Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1642 conjugacy classes of subgroups.
The subgroup lattice has 1038 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20289499 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20288496 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20284120 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20284079 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20284061 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20275776 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #20275772 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #20275753 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #20275749 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #20275264 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #20275218 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #20275214 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #20275095 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #20274689 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C53×#3020 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #16811459 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×#13133264 | C22 | 1 | 1 | yes | characteristic |
| 18 | #16811439 | — | 2 | 2 | no | — |
| 19 | #16811437 | — | 2 | 2 | no | — |
| 20 | #16811433 | — | 2 | 2 | no | — |
| 21 | #16811430 | — | 2 | 2 | no | — |
| 22 | #16811421 | C22 | 1 | 1 | yes | characteristic |
| 23 | #16811421 | C22 | 1 | 1 | yes | characteristic |
| 24 | #16811419 | — | 2 | 2 | no | — |
| 25 | C2×#13133250 | C22 | 1 | 1 | yes | characteristic |
| 26 | C2×#13133247 | C22 | 1 | 1 | yes | characteristic |
| 27 | #137×D53 | — | 2 | 2 | no | — |
| 28 | #16811389 | C22 | 1 | 1 | yes | characteristic |
| 29 | Q8×C22⋊D53 | — | 2 | 2 | no | — |
| 30 | #16811272 | — | 2 | 2 | no | — |
| 31 | #16811272 | — | 2 | 4 | no | — |
| 32 | #16811197 | — | 2 | 1 | no | — |
| 33 | #16811197 | C22 | 1 | 1 | yes | characteristic |
| 34 | #16811197 | C22 | 1 | 1 | yes | characteristic |
| 35 | #16811194 | — | 2 | 1 | no | — |
| 36 | #16811194 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #16811169 | — | 2 | 1 | no | — |
| 38 | #16811169 | C22 | 1 | 1 | yes | characteristic |
| 39 | C2×#13133215 | — | 2 | 1 | no | — |
| 40 | C2×#13133215 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #41×Dic53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #16810812 | — | 2 | 4 | no | — |
| 43 | #16810806 | — | 2 | 2 | no | — |
| 44 | #16810804 | — | 2 | 1 | no | — |
| 45 | #16810799 | — | 2 | 1 | no | — |
| 46 | #16810796 | — | 2 | 2 | no | — |
| 47 | #16810794 | — | 2 | 1 | no | — |
| 48 | #16810789 | — | 2 | 1 | no | — |
| 49 | #16810640 | C22 | 1 | 1 | yes | characteristic, complemented |
| 50 | #16810640 | C22 | 1 | 1 | yes | characteristic, complemented |
| 51 | C2×#13133144 | C22 | 1 | 1 | yes | characteristic |
| 52 | C2×#13133143 | C22 | 1 | 1 | yes | characteristic |
| 53 | #16810633 | C22 | 1 | 1 | yes | characteristic, complemented |
| 54 | #16810631 | C22 | 1 | 1 | yes | characteristic, complemented |
| 55 | #16810605 | C22 | 1 | 1 | yes | characteristic |
| 56 | C2×#13133136 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | #16810597 | C22 | 1 | 1 | yes | characteristic |
| 58 | #16810596 | C22 | 1 | 1 | yes | characteristic |
| 59 | #16810596 | C22 | 1 | 1 | yes | characteristic |
| 60 | #16810395 | C22 | 1 | 1 | yes | characteristic, complemented |
| 61 | #16810394 | C22 | 1 | 1 | yes | characteristic, complemented |
| 62 | #16810384 | C22 | 1 | 1 | yes | characteristic, complemented |
| 63 | #16810382 | C22 | 1 | 1 | yes | characteristic, complemented |
| 64 | C2×2−1+4×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 65 | C53×#575 | C22 | 1 | 1 | yes | characteristic |
| 66 | C53×#575 | C22 | 1 | 1 | yes | characteristic |
| 67 | C53×#536 | C22 | 1 | 1 | yes | characteristic |
| 68 | C53×#456 | — | 2 | 2 | no | — |
| 69 | C53×#454 | — | 2 | 2 | no | — |
| 70 | C53×#421 | C22 | 1 | 1 | yes | characteristic, complemented |
| 71 | C53×#421 | C22 | 1 | 1 | yes | characteristic, complemented |
| 72 | C2×#101×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 73 | #13133265 | — | 2 | 1 | no | — |
| 74 | #13133264 | — | 2 | 2 | no | — |
| 75 | #13133264 | — | 2 | 2 | no | — |
| 76 | #13133264 | — | 2 | 1 | no | — |
| 77 | #13133264 | — | 2 | 1 | no | — |
| 78 | #13133264 | — | 4 | 1 | no | — |
| 79 | #13133264 | — | 4 | 1 | no | — |
| 80 | #13133263 | — | 2 | 1 | no | — |
| 81 | #13133263 | — | 2 | 1 | no | — |
| 82 | #13133262 | — | 2 | 1 | no | — |
| 83 | #13133262 | — | 2 | 2 | no | — |
| 84 | C2×#11719945 | — | 2 | 1 | no | — |
| 85 | C2×#11719945 | — | 4 | 1 | no | — |
| 86 | C2×#11719945 | C23 | 1 | 1 | yes | characteristic |
| 87 | C2×#11719945 | C23 | 1 | 1 | yes | characteristic |
| 88 | C2×#11719947 | — | 2 | 2 | no | — |
| 89 | C2×#11719947 | D4 | 1 | 2 | yes | — |
| 90 | #41×D53 | — | 2 | 2 | no | — |
| 91 | #41×D53 | — | 4 | 1 | no | — |
| 92 | C22×Dic106 | — | 2 | 1 | no | — |
| 93 | C22×Dic106 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×Q8×D53 | D4 | 1 | 2 | yes | — |
| 95 | #13133250 | — | 2 | 2 | no | — |
| 96 | #13133250 | — | 2 | 2 | no | — |
| 97 | #13133249 | — | 2 | 4 | no | — |
| 98 | #13133248 | — | 2 | 1 | no | — |
| 99 | #13133248 | — | 2 | 1 | no | — |
| 100 | #13133247 | — | 2 | 2 | no | — |
| 101 | #13133247 | — | 2 | 2 | no | — |
| 102 | #13133247 | — | 2 | 1 | no | — |
| 103 | #13133247 | D4 | 1 | 2 | yes | complemented |
| 104 | #13133246 | — | 2 | 4 | no | — |
| 105 | #13133246 | — | 2 | 4 | no | — |
| 106 | #13133243 | — | 2 | 1 | no | — |
| 107 | #13133243 | — | 2 | 1 | no | — |
| 108 | #13133242 | — | 2 | 1 | no | — |
| 109 | #13133242 | D4 | 1 | 2 | yes | complemented |
| 110 | #13133241 | — | 2 | 4 | no | — |
| 111 | #13133238 | — | 2 | 4 | no | — |
| 112 | #13133237 | — | 2 | 2 | no | — |
| 113 | #13133237 | — | 4 | 1 | no | — |
| 114 | #13133236 | — | 2 | 4 | no | — |
| 115 | C2×Dic212 | — | 2 | 1 | no | — |
| 116 | C2×#11719925 | — | 2 | 1 | no | — |
| 117 | Q16×D53 | — | 2 | 4 | no | — |
| 118 | C2×#11719913 | — | 2 | 1 | no | — |
| 119 | C2×#11719923 | — | 2 | 1 | no | — |
| 120 | SD16×D53 | — | 2 | 4 | no | — |
| 121 | #13133225 | — | 2 | 2 | no | — |
| 122 | #13133223 | — | 2 | 2 | no | — |
| 123 | C2×#11719917 | C23 | 1 | 1 | yes | characteristic |
| 124 | C2×#11719917 | C23 | 1 | 1 | yes | characteristic |
| 125 | M16×D53 | — | 2 | 2 | no | — |
| 126 | #13133215 | — | 2 | 4 | no | — |
| 127 | #13133215 | — | 2 | 1 | no | — |
| 128 | #13133215 | — | 2 | 1 | no | — |
| 129 | #13133215 | — | 2 | 1 | no | — |
| 130 | #13133215 | — | 2 | 2 | no | — |
| 131 | #13133215 | — | 2 | 1 | no | — |
| 132 | #13133215 | — | 2 | 1 | no | — |
| 133 | #13133215 | D4 | 1 | 1 | yes | characteristic |
| 134 | #13133213 | D4 | 1 | 1 | yes | characteristic |
| 135 | #13133206 | — | 2 | 1 | no | — |
| 136 | #13133206 | — | 2 | 1 | no | — |
| 137 | #13133206 | D4 | 1 | 1 | yes | characteristic |
| 138 | #13133204 | — | 2 | 1 | no | — |
| 139 | #13133204 | D4 | 1 | 1 | yes | characteristic |
| 140 | #13133200 | — | 2 | 4 | no | — |
| 141 | #13133200 | — | 2 | 2 | no | — |
| 142 | #13133200 | D4 | 1 | 4 | yes | — |
| 143 | #13133198 | — | 2 | 4 | no | — |
| 144 | #13133198 | — | 2 | 2 | no | — |
| 145 | #13133196 | — | 2 | 4 | no | — |
| 146 | #13133196 | — | 2 | 2 | no | — |
| 147 | #13133193 | — | 2 | 4 | no | — |
| 148 | #13133193 | — | 2 | 2 | no | — |
| 149 | #13133193 | — | 4 | 1 | no | — |
| 150 | #13133189 | — | 2 | 4 | no | — |
| 151 | #13133189 | — | 2 | 2 | no | — |
| 152 | Q8×Dic53 | — | 2 | 1 | no | — |
| 153 | D4×Dic53 | — | 2 | 2 | no | — |
| 154 | D4×Dic53 | — | 2 | 1 | no | — |
| 155 | C4×C22⋊D53 | — | 2 | 4 | no | — |
| 156 | C4×C22⋊D53 | — | 2 | 2 | no | — |
| 157 | #13133176 | — | 2 | 1 | no | — |
| 158 | #13133176 | C23 | 1 | 1 | yes | characteristic |
| 159 | #13133176 | C23 | 1 | 1 | yes | characteristic |
| 160 | C2×#11719919 | — | 2 | 4 | no | — |
| 161 | C2×#11719919 | — | 2 | 2 | no | — |
| 162 | C2×C4×Dic53 | — | 2 | 1 | no | — |
| 163 | C2×C4×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 164 | #13133144 | — | 2 | 1 | no | — |
| 165 | #13133144 | — | 2 | 1 | no | — |
| 166 | #13133144 | — | 2 | 2 | no | — |
| 167 | #13133144 | — | 2 | 2 | no | — |
| 168 | #13133143 | — | 2 | 1 | no | — |
| 169 | #13133143 | — | 2 | 1 | no | — |
| 170 | #13133142 | — | 4 | 1 | no | — |
| 171 | #13133140 | — | 4 | 1 | no | — |
| 172 | #13133136 | — | 2 | 2 | no | — |
| 173 | #13133135 | — | 2 | 1 | no | — |
| 174 | #13133133 | — | 2 | 1 | no | — |
| 175 | #13133132 | — | 2 | 2 | no | — |
| 176 | #13133131 | — | 2 | 2 | no | — |
| 177 | #13133131 | — | 2 | 2 | no | — |
| 178 | 2−1+4×C53 | — | 2 | 2 | no | — |
| 179 | 2−1+4×C53 | — | 2 | 2 | no | — |
| 180 | 2−1+4×C53 | — | 4 | 1 | no | — |
| 181 | 2−1+4×C53 | — | 4 | 1 | no | — |
| 182 | C2×#41×C53 | — | 2 | 1 | no | — |
| 183 | C2×#41×C53 | — | 2 | 1 | no | — |
| 184 | C2×#41×C53 | — | 2 | 2 | no | — |
| 185 | C2×#41×C53 | C23 | 1 | 1 | yes | characteristic |
| 186 | C2×#41×C53 | C23 | 1 | 1 | yes | characteristic |
| 187 | C2×#41×C53 | C23 | 1 | 1 | yes | characteristic |
| 188 | C22×Q8×C53 | — | 2 | 1 | no | — |
| 189 | C22×Q8×C53 | — | 2 | 1 | no | — |
| 190 | C22×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 191 | #137×C53 | — | 2 | 1 | no | — |
| 192 | #137×C53 | — | 2 | 1 | no | — |
| 193 | #137×C53 | — | 2 | 1 | no | — |
| 194 | #137×C53 | D4 | 1 | 2 | yes | complemented |
| 195 | AGL(1,ℤ/8)×C53 | — | 2 | 1 | no | — |
| 196 | AGL(1,ℤ/8)×C53 | — | 2 | 1 | no | — |
| 197 | AGL(1,ℤ/8)×C53 | — | 2 | 1 | no | — |
| 198 | AGL(1,ℤ/8)×C53 | D4 | 1 | 2 | yes | complemented |
| 199 | #135×C53 | — | 2 | 2 | no | — |
| 200 | #135×C53 | — | 4 | 1 | no | — |
| 201 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 202 | C2×M16×C53 | C23 | 1 | 1 | yes | characteristic |
| 203 | C4⋊Q8×C53 | — | 2 | 1 | no | — |
| 204 | #124×C53 | — | 2 | 1 | no | — |
| 205 | #123×C53 | — | 2 | 2 | no | — |
| 206 | C22⋊Q8×C53 | — | 4 | 1 | no | — |
| 207 | #117×C53 | C23 | 1 | 1 | yes | characteristic |
| 208 | #104×C53 | — | 2 | 2 | no | — |
| 209 | #104×C53 | — | 2 | 2 | no | — |
| 210 | #101×C53 | — | 2 | 2 | no | — |
| 211 | #41×C53 | — | 2 | 1 | no | — |
| 212 | #41×C53 | — | 2 | 1 | no | — |
| 213 | #41×C53 | — | 2 | 1 | no | — |
| 214 | #41×C53 | — | 2 | 1 | no | — |
| 215 | #41×C53 | — | 2 | 1 | no | — |
| 216 | #41×C53 | — | 2 | 1 | no | — |
| 217 | #41×C53 | — | 2 | 1 | no | — |
| 218 | #41×C53 | — | 2 | 1 | no | — |
| 219 | #41×C53 | — | 2 | 1 | no | — |
| 220 | #41×C53 | — | 2 | 1 | no | — |
| 221 | #41×C53 | — | 4 | 2 | no | — |
| 222 | #41×C53 | — | 4 | 2 | no | — |
| 223 | #41×C53 | — | 4 | 4 | no | — |
| 224 | #41×C53 | — | 4 | 4 | no | — |
| 225 | #41×C53 | — | 4 | 2 | no | — |
| 226 | #41×C53 | — | 4 | 2 | no | — |
| 227 | #41×C53 | C2×D4 | 1 | 2 | yes | — |
| 228 | #41×C53 | C2×D4 | 1 | 2 | yes | — |
| 229 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 230 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 231 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 232 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 233 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 234 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 235 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 236 | C2×Q8×C53 | — | 4 | 2 | no | — |
| 237 | C2×Q8×C53 | — | 4 | 2 | no | — |
| 238 | C2×Q8×C53 | — | 4 | 2 | no | — |
| 239 | C2×Q8×C53 | — | 4 | 2 | no | — |
| 240 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 241 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 242 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 243 | C2×D4×C53 | — | 2 | 1 | no | — |
| 244 | C2×D4×C53 | — | 2 | 2 | no | — |
| 245 | C2×D4×C53 | — | 2 | 1 | no | — |
| 246 | C2×D4×C53 | — | 2 | 1 | no | — |
| 247 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 248 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 249 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 250 | C22×C4×C53 | — | 2 | 1 | no | — |
| 251 | C22×C4×C53 | — | 2 | 2 | no | — |
| 252 | C22×C4×C53 | — | 2 | 2 | no | — |
| 253 | C22×C4×C53 | — | 2 | 1 | no | — |
| 254 | C22×C4×C53 | — | 2 | 1 | no | — |
| 255 | C22×C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 256 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 257 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 258 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 259 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 260 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 261 | C2×C22⋊D53 | C2×D4 | 1 | 2 | yes | — |
| 262 | C22×Dic53 | — | 2 | 2 | no | — |
| 263 | C22×Dic53 | — | 2 | 1 | no | — |
| 264 | C22×Dic53 | — | 2 | 1 | no | — |
| 265 | C22×Dic53 | — | 2 | 2 | no | — |
| 266 | #11719949 | — | 2 | 2 | no | — |
| 267 | #11719949 | — | 4 | 1 | no | — |
| 268 | Q8×D53 | — | 2 | 2 | no | — |
| 269 | Q8×D53 | — | 2 | 4 | no | — |
| 270 | Q8×D53 | — | 4 | 2 | no | — |
| 271 | Q8×D53 | — | 4 | 1 | no | — |
| 272 | #11719947 | — | 2 | 2 | no | — |
| 273 | #11719947 | — | 2 | 4 | no | — |
| 274 | #11719947 | — | 4 | 2 | no | — |
| 275 | #11719947 | — | 4 | 1 | no | — |
| 276 | #11719947 | — | 4 | 2 | no | — |
| 277 | #11719947 | — | 4 | 4 | no | — |
| 278 | #11719947 | — | 4 | 4 | no | — |
| 279 | #11719947 | — | 4 | 2 | no | — |
| 280 | D4×D53 | — | 2 | 2 | no | — |
| 281 | D4×D53 | — | 4 | 1 | no | — |
| 282 | D4×D53 | — | 4 | 2 | no | — |
| 283 | D4×D53 | — | 4 | 2 | no | — |
| 284 | #11719945 | — | 2 | 1 | no | — |
| 285 | #11719945 | — | 2 | 1 | no | — |
| 286 | #11719945 | — | 2 | 1 | no | — |
| 287 | #11719945 | — | 2 | 1 | no | — |
| 288 | #11719945 | — | 2 | 1 | no | — |
| 289 | #11719945 | — | 2 | 1 | no | — |
| 290 | #11719945 | — | 2 | 1 | no | — |
| 291 | #11719945 | — | 2 | 1 | no | — |
| 292 | #11719945 | — | 4 | 1 | no | — |
| 293 | #11719945 | — | 4 | 1 | no | — |
| 294 | #11719945 | — | 4 | 2 | no | — |
| 295 | #11719945 | — | 4 | 2 | no | — |
| 296 | #11719945 | — | 4 | 2 | no | — |
| 297 | #11719945 | — | 4 | 2 | no | — |
| 298 | C2×D212 | — | 4 | 1 | no | — |
| 299 | C2×D212 | C2×D4 | 1 | 1 | yes | characteristic |
| 300 | C2×D212 | C2×D4 | 1 | 1 | yes | characteristic |
| 301 | C2×C4×D53 | — | 2 | 2 | no | — |
| 302 | C2×C4×D53 | — | 2 | 1 | no | — |
| 303 | C2×C4×D53 | — | 4 | 2 | no | — |
| 304 | C2×C4×D53 | C2×D4 | 1 | 2 | yes | — |
| 305 | C2×Dic106 | — | 2 | 1 | no | — |
| 306 | C2×Dic106 | — | 2 | 1 | no | — |
| 307 | C2×Dic106 | — | 2 | 1 | no | — |
| 308 | C2×Dic106 | — | 2 | 1 | no | — |
| 309 | C2×Dic106 | — | 2 | 1 | no | — |
| 310 | C2×Dic106 | — | 2 | 2 | no | — |
| 311 | C2×Dic106 | — | 4 | 1 | no | — |
| 312 | C2×Dic106 | — | 4 | 2 | no | — |
| 313 | C2×Dic106 | — | 4 | 2 | no | — |
| 314 | C2×Dic106 | C2×D4 | 1 | 2 | yes | — |
| 315 | C2×Dic106 | C2×D4 | 1 | 1 | yes | characteristic |
| 316 | C2×Dic106 | C2×D4 | 1 | 1 | yes | characteristic |
| 317 | Q16×C53 | — | 2 | 2 | no | — |
| 318 | Q16×C53 | — | 4 | 1 | no | — |
| 319 | SD16×C53 | — | 2 | 2 | no | — |
| 320 | SD16×C53 | — | 2 | 2 | no | — |
| 321 | SD16×C53 | — | 4 | 1 | no | — |
| 322 | SD16×C53 | — | 4 | 1 | no | — |
| 323 | D8×C53 | — | 2 | 2 | no | — |
| 324 | D8×C53 | — | 4 | 1 | no | — |
| 325 | M16×C53 | — | 2 | 1 | no | — |
| 326 | M16×C53 | — | 2 | 1 | no | — |
| 327 | M16×C53 | — | 2 | 1 | no | — |
| 328 | M16×C53 | C2×D4 | 1 | 2 | yes | — |
| 329 | C2×C8×C53 | — | 2 | 1 | no | — |
| 330 | C2×C8×C53 | — | 2 | 1 | no | — |
| 331 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 332 | C4⋊C4×C53 | — | 4 | 2 | no | — |
| 333 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 334 | C22⋊C4×C53 | — | 4 | 2 | no | — |
| 335 | C42×C53 | — | 2 | 1 | no | — |
| 336 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 337 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 338 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 339 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 340 | C22⋊Dic53 | C2×D4 | 1 | 2 | yes | — |
| 341 | #11719925 | — | 2 | 4 | no | — |
| 342 | #11719925 | — | 2 | 2 | no | — |
| 343 | #11719925 | — | 4 | 1 | no | — |
| 344 | #11719924 | — | 2 | 2 | no | — |
| 345 | #11719924 | — | 4 | 1 | no | — |
| 346 | #11719923 | — | 2 | 4 | no | — |
| 347 | #11719923 | — | 2 | 2 | no | — |
| 348 | #11719923 | — | 4 | 1 | no | — |
| 349 | #11719922 | — | 2 | 2 | no | — |
| 350 | #11719922 | — | 4 | 1 | no | — |
| 351 | #11719921 | — | 2 | 2 | no | — |
| 352 | #11719921 | — | 2 | 4 | no | — |
| 353 | #11719921 | — | 4 | 2 | no | — |
| 354 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 355 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 356 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 357 | #11719919 | — | 2 | 4 | no | — |
| 358 | #11719919 | — | 2 | 4 | no | — |
| 359 | #11719919 | — | 2 | 4 | no | — |
| 360 | #11719919 | — | 2 | 2 | no | — |
| 361 | #11719919 | — | 2 | 4 | no | — |
| 362 | #11719919 | — | 4 | 2 | no | — |
| 363 | C4×Dic53 | — | 2 | 2 | no | — |
| 364 | C4×Dic53 | — | 2 | 1 | no | — |
| 365 | C4×Dic53 | — | 2 | 1 | no | — |
| 366 | C4×Dic53 | — | 2 | 1 | no | — |
| 367 | C4×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 368 | C4×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 369 | #11719917 | — | 2 | 1 | no | — |
| 370 | #11719917 | — | 2 | 1 | no | — |
| 371 | #11719917 | — | 2 | 1 | no | — |
| 372 | #11719917 | C2×D4 | 1 | 2 | yes | — |
| 373 | C2×#88322 | — | 2 | 1 | no | — |
| 374 | C2×#88322 | — | 2 | 1 | no | — |
| 375 | Dic212 | — | 2 | 4 | no | — |
| 376 | #11719913 | — | 2 | 4 | no | — |
| 377 | #11719912 | — | 2 | 4 | no | — |
| 378 | C8×D53 | — | 2 | 4 | no | — |
| 379 | C23×C53 | — | 2 | 1 | no | — |
| 380 | C23×C53 | — | 2 | 1 | no | — |
| 381 | C23×C53 | — | 2 | 1 | no | — |
| 382 | C23×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 383 | C22×D53 | — | 2 | 1 | no | — |
| 384 | C22×D53 | — | 4 | 2 | no | — |
| 385 | C22×D53 | #120 | 1 | 2 | yes | — |
| 386 | Q8×C53 | — | 2 | 1 | no | — |
| 387 | Q8×C53 | — | 2 | 1 | no | — |
| 388 | Q8×C53 | — | 2 | 1 | no | — |
| 389 | Q8×C53 | — | 2 | 1 | no | — |
| 390 | Q8×C53 | — | 2 | 1 | no | — |
| 391 | Q8×C53 | — | 4 | 4 | no | — |
| 392 | Q8×C53 | — | 4 | 1 | no | — |
| 393 | Q8×C53 | — | 4 | 1 | no | — |
| 394 | Q8×C53 | — | 4 | 1 | no | — |
| 395 | Q8×C53 | — | 4 | 1 | no | — |
| 396 | Q8×C53 | #120 | 1 | 2 | yes | — |
| 397 | D4×C53 | — | 2 | 2 | no | — |
| 398 | D4×C53 | — | 2 | 2 | no | — |
| 399 | D4×C53 | — | 2 | 1 | no | — |
| 400 | D4×C53 | — | 2 | 1 | no | — |
| 401 | D4×C53 | — | 2 | 1 | no | — |
| 402 | D4×C53 | — | 2 | 1 | no | — |
| 403 | D4×C53 | — | 2 | 1 | no | — |
| 404 | D4×C53 | — | 4 | 4 | no | — |
| 405 | D4×C53 | — | 4 | 1 | no | — |
| 406 | D4×C53 | — | 4 | 1 | no | — |
| 407 | D4×C53 | — | 4 | 1 | no | — |
| 408 | D4×C53 | — | 4 | 1 | no | — |
| 409 | D4×C53 | #120 | 1 | 2 | yes | — |
| 410 | C2×C4×C53 | — | 2 | 1 | no | — |
| 411 | C2×C4×C53 | — | 2 | 2 | no | — |
| 412 | C2×C4×C53 | — | 2 | 2 | no | — |
| 413 | C2×C4×C53 | — | 2 | 1 | no | — |
| 414 | C2×C4×C53 | — | 2 | 2 | no | — |
| 415 | C2×C4×C53 | — | 2 | 1 | no | — |
| 416 | C2×C4×C53 | — | 2 | 2 | no | — |
| 417 | C2×C4×C53 | — | 2 | 2 | no | — |
| 418 | C2×C4×C53 | — | 4 | 4 | no | — |
| 419 | C2×C4×C53 | — | 4 | 4 | no | — |
| 420 | C2×C4×C53 | — | 4 | 1 | no | — |
| 421 | C2×C4×C53 | — | 4 | 1 | no | — |
| 422 | C2×C4×C53 | — | 4 | 1 | no | — |
| 423 | C2×C4×C53 | — | 4 | 1 | no | — |
| 424 | C2×C4×C53 | — | 4 | 1 | no | — |
| 425 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 426 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 427 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 428 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 429 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 430 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 431 | C22⋊D53 | — | 2 | 2 | no | — |
| 432 | C22⋊D53 | — | 2 | 2 | no | — |
| 433 | C22⋊D53 | — | 4 | 2 | no | — |
| 434 | C22⋊D53 | — | 4 | 4 | no | — |
| 435 | C22⋊D53 | — | 4 | 4 | no | — |
| 436 | C22⋊D53 | — | 4 | 2 | no | — |
| 437 | C22⋊D53 | — | 4 | 1 | no | — |
| 438 | C22⋊D53 | — | 4 | 1 | no | — |
| 439 | C2×Dic53 | — | 2 | 1 | no | — |
| 440 | C2×Dic53 | — | 2 | 2 | no | — |
| 441 | C2×Dic53 | — | 2 | 2 | no | — |
| 442 | C2×Dic53 | — | 2 | 1 | no | — |
| 443 | C2×Dic53 | — | 2 | 1 | no | — |
| 444 | C2×Dic53 | — | 4 | 4 | no | — |
| 445 | C2×Dic53 | — | 4 | 2 | no | — |
| 446 | C2×Dic53 | — | 4 | 2 | no | — |
| 447 | C2×Dic53 | — | 4 | 4 | no | — |
| 448 | C2×Dic53 | — | 4 | 1 | no | — |
| 449 | C2×Dic53 | — | 4 | 1 | no | — |
| 450 | C2×Dic53 | — | 4 | 1 | no | — |
| 451 | C2×Dic53 | #120 | 1 | 2 | yes | — |
| 452 | D212 | — | 2 | 1 | no | — |
| 453 | D212 | — | 2 | 1 | no | — |
| 454 | D212 | — | 2 | 1 | no | — |
| 455 | D212 | — | 2 | 1 | no | — |
| 456 | D212 | — | 4 | 2 | no | — |
| 457 | C4×D53 | — | 2 | 2 | no | — |
| 458 | C4×D53 | — | 2 | 2 | no | — |
| 459 | C4×D53 | — | 4 | 2 | no | — |
| 460 | C4×D53 | — | 4 | 4 | no | — |
| 461 | C4×D53 | — | 4 | 2 | no | — |
| 462 | C4×D53 | — | 4 | 1 | no | — |
| 463 | C4×D53 | — | 4 | 1 | no | — |
| 464 | Dic106 | — | 2 | 1 | no | — |
| 465 | Dic106 | — | 2 | 1 | no | — |
| 466 | Dic106 | — | 2 | 2 | no | — |
| 467 | Dic106 | — | 2 | 1 | no | — |
| 468 | Dic106 | — | 2 | 2 | no | — |
| 469 | Dic106 | — | 2 | 1 | no | — |
| 470 | Dic106 | — | 4 | 4 | no | — |
| 471 | Dic106 | — | 4 | 2 | no | — |
| 472 | Dic106 | — | 4 | 1 | no | — |
| 473 | Dic106 | — | 4 | 1 | no | — |
| 474 | C8×C53 | — | 2 | 2 | no | — |
| 475 | C8×C53 | — | 4 | 1 | no | — |
| 476 | #88322 | — | 2 | 2 | no | — |
| 477 | #88322 | — | 4 | 1 | no | — |
| 478 | #23875 | — | 53 | 1 | no | maximal, Sylow |
| 479 | C22×C53 | — | 2 | 2 | no | — |
| 480 | C22×C53 | — | 4 | 1 | no | — |
| 481 | C22×C53 | — | 4 | 2 | no | — |
| 482 | C22×C53 | — | 4 | 2 | no | — |
| 483 | C22×C53 | — | 4 | 1 | no | — |
| 484 | C22×C53 | — | 4 | 1 | no | — |
| 485 | C22×C53 | — | 8 | 1 | no | — |
| 486 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 487 | C22×C53 | D42 | 1 | 1 | yes | characteristic |
| 488 | C22×C53 | D42 | 1 | 1 | yes | characteristic |
| 489 | C2×D53 | — | 2 | 2 | no | — |
| 490 | C2×D53 | — | 4 | 2 | no | — |
| 491 | C2×D53 | — | 4 | 1 | no | — |
| 492 | C2×D53 | — | 8 | 1 | no | — |
| 493 | C2×D53 | — | 16 | 2 | no | — |
| 494 | C4×C53 | — | 2 | 2 | no | — |
| 495 | C4×C53 | — | 4 | 1 | no | — |
| 496 | C4×C53 | — | 4 | 2 | no | — |
| 497 | C4×C53 | — | 4 | 1 | no | — |
| 498 | C4×C53 | — | 8 | 1 | no | — |
| 499 | C4×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 500 | C4×C53 | #534 | 1 | 1 | yes | characteristic |
| 501 | C4×C53 | D42 | 1 | 1 | yes | characteristic |
| 502 | C4×C53 | D42 | 1 | 1 | yes | characteristic |
| 503 | Dic53 | — | 2 | 2 | no | — |
| 504 | Dic53 | — | 2 | 2 | no | — |
| 505 | Dic53 | — | 4 | 2 | no | — |
| 506 | Dic53 | — | 4 | 1 | no | — |
| 507 | Dic53 | — | 4 | 2 | no | — |
| 508 | Dic53 | — | 4 | 1 | no | — |
| 509 | Dic53 | — | 8 | 1 | no | — |
| 510 | #3586 | — | 53 | 1 | no | — |
| 511 | #3499 | — | 53 | 1 | no | — |
| 512 | #3028 | — | 53 | 1 | no | — |
| 513 | #3020 | — | 53 | 1 | no | — |
| 514 | #3020 | D53 | 1 | 1 | yes | characteristic, complemented |
| 515 | #3018 | — | 53 | 1 | no | — |
| 516 | #2009 | — | 53 | 1 | no | — |
| 517 | #2009 | — | 53 | 1 | no | — |
| 518 | #2005 | — | 53 | 1 | no | — |
| 519 | #2005 | — | 53 | 1 | no | — |
| 520 | #1915 | — | 53 | 1 | no | — |
| 521 | #1906 | — | 53 | 1 | no | — |
| 522 | #1906 | — | 53 | 1 | no | — |
| 523 | #1884 | — | 53 | 1 | no | — |
| 524 | #1796 | — | 53 | 1 | no | — |
| 525 | C2×C53 | — | 2 | 1 | no | — |
| 526 | C2×C53 | — | 2 | 1 | no | — |
| 527 | C2×C53 | — | 2 | 1 | no | — |
| 528 | C2×C53 | — | 4 | 2 | no | — |
| 529 | C2×C53 | — | 8 | 1 | no | — |
| 530 | C2×C53 | — | 8 | 1 | no | — |
| 531 | C2×C53 | #2403 | 1 | 1 | yes | characteristic |
| 532 | D53 | — | 4 | 2 | no | — |
| 533 | D53 | — | 8 | 1 | no | — |
| 534 | #585 | — | 53 | 1 | no | — |
| 535 | C2×2−1+4 | — | 53 | 1 | no | — |
| 536 | C2×2−1+4 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 537 | #578 | — | 106 | 2 | no | — |
| 538 | #578 | — | 106 | 2 | no | — |
| 539 | #577 | — | 106 | 2 | no | — |
| 540 | #577 | — | 106 | 2 | no | — |
| 541 | #575 | — | 53 | 1 | no | — |
| 542 | #575 | — | 53 | 1 | no | — |
| 543 | #575 | — | 106 | 2 | no | — |
| 544 | #575 | C2×D53 | 1 | 1 | yes | characteristic |
| 545 | #575 | C2×D53 | 1 | 1 | yes | characteristic |
| 546 | C2×#137 | — | 53 | 1 | no | — |
| 547 | C2×#137 | — | 53 | 1 | no | — |
| 548 | C2×#137 | — | 106 | 2 | no | — |
| 549 | #568 | — | 53 | 1 | no | — |
| 550 | D4×Q8 | — | 106 | 2 | no | — |
| 551 | #547 | — | 106 | 4 | no | — |
| 552 | #547 | — | 106 | 2 | no | — |
| 553 | #536 | — | 53 | 1 | no | — |
| 554 | #536 | — | 53 | 1 | no | — |
| 555 | #536 | — | 53 | 1 | no | — |
| 556 | #536 | — | 106 | 1 | no | — |
| 557 | #536 | — | 106 | 1 | no | — |
| 558 | #536 | C2×D53 | 1 | 1 | yes | characteristic |
| 559 | #532 | — | 53 | 1 | no | — |
| 560 | #532 | — | 106 | 1 | no | — |
| 561 | C2×C4⋊Q8 | — | 53 | 1 | no | — |
| 562 | C2×C4⋊Q8 | — | 106 | 1 | no | — |
| 563 | C4×#41 | — | 53 | 1 | no | — |
| 564 | #458 | — | 106 | 4 | no | — |
| 565 | #456 | — | 2 | 2 | no | — |
| 566 | #456 | — | 106 | 1 | no | — |
| 567 | #456 | — | 106 | 2 | no | — |
| 568 | #455 | — | 106 | 1 | no | — |
| 569 | #454 | — | 2 | 2 | no | — |
| 570 | #454 | — | 106 | 1 | no | — |
| 571 | #454 | — | 106 | 2 | no | — |
| 572 | #453 | — | 106 | 1 | no | — |
| 573 | #421 | — | 53 | 1 | no | — |
| 574 | #421 | — | 53 | 1 | no | — |
| 575 | #421 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 576 | #421 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 577 | C2×#104 | — | 53 | 1 | no | — |
| 578 | C2×#104 | — | 53 | 1 | no | — |
| 579 | #419 | — | 53 | 1 | no | — |
| 580 | #419 | — | 53 | 1 | no | — |
| 581 | #413 | — | 53 | 1 | no | — |
| 582 | C2×#101 | — | 53 | 1 | no | — |
| 583 | C2×#101 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 584 | #410 | — | 53 | 1 | no | — |
| 585 | #410 | — | 53 | 1 | no | — |
| 586 | #410 | — | 53 | 1 | no | — |
| 587 | #344 | — | 53 | 1 | no | — |
| 588 | #344 | — | 53 | 1 | no | — |
| 589 | #339 | — | 53 | 1 | no | — |
| 590 | #339 | — | 53 | 1 | no | — |
| 591 | C53 | #23875 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 592 | 2−1+4 | — | 2 | 2 | no | — |
| 593 | 2−1+4 | — | 2 | 2 | no | — |
| 594 | 2−1+4 | — | 4 | 1 | no | — |
| 595 | 2−1+4 | — | 4 | 1 | no | — |
| 596 | 2−1+4 | — | 106 | 1 | no | — |
| 597 | 2−1+4 | — | 106 | 1 | no | — |
| 598 | 2−1+4 | — | 106 | 2 | no | — |
| 599 | 2−1+4 | — | 106 | 2 | no | — |
| 600 | 2−1+4 | — | 106 | 1 | no | — |
| 601 | 2−1+4 | — | 212 | 1 | no | — |
| 602 | 2−1+4 | — | 212 | 1 | no | — |
| 603 | H(5,𝔽2) | — | 106 | 2 | no | — |
| 604 | H(5,𝔽2) | — | 106 | 1 | no | — |
| 605 | H(5,𝔽2) | — | 106 | 1 | no | — |
| 606 | H(5,𝔽2) | — | 106 | 1 | no | — |
| 607 | C2×#41 | — | 2 | 1 | no | — |
| 608 | C2×#41 | — | 2 | 1 | no | — |
| 609 | C2×#41 | — | 2 | 2 | no | — |
| 610 | C2×#41 | — | 53 | 1 | no | — |
| 611 | C2×#41 | — | 53 | 2 | no | — |
| 612 | C2×#41 | — | 53 | 1 | no | — |
| 613 | C2×#41 | — | 106 | 1 | no | — |
| 614 | C2×#41 | — | 106 | 2 | no | — |
| 615 | C2×#41 | — | 106 | 2 | no | — |
| 616 | C2×#41 | — | 212 | 1 | no | — |
| 617 | C2×#41 | — | 212 | 1 | no | — |
| 618 | C2×#41 | C22×D53 | 1 | 1 | yes | characteristic |
| 619 | C2×#41 | C22×D53 | 1 | 1 | yes | characteristic |
| 620 | C2×#41 | C22×D53 | 1 | 1 | yes | characteristic |
| 621 | C22×Q8 | — | 2 | 1 | no | — |
| 622 | C22×Q8 | — | 2 | 1 | no | — |
| 623 | C22×Q8 | — | 53 | 2 | no | — |
| 624 | C22×Q8 | — | 53 | 1 | no | — |
| 625 | C22×Q8 | — | 106 | 1 | no | — |
| 626 | C22×Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 627 | #137 | — | 2 | 1 | no | — |
| 628 | #137 | — | 2 | 1 | no | — |
| 629 | #137 | — | 2 | 1 | no | — |
| 630 | #137 | — | 53 | 2 | no | — |
| 631 | #137 | — | 106 | 2 | no | — |
| 632 | #137 | — | 106 | 2 | no | — |
| 633 | #137 | — | 106 | 4 | no | — |
| 634 | #137 | — | 106 | 4 | no | — |
| 635 | #137 | — | 106 | 4 | no | — |
| 636 | #137 | — | 106 | 2 | no | — |
| 637 | #137 | — | 106 | 1 | no | — |
| 638 | #137 | — | 106 | 1 | no | — |
| 639 | #137 | — | 106 | 1 | no | — |
| 640 | #137 | — | 106 | 2 | no | — |
| 641 | #137 | C22⋊D53 | 1 | 2 | yes | complemented |
| 642 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 643 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 644 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 645 | AGL(1,ℤ/8) | — | 53 | 2 | no | — |
| 646 | AGL(1,ℤ/8) | — | 106 | 4 | no | — |
| 647 | AGL(1,ℤ/8) | — | 106 | 1 | no | — |
| 648 | AGL(1,ℤ/8) | — | 106 | 1 | no | — |
| 649 | AGL(1,ℤ/8) | — | 106 | 1 | no | — |
| 650 | AGL(1,ℤ/8) | C22⋊D53 | 1 | 2 | yes | complemented |
| 651 | #135 | — | 2 | 2 | no | — |
| 652 | #135 | — | 4 | 1 | no | — |
| 653 | #135 | — | 106 | 4 | no | — |
| 654 | #135 | — | 106 | 4 | no | — |
| 655 | #135 | — | 106 | 2 | no | — |
| 656 | #135 | — | 212 | 1 | no | — |
| 657 | C2×Q16 | — | 106 | 1 | no | — |
| 658 | C2×Q16 | — | 106 | 4 | no | — |
| 659 | C2×Q16 | — | 106 | 1 | no | — |
| 660 | C2×SD16 | — | 106 | 1 | no | — |
| 661 | C2×SD16 | — | 106 | 4 | no | — |
| 662 | C2×SD16 | — | 106 | 1 | no | — |
| 663 | #131 | — | 106 | 2 | no | — |
| 664 | #131 | — | 106 | 2 | no | — |
| 665 | C2×M16 | — | 53 | 1 | no | — |
| 666 | C2×M16 | — | 53 | 1 | no | — |
| 667 | C2×M16 | — | 106 | 2 | no | — |
| 668 | C2×M16 | C22×D53 | 1 | 1 | yes | characteristic |
| 669 | C2×M16 | C22×D53 | 1 | 1 | yes | characteristic |
| 670 | C4⋊Q8 | — | 2 | 1 | no | — |
| 671 | C4⋊Q8 | — | 53 | 1 | no | — |
| 672 | C4⋊Q8 | — | 106 | 1 | no | — |
| 673 | C4⋊Q8 | — | 106 | 1 | no | — |
| 674 | C4⋊Q8 | — | 106 | 2 | no | — |
| 675 | C4⋊Q8 | — | 106 | 1 | no | — |
| 676 | C4⋊Q8 | — | 106 | 4 | no | — |
| 677 | C4⋊Q8 | — | 106 | 1 | no | — |
| 678 | C4⋊Q8 | — | 106 | 1 | no | — |
| 679 | #127 | — | 53 | 1 | no | — |
| 680 | #124 | — | 2 | 1 | no | — |
| 681 | #124 | — | 53 | 1 | no | — |
| 682 | #124 | — | 53 | 1 | no | — |
| 683 | #124 | — | 106 | 1 | no | — |
| 684 | #124 | — | 106 | 1 | no | — |
| 685 | #124 | — | 106 | 1 | no | — |
| 686 | #123 | — | 2 | 2 | no | — |
| 687 | #123 | — | 53 | 4 | no | — |
| 688 | #123 | — | 106 | 2 | no | — |
| 689 | #123 | — | 106 | 4 | no | — |
| 690 | #123 | — | 106 | 4 | no | — |
| 691 | #123 | — | 106 | 2 | no | — |
| 692 | C22⋊Q8 | — | 4 | 1 | no | — |
| 693 | C22⋊Q8 | — | 106 | 2 | no | — |
| 694 | C22⋊Q8 | — | 106 | 4 | no | — |
| 695 | C22⋊Q8 | — | 106 | 2 | no | — |
| 696 | C22⋊Q8 | — | 106 | 4 | no | — |
| 697 | C22⋊Q8 | — | 212 | 1 | no | — |
| 698 | #121 | — | 106 | 2 | no | — |
| 699 | #121 | — | 106 | 4 | no | — |
| 700 | C4×Q8 | — | 106 | 1 | no | — |
| 701 | C4×D4 | — | 106 | 2 | no | — |
| 702 | C4×D4 | — | 106 | 2 | no | — |
| 703 | C4×D4 | — | 106 | 4 | no | — |
| 704 | C4×D4 | — | 106 | 1 | no | — |
| 705 | #117 | — | 53 | 1 | no | — |
| 706 | #117 | — | 53 | 1 | no | — |
| 707 | #117 | — | 106 | 1 | no | — |
| 708 | #117 | C22×D53 | 1 | 1 | yes | characteristic |
| 709 | C2×C4⋊C4 | — | 106 | 4 | no | — |
| 710 | C2×C4⋊C4 | — | 106 | 2 | no | — |
| 711 | C2×C42 | — | 53 | 1 | no | — |
| 712 | C2×C42 | — | 106 | 1 | no | — |
| 713 | #104 | — | 2 | 2 | no | — |
| 714 | #104 | — | 2 | 2 | no | — |
| 715 | #104 | — | 106 | 1 | no | — |
| 716 | #104 | — | 106 | 1 | no | — |
| 717 | #104 | — | 106 | 1 | no | — |
| 718 | #104 | — | 106 | 1 | no | — |
| 719 | #104 | — | 106 | 2 | no | — |
| 720 | #104 | — | 106 | 2 | no | — |
| 721 | #103 | — | 212 | 1 | no | — |
| 722 | #103 | — | 212 | 1 | no | — |
| 723 | #101 | — | 2 | 2 | no | — |
| 724 | #101 | — | 106 | 1 | no | — |
| 725 | #101 | — | 106 | 2 | no | — |
| 726 | #100 | — | 106 | 1 | no | — |
| 727 | #99 | — | 106 | 2 | no | — |
| 728 | #99 | — | 106 | 2 | no | — |
| 729 | #99 | — | 106 | 2 | no | — |
| 730 | #41 | — | 2 | 1 | no | — |
| 731 | #41 | — | 2 | 1 | no | — |
| 732 | #41 | — | 2 | 1 | no | — |
| 733 | #41 | — | 2 | 1 | no | — |
| 734 | #41 | — | 2 | 1 | no | — |
| 735 | #41 | — | 2 | 1 | no | — |
| 736 | #41 | — | 2 | 1 | no | — |
| 737 | #41 | — | 2 | 1 | no | — |
| 738 | #41 | — | 2 | 1 | no | — |
| 739 | #41 | — | 2 | 1 | no | — |
| 740 | #41 | — | 4 | 2 | no | — |
| 741 | #41 | — | 4 | 2 | no | — |
| 742 | #41 | — | 4 | 4 | no | — |
| 743 | #41 | — | 4 | 4 | no | — |
| 744 | #41 | — | 4 | 2 | no | — |
| 745 | #41 | — | 4 | 2 | no | — |
| 746 | #41 | — | 106 | 1 | no | — |
| 747 | #41 | — | 106 | 1 | no | — |
| 748 | #41 | — | 106 | 1 | no | — |
| 749 | #41 | — | 106 | 1 | no | — |
| 750 | #41 | — | 106 | 2 | no | — |
| 751 | #41 | — | 106 | 2 | no | — |
| 752 | #41 | — | 106 | 4 | no | — |
| 753 | #41 | — | 106 | 1 | no | — |
| 754 | #41 | — | 106 | 1 | no | — |
| 755 | #41 | — | 106 | 1 | no | — |
| 756 | #41 | — | 106 | 1 | no | — |
| 757 | #41 | — | 212 | 2 | no | — |
| 758 | #41 | — | 212 | 2 | no | — |
| 759 | #41 | — | 212 | 2 | no | — |
| 760 | #41 | — | 212 | 2 | no | — |
| 761 | #41 | — | 212 | 1 | no | — |
| 762 | #41 | — | 212 | 1 | no | — |
| 763 | #41 | — | 212 | 2 | no | — |
| 764 | #41 | — | 212 | 2 | no | — |
| 765 | #41 | — | 212 | 2 | no | — |
| 766 | #41 | — | 212 | 4 | no | — |
| 767 | #41 | — | 212 | 4 | no | — |
| 768 | #41 | — | 212 | 1 | no | — |
| 769 | #41 | — | 212 | 1 | no | — |
| 770 | #41 | D4×D53 | 1 | 2 | yes | — |
| 771 | #41 | C2×C22⋊D53 | 1 | 2 | yes | — |
| 772 | C2×Q8 | — | 2 | 2 | no | — |
| 773 | C2×Q8 | — | 2 | 1 | no | — |
| 774 | C2×Q8 | — | 2 | 1 | no | — |
| 775 | C2×Q8 | — | 2 | 1 | no | — |
| 776 | C2×Q8 | — | 2 | 1 | no | — |
| 777 | C2×Q8 | — | 2 | 1 | no | — |
| 778 | C2×Q8 | — | 2 | 1 | no | — |
| 779 | C2×Q8 | — | 4 | 2 | no | — |
| 780 | C2×Q8 | — | 4 | 2 | no | — |
| 781 | C2×Q8 | — | 4 | 2 | no | — |
| 782 | C2×Q8 | — | 4 | 2 | no | — |
| 783 | C2×Q8 | — | 53 | 1 | no | — |
| 784 | C2×Q8 | — | 53 | 2 | no | — |
| 785 | C2×Q8 | — | 53 | 1 | no | — |
| 786 | C2×Q8 | — | 106 | 2 | no | — |
| 787 | C2×Q8 | — | 106 | 1 | no | — |
| 788 | C2×Q8 | — | 106 | 2 | no | — |
| 789 | C2×Q8 | — | 106 | 4 | no | — |
| 790 | C2×Q8 | — | 106 | 1 | no | — |
| 791 | C2×Q8 | — | 106 | 1 | no | — |
| 792 | C2×Q8 | — | 106 | 1 | no | — |
| 793 | C2×Q8 | — | 106 | 1 | no | — |
| 794 | C2×Q8 | — | 212 | 2 | no | — |
| 795 | C2×Q8 | — | 212 | 2 | no | — |
| 796 | C2×Q8 | — | 212 | 1 | no | — |
| 797 | C2×Q8 | — | 212 | 2 | no | — |
| 798 | C2×Q8 | — | 212 | 1 | no | — |
| 799 | C2×Q8 | D4×D53 | 1 | 1 | yes | characteristic |
| 800 | C2×Q8 | D4×D53 | 1 | 1 | yes | characteristic |
| 801 | C2×Q8 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 802 | C2×D4 | — | 2 | 1 | no | — |
| 803 | C2×D4 | — | 2 | 2 | no | — |
| 804 | C2×D4 | — | 2 | 1 | no | — |
| 805 | C2×D4 | — | 2 | 1 | no | — |
| 806 | C2×D4 | — | 53 | 2 | no | — |
| 807 | C2×D4 | — | 53 | 1 | no | — |
| 808 | C2×D4 | — | 53 | 1 | no | — |
| 809 | C2×D4 | — | 106 | 2 | no | — |
| 810 | C2×D4 | — | 106 | 2 | no | — |
| 811 | C2×D4 | — | 106 | 2 | no | — |
| 812 | C2×D4 | — | 106 | 1 | no | — |
| 813 | C2×D4 | — | 212 | 1 | no | — |
| 814 | C2×D4 | — | 212 | 1 | no | — |
| 815 | C2×D4 | — | 212 | 2 | no | — |
| 816 | C2×D4 | — | 212 | 2 | no | — |
| 817 | C2×D4 | — | 212 | 2 | no | — |
| 818 | C2×D4 | D4×D53 | 1 | 1 | yes | characteristic |
| 819 | C2×D4 | D4×D53 | 1 | 1 | yes | characteristic |
| 820 | C2×D4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 821 | C22×C4 | — | 2 | 1 | no | — |
| 822 | C22×C4 | — | 2 | 2 | no | — |
| 823 | C22×C4 | — | 2 | 2 | no | — |
| 824 | C22×C4 | — | 2 | 1 | no | — |
| 825 | C22×C4 | — | 2 | 1 | no | — |
| 826 | C22×C4 | — | 53 | 2 | no | — |
| 827 | C22×C4 | — | 106 | 2 | no | — |
| 828 | C22×C4 | — | 106 | 2 | no | — |
| 829 | C22×C4 | — | 106 | 2 | no | — |
| 830 | C22×C4 | — | 106 | 1 | no | — |
| 831 | C22×C4 | — | 106 | 1 | no | — |
| 832 | C22×C4 | — | 106 | 1 | no | — |
| 833 | C22×C4 | — | 212 | 2 | no | — |
| 834 | C22×C4 | D4×D53 | 1 | 2 | yes | — |
| 835 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 836 | Q16 | — | 2 | 2 | no | — |
| 837 | Q16 | — | 4 | 1 | no | — |
| 838 | Q16 | — | 106 | 4 | no | — |
| 839 | Q16 | — | 106 | 4 | no | — |
| 840 | Q16 | — | 106 | 2 | no | — |
| 841 | Q16 | — | 212 | 1 | no | — |
| 842 | SD16 | — | 2 | 2 | no | — |
| 843 | SD16 | — | 2 | 2 | no | — |
| 844 | SD16 | — | 4 | 1 | no | — |
| 845 | SD16 | — | 4 | 1 | no | — |
| 846 | SD16 | — | 106 | 4 | no | — |
| 847 | SD16 | — | 106 | 4 | no | — |
| 848 | SD16 | — | 106 | 2 | no | — |
| 849 | SD16 | — | 106 | 2 | no | — |
| 850 | SD16 | — | 212 | 1 | no | — |
| 851 | SD16 | — | 212 | 1 | no | — |
| 852 | D8 | — | 2 | 2 | no | — |
| 853 | D8 | — | 4 | 1 | no | — |
| 854 | D8 | — | 106 | 2 | no | — |
| 855 | D8 | — | 212 | 1 | no | — |
| 856 | M16 | — | 2 | 1 | no | — |
| 857 | M16 | — | 2 | 1 | no | — |
| 858 | M16 | — | 2 | 1 | no | — |
| 859 | M16 | — | 53 | 2 | no | — |
| 860 | M16 | — | 106 | 4 | no | — |
| 861 | M16 | — | 106 | 1 | no | — |
| 862 | M16 | — | 106 | 1 | no | — |
| 863 | M16 | — | 106 | 1 | no | — |
| 864 | M16 | C2×C22⋊D53 | 1 | 2 | yes | — |
| 865 | C2×C8 | — | 2 | 1 | no | — |
| 866 | C2×C8 | — | 2 | 1 | no | — |
| 867 | C2×C8 | — | 106 | 4 | no | — |
| 868 | C2×C8 | — | 106 | 1 | no | — |
| 869 | C2×C8 | — | 106 | 1 | no | — |
| 870 | C4⋊C4 | — | 2 | 1 | no | — |
| 871 | C4⋊C4 | — | 4 | 2 | no | — |
| 872 | C4⋊C4 | — | 106 | 2 | no | — |
| 873 | C4⋊C4 | — | 106 | 4 | no | — |
| 874 | C4⋊C4 | — | 106 | 4 | no | — |
| 875 | C4⋊C4 | — | 106 | 4 | no | — |
| 876 | C4⋊C4 | — | 106 | 4 | no | — |
| 877 | C4⋊C4 | — | 106 | 2 | no | — |
| 878 | C4⋊C4 | — | 106 | 1 | no | — |
| 879 | C4⋊C4 | — | 106 | 1 | no | — |
| 880 | C4⋊C4 | — | 212 | 2 | no | — |
| 881 | C22⋊C4 | — | 2 | 1 | no | — |
| 882 | C22⋊C4 | — | 4 | 2 | no | — |
| 883 | C22⋊C4 | — | 53 | 2 | no | — |
| 884 | C22⋊C4 | — | 106 | 4 | no | — |
| 885 | C22⋊C4 | — | 106 | 2 | no | — |
| 886 | C22⋊C4 | — | 106 | 2 | no | — |
| 887 | C22⋊C4 | — | 106 | 2 | no | — |
| 888 | C22⋊C4 | — | 106 | 4 | no | — |
| 889 | C22⋊C4 | — | 106 | 1 | no | — |
| 890 | C22⋊C4 | — | 212 | 2 | no | — |
| 891 | C42 | — | 2 | 1 | no | — |
| 892 | C42 | — | 53 | 1 | no | — |
| 893 | C42 | — | 53 | 1 | no | — |
| 894 | C42 | — | 106 | 2 | no | — |
| 895 | C42 | — | 106 | 1 | no | — |
| 896 | C42 | — | 106 | 1 | no | — |
| 897 | C42 | — | 106 | 1 | no | — |
| 898 | C23 | — | 2 | 1 | no | — |
| 899 | C23 | — | 2 | 1 | no | — |
| 900 | C23 | — | 2 | 1 | no | — |
| 901 | C23 | — | 53 | 2 | no | — |
| 902 | C23 | — | 106 | 1 | no | — |
| 903 | C23 | — | 212 | 2 | no | — |
| 904 | C23 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 905 | Q8 | — | 2 | 1 | no | — |
| 906 | Q8 | — | 2 | 1 | no | — |
| 907 | Q8 | — | 2 | 1 | no | — |
| 908 | Q8 | — | 2 | 1 | no | — |
| 909 | Q8 | — | 2 | 1 | no | — |
| 910 | Q8 | — | 4 | 4 | no | — |
| 911 | Q8 | — | 4 | 1 | no | — |
| 912 | Q8 | — | 4 | 1 | no | — |
| 913 | Q8 | — | 4 | 1 | no | — |
| 914 | Q8 | — | 4 | 1 | no | — |
| 915 | Q8 | — | 106 | 1 | no | — |
| 916 | Q8 | — | 106 | 1 | no | — |
| 917 | Q8 | — | 106 | 2 | no | — |
| 918 | Q8 | — | 106 | 1 | no | — |
| 919 | Q8 | — | 106 | 2 | no | — |
| 920 | Q8 | — | 106 | 1 | no | — |
| 921 | Q8 | — | 212 | 4 | no | — |
| 922 | Q8 | — | 212 | 2 | no | — |
| 923 | Q8 | — | 212 | 1 | no | — |
| 924 | Q8 | — | 212 | 1 | no | — |
| 925 | Q8 | #13133185 | 1 | 2 | yes | — |
| 926 | D4 | — | 2 | 2 | no | — |
| 927 | D4 | — | 2 | 2 | no | — |
| 928 | D4 | — | 2 | 1 | no | — |
| 929 | D4 | — | 2 | 1 | no | — |
| 930 | D4 | — | 2 | 1 | no | — |
| 931 | D4 | — | 2 | 1 | no | — |
| 932 | D4 | — | 2 | 1 | no | — |
| 933 | D4 | — | 4 | 4 | no | — |
| 934 | D4 | — | 4 | 1 | no | — |
| 935 | D4 | — | 4 | 1 | no | — |
| 936 | D4 | — | 4 | 1 | no | — |
| 937 | D4 | — | 4 | 1 | no | — |
| 938 | D4 | — | 106 | 2 | no | — |
| 939 | D4 | — | 106 | 2 | no | — |
| 940 | D4 | — | 106 | 1 | no | — |
| 941 | D4 | — | 106 | 1 | no | — |
| 942 | D4 | — | 106 | 1 | no | — |
| 943 | D4 | — | 106 | 1 | no | — |
| 944 | D4 | — | 212 | 2 | no | — |
| 945 | D4 | — | 212 | 4 | no | — |
| 946 | D4 | — | 212 | 2 | no | — |
| 947 | D4 | — | 212 | 4 | no | — |
| 948 | D4 | — | 212 | 2 | no | — |
| 949 | D4 | — | 212 | 1 | no | — |
| 950 | D4 | — | 212 | 1 | no | — |
| 951 | D4 | #13133185 | 1 | 2 | yes | — |
| 952 | C2×C4 | — | 2 | 1 | no | — |
| 953 | C2×C4 | — | 2 | 2 | no | — |
| 954 | C2×C4 | — | 2 | 2 | no | — |
| 955 | C2×C4 | — | 2 | 1 | no | — |
| 956 | C2×C4 | — | 2 | 2 | no | — |
| 957 | C2×C4 | — | 2 | 2 | no | — |
| 958 | C2×C4 | — | 2 | 2 | no | — |
| 959 | C2×C4 | — | 2 | 1 | no | — |
| 960 | C2×C4 | — | 4 | 4 | no | — |
| 961 | C2×C4 | — | 4 | 4 | no | — |
| 962 | C2×C4 | — | 4 | 1 | no | — |
| 963 | C2×C4 | — | 4 | 1 | no | — |
| 964 | C2×C4 | — | 4 | 1 | no | — |
| 965 | C2×C4 | — | 4 | 1 | no | — |
| 966 | C2×C4 | — | 4 | 1 | no | — |
| 967 | C2×C4 | — | 53 | 2 | no | — |
| 968 | C2×C4 | — | 106 | 1 | no | — |
| 969 | C2×C4 | — | 106 | 2 | no | — |
| 970 | C2×C4 | — | 106 | 2 | no | — |
| 971 | C2×C4 | — | 106 | 1 | no | — |
| 972 | C2×C4 | — | 106 | 2 | no | — |
| 973 | C2×C4 | — | 106 | 2 | no | — |
| 974 | C2×C4 | — | 106 | 1 | no | — |
| 975 | C2×C4 | — | 212 | 4 | no | — |
| 976 | C2×C4 | — | 212 | 2 | no | — |
| 977 | C2×C4 | — | 212 | 2 | no | — |
| 978 | C2×C4 | — | 212 | 4 | no | — |
| 979 | C2×C4 | — | 212 | 2 | no | — |
| 980 | C2×C4 | — | 212 | 4 | no | — |
| 981 | C2×C4 | — | 212 | 2 | no | — |
| 982 | C2×C4 | — | 212 | 1 | no | — |
| 983 | C2×C4 | — | 212 | 1 | no | — |
| 984 | C2×C4 | — | 212 | 1 | no | — |
| 985 | C2×C4 | — | 212 | 1 | no | — |
| 986 | C2×C4 | — | 212 | 1 | no | — |
| 987 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 988 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 989 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 990 | C2×C4 | C22×C22⋊D53 | 1 | 1 | yes | characteristic |
| 991 | C2×C4 | #13133262 | 1 | 1 | yes | characteristic |
| 992 | C2×C4 | #13133262 | 1 | 1 | yes | characteristic |
| 993 | C8 | — | 2 | 2 | no | — |
| 994 | C8 | — | 4 | 1 | no | — |
| 995 | C8 | — | 106 | 2 | no | — |
| 996 | C8 | — | 212 | 1 | no | — |
| 997 | C22 | — | 2 | 2 | no | — |
| 998 | C22 | — | 4 | 1 | no | — |
| 999 | C22 | — | 4 | 2 | no | — |
| 1000 | C22 | — | 4 | 2 | no | — |
| 1001 | C22 | — | 4 | 1 | no | — |
| 1002 | C22 | — | 4 | 1 | no | — |
| 1003 | C22 | — | 8 | 1 | no | — |
| 1004 | C22 | — | 848 | 2 | no | — |
| 1005 | C22 | — | 106 | 2 | no | — |
| 1006 | C22 | — | 424 | 1 | no | — |
| 1007 | C22 | — | 212 | 2 | no | — |
| 1008 | C22 | — | 212 | 1 | no | — |
| 1009 | C22 | #120×D53 | 1 | 1 | yes | characteristic |
| 1010 | C22 | #16811255 | 1 | 1 | yes | characteristic |
| 1011 | C22 | D4×C22⋊D53 | 1 | 1 | yes | characteristic |
| 1012 | C4 | — | 2 | 2 | no | — |
| 1013 | C4 | — | 4 | 2 | no | — |
| 1014 | C4 | — | 4 | 1 | no | — |
| 1015 | C4 | — | 4 | 1 | no | — |
| 1016 | C4 | — | 8 | 1 | no | — |
| 1017 | C4 | — | 106 | 2 | no | — |
| 1018 | C4 | — | 106 | 2 | no | — |
| 1019 | C4 | — | 424 | 1 | no | — |
| 1020 | C4 | — | 212 | 1 | no | — |
| 1021 | C4 | — | 212 | 2 | no | — |
| 1022 | C4 | — | 212 | 1 | no | — |
| 1023 | C4 | — | 212 | 2 | no | — |
| 1024 | C4 | C2×#13133185 | 1 | 1 | yes | characteristic |
| 1025 | C4 | #16811183 | 1 | 1 | yes | characteristic |
| 1026 | C4 | #16811255 | 1 | 1 | yes | characteristic |
| 1027 | C4 | D4×C22⋊D53 | 1 | 1 | yes | characteristic |
| 1028 | C2 | — | 2 | 1 | no | — |
| 1029 | C2 | — | 2 | 1 | no | — |
| 1030 | C2 | — | 2 | 1 | no | — |
| 1031 | C2 | — | 4 | 2 | no | — |
| 1032 | C2 | — | 8 | 1 | no | — |
| 1033 | C2 | — | 8 | 1 | no | — |
| 1034 | C2 | — | 424 | 1 | no | — |
| 1035 | C2 | — | 212 | 2 | no | — |
| 1036 | C2 | #20278026 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20289499 | C2 | semidirect |
| 2. #20288496 | C2 | semidirect |
| 3. #20284120 | C2 | semidirect |
| 4. #20284079 | C2 | semidirect |
| 5. #20284061 | C2 | semidirect |
| 6. #20275776 | C2 | semidirect |
| 7. #20275772 | C2 | semidirect |
| 8. #20275753 | C2 | semidirect |
| 9. #20275749 | C2 | semidirect |
| 10. #20275264 | C2 | semidirect |
| 11. #20275218 | C2 | semidirect |
| 12. #20275214 | C2 | semidirect |
| 13. #20275095 | C2 | semidirect |
| 14. #20274689 | C2 | semidirect |
| 15. C53×#3020 | C2 | semidirect |
| 36. #16811194 | C22 | semidirect |
| 40. C2×#13133215 | C22 | semidirect |
| 41. #41×Dic53 | C22 | semidirect |
| 49. #16810640 | C22 | semidirect |
| 50. #16810640 | C22 | semidirect |
| 53. #16810633 | C22 | semidirect |
| 54. #16810631 | C22 | semidirect |
| 56. C2×#13133136 | C22 | semidirect |
| 60. #16810395 | C22 | semidirect |
| 61. #16810394 | C22 | semidirect |
| 62. #16810384 | C22 | semidirect |
| 63. #16810382 | C22 | semidirect |
| 64. C2×2−1+4×C53 | C22 | semidirect |
| 70. C53×#421 | C22 | semidirect |
| 71. C53×#421 | C22 | semidirect |
| 72. C2×#101×C53 | C22 | semidirect |
| 103. #13133247 | D4 | semidirect |
| 109. #13133242 | D4 | semidirect |
| 194. #137×C53 | D4 | semidirect |
| 198. AGL(1,ℤ/8)×C53 | D4 | semidirect |
| 514. #3020 | D53 | semidirect |
| 536. C2×2−1+4 | C2×D53 | semidirect |
| 575. #421 | C2×D53 | semidirect |
| 576. #421 | C2×D53 | semidirect |
| 583. C2×#101 | C2×D53 | semidirect |
| 591. C53 | #23875 | semidirect |
| 641. #137 | C22⋊D53 | semidirect |
| 650. AGL(1,ℤ/8) | C22⋊D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289499 | 2 |
| #20288496 | 2 |
| #20284120 | 2 |
| #20284079 | 2 |
| #20284061 | 2 |
| #20275776 | 2 |
| #20275772 | 2 |
| #20275753 | 2 |
| #20275749 | 2 |
| #20275264 | 2 |
| #20275218 | 2 |
| #20275214 | 2 |
| #20275095 | 2 |
| #20274689 | 2 |
| C53×#3020 | 2 |
| #23875 | 53 |