Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2620 conjugacy classes of subgroups.
The subgroup lattice has 842 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20289487 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #20286516 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20286511 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #20286509 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #20286508 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20286498 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #20286495 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | #20285138 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #20284430 | C2 | 1 | 4 | yes | maximal, complemented |
| 10 | #20284067 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #20284060 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #443×D53 | C2 | 1 | 2 | yes | maximal, complemented |
| 13 | C53×#3291 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #16811460 | C22 | 1 | 2 | yes | complemented |
| 15 | #16811458 | C22 | 1 | 2 | yes | complemented |
| 16 | #16811439 | — | 2 | 4 | no | — |
| 17 | #16811439 | C22 | 1 | 4 | yes | complemented |
| 18 | #16811438 | C22 | 1 | 4 | yes | complemented |
| 19 | #16811435 | C22 | 1 | 4 | yes | complemented |
| 20 | #16811430 | — | 2 | 4 | no | — |
| 21 | #16811430 | C22 | 1 | 4 | yes | complemented |
| 22 | #16811429 | — | 2 | 4 | no | — |
| 23 | #16811429 | C22 | 1 | 4 | yes | complemented |
| 24 | #16811427 | — | 2 | 4 | no | — |
| 25 | #16811427 | C22 | 1 | 4 | yes | complemented |
| 26 | #16811426 | C22 | 1 | 4 | yes | complemented |
| 27 | #16811422 | — | 2 | 4 | no | — |
| 28 | #16811422 | C22 | 1 | 4 | yes | complemented |
| 29 | #16811419 | — | 2 | 4 | no | — |
| 30 | #16811419 | C22 | 1 | 4 | yes | complemented |
| 31 | C2×#13133238 | — | 2 | 4 | no | — |
| 32 | C2×#13133238 | C22 | 1 | 4 | yes | complemented |
| 33 | #135×D53 | — | 2 | 4 | no | — |
| 34 | #135×D53 | C22 | 1 | 2 | yes | — |
| 35 | #131×D53 | C22 | 1 | 4 | yes | complemented |
| 36 | #16811174 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | #16811171 | C22 | 1 | 1 | yes | characteristic, complemented |
| 38 | #16811004 | C22 | 1 | 4 | yes | complemented |
| 39 | #16811002 | C22 | 1 | 1 | yes | characteristic, complemented |
| 40 | #16810999 | C22 | 1 | 1 | yes | characteristic, complemented |
| 41 | #16810996 | C22 | 1 | 1 | yes | characteristic, complemented |
| 42 | #16810897 | C22 | 1 | 4 | yes | complemented |
| 43 | #16810896 | C22 | 1 | 4 | yes | complemented |
| 44 | #16810892 | C22 | 1 | 4 | yes | complemented |
| 45 | #16810891 | C22 | 1 | 4 | yes | complemented |
| 46 | #16810887 | C22 | 1 | 4 | yes | complemented |
| 47 | #16810886 | C22 | 1 | 4 | yes | complemented |
| 48 | #16810883 | C22 | 1 | 4 | yes | complemented |
| 49 | #16810807 | C22 | 1 | 4 | yes | complemented |
| 50 | #16810805 | C22 | 1 | 2 | yes | complemented |
| 51 | #16810803 | C22 | 1 | 2 | yes | complemented |
| 52 | #16810801 | C22 | 1 | 2 | yes | complemented |
| 53 | #16810799 | C22 | 1 | 4 | yes | complemented |
| 54 | #16810798 | C22 | 1 | 2 | yes | complemented |
| 55 | #16810796 | C22 | 1 | 2 | yes | complemented |
| 56 | #16810794 | C22 | 1 | 4 | yes | complemented |
| 57 | #16810792 | C22 | 1 | 4 | yes | complemented |
| 58 | #16810790 | C22 | 1 | 2 | yes | complemented |
| 59 | #16810741 | C22 | 1 | 2 | yes | complemented |
| 60 | #16810740 | C22 | 1 | 2 | yes | complemented |
| 61 | #16810739 | C22 | 1 | 2 | yes | complemented |
| 62 | #16810738 | C22 | 1 | 4 | yes | complemented |
| 63 | #16810737 | C22 | 1 | 4 | yes | complemented |
| 64 | #108×D53 | C22 | 1 | 2 | yes | complemented |
| 65 | #104×D53 | C22 | 1 | 4 | yes | complemented |
| 66 | #16810606 | C22 | 1 | 2 | yes | complemented |
| 67 | #16810604 | C22 | 1 | 2 | yes | complemented |
| 68 | C4×C8×D53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 69 | C53×#577 | C22 | 1 | 4 | yes | complemented |
| 70 | C53×#492 | C22 | 1 | 1 | yes | characteristic, complemented |
| 71 | C53×#471 | C22 | 1 | 4 | yes | complemented |
| 72 | C53×#456 | C22 | 1 | 2 | yes | complemented |
| 73 | C53×#453 | C22 | 1 | 2 | yes | complemented |
| 74 | C53×#443 | C22 | 1 | 2 | yes | complemented |
| 75 | #13133265 | — | 2 | 4 | no | — |
| 76 | #13133265 | C23 | 1 | 2 | yes | — |
| 77 | #13133264 | — | 2 | 4 | no | — |
| 78 | #13133264 | C23 | 1 | 4 | yes | — |
| 79 | #13133263 | — | 2 | 4 | no | — |
| 80 | #13133263 | — | 4 | 2 | no | — |
| 81 | #13133263 | C23 | 1 | 4 | yes | — |
| 82 | #13133262 | — | 2 | 4 | no | — |
| 83 | #13133262 | — | 4 | 2 | no | — |
| 84 | #13133262 | C23 | 1 | 2 | yes | — |
| 85 | C2×#11719949 | — | 2 | 4 | no | — |
| 86 | C2×#11719949 | C23 | 1 | 2 | yes | — |
| 87 | C2×#11719947 | — | 2 | 4 | no | — |
| 88 | C2×#11719947 | — | 4 | 2 | no | — |
| 89 | C2×#11719947 | C23 | 1 | 2 | yes | — |
| 90 | #41×D53 | — | 2 | 4 | no | — |
| 91 | #41×D53 | — | 2 | 4 | no | — |
| 92 | #41×D53 | — | 4 | 2 | no | — |
| 93 | #41×D53 | C23 | 1 | 4 | yes | — |
| 94 | #13133250 | — | 2 | 4 | no | — |
| 95 | #13133250 | C23 | 1 | 4 | yes | — |
| 96 | #13133249 | — | 2 | 4 | no | — |
| 97 | #13133249 | — | 2 | 4 | no | — |
| 98 | #13133249 | — | 2 | 4 | no | — |
| 99 | #13133248 | — | 2 | 4 | no | — |
| 100 | #13133248 | C23 | 1 | 4 | yes | — |
| 101 | #13133247 | — | 2 | 4 | no | — |
| 102 | #13133247 | C23 | 1 | 4 | yes | — |
| 103 | #13133246 | — | 2 | 4 | no | — |
| 104 | #13133246 | — | 2 | 4 | no | — |
| 105 | #13133246 | — | 2 | 4 | no | — |
| 106 | #13133245 | — | 2 | 4 | no | — |
| 107 | #13133245 | C23 | 1 | 4 | yes | — |
| 108 | #13133244 | — | 2 | 4 | no | — |
| 109 | #13133244 | — | 2 | 4 | no | — |
| 110 | #13133244 | — | 2 | 4 | no | — |
| 111 | #13133243 | — | 2 | 4 | no | — |
| 112 | #13133243 | C23 | 1 | 4 | yes | — |
| 113 | #13133242 | — | 2 | 4 | no | — |
| 114 | #13133242 | C23 | 1 | 4 | yes | — |
| 115 | #13133241 | — | 2 | 4 | no | — |
| 116 | #13133241 | — | 2 | 4 | no | — |
| 117 | #13133241 | — | 2 | 4 | no | — |
| 118 | #13133240 | — | 2 | 4 | no | — |
| 119 | #13133240 | D4 | 1 | 2 | yes | complemented |
| 120 | #13133239 | — | 2 | 4 | no | — |
| 121 | #13133239 | C23 | 1 | 2 | yes | — |
| 122 | #13133238 | — | 2 | 4 | no | — |
| 123 | #13133238 | — | 2 | 4 | no | — |
| 124 | #13133238 | — | 2 | 4 | no | — |
| 125 | #13133238 | — | 2 | 4 | no | — |
| 126 | #13133238 | — | 2 | 4 | no | — |
| 127 | #13133238 | — | 2 | 4 | no | — |
| 128 | #13133238 | — | 2 | 4 | no | — |
| 129 | #13133238 | — | 2 | 4 | no | — |
| 130 | #13133238 | — | 2 | 4 | no | — |
| 131 | #13133238 | — | 2 | 4 | no | — |
| 132 | #13133238 | D4 | 1 | 4 | yes | complemented |
| 133 | #13133237 | — | 2 | 4 | no | — |
| 134 | #13133237 | — | 2 | 4 | no | — |
| 135 | #13133237 | C23 | 1 | 4 | yes | — |
| 136 | #13133236 | — | 2 | 4 | no | — |
| 137 | #13133236 | D4 | 1 | 2 | yes | complemented |
| 138 | C2×#11719925 | — | 2 | 4 | no | — |
| 139 | C2×#11719925 | C23 | 1 | 4 | yes | — |
| 140 | Q16×D53 | — | 2 | 4 | no | — |
| 141 | Q16×D53 | D4 | 1 | 2 | yes | complemented |
| 142 | C2×#11719913 | — | 2 | 4 | no | — |
| 143 | C2×#11719913 | C23 | 1 | 4 | yes | — |
| 144 | SD16×D53 | — | 2 | 4 | no | — |
| 145 | SD16×D53 | — | 2 | 4 | no | — |
| 146 | SD16×D53 | D4 | 1 | 4 | yes | complemented |
| 147 | C2×#11719922 | — | 2 | 4 | no | — |
| 148 | C2×#11719922 | C23 | 1 | 4 | yes | — |
| 149 | D8×D53 | — | 2 | 4 | no | — |
| 150 | D8×D53 | D4 | 1 | 2 | yes | complemented |
| 151 | #13133225 | — | 2 | 4 | no | — |
| 152 | #13133225 | C23 | 1 | 4 | yes | — |
| 153 | #13133224 | C23 | 1 | 4 | yes | — |
| 154 | #13133223 | — | 2 | 4 | no | — |
| 155 | #13133223 | C23 | 1 | 4 | yes | — |
| 156 | M16×D53 | — | 2 | 4 | no | — |
| 157 | M16×D53 | C23 | 1 | 4 | yes | — |
| 158 | C2×C8×D53 | — | 2 | 4 | no | — |
| 159 | C2×C8×D53 | C23 | 1 | 2 | yes | — |
| 160 | #13133217 | C23 | 1 | 1 | yes | characteristic |
| 161 | #13133214 | C23 | 1 | 1 | yes | characteristic |
| 162 | #13133206 | C23 | 1 | 2 | yes | — |
| 163 | #13133204 | C23 | 1 | 2 | yes | — |
| 164 | #13133192 | — | 4 | 1 | no | — |
| 165 | #13133188 | — | 4 | 1 | no | — |
| 166 | D4×Dic53 | — | 4 | 1 | no | — |
| 167 | #13133179 | — | 4 | 1 | no | — |
| 168 | C42×D53 | C23 | 1 | 1 | yes | characteristic |
| 169 | #13133153 | C23 | 1 | 2 | yes | — |
| 170 | #13133152 | C23 | 1 | 4 | yes | — |
| 171 | #13133145 | C23 | 1 | 4 | yes | — |
| 172 | #13133144 | C23 | 1 | 4 | yes | — |
| 173 | #13133143 | C23 | 1 | 4 | yes | — |
| 174 | #13133136 | C23 | 1 | 2 | yes | — |
| 175 | #13133135 | C23 | 1 | 4 | yes | — |
| 176 | #13133134 | C23 | 1 | 2 | yes | — |
| 177 | #13133133 | C23 | 1 | 4 | yes | — |
| 178 | C4×#88322 | C23 | 1 | 1 | yes | characteristic |
| 179 | C8×Dic53 | C23 | 1 | 2 | yes | — |
| 180 | 2−1+4×C53 | C23 | 1 | 2 | yes | — |
| 181 | H(5,𝔽2)×C53 | C23 | 1 | 2 | yes | — |
| 182 | #137×C53 | — | 2 | 4 | no | — |
| 183 | #137×C53 | C23 | 1 | 4 | yes | — |
| 184 | AGL(1,ℤ/8)×C53 | — | 2 | 4 | no | — |
| 185 | AGL(1,ℤ/8)×C53 | C23 | 1 | 4 | yes | — |
| 186 | #135×C53 | — | 2 | 4 | no | — |
| 187 | #135×C53 | C23 | 1 | 2 | yes | — |
| 188 | C2×SD16×C53 | — | 2 | 4 | no | — |
| 189 | C2×SD16×C53 | C23 | 1 | 4 | yes | — |
| 190 | #131×C53 | C23 | 1 | 4 | yes | — |
| 191 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 192 | #127×C53 | C23 | 1 | 1 | yes | characteristic |
| 193 | #108×C53 | C23 | 1 | 2 | yes | — |
| 194 | #104×C53 | C23 | 1 | 4 | yes | — |
| 195 | #101×C53 | C23 | 1 | 2 | yes | — |
| 196 | #100×C53 | C23 | 1 | 2 | yes | — |
| 197 | C4×C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 198 | #41×C53 | — | 2 | 4 | no | — |
| 199 | #41×C53 | — | 2 | 4 | no | — |
| 200 | #41×C53 | — | 4 | 2 | no | — |
| 201 | #41×C53 | C24 | 1 | 4 | yes | — |
| 202 | C2×Q8×C53 | — | 2 | 4 | no | — |
| 203 | C2×Q8×C53 | C24 | 1 | 2 | yes | — |
| 204 | C2×D4×C53 | — | 2 | 4 | no | — |
| 205 | C2×D4×C53 | — | 4 | 1 | no | — |
| 206 | C2×D4×C53 | — | 4 | 2 | no | — |
| 207 | C2×D4×C53 | C24 | 1 | 2 | yes | — |
| 208 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 209 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 210 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 211 | C2×C22⋊D53 | — | 4 | 4 | no | — |
| 212 | C22×Dic53 | — | 2 | 2 | no | — |
| 213 | C22×Dic53 | — | 4 | 2 | no | — |
| 214 | #11719949 | — | 2 | 4 | no | — |
| 215 | #11719949 | — | 2 | 4 | no | — |
| 216 | #11719949 | — | 2 | 4 | no | — |
| 217 | #11719949 | — | 2 | 4 | no | — |
| 218 | #11719949 | — | 4 | 2 | no | — |
| 219 | #11719949 | — | 4 | 4 | no | — |
| 220 | #11719949 | C2×D4 | 1 | 4 | yes | — |
| 221 | Q8×D53 | — | 2 | 4 | no | — |
| 222 | Q8×D53 | — | 2 | 4 | no | — |
| 223 | Q8×D53 | — | 4 | 2 | no | — |
| 224 | Q8×D53 | C2×D4 | 1 | 4 | yes | — |
| 225 | #11719947 | — | 2 | 4 | no | — |
| 226 | #11719947 | — | 2 | 4 | no | — |
| 227 | #11719947 | — | 2 | 4 | no | — |
| 228 | #11719947 | — | 2 | 4 | no | — |
| 229 | #11719947 | — | 2 | 4 | no | — |
| 230 | #11719947 | — | 4 | 4 | no | — |
| 231 | #11719947 | — | 4 | 4 | no | — |
| 232 | #11719947 | — | 4 | 4 | no | — |
| 233 | #11719947 | — | 4 | 2 | no | — |
| 234 | #11719947 | — | 4 | 4 | no | — |
| 235 | #11719947 | C2×D4 | 1 | 4 | yes | — |
| 236 | D4×D53 | — | 2 | 4 | no | — |
| 237 | D4×D53 | — | 2 | 4 | no | — |
| 238 | D4×D53 | — | 2 | 4 | no | — |
| 239 | D4×D53 | — | 4 | 4 | no | — |
| 240 | D4×D53 | — | 4 | 2 | no | — |
| 241 | D4×D53 | — | 4 | 4 | no | — |
| 242 | D4×D53 | — | 4 | 4 | no | — |
| 243 | D4×D53 | C2×D4 | 1 | 4 | yes | — |
| 244 | #11719945 | — | 2 | 4 | no | — |
| 245 | #11719945 | — | 2 | 4 | no | — |
| 246 | #11719945 | — | 2 | 4 | no | — |
| 247 | #11719945 | — | 4 | 4 | no | — |
| 248 | #11719945 | — | 4 | 4 | no | — |
| 249 | #11719945 | — | 4 | 4 | no | — |
| 250 | #11719945 | — | 4 | 2 | no | — |
| 251 | #11719945 | C24 | 1 | 4 | yes | — |
| 252 | C2×D212 | — | 2 | 4 | no | — |
| 253 | C2×D212 | — | 2 | 2 | no | — |
| 254 | C2×D212 | — | 4 | 4 | no | — |
| 255 | C2×D212 | — | 4 | 1 | no | — |
| 256 | C2×D212 | C24 | 1 | 2 | yes | — |
| 257 | C2×C4×D53 | — | 2 | 4 | no | — |
| 258 | C2×C4×D53 | — | 2 | 1 | no | — |
| 259 | C2×C4×D53 | — | 2 | 2 | no | — |
| 260 | C2×C4×D53 | — | 4 | 2 | no | — |
| 261 | C2×C4×D53 | — | 4 | 4 | no | — |
| 262 | C2×C4×D53 | C24 | 1 | 1 | yes | characteristic |
| 263 | C2×Dic106 | — | 2 | 4 | no | — |
| 264 | C2×Dic106 | — | 4 | 2 | no | — |
| 265 | C2×Dic106 | C24 | 1 | 2 | yes | — |
| 266 | Q16×C53 | — | 2 | 4 | no | — |
| 267 | Q16×C53 | C2×D4 | 1 | 2 | yes | — |
| 268 | SD16×C53 | — | 2 | 4 | no | — |
| 269 | SD16×C53 | — | 2 | 4 | no | — |
| 270 | SD16×C53 | — | 2 | 4 | no | — |
| 271 | SD16×C53 | — | 2 | 4 | no | — |
| 272 | SD16×C53 | C2×D4 | 1 | 4 | yes | — |
| 273 | D8×C53 | — | 2 | 4 | no | — |
| 274 | D8×C53 | C2×D4 | 1 | 2 | yes | — |
| 275 | M16×C53 | — | 2 | 4 | no | — |
| 276 | M16×C53 | C24 | 1 | 4 | yes | — |
| 277 | C2×C8×C53 | — | 2 | 4 | no | — |
| 278 | C2×C8×C53 | C24 | 1 | 2 | yes | — |
| 279 | C4⋊C4×C53 | — | 4 | 1 | no | — |
| 280 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 281 | C22⋊Dic53 | — | 4 | 2 | no | — |
| 282 | #11719925 | — | 2 | 4 | no | — |
| 283 | #11719925 | — | 2 | 4 | no | — |
| 284 | #11719925 | — | 2 | 4 | no | — |
| 285 | #11719925 | — | 2 | 4 | no | — |
| 286 | #11719925 | C2×D4 | 1 | 4 | yes | — |
| 287 | #11719924 | — | 2 | 4 | no | — |
| 288 | #11719924 | — | 2 | 4 | no | — |
| 289 | #11719924 | C2×D4 | 1 | 4 | yes | — |
| 290 | #11719923 | — | 2 | 4 | no | — |
| 291 | #11719923 | — | 2 | 4 | no | — |
| 292 | #11719923 | C2×D4 | 1 | 4 | yes | — |
| 293 | #11719922 | — | 2 | 4 | no | — |
| 294 | #11719922 | — | 2 | 4 | no | — |
| 295 | #11719922 | — | 2 | 4 | no | — |
| 296 | #11719922 | — | 2 | 4 | no | — |
| 297 | #11719922 | C2×D4 | 1 | 4 | yes | — |
| 298 | #11719921 | — | 4 | 2 | no | — |
| 299 | C4⋊Dic53 | — | 4 | 1 | no | — |
| 300 | C4×Dic53 | — | 2 | 1 | no | — |
| 301 | C4×Dic53 | C24 | 1 | 1 | yes | characteristic |
| 302 | #11719917 | — | 2 | 4 | no | — |
| 303 | #11719917 | C24 | 1 | 4 | yes | — |
| 304 | C2×#88322 | — | 2 | 4 | no | — |
| 305 | C2×#88322 | C24 | 1 | 2 | yes | — |
| 306 | Dic212 | — | 2 | 4 | no | — |
| 307 | Dic212 | C2×D4 | 1 | 2 | yes | — |
| 308 | D424 | — | 2 | 4 | no | — |
| 309 | D424 | C2×D4 | 1 | 2 | yes | — |
| 310 | #11719913 | — | 2 | 4 | no | — |
| 311 | #11719913 | — | 2 | 4 | no | — |
| 312 | #11719913 | — | 2 | 4 | no | — |
| 313 | #11719913 | — | 2 | 4 | no | — |
| 314 | #11719913 | C2×D4 | 1 | 4 | yes | — |
| 315 | #11719912 | — | 2 | 4 | no | — |
| 316 | #11719912 | — | 2 | 4 | no | — |
| 317 | #11719912 | — | 2 | 4 | no | — |
| 318 | C8×D53 | — | 2 | 4 | no | — |
| 319 | C8×D53 | — | 2 | 4 | no | — |
| 320 | C8×D53 | — | 2 | 4 | no | — |
| 321 | C8×D53 | C2×D4 | 1 | 2 | yes | — |
| 322 | C8×D53 | C2×D4 | 1 | 2 | yes | — |
| 323 | C8×D53 | C2×D4 | 1 | 2 | yes | — |
| 324 | C8×D53 | C2×D4 | 1 | 2 | yes | — |
| 325 | C23×C53 | — | 2 | 2 | no | — |
| 326 | C23×C53 | — | 4 | 2 | no | — |
| 327 | C22×D53 | — | 2 | 4 | no | — |
| 328 | C22×D53 | — | 2 | 2 | no | — |
| 329 | C22×D53 | — | 4 | 2 | no | — |
| 330 | C22×D53 | — | 4 | 4 | no | — |
| 331 | C22×D53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 332 | Q8×C53 | — | 2 | 4 | no | — |
| 333 | Q8×C53 | — | 4 | 2 | no | — |
| 334 | Q8×C53 | C22×D4 | 1 | 4 | yes | — |
| 335 | D4×C53 | — | 2 | 4 | no | — |
| 336 | D4×C53 | — | 2 | 4 | no | — |
| 337 | D4×C53 | — | 4 | 4 | no | — |
| 338 | D4×C53 | — | 4 | 2 | no | — |
| 339 | D4×C53 | — | 8 | 2 | no | — |
| 340 | D4×C53 | C22×D4 | 1 | 4 | yes | — |
| 341 | C2×C4×C53 | — | 2 | 1 | no | — |
| 342 | C2×C4×C53 | — | 2 | 4 | no | — |
| 343 | C2×C4×C53 | — | 2 | 2 | no | — |
| 344 | C2×C4×C53 | — | 4 | 2 | no | — |
| 345 | C2×C4×C53 | — | 4 | 4 | no | — |
| 346 | C2×C4×C53 | C25 | 1 | 1 | yes | characteristic |
| 347 | C22⋊D53 | — | 2 | 4 | no | — |
| 348 | C22⋊D53 | — | 2 | 4 | no | — |
| 349 | C22⋊D53 | — | 2 | 4 | no | — |
| 350 | C22⋊D53 | — | 4 | 4 | no | — |
| 351 | C22⋊D53 | — | 4 | 4 | no | — |
| 352 | C22⋊D53 | — | 4 | 4 | no | — |
| 353 | C22⋊D53 | — | 4 | 4 | no | — |
| 354 | C2×Dic53 | — | 2 | 4 | no | — |
| 355 | C2×Dic53 | — | 2 | 2 | no | — |
| 356 | C2×Dic53 | — | 2 | 1 | no | — |
| 357 | C2×Dic53 | — | 4 | 2 | no | — |
| 358 | C2×Dic53 | — | 4 | 4 | no | — |
| 359 | C2×Dic53 | — | 4 | 2 | no | — |
| 360 | C2×Dic53 | — | 4 | 2 | no | — |
| 361 | C2×Dic53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 362 | D212 | — | 2 | 4 | no | — |
| 363 | D212 | — | 2 | 4 | no | — |
| 364 | D212 | — | 4 | 4 | no | — |
| 365 | D212 | — | 4 | 2 | no | — |
| 366 | D212 | — | 4 | 4 | no | — |
| 367 | D212 | — | 8 | 2 | no | — |
| 368 | D212 | C22×D4 | 1 | 4 | yes | — |
| 369 | C4×D53 | — | 2 | 4 | no | — |
| 370 | C4×D53 | — | 2 | 4 | no | — |
| 371 | C4×D53 | — | 2 | 4 | no | — |
| 372 | C4×D53 | — | 4 | 4 | no | — |
| 373 | C4×D53 | — | 4 | 4 | no | — |
| 374 | C4×D53 | — | 4 | 4 | no | — |
| 375 | C4×D53 | — | 4 | 2 | no | — |
| 376 | C4×D53 | — | 4 | 2 | no | — |
| 377 | C4×D53 | — | 4 | 2 | no | — |
| 378 | C4×D53 | C22×D4 | 1 | 2 | yes | — |
| 379 | C4×D53 | C22×D4 | 1 | 2 | yes | — |
| 380 | Dic106 | — | 2 | 4 | no | — |
| 381 | Dic106 | — | 2 | 4 | no | — |
| 382 | Dic106 | — | 4 | 2 | no | — |
| 383 | Dic106 | — | 4 | 4 | no | — |
| 384 | Dic106 | C22×D4 | 1 | 4 | yes | — |
| 385 | C8×C53 | — | 2 | 4 | no | — |
| 386 | C8×C53 | C22×D4 | 1 | 2 | yes | — |
| 387 | C8×C53 | C22×D4 | 1 | 2 | yes | — |
| 388 | #88322 | — | 2 | 4 | no | — |
| 389 | #88322 | C22×D4 | 1 | 2 | yes | — |
| 390 | #88322 | C22×D4 | 1 | 2 | yes | — |
| 391 | #61105 | — | 53 | 1 | no | maximal, Sylow |
| 392 | C22×C53 | — | 2 | 4 | no | — |
| 393 | C22×C53 | — | 4 | 2 | no | — |
| 394 | C22×C53 | — | 8 | 2 | no | — |
| 395 | C22×C53 | — | 16 | 2 | no | — |
| 396 | C22×C53 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 397 | C2×D53 | — | 2 | 4 | no | — |
| 398 | C2×D53 | — | 4 | 1 | no | — |
| 399 | C2×D53 | — | 4 | 2 | no | — |
| 400 | C2×D53 | — | 8 | 4 | no | — |
| 401 | C2×D53 | — | 8 | 2 | no | — |
| 402 | C2×D53 | — | 16 | 2 | no | — |
| 403 | C2×D53 | — | 16 | 4 | no | — |
| 404 | C2×D53 | D42 | 1 | 2 | yes | — |
| 405 | C4×C53 | — | 2 | 2 | no | — |
| 406 | C4×C53 | — | 2 | 4 | no | — |
| 407 | C4×C53 | — | 4 | 2 | no | — |
| 408 | C4×C53 | C23×D4 | 1 | 2 | yes | — |
| 409 | Dic53 | — | 2 | 4 | no | — |
| 410 | Dic53 | — | 4 | 1 | no | — |
| 411 | Dic53 | — | 4 | 2 | no | — |
| 412 | Dic53 | D42 | 1 | 1 | yes | characteristic |
| 413 | Dic53 | D42 | 1 | 1 | yes | characteristic |
| 414 | #3584 | — | 53 | 4 | no | — |
| 415 | #3293 | — | 53 | 2 | no | — |
| 416 | #3292 | — | 53 | 2 | no | — |
| 417 | #3291 | — | 53 | 1 | no | — |
| 418 | #3291 | — | 53 | 2 | no | — |
| 419 | #3291 | D53 | 1 | 1 | yes | characteristic, complemented |
| 420 | #3290 | — | 53 | 4 | no | — |
| 421 | #3290 | — | 53 | 4 | no | — |
| 422 | #3147 | — | 53 | 1 | no | — |
| 423 | #3067 | — | 53 | 4 | no | — |
| 424 | #3018 | — | 53 | 2 | no | — |
| 425 | #3018 | — | 53 | 2 | no | — |
| 426 | C2×#443 | — | 53 | 2 | no | — |
| 427 | C2×C53 | — | 2 | 1 | no | — |
| 428 | C2×C53 | — | 4 | 4 | no | — |
| 429 | C2×C53 | — | 8 | 2 | no | — |
| 430 | C2×C53 | C2×D42 | 1 | 1 | yes | characteristic |
| 431 | D53 | — | 2 | 2 | no | — |
| 432 | D53 | — | 4 | 4 | no | — |
| 433 | D53 | — | 8 | 2 | no | — |
| 434 | #585 | — | 53 | 2 | no | — |
| 435 | #585 | — | 53 | 2 | no | — |
| 436 | #578 | — | 53 | 4 | no | — |
| 437 | #578 | — | 53 | 4 | no | — |
| 438 | #578 | — | 106 | 4 | no | — |
| 439 | #577 | — | 53 | 4 | no | — |
| 440 | #577 | — | 53 | 4 | no | — |
| 441 | #577 | — | 53 | 4 | no | — |
| 442 | #577 | — | 106 | 4 | no | — |
| 443 | #577 | — | 106 | 4 | no | — |
| 444 | #577 | C2×D53 | 1 | 4 | yes | complemented |
| 445 | #576 | — | 53 | 4 | no | — |
| 446 | #576 | — | 53 | 4 | no | — |
| 447 | #576 | — | 106 | 4 | no | — |
| 448 | #575 | — | 53 | 4 | no | — |
| 449 | #575 | — | 53 | 4 | no | — |
| 450 | #575 | — | 106 | 4 | no | — |
| 451 | #575 | — | 106 | 4 | no | — |
| 452 | C2×#135 | — | 53 | 2 | no | — |
| 453 | C2×#135 | — | 53 | 4 | no | — |
| 454 | C2×#135 | — | 106 | 4 | no | — |
| 455 | C2×#135 | — | 106 | 4 | no | — |
| 456 | C2×#131 | — | 53 | 4 | no | — |
| 457 | #532 | — | 53 | 1 | no | — |
| 458 | #532 | — | 53 | 1 | no | — |
| 459 | #495 | — | 53 | 4 | no | — |
| 460 | #494 | — | 53 | 1 | no | — |
| 461 | #493 | — | 53 | 1 | no | — |
| 462 | #492 | — | 53 | 1 | no | — |
| 463 | #492 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 464 | #473 | — | 53 | 4 | no | — |
| 465 | #473 | — | 53 | 4 | no | — |
| 466 | #472 | — | 53 | 4 | no | — |
| 467 | #472 | — | 53 | 4 | no | — |
| 468 | #471 | — | 53 | 4 | no | — |
| 469 | #471 | — | 53 | 4 | no | — |
| 470 | #471 | — | 53 | 4 | no | — |
| 471 | #471 | C2×D53 | 1 | 4 | yes | complemented |
| 472 | #456 | — | 53 | 2 | no | — |
| 473 | #456 | — | 53 | 4 | no | — |
| 474 | #456 | C2×D53 | 1 | 2 | yes | complemented |
| 475 | #455 | — | 53 | 2 | no | — |
| 476 | #455 | — | 53 | 4 | no | — |
| 477 | #455 | — | 53 | 2 | no | — |
| 478 | #454 | — | 53 | 2 | no | — |
| 479 | #454 | — | 53 | 4 | no | — |
| 480 | #454 | — | 53 | 2 | no | — |
| 481 | #453 | — | 53 | 2 | no | — |
| 482 | #453 | — | 53 | 4 | no | — |
| 483 | #453 | C2×D53 | 1 | 2 | yes | complemented |
| 484 | #443 | — | 53 | 2 | no | — |
| 485 | #443 | — | 53 | 4 | no | — |
| 486 | #443 | — | 53 | 2 | no | — |
| 487 | #443 | — | 53 | 4 | no | — |
| 488 | #443 | — | 53 | 2 | no | — |
| 489 | #443 | C2×D53 | 1 | 2 | yes | complemented |
| 490 | C2×#108 | — | 53 | 2 | no | — |
| 491 | C2×#104 | — | 53 | 4 | no | — |
| 492 | #413 | — | 53 | 2 | no | — |
| 493 | #413 | — | 53 | 2 | no | — |
| 494 | C2×C4×C8 | — | 53 | 1 | no | — |
| 495 | C53 | #61105 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 496 | 2−1+4 | — | 53 | 4 | no | — |
| 497 | 2−1+4 | — | 53 | 2 | no | — |
| 498 | 2−1+4 | — | 106 | 4 | no | — |
| 499 | 2−1+4 | — | 106 | 4 | no | — |
| 500 | 2−1+4 | C22×D53 | 1 | 2 | yes | — |
| 501 | H(5,𝔽2) | — | 53 | 4 | no | — |
| 502 | H(5,𝔽2) | — | 53 | 2 | no | — |
| 503 | H(5,𝔽2) | — | 106 | 4 | no | — |
| 504 | H(5,𝔽2) | — | 106 | 4 | no | — |
| 505 | H(5,𝔽2) | — | 212 | 2 | no | — |
| 506 | H(5,𝔽2) | — | 212 | 2 | no | — |
| 507 | H(5,𝔽2) | C22×D53 | 1 | 2 | yes | — |
| 508 | C2×#41 | — | 53 | 4 | no | — |
| 509 | C2×#41 | — | 53 | 2 | no | — |
| 510 | C2×#41 | — | 53 | 2 | no | — |
| 511 | C2×#41 | — | 106 | 4 | no | — |
| 512 | C2×#41 | — | 106 | 4 | no | — |
| 513 | C2×#41 | — | 106 | 4 | no | — |
| 514 | C2×#41 | — | 106 | 4 | no | — |
| 515 | C2×#41 | — | 212 | 2 | no | — |
| 516 | C2×#41 | — | 212 | 2 | no | — |
| 517 | #137 | — | 2 | 4 | no | — |
| 518 | #137 | — | 53 | 4 | no | — |
| 519 | #137 | — | 53 | 4 | no | — |
| 520 | #137 | — | 53 | 4 | no | — |
| 521 | #137 | — | 106 | 4 | no | — |
| 522 | #137 | — | 106 | 4 | no | — |
| 523 | #137 | — | 106 | 4 | no | — |
| 524 | #137 | — | 106 | 4 | no | — |
| 525 | #137 | — | 106 | 4 | no | — |
| 526 | #137 | — | 106 | 4 | no | — |
| 527 | #137 | — | 106 | 4 | no | — |
| 528 | #137 | — | 106 | 4 | no | — |
| 529 | #137 | — | 106 | 4 | no | — |
| 530 | #137 | C22×D53 | 1 | 4 | yes | — |
| 531 | AGL(1,ℤ/8) | — | 2 | 4 | no | — |
| 532 | AGL(1,ℤ/8) | — | 53 | 4 | no | — |
| 533 | AGL(1,ℤ/8) | — | 53 | 4 | no | — |
| 534 | AGL(1,ℤ/8) | — | 53 | 4 | no | — |
| 535 | AGL(1,ℤ/8) | — | 106 | 4 | no | — |
| 536 | AGL(1,ℤ/8) | — | 106 | 4 | no | — |
| 537 | AGL(1,ℤ/8) | — | 106 | 4 | no | — |
| 538 | AGL(1,ℤ/8) | — | 106 | 4 | no | — |
| 539 | AGL(1,ℤ/8) | — | 106 | 4 | no | — |
| 540 | AGL(1,ℤ/8) | — | 106 | 4 | no | — |
| 541 | AGL(1,ℤ/8) | — | 106 | 4 | no | — |
| 542 | AGL(1,ℤ/8) | — | 106 | 4 | no | — |
| 543 | AGL(1,ℤ/8) | — | 106 | 4 | no | — |
| 544 | AGL(1,ℤ/8) | C22×D53 | 1 | 4 | yes | — |
| 545 | #135 | — | 2 | 4 | no | — |
| 546 | #135 | — | 53 | 4 | no | — |
| 547 | #135 | — | 53 | 2 | no | — |
| 548 | #135 | — | 53 | 4 | no | — |
| 549 | #135 | — | 53 | 2 | no | — |
| 550 | #135 | — | 53 | 2 | no | — |
| 551 | #135 | — | 106 | 4 | no | — |
| 552 | #135 | — | 106 | 4 | no | — |
| 553 | #135 | — | 106 | 4 | no | — |
| 554 | #135 | — | 106 | 4 | no | — |
| 555 | #135 | — | 106 | 4 | no | — |
| 556 | #135 | — | 106 | 4 | no | — |
| 557 | #135 | — | 106 | 4 | no | — |
| 558 | #135 | — | 106 | 4 | no | — |
| 559 | #135 | — | 106 | 4 | no | — |
| 560 | #135 | — | 106 | 4 | no | — |
| 561 | #135 | — | 106 | 4 | no | — |
| 562 | #135 | — | 106 | 4 | no | — |
| 563 | #135 | — | 106 | 4 | no | — |
| 564 | #135 | — | 106 | 4 | no | — |
| 565 | #135 | — | 106 | 4 | no | — |
| 566 | #135 | C22×D53 | 1 | 2 | yes | — |
| 567 | C2×Q16 | — | 53 | 2 | no | — |
| 568 | C2×Q16 | — | 53 | 4 | no | — |
| 569 | C2×Q16 | — | 106 | 4 | no | — |
| 570 | C2×Q16 | — | 106 | 4 | no | — |
| 571 | C2×SD16 | — | 2 | 4 | no | — |
| 572 | C2×SD16 | — | 53 | 4 | no | — |
| 573 | C2×SD16 | — | 53 | 4 | no | — |
| 574 | C2×SD16 | — | 106 | 4 | no | — |
| 575 | C2×SD16 | — | 106 | 4 | no | — |
| 576 | C2×SD16 | — | 106 | 4 | no | — |
| 577 | C2×SD16 | C22×D53 | 1 | 4 | yes | — |
| 578 | C2×D8 | — | 53 | 2 | no | — |
| 579 | C2×D8 | — | 53 | 4 | no | — |
| 580 | C2×D8 | — | 106 | 4 | no | — |
| 581 | C2×D8 | — | 106 | 4 | no | — |
| 582 | #131 | — | 53 | 4 | no | — |
| 583 | #131 | — | 53 | 4 | no | — |
| 584 | #131 | — | 53 | 4 | no | — |
| 585 | #131 | — | 106 | 4 | no | — |
| 586 | #131 | — | 106 | 4 | no | — |
| 587 | #131 | C22×D53 | 1 | 4 | yes | — |
| 588 | C2×M16 | — | 53 | 4 | no | — |
| 589 | C2×M16 | — | 106 | 4 | no | — |
| 590 | C22×C8 | — | 53 | 2 | no | — |
| 591 | C22×C8 | — | 106 | 4 | no | — |
| 592 | C4⋊Q8 | — | 53 | 1 | no | — |
| 593 | C4⋊Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 594 | #127 | — | 53 | 1 | no | — |
| 595 | #127 | C22×D53 | 1 | 1 | yes | characteristic |
| 596 | #124 | — | 53 | 2 | no | — |
| 597 | #124 | — | 53 | 2 | no | — |
| 598 | #121 | — | 212 | 1 | no | — |
| 599 | #121 | — | 212 | 1 | no | — |
| 600 | C4×D4 | — | 212 | 1 | no | — |
| 601 | C4×D4 | — | 212 | 1 | no | — |
| 602 | C2×C42 | — | 53 | 1 | no | — |
| 603 | #108 | — | 53 | 4 | no | — |
| 604 | #108 | — | 53 | 2 | no | — |
| 605 | #108 | C22×D53 | 1 | 2 | yes | — |
| 606 | #104 | — | 53 | 4 | no | — |
| 607 | #104 | — | 53 | 4 | no | — |
| 608 | #104 | — | 53 | 4 | no | — |
| 609 | #104 | C22×D53 | 1 | 4 | yes | — |
| 610 | #101 | — | 53 | 2 | no | — |
| 611 | #101 | — | 53 | 4 | no | — |
| 612 | #101 | C22×D53 | 1 | 2 | yes | — |
| 613 | #100 | — | 53 | 2 | no | — |
| 614 | #100 | — | 53 | 4 | no | — |
| 615 | #100 | C22×D53 | 1 | 2 | yes | — |
| 616 | C4×C8 | — | 53 | 2 | no | — |
| 617 | C4×C8 | — | 53 | 1 | no | — |
| 618 | C4×C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 619 | #41 | — | 2 | 4 | no | — |
| 620 | #41 | — | 2 | 4 | no | — |
| 621 | #41 | — | 4 | 2 | no | — |
| 622 | #41 | — | 53 | 4 | no | — |
| 623 | #41 | — | 53 | 4 | no | — |
| 624 | #41 | — | 53 | 4 | no | — |
| 625 | #41 | — | 106 | 4 | no | — |
| 626 | #41 | — | 106 | 4 | no | — |
| 627 | #41 | — | 106 | 4 | no | — |
| 628 | #41 | — | 106 | 4 | no | — |
| 629 | #41 | — | 106 | 4 | no | — |
| 630 | #41 | — | 106 | 4 | no | — |
| 631 | #41 | — | 106 | 4 | no | — |
| 632 | #41 | — | 106 | 4 | no | — |
| 633 | #41 | — | 106 | 4 | no | — |
| 634 | #41 | — | 106 | 4 | no | — |
| 635 | #41 | — | 106 | 4 | no | — |
| 636 | #41 | — | 106 | 4 | no | — |
| 637 | #41 | — | 212 | 2 | no | — |
| 638 | #41 | — | 212 | 4 | no | — |
| 639 | #41 | — | 212 | 4 | no | — |
| 640 | #41 | — | 212 | 4 | no | — |
| 641 | #41 | — | 212 | 4 | no | — |
| 642 | #41 | — | 212 | 2 | no | — |
| 643 | #41 | — | 212 | 2 | no | — |
| 644 | #41 | — | 212 | 4 | no | — |
| 645 | #41 | — | 212 | 4 | no | — |
| 646 | #41 | — | 212 | 4 | no | — |
| 647 | #41 | — | 212 | 4 | no | — |
| 648 | #41 | C23×D53 | 1 | 4 | yes | — |
| 649 | C2×Q8 | — | 2 | 4 | no | — |
| 650 | C2×Q8 | — | 53 | 4 | no | — |
| 651 | C2×Q8 | — | 53 | 2 | no | — |
| 652 | C2×Q8 | — | 106 | 4 | no | — |
| 653 | C2×Q8 | — | 106 | 4 | no | — |
| 654 | C2×Q8 | — | 106 | 4 | no | — |
| 655 | C2×Q8 | — | 212 | 2 | no | — |
| 656 | C2×Q8 | — | 212 | 2 | no | — |
| 657 | C2×Q8 | C23×D53 | 1 | 2 | yes | — |
| 658 | C2×D4 | — | 2 | 4 | no | — |
| 659 | C2×D4 | — | 4 | 1 | no | — |
| 660 | C2×D4 | — | 4 | 2 | no | — |
| 661 | C2×D4 | — | 53 | 4 | no | — |
| 662 | C2×D4 | — | 53 | 2 | no | — |
| 663 | C2×D4 | — | 106 | 4 | no | — |
| 664 | C2×D4 | — | 106 | 2 | no | — |
| 665 | C2×D4 | — | 106 | 4 | no | — |
| 666 | C2×D4 | — | 106 | 4 | no | — |
| 667 | C2×D4 | — | 106 | 4 | no | — |
| 668 | C2×D4 | — | 106 | 2 | no | — |
| 669 | C2×D4 | — | 212 | 1 | no | — |
| 670 | C2×D4 | — | 212 | 4 | no | — |
| 671 | C2×D4 | — | 212 | 4 | no | — |
| 672 | C2×D4 | — | 212 | 2 | no | — |
| 673 | C2×D4 | — | 212 | 4 | no | — |
| 674 | C2×D4 | — | 212 | 4 | no | — |
| 675 | C2×D4 | — | 212 | 2 | no | — |
| 676 | C2×D4 | — | 212 | 2 | no | — |
| 677 | C2×D4 | — | 212 | 4 | no | — |
| 678 | C2×D4 | C23×D53 | 1 | 2 | yes | — |
| 679 | C22×C4 | — | 53 | 1 | no | — |
| 680 | C22×C4 | — | 106 | 4 | no | — |
| 681 | C22×C4 | — | 106 | 2 | no | — |
| 682 | C22×C4 | — | 106 | 1 | no | — |
| 683 | C22×C4 | — | 106 | 2 | no | — |
| 684 | C22×C4 | — | 212 | 2 | no | — |
| 685 | C22×C4 | — | 212 | 4 | no | — |
| 686 | C22×C4 | — | 212 | 2 | no | — |
| 687 | Q16 | — | 2 | 4 | no | — |
| 688 | Q16 | — | 53 | 4 | no | — |
| 689 | Q16 | — | 53 | 2 | no | — |
| 690 | Q16 | — | 106 | 4 | no | — |
| 691 | Q16 | — | 106 | 4 | no | — |
| 692 | Q16 | — | 106 | 4 | no | — |
| 693 | Q16 | — | 106 | 4 | no | — |
| 694 | Q16 | — | 106 | 4 | no | — |
| 695 | Q16 | D4×D53 | 1 | 2 | yes | — |
| 696 | SD16 | — | 2 | 4 | no | — |
| 697 | SD16 | — | 2 | 4 | no | — |
| 698 | SD16 | — | 2 | 4 | no | — |
| 699 | SD16 | — | 2 | 4 | no | — |
| 700 | SD16 | — | 53 | 4 | no | — |
| 701 | SD16 | — | 53 | 4 | no | — |
| 702 | SD16 | — | 53 | 4 | no | — |
| 703 | SD16 | — | 106 | 4 | no | — |
| 704 | SD16 | — | 106 | 4 | no | — |
| 705 | SD16 | — | 106 | 4 | no | — |
| 706 | SD16 | — | 106 | 4 | no | — |
| 707 | SD16 | — | 106 | 4 | no | — |
| 708 | SD16 | — | 106 | 4 | no | — |
| 709 | SD16 | — | 106 | 4 | no | — |
| 710 | SD16 | — | 106 | 4 | no | — |
| 711 | SD16 | D4×D53 | 1 | 4 | yes | — |
| 712 | D8 | — | 2 | 4 | no | — |
| 713 | D8 | — | 53 | 4 | no | — |
| 714 | D8 | — | 53 | 2 | no | — |
| 715 | D8 | — | 106 | 4 | no | — |
| 716 | D8 | — | 106 | 4 | no | — |
| 717 | D8 | — | 106 | 4 | no | — |
| 718 | D8 | — | 106 | 4 | no | — |
| 719 | D8 | — | 106 | 4 | no | — |
| 720 | D8 | D4×D53 | 1 | 2 | yes | — |
| 721 | M16 | — | 2 | 4 | no | — |
| 722 | M16 | — | 53 | 4 | no | — |
| 723 | M16 | — | 106 | 4 | no | — |
| 724 | M16 | — | 106 | 4 | no | — |
| 725 | M16 | — | 106 | 4 | no | — |
| 726 | M16 | — | 106 | 4 | no | — |
| 727 | M16 | C23×D53 | 1 | 4 | yes | — |
| 728 | C2×C8 | — | 2 | 4 | no | — |
| 729 | C2×C8 | — | 53 | 2 | no | — |
| 730 | C2×C8 | — | 53 | 2 | no | — |
| 731 | C2×C8 | — | 53 | 2 | no | — |
| 732 | C2×C8 | — | 53 | 2 | no | — |
| 733 | C2×C8 | — | 53 | 2 | no | — |
| 734 | C2×C8 | — | 106 | 4 | no | — |
| 735 | C2×C8 | — | 106 | 4 | no | — |
| 736 | C2×C8 | — | 106 | 4 | no | — |
| 737 | C2×C8 | — | 106 | 4 | no | — |
| 738 | C2×C8 | C23×D53 | 1 | 2 | yes | — |
| 739 | C4⋊C4 | — | 4 | 1 | no | — |
| 740 | C4⋊C4 | — | 212 | 1 | no | — |
| 741 | C22⋊C4 | — | 212 | 2 | no | — |
| 742 | C22⋊C4 | — | 212 | 2 | no | — |
| 743 | C42 | — | 53 | 1 | no | — |
| 744 | C42 | — | 106 | 1 | no | — |
| 745 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 746 | C23 | — | 2 | 2 | no | — |
| 747 | C23 | — | 4 | 2 | no | — |
| 748 | C23 | — | 53 | 1 | no | — |
| 749 | C23 | — | 106 | 4 | no | — |
| 750 | C23 | — | 106 | 2 | no | — |
| 751 | C23 | — | 212 | 4 | no | — |
| 752 | C23 | — | 212 | 2 | no | — |
| 753 | Q8 | — | 2 | 4 | no | — |
| 754 | Q8 | — | 4 | 2 | no | — |
| 755 | Q8 | — | 53 | 4 | no | — |
| 756 | Q8 | — | 106 | 4 | no | — |
| 757 | Q8 | — | 106 | 4 | no | — |
| 758 | Q8 | — | 212 | 4 | no | — |
| 759 | Q8 | — | 212 | 2 | no | — |
| 760 | Q8 | C2×D4×D53 | 1 | 4 | yes | — |
| 761 | D4 | — | 2 | 4 | no | — |
| 762 | D4 | — | 2 | 4 | no | — |
| 763 | D4 | — | 4 | 4 | no | — |
| 764 | D4 | — | 4 | 2 | no | — |
| 765 | D4 | — | 8 | 2 | no | — |
| 766 | D4 | — | 53 | 4 | no | — |
| 767 | D4 | — | 106 | 4 | no | — |
| 768 | D4 | — | 106 | 4 | no | — |
| 769 | D4 | — | 106 | 4 | no | — |
| 770 | D4 | — | 106 | 4 | no | — |
| 771 | D4 | — | 106 | 4 | no | — |
| 772 | D4 | — | 424 | 2 | no | — |
| 773 | D4 | — | 212 | 4 | no | — |
| 774 | D4 | — | 212 | 4 | no | — |
| 775 | D4 | — | 212 | 2 | no | — |
| 776 | D4 | — | 212 | 4 | no | — |
| 777 | D4 | — | 212 | 4 | no | — |
| 778 | D4 | — | 212 | 4 | no | — |
| 779 | D4 | — | 212 | 4 | no | — |
| 780 | D4 | C2×D4×D53 | 1 | 4 | yes | — |
| 781 | C2×C4 | — | 2 | 1 | no | — |
| 782 | C2×C4 | — | 2 | 4 | no | — |
| 783 | C2×C4 | — | 2 | 2 | no | — |
| 784 | C2×C4 | — | 4 | 2 | no | — |
| 785 | C2×C4 | — | 4 | 4 | no | — |
| 786 | C2×C4 | — | 53 | 1 | no | — |
| 787 | C2×C4 | — | 53 | 2 | no | — |
| 788 | C2×C4 | — | 53 | 2 | no | — |
| 789 | C2×C4 | — | 106 | 4 | no | — |
| 790 | C2×C4 | — | 106 | 4 | no | — |
| 791 | C2×C4 | — | 106 | 4 | no | — |
| 792 | C2×C4 | — | 106 | 4 | no | — |
| 793 | C2×C4 | — | 106 | 1 | no | — |
| 794 | C2×C4 | — | 106 | 2 | no | — |
| 795 | C2×C4 | — | 212 | 4 | no | — |
| 796 | C2×C4 | — | 212 | 4 | no | — |
| 797 | C2×C4 | — | 212 | 2 | no | — |
| 798 | C2×C4 | — | 212 | 2 | no | — |
| 799 | C2×C4 | — | 212 | 2 | no | — |
| 800 | C2×C4 | — | 212 | 4 | no | — |
| 801 | C2×C4 | — | 212 | 2 | no | — |
| 802 | C2×C4 | — | 212 | 2 | no | — |
| 803 | C2×C4 | — | 212 | 2 | no | — |
| 804 | C2×C4 | — | 212 | 4 | no | — |
| 805 | C2×C4 | C24×D53 | 1 | 1 | yes | characteristic |
| 806 | C8 | — | 2 | 4 | no | — |
| 807 | C8 | — | 53 | 2 | no | — |
| 808 | C8 | — | 53 | 2 | no | — |
| 809 | C8 | — | 106 | 4 | no | — |
| 810 | C8 | C2×D4×D53 | 1 | 2 | yes | — |
| 811 | C8 | C2×D4×D53 | 1 | 2 | yes | — |
| 812 | C22 | — | 2 | 4 | no | — |
| 813 | C22 | — | 4 | 2 | no | — |
| 814 | C22 | — | 8 | 2 | no | — |
| 815 | C22 | — | 16 | 2 | no | — |
| 816 | C22 | — | 53 | 2 | no | — |
| 817 | C22 | — | 848 | 4 | no | — |
| 818 | C22 | — | 848 | 2 | no | — |
| 819 | C22 | — | 106 | 4 | no | — |
| 820 | C22 | — | 424 | 2 | no | — |
| 821 | C22 | — | 424 | 4 | no | — |
| 822 | C22 | — | 212 | 1 | no | — |
| 823 | C22 | — | 212 | 2 | no | — |
| 824 | C22 | H(5,𝔽2)×D53 | 1 | 1 | yes | characteristic |
| 825 | C4 | — | 2 | 2 | no | — |
| 826 | C4 | — | 2 | 4 | no | — |
| 827 | C4 | — | 4 | 2 | no | — |
| 828 | C4 | — | 53 | 1 | no | — |
| 829 | C4 | — | 53 | 1 | no | — |
| 830 | C4 | — | 106 | 4 | no | — |
| 831 | C4 | — | 212 | 1 | no | — |
| 832 | C4 | — | 212 | 2 | no | — |
| 833 | C4 | C22×D4×D53 | 1 | 2 | yes | — |
| 834 | C2 | — | 2 | 1 | no | — |
| 835 | C2 | — | 4 | 4 | no | — |
| 836 | C2 | — | 8 | 2 | no | — |
| 837 | C2 | — | 106 | 2 | no | — |
| 838 | C2 | — | 424 | 2 | no | — |
| 839 | C2 | — | 212 | 4 | no | — |
| 840 | C2 | D42×D53 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20289487 | C2 | semidirect |
| 2. #20286516 | C2 | semidirect |
| 3. #20286511 | C2 | semidirect |
| 4. #20286509 | C2 | semidirect |
| 5. #20286508 | C2 | semidirect |
| 6. #20286498 | C2 | semidirect |
| 7. #20286495 | C2 | semidirect |
| 8. #20285138 | C2 | semidirect |
| 9. #20284430 | C2 | semidirect |
| 10. #20284067 | C2 | semidirect |
| 11. #20284060 | C2 | semidirect |
| 12. #443×D53 | C2 | semidirect |
| 13. C53×#3291 | C2 | semidirect |
| 14. #16811460 | C22 | semidirect |
| 15. #16811458 | C22 | semidirect |
| 17. #16811439 | C22 | semidirect |
| 18. #16811438 | C22 | semidirect |
| 19. #16811435 | C22 | semidirect |
| 21. #16811430 | C22 | semidirect |
| 23. #16811429 | C22 | semidirect |
| 25. #16811427 | C22 | semidirect |
| 26. #16811426 | C22 | semidirect |
| 28. #16811422 | C22 | semidirect |
| 30. #16811419 | C22 | semidirect |
| 32. C2×#13133238 | C22 | semidirect |
| 35. #131×D53 | C22 | semidirect |
| 36. #16811174 | C22 | semidirect |
| 37. #16811171 | C22 | semidirect |
| 38. #16811004 | C22 | semidirect |
| 39. #16811002 | C22 | semidirect |
| 40. #16810999 | C22 | semidirect |
| 41. #16810996 | C22 | semidirect |
| 42. #16810897 | C22 | semidirect |
| 43. #16810896 | C22 | semidirect |
| 44. #16810892 | C22 | semidirect |
| 45. #16810891 | C22 | semidirect |
| 46. #16810887 | C22 | semidirect |
| 47. #16810886 | C22 | semidirect |
| 48. #16810883 | C22 | semidirect |
| 49. #16810807 | C22 | semidirect |
| 50. #16810805 | C22 | semidirect |
| 51. #16810803 | C22 | semidirect |
| 52. #16810801 | C22 | semidirect |
| 53. #16810799 | C22 | semidirect |
| 54. #16810798 | C22 | semidirect |
| 55. #16810796 | C22 | semidirect |
| 56. #16810794 | C22 | semidirect |
| 57. #16810792 | C22 | semidirect |
| 58. #16810790 | C22 | semidirect |
| 59. #16810741 | C22 | semidirect |
| 60. #16810740 | C22 | semidirect |
| 61. #16810739 | C22 | semidirect |
| 62. #16810738 | C22 | semidirect |
| 63. #16810737 | C22 | semidirect |
| 64. #108×D53 | C22 | semidirect |
| 65. #104×D53 | C22 | semidirect |
| 66. #16810606 | C22 | semidirect |
| 67. #16810604 | C22 | semidirect |
| 68. C4×C8×D53 | C22 | semidirect |
| 69. C53×#577 | C22 | semidirect |
| 70. C53×#492 | C22 | semidirect |
| 71. C53×#471 | C22 | semidirect |
| 72. C53×#456 | C22 | semidirect |
| 73. C53×#453 | C22 | semidirect |
| 74. C53×#443 | C22 | semidirect |
| 119. #13133240 | D4 | semidirect |
| 132. #13133238 | D4 | semidirect |
| 137. #13133236 | D4 | semidirect |
| 141. Q16×D53 | D4 | semidirect |
| 146. SD16×D53 | D4 | semidirect |
| 150. D8×D53 | D4 | semidirect |
| 419. #3291 | D53 | semidirect |
| 444. #577 | C2×D53 | semidirect |
| 463. #492 | C2×D53 | semidirect |
| 471. #471 | C2×D53 | semidirect |
| 474. #456 | C2×D53 | semidirect |
| 483. #453 | C2×D53 | semidirect |
| 489. #443 | C2×D53 | semidirect |
| 495. C53 | #61105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20289487 | 2 |
| #20286516 | 2 |
| #20286511 | 2 |
| #20286509 | 2 |
| #20286508 | 2 |
| #20286498 | 2 |
| #20286495 | 2 |
| #20285138 | 2 |
| #20284430 | 2 |
| #20284067 | 2 |
| #20284060 | 2 |
| #443×D53 | 2 |
| C53×#3291 | 2 |
| #61105 | 53 |