 | 8 | no | — |
| 473 | #577 | — | 106 | 8 | no | — |
| 474 | C2×#137 | — | 53 | 3 | no | — |
| 475 | C2×#137 | — | 53 | 3 | no | — |
| 476 | C2×#137 | — | 53 | 3 | no | — |
| 477 | C2×AGL(1,ℤ/8) | — | 53 | 3 | no | — |
| 478 | C2×#135 | — | 53 | 3 | no | — |
| 479 | C2×#135 | — | 53 | 3 | no | — |
| 480 | C22×Q16 | — | 53 | 3 | no | — |
| 481 | C22×SD16 | — | 53 | 3 | no | — |
| 482 | C2×#131 | — | 53 | 1 | no | — |
| 483 | C2×#131 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 484 | D4×Q8 | — | 106 | 1 | no | — |
| 485 | #548 | — | 106 | 1 | no | — |
| 486 | #547 | — | 106 | 3 | no | — |
| 487 | #546 | — | 106 | 3 | no | — |
| 488 | #537 | — | 53 | 3 | no | — |
| 489 | #536 | — | 53 | 3 | no | — |
| 490 | #525 | — | 53 | 3 | no | — |
| 491 | C2×C22⋊Q8 | — | 53 | 3 | no | — |
| 492 | #520 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 493 | #452 | — | 53 | 3 | no | — |
| 494 | #452 | — | 53 | 6 | no | — |
| 495 | #452 | — | 53 | 6 | no | — |
| 496 | #452 | — | 53 | 6 | no | — |
| 497 | #452 | — | 53 | 6 | no | — |
| 498 | #452 | — | 53 | 3 | no | — |
| 499 | #451 | — | 53 | 3 | no | — |
| 500 | #451 | — | 53 | 6 | no | — |
| 501 | #450 | — | 53 | 3 | no | — |
| 502 | #450 | — | 53 | 6 | no | — |
| 503 | #449 | — | 53 | 3 | no | — |
| 504 | #449 | — | 53 | 6 | no | — |
| 505 | #449 | — | 53 | 1 | no | — |
| 506 | #448 | — | 53 | 3 | no | — |
| 507 | #447 | — | 53 | 3 | no | — |
| 508 | #419 | C2×D53 | 1 | 3 | yes | complemented |
| 509 | #418 | — | 53 | 3 | no | — |
| 510 | #417 | — | 53 | 3 | no | — |
| 511 | #417 | C2×D53 | 1 | 3 | yes | complemented |
| 512 | #416 | — | 53 | 3 | no | — |
| 513 | #416 | C2×D53 | 1 | 3 | yes | complemented |
| 514 | C2×#103 | C2×D53 | 1 | 3 | yes | complemented |
| 515 | C2×#102 | — | 53 | 3 | no | — |
| 516 | #408 | — | 53 | 3 | no | — |
| 517 | #408 | — | 53 | 3 | no | — |
| 518 | #407 | — | 53 | 3 | no | — |
| 519 | C2×C22⋊C8 | — | 53 | 3 | no | — |
| 520 | C53 | #60377 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 521 | 2−1+4 | — | 2 | 4 | no | — |
| 522 | 2−1+4 | — | 106 | 12 | no | — |
| 523 | 2−1+4 | — | 106 | 16 | no | — |
| 524 | 2−1+4 | — | 106 | 12 | no | — |
| 525 | 2−1+4 | — | 106 | 4 | no | — |
| 526 | 2−1+4 | — | 106 | 4 | no | — |
| 527 | 2−1+4 | D212 | 1 | 8 | yes | complemented |
| 528 | H(5,𝔽2) | — | 53 | 8 | no | — |
| 529 | H(5,𝔽2) | — | 106 | 12 | no | — |
| 530 | H(5,𝔽2) | — | 106 | 48 | no | — |
| 531 | H(5,𝔽2) | — | 106 | 12 | no | — |
| 532 | H(5,𝔽2) | — | 106 | 4 | no | — |
| 533 | C2×#41 | — | 2 | 3 | no | — |
| 534 | C2×#41 | — | 53 | 1 | no | — |
| 535 | C2×#41 | — | 53 | 3 | no | — |
| 536 | C2×#41 | — | 53 | 3 | no | — |
| 537 | C2×#41 | — | 53 | 3 | no | — |
| 538 | C2×#41 | — | 53 | 6 | no | — |
| 539 | C2×#41 | — | 53 | 1 | no | — |
| 540 | C2×#41 | — | 53 | 3 | no | — |
| 541 | C2×#41 | — | 53 | 3 | no | — |
| 542 | C2×#41 | — | 106 | 3 | no | — |
| 543 | C2×#41 | — | 106 | 6 | no | — |
| 544 | C2×#41 | — | 106 | 3 | no | — |
| 545 | C2×#41 | — | 106 | 3 | no | — |
| 546 | C2×#41 | — | 106 | 3 | no | — |
| 547 | C2×#41 | — | 106 | 3 | no | — |
| 548 | C2×#41 | — | 106 | 12 | no | — |
| 549 | C2×#41 | — | 106 | 3 | no | — |
| 550 | C2×#41 | — | 106 | 16 | no | — |
| 551 | C2×#41 | — | 106 | 12 | no | — |
| 552 | C2×#41 | — | 106 | 48 | no | — |
| 553 | C2×#41 | — | 106 | 12 | no | — |
| 554 | C2×#41 | — | 106 | 4 | no | — |
| 555 | C2×#41 | — | 106 | 4 | no | — |
| 556 | C2×#41 | — | 106 | 12 | no | — |
| 557 | C2×#41 | — | 106 | 1 | no | — |
| 558 | C2×#41 | — | 106 | 3 | no | — |
| 559 | C2×#41 | C22×D53 | 1 | 3 | yes | — |
| 560 | C2×#41 | C22×D53 | 1 | 1 | yes | characteristic |
| 561 | C22×Q8 | — | 2 | 1 | no | — |
| 562 | C22×Q8 | — | 53 | 1 | no | — |
| 563 | C22×Q8 | — | 53 | 3 | no | — |
| 564 | C22×Q8 | — | 53 | 3 | no | — |
| 565 | C22×Q8 | — | 106 | 3 | no | — |
| 566 | C22×Q8 | — | 106 | 1 | no | — |
| 567 | C22×Q8 | C22×D53 | 1 | 3 | yes | — |
| 568 | C22×D4 | — | 53 | 3 | no | — |
| 569 | C22×D4 | — | 53 | 3 | no | — |
| 570 | C22×D4 | — | 53 | 3 | no | — |
| 571 | C22×D4 | — | 106 | 3 | no | — |
| 572 | C22×D4 | — | 106 | 3 | no | — |
| 573 | C22×D4 | — | 106 | 6 | no | — |
| 574 | C22×D4 | — | 106 | 3 | no | — |
| 575 | C22×D4 | — | 106 | 3 | no | — |
| 576 | C23×C4 | — | 53 | 3 | no | — |
| 577 | C23×C4 | — | 106 | 3 | no | — |
| 578 | C23×C4 | — | 106 | 3 | no | — |
| 579 | #137 | — | 106 | 12 | no | — |
| 580 | #137 | — | 106 | 12 | no | — |
| 581 | #137 | — | 106 | 12 | no | — |
| 582 | AGL(1,ℤ/8) | — | 106 | 12 | no | — |
| 583 | #135 | — | 106 | 12 | no | — |
| 584 | #135 | — | 106 | 12 | no | — |
| 585 | C2×Q16 | — | 53 | 3 | no | — |
| 586 | C2×Q16 | — | 53 | 6 | no | — |
| 587 | C2×Q16 | — | 53 | 3 | no | — |
| 588 | C2×Q16 | — | 106 | 12 | no | — |
| 589 | C2×SD16 | — | 53 | 3 | no | — |
| 590 | C2×SD16 | — | 53 | 3 | no | — |
| 591 | C2×SD16 | — | 53 | 3 | no | — |
| 592 | C2×SD16 | — | 53 | 6 | no | — |
| 593 | C2×SD16 | — | 53 | 1 | no | — |
| 594 | C2×SD16 | — | 106 | 12 | no | — |
| 595 | C2×D8 | — | 53 | 1 | no | — |
| 596 | C2×D8 | — | 53 | 3 | no | — |
| 597 | #131 | — | 2 | 4 | no | — |
| 598 | #131 | — | 106 | 4 | no | — |
| 599 | C2×M16 | — | 53 | 3 | no | — |
| 600 | C2×M16 | C22×D53 | 1 | 3 | yes | — |
| 601 | C22×C8 | — | 53 | 3 | no | — |
| 602 | C22×C8 | C22×D53 | 1 | 3 | yes | — |
| 603 | C4⋊Q8 | — | 106 | 3 | no | — |
| 604 | #124 | — | 106 | 3 | no | — |
| 605 | #123 | — | 106 | 3 | no | — |
| 606 | #123 | — | 106 | 6 | no | — |
| 607 | C22⋊Q8 | — | 53 | 3 | no | — |
| 608 | C22⋊Q8 | — | 53 | 6 | no | — |
| 609 | C22⋊Q8 | — | 53 | 3 | no | — |
| 610 | C22⋊Q8 | — | 106 | 3 | no | — |
| 611 | C22⋊Q8 | — | 106 | 3 | no | — |
| 612 | C22⋊Q8 | — | 106 | 3 | no | — |
| 613 | #121 | — | 53 | 1 | no | — |
| 614 | #121 | — | 53 | 3 | no | — |
| 615 | #121 | — | 106 | 3 | no | — |
| 616 | #121 | — | 106 | 6 | no | — |
| 617 | #120 | — | 106 | 3 | no | — |
| 618 | C4×Q8 | — | 2 | 1 | no | — |
| 619 | C4×D4 | — | 2 | 3 | no | — |
| 620 | C4×D4 | — | 106 | 3 | no | — |
| 621 | C4×D4 | — | 106 | 3 | no | — |
| 622 | #117 | C22×D53 | 1 | 3 | yes | — |
| 623 | C2×C4⋊C4 | — | 106 | 3 | no | — |
| 624 | C2×C4⋊C4 | C22×D53 | 1 | 3 | yes | — |
| 625 | C2×C22⋊C4 | — | 106 | 3 | no | — |
| 626 | #103 | — | 53 | 1 | no | — |
| 627 | #103 | — | 53 | 3 | no | — |
| 628 | #103 | C22×D53 | 1 | 3 | yes | — |
| 629 | #103 | C22×D53 | 1 | 6 | yes | — |
| 630 | #103 | C22×D53 | 1 | 3 | yes | — |
| 631 | #102 | — | 53 | 3 | no | — |
| 632 | #102 | — | 53 | 6 | no | — |
| 633 | #102 | — | 53 | 3 | no | — |
| 634 | #102 | C22×D53 | 1 | 1 | yes | characteristic |
| 635 | #102 | C22×D53 | 1 | 3 | yes | — |
| 636 | C22⋊C8 | — | 53 | 1 | no | — |
| 637 | C22⋊C8 | — | 53 | 3 | no | — |
| 638 | C22⋊C8 | — | 53 | 3 | no | — |
| 639 | C22⋊C8 | — | 53 | 3 | no | — |
| 640 | C22⋊C8 | — | 53 | 6 | no | — |
| 641 | C24 | — | 53 | 3 | no | — |
| 642 | C24 | — | 106 | 3 | no | — |
| 643 | C24 | — | 106 | 3 | no | — |
| 644 | #41 | — | 2 | 24 | no | — |
| 645 | #41 | — | 2 | 6 | no | — |
| 646 | #41 | — | 53 | 12 | no | — |
| 647 | #41 | — | 106 | 48 | no | — |
| 648 | #41 | — | 106 | 24 | no | — |
| 649 | #41 | — | 106 | 24 | no | — |
| 650 | #41 | — | 106 | 2 | no | — |
| 651 | #41 | — | 106 | 24 | no | — |
| 652 | #41 | — | 106 | 6 | no | — |
| 653 | #41 | — | 106 | 12 | no | — |
| 654 | #41 | — | 106 | 24 | no | — |
| 655 | #41 | — | 106 | 24 | no | — |
| 656 | #41 | — | 106 | 24 | no | — |
| 657 | #41 | — | 106 | 4 | no | — |
| 658 | #41 | — | 106 | 8 | no | — |
| 659 | #41 | — | 106 | 6 | no | — |
| 660 | #41 | — | 106 | 12 | no | — |
| 661 | #41 | — | 106 | 12 | no | — |
| 662 | #41 | — | 106 | 2 | no | — |
| 663 | #41 | — | 106 | 6 | no | — |
| 664 | #41 | — | 106 | 6 | no | — |
| 665 | #41 | — | 106 | 6 | no | — |
| 666 | #41 | — | 106 | 6 | no | — |
| 667 | #41 | — | 106 | 6 | no | — |
| 668 | #41 | — | 212 | 12 | no | — |
| 669 | #41 | C2×D212 | 1 | 12 | yes | — |
| 670 | #41 | C2×D212 | 1 | 4 | yes | — |
| 671 | #41 | D4×D53 | 1 | 4 | yes | — |
| 672 | C2×Q8 | — | 2 | 8 | no | — |
| 673 | C2×Q8 | — | 2 | 3 | no | — |
| 674 | C2×Q8 | — | 2 | 6 | no | — |
| 675 | C2×Q8 | — | 53 | 3 | no | — |
| 676 | C2×Q8 | — | 53 | 1 | no | — |
| 677 | C2×Q8 | — | 53 | 3 | no | — |
| 678 | C2×Q8 | — | 106 | 3 | no | — |
| 679 | C2×Q8 | — | 106 | 6 | no | — |
| 680 | C2×Q8 | — | 106 | 24 | no | — |
| 681 | C2×Q8 | — | 106 | 4 | no | — |
| 682 | C2×Q8 | — | 106 | 6 | no | — |
| 683 | C2×Q8 | — | 106 | 3 | no | — |
| 684 | C2×Q8 | — | 106 | 6 | no | — |
| 685 | C2×Q8 | — | 106 | 6 | no | — |
| 686 | C2×Q8 | — | 212 | 4 | no | — |
| 687 | C2×Q8 | C2×D212 | 1 | 12 | yes | — |
| 688 | C2×Q8 | D4×D53 | 1 | 1 | yes | characteristic |
| 689 | C2×Q8 | C23×D53 | 1 | 3 | yes | — |
| 690 | C2×D4 | — | 2 | 3 | no | — |
| 691 | C2×D4 | — | 53 | 6 | no | — |
| 692 | C2×D4 | — | 53 | 12 | no | — |
| 693 | C2×D4 | — | 53 | 3 | no | — |
| 694 | C2×D4 | — | 53 | 3 | no | — |
| 695 | C2×D4 | — | 53 | 1 | no | — |
| 696 | C2×D4 | — | 106 | 3 | no | — |
| 697 | C2×D4 | — | 106 | 6 | no | — |
| 698 | C2×D4 | — | 106 | 24 | no | — |
| 699 | C2×D4 | — | 106 | 24 | no | — |
| 700 | C2×D4 | — | 106 | 3 | no | — |
| 701 | C2×D4 | — | 106 | 1 | no | — |
| 702 | C2×D4 | — | 106 | 3 | no | — |
| 703 | C2×D4 | — | 106 | 6 | no | — |
| 704 | C2×D4 | — | 106 | 48 | no | — |
| 705 | C2×D4 | — | 106 | 24 | no | — |
| 706 | C2×D4 | — | 106 | 1 | no | — |
| 707 | C2×D4 | — | 106 | 3 | no | — |
| 708 | C2×D4 | — | 106 | 12 | no | — |
| 709 | C2×D4 | — | 106 | 24 | no | — |
| 710 | C2×D4 | — | 106 | 6 | no | — |
| 711 | C2×D4 | — | 106 | 3 | no | — |
| 712 | C2×D4 | — | 106 | 3 | no | — |
| 713 | C2×D4 | — | 106 | 6 | no | — |
| 714 | C2×D4 | D4×D53 | 1 | 3 | yes | — |
| 715 | C2×D4 | C23×D53 | 1 | 1 | yes | characteristic |
| 716 | C22×C4 | — | 2 | 3 | no | — |
| 717 | C22×C4 | — | 2 | 3 | no | — |
| 718 | C22×C4 | — | 2 | 3 | no | — |
| 719 | C22×C4 | — | 53 | 3 | no | — |
| 720 | C22×C4 | — | 53 | 3 | no | — |
| 721 | C22×C4 | — | 53 | 3 | no | — |
| 722 | C22×C4 | — | 53 | 1 | no | — |
| 723 | C22×C4 | — | 53 | 3 | no | — |
| 724 | C22×C4 | — | 106 | 3 | no | — |
| 725 | C22×C4 | — | 106 | 6 | no | — |
| 726 | C22×C4 | — | 106 | 3 | no | — |
| 727 | C22×C4 | — | 106 | 24 | no | — |
| 728 | C22×C4 | — | 106 | 24 | no | — |
| 729 | C22×C4 | — | 106 | 1 | no | — |
| 730 | C22×C4 | — | 106 | 6 | no | — |
| 731 | C22×C4 | — | 106 | 3 | no | — |
| 732 | C22×C4 | — | 106 | 6 | no | — |
| 733 | C22×C4 | — | 106 | 3 | no | — |
| 734 | C22×C4 | — | 106 | 3 | no | — |
| 735 | C22×C4 | C23×D53 | 1 | 3 | yes | — |
| 736 | Q16 | — | 106 | 6 | no | — |
| 737 | Q16 | — | 106 | 6 | no | — |
| 738 | Q16 | — | 106 | 12 | no | — |
| 739 | SD16 | — | 106 | 6 | no | — |
| 740 | SD16 | — | 106 | 12 | no | — |
| 741 | SD16 | — | 106 | 2 | no | — |
| 742 | SD16 | — | 106 | 6 | no | — |
| 743 | SD16 | — | 106 | 6 | no | — |
| 744 | D8 | — | 106 | 6 | no | — |
| 745 | D8 | — | 106 | 2 | no | — |
| 746 | M16 | — | 2 | 6 | no | — |
| 747 | M16 | — | 106 | 6 | no | — |
| 748 | C2×C8 | — | 2 | 6 | no | — |
| 749 | C2×C8 | — | 53 | 1 | no | — |
| 750 | C2×C8 | — | 53 | 3 | no | — |
| 751 | C2×C8 | — | 106 | 6 | no | — |
| 752 | C2×C8 | C23×D53 | 1 | 1 | yes | characteristic |
| 753 | C2×C8 | C23×D53 | 1 | 3 | yes | — |
| 754 | C4⋊C4 | — | 2 | 3 | no | — |
| 755 | C4⋊C4 | — | 106 | 3 | no | — |
| 756 | C4⋊C4 | — | 106 | 6 | no | — |
| 757 | C4⋊C4 | — | 106 | 3 | no | — |
| 758 | C4⋊C4 | C23×D53 | 1 | 3 | yes | — |
| 759 | C4⋊C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 760 | C22⋊C4 | — | 2 | 3 | no | — |
| 761 | C22⋊C4 | — | 106 | 1 | no | — |
| 762 | C22⋊C4 | — | 106 | 3 | no | — |
| 763 | C22⋊C4 | — | 106 | 3 | no | — |
| 764 | C22⋊C4 | — | 106 | 6 | no | — |
| 765 | C22⋊C4 | — | 106 | 3 | no | — |
| 766 | C42 | — | 2 | 3 | no | — |
| 767 | C23 | — | 2 | 1 | no | — |
| 768 | C23 | — | 53 | 1 | no | — |
| 769 | C23 | — | 53 | 3 | no | — |
| 770 | C23 | — | 106 | 12 | no | — |
| 771 | C23 | — | 106 | 12 | no | — |
| 772 | C23 | — | 106 | 6 | no | — |
| 773 | C23 | — | 106 | 3 | no | — |
| 774 | C23 | — | 106 | 1 | no | — |
| 775 | C23 | — | 424 | 3 | no | — |
| 776 | C23 | — | 424 | 3 | no | — |
| 777 | C23 | — | 424 | 3 | no | — |
| 778 | C23 | — | 424 | 3 | no | — |
| 779 | C23 | — | 212 | 3 | no | — |
| 780 | C23 | — | 212 | 3 | no | — |
| 781 | C23 | C2×D4×D53 | 1 | 3 | yes | — |
| 782 | Q8 | — | 2 | 12 | no | — |
| 783 | Q8 | — | 2 | 3 | no | — |
| 784 | Q8 | — | 53 | 2 | no | — |
| 785 | Q8 | — | 106 | 12 | no | — |
| 786 | Q8 | — | 106 | 6 | no | — |
| 787 | Q8 | — | 106 | 1 | no | — |
| 788 | Q8 | — | 106 | 3 | no | — |
| 789 | Q8 | — | 106 | 3 | no | — |
| 790 | Q8 | — | 212 | 6 | no | — |
| 791 | Q8 | #13133187 | 1 | 4 | yes | — |
| 792 | Q8 | C22×D212 | 1 | 6 | yes | — |
| 793 | D4 | — | 2 | 12 | no | — |
| 794 | D4 | — | 2 | 1 | no | — |
| 795 | D4 | — | 53 | 6 | no | — |
| 796 | D4 | — | 106 | 12 | no | — |
| 797 | D4 | — | 106 | 24 | no | — |
| 798 | D4 | — | 106 | 12 | no | — |
| 799 | D4 | — | 106 | 4 | no | — |
| 800 | D4 | — | 106 | 12 | no | — |
| 801 | D4 | — | 106 | 12 | no | — |
| 802 | D4 | — | 106 | 12 | no | — |
| 803 | D4 | — | 106 | 6 | no | — |
| 804 | D4 | — | 106 | 1 | no | — |
| 805 | D4 | — | 106 | 3 | no | — |
| 806 | D4 | — | 106 | 1 | no | — |
| 807 | D4 | — | 424 | 3 | no | — |
| 808 | D4 | — | 212 | 2 | no | — |
| 809 | D4 | — | 212 | 6 | no | — |
| 810 | D4 | #13133187 | 1 | 12 | yes | — |
| 811 | D4 | C22×D212 | 1 | 2 | yes | — |
| 812 | C2×C4 | — | 2 | 12 | no | — |
| 813 | C2×C4 | — | 2 | 3 | no | — |
| 814 | C2×C4 | — | 2 | 12 | no | — |
| 815 | C2×C4 | — | 2 | 1 | no | — |
| 816 | C2×C4 | — | 2 | 3 | no | — |
| 817 | C2×C4 | — | 8 | 3 | no | — |
| 818 | C2×C4 | — | 53 | 1 | no | — |
| 819 | C2×C4 | — | 53 | 3 | no | — |
| 820 | C2×C4 | — | 106 | 12 | no | — |
| 821 | C2×C4 | — | 106 | 24 | no | — |
| 822 | C2×C4 | — | 106 | 12 | no | — |
| 823 | C2×C4 | — | 106 | 4 | no | — |
| 824 | C2×C4 | — | 106 | 6 | no | — |
| 825 | C2×C4 | — | 106 | 1 | no | — |
| 826 | C2×C4 | — | 106 | 6 | no | — |
| 827 | C2×C4 | — | 106 | 6 | no | — |
| 828 | C2×C4 | — | 106 | 12 | no | — |
| 829 | C2×C4 | — | 106 | 1 | no | — |
| 830 | C2×C4 | — | 106 | 3 | no | — |
| 831 | C2×C4 | — | 106 | 1 | no | — |
| 832 | C2×C4 | — | 106 | 3 | no | — |
| 833 | C2×C4 | — | 106 | 3 | no | — |
| 834 | C2×C4 | — | 212 | 6 | no | — |
| 835 | C2×C4 | — | 212 | 6 | no | — |
| 836 | C2×C4 | C2×D4×D53 | 1 | 3 | yes | — |
| 837 | C2×C4 | C2×D4×D53 | 1 | 6 | yes | — |
| 838 | C2×C4 | C22×D212 | 1 | 6 | yes | — |
| 839 | C2×C4 | C24×D53 | 1 | 1 | yes | characteristic |
| 840 | C8 | — | 2 | 1 | no | — |
| 841 | C8 | — | 2 | 3 | no | — |
| 842 | C8 | — | 106 | 1 | no | — |
| 843 | C8 | — | 106 | 3 | no | — |
| 844 | C22 | — | 2 | 3 | no | — |
| 845 | C22 | — | 2 | 3 | no | — |
| 846 | C22 | — | 2 | 2 | no | — |
| 847 | C22 | — | 4 | 1 | no | — |
| 848 | C22 | — | 4 | 1 | no | — |
| 849 | C22 | — | 106 | 6 | no | — |
| 850 | C22 | — | 106 | 3 | no | — |
| 851 | C22 | — | 106 | 1 | no | — |
| 852 | C22 | — | 106 | 3 | no | — |
| 853 | C22 | — | 106 | 1 | no | — |
| 854 | C22 | — | 106 | 1 | no | — |
| 855 | C22 | — | 106 | 3 | no | — |
| 856 | C22 | — | 424 | 12 | no | — |
| 857 | C22 | — | 424 | 6 | no | — |
| 858 | C22 | — | 424 | 12 | no | — |
| 859 | C22 | — | 212 | 1 | no | — |
| 860 | C22 | — | 212 | 1 | no | — |
| 861 | C22 | — | 212 | 1 | no | — |
| 862 | C22 | — | 212 | 3 | no | — |
| 863 | C22 | — | 212 | 3 | no | — |
| 864 | C22 | C2×#13133187 | 1 | 6 | yes | — |
| 865 | C22 | C22×D4×D53 | 1 | 1 | yes | characteristic |
| 866 | C4 | — | 2 | 6 | no | — |
| 867 | C4 | — | 4 | 3 | no | — |
| 868 | C4 | — | 4 | 1 | no | — |
| 869 | C4 | — | 106 | 1 | no | — |
| 870 | C4 | — | 106 | 3 | no | — |
| 871 | C4 | — | 106 | 2 | no | — |
| 872 | C4 | — | 212 | 3 | no | — |
| 873 | C4 | C2×#13133187 | 1 | 6 | yes | — |
| 874 | C4 | C22×D4×D53 | 1 | 1 | yes | characteristic |
| 875 | C4 | C23×D212 | 1 | 1 | yes | characteristic |
| 876 | C2 | — | 2 | 6 | no | — |
| 877 | C2 | — | 4 | 2 | no | — |
| 878 | C2 | — | 424 | 1 | no | — |
| 879 | C2 | — | 212 | 3 | no | — |
| 880 | C2 | — | 212 | 1 | no | — |
| 881 | C2 | — | 212 | 6 | no | — |
| 882 | C2 | C22×#13133187 | 1 | 1 | yes | characteristic |
| 883 | C2 | #20289487 | 1 | 1 | yes | characteristic |
| 884 | C2 | #20289500 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16811460 | C2 | semidirect |
| 2. C2×#16811438 | C2 | semidirect |
| 3. C2×#16811435 | C2 | semidirect |
| 4. #20288396 | C2 | semidirect |
| 5. #20284035 | C2 | semidirect |
| 6. #20284021 | C2 | semidirect |
| 7. #20284011 | C2 | semidirect |
| 8. #20283995 | C2 | semidirect |
| 9. #20283976 | C2 | semidirect |
| 10. #20283961 | C2 | semidirect |
| 11. #20283935 | C2 | semidirect |
| 12. C2×#16810788 | C2 | semidirect |
| 13. #20283238 | C2 | semidirect |
| 14. #20283162 | C2 | semidirect |
| 15. C53×#2898 | C2 | semidirect |
| 20. C2×#13133264 | C22 | semidirect |
| 31. C2×#13133250 | C22 | semidirect |
| 32. C2×#13133248 | C22 | semidirect |
| 33. C2×#13133247 | C22 | semidirect |
| 34. C2×#13133245 | C22 | semidirect |
| 35. C2×#13133239 | C22 | semidirect |
| 36. C2×#13133237 | C22 | semidirect |
| 37. C22×#11719925 | C22 | semidirect |
| 38. C22×#11719913 | C22 | semidirect |
| 39. C2×#13133224 | C22 | semidirect |
| 44. #16811204 | C22 | semidirect |
| 45. #16811199 | C22 | semidirect |
| 46. #16811135 | C22 | semidirect |
| 47. C2×#13133197 | C22 | semidirect |
| 48. #16810788 | C22 | semidirect |
| 49. #16810788 | C22 | semidirect |
| 50. #16810788 | C22 | semidirect |
| 51. #16810788 | C22 | semidirect |
| 52. #16810788 | C22 | semidirect |
| 53. #16810786 | C22 | semidirect |
| 54. #16810780 | C22 | semidirect |
| 55. #16810780 | C22 | semidirect |
| 56. #16810775 | C22 | semidirect |
| 57. #16810775 | C22 | semidirect |
| 58. #16810771 | C22 | semidirect |
| 59. #16810771 | C22 | semidirect |
| 60. #16810769 | C22 | semidirect |
| 61. #16810763 | C22 | semidirect |
| 62. #16810758 | C22 | semidirect |
| 63. #16810627 | C22 | semidirect |
| 64. #16810622 | C22 | semidirect |
| 65. #16810617 | C22 | semidirect |
| 66. C2×#13133137 | C22 | semidirect |
| 67. #16810591 | C22 | semidirect |
| 68. #16810589 | C22 | semidirect |
| 69. #16810586 | C22 | semidirect |
| 70. C2×#13133129 | C22 | semidirect |
| 72. C2×#131×C53 | C22 | semidirect |
| 73. C53×#520 | C22 | semidirect |
| 74. C53×#419 | C22 | semidirect |
| 75. C53×#417 | C22 | semidirect |
| 76. C53×#416 | C22 | semidirect |
| 77. C2×#103×C53 | C22 | semidirect |
| 87. #13133263 | D4 | semidirect |
| 180. 2−1+4×C53 | D4 | semidirect |
| 446. #2898 | D53 | semidirect |
| 483. C2×#131 | C2×D53 | semidirect |
| 492. #520 | C2×D53 | semidirect |
| 508. #419 | C2×D53 | semidirect |
| 511. #417 | C2×D53 | semidirect |
| 513. #416 | C2×D53 | semidirect |
| 514. C2×#103 | C2×D53 | semidirect |
| 520. C53 | #60377 | semidirect |
| 527. 2−1+4 | D212 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811460 | 2 |
| C2×#16811438 | 2 |
| C2×#16811435 | 2 |
| #20288396 | 2 |
| #20284035 | 2 |
| #20284021 | 2 |
| #20284011 | 2 |
| #20283995 | 2 |
| #20283976 | 2 |
| #20283961 | 2 |
| #20283935 | 2 |
| C2×#16810788 | 2 |
| #20283238 | 2 |
| #20283162 | 2 |
| C53×#2898 | 2 |
| #60377 | 53 |