Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
888 conjugacy classes of subgroups.
The subgroup lattice has 694 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20291042 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | D53⋊#360 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#16811539 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20291030 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20290958 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20290603 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #20289483 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | C2×#13133292 | C22 | 1 | 1 | yes | characteristic, complemented |
| 9 | D53⋊M32 | C22 | 1 | 1 | yes | characteristic, complemented |
| 10 | D53⋊#108 | C22 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×#13133285 | C22 | 1 | 1 | yes | characteristic, complemented |
| 12 | #16811614 | — | 2 | 1 | no | — |
| 13 | #16811542 | — | 2 | 1 | no | — |
| 14 | #16811541 | — | 2 | 1 | no | — |
| 15 | #16811540 | — | 2 | 1 | no | — |
| 16 | #16811539 | — | 2 | 2 | no | — |
| 17 | #16811539 | — | 2 | 1 | no | — |
| 18 | #16811537 | — | 2 | 2 | no | — |
| 19 | #16811522 | — | 2 | 1 | no | — |
| 20 | #16811521 | — | 2 | 1 | no | — |
| 21 | #16811502 | — | 2 | 1 | no | — |
| 22 | #16811458 | — | 2 | 1 | no | — |
| 23 | #16811440 | C4 | 1 | 1 | yes | characteristic, complemented |
| 24 | #16811437 | — | 2 | 1 | no | — |
| 25 | #16811437 | C4 | 1 | 1 | yes | characteristic, complemented |
| 26 | #16811434 | — | 2 | 1 | no | — |
| 27 | #16811433 | — | 2 | 2 | no | — |
| 28 | #16811433 | — | 2 | 1 | no | — |
| 29 | #16811424 | — | 2 | 1 | no | — |
| 30 | #16811424 | C4 | 1 | 1 | yes | characteristic, complemented |
| 31 | #16811419 | — | 2 | 2 | no | — |
| 32 | #16811419 | — | 2 | 1 | no | — |
| 33 | C2×#13133236 | — | 2 | 1 | no | — |
| 34 | C2×#13133236 | C22 | 1 | 1 | yes | characteristic |
| 35 | #135×D53 | — | 2 | 1 | no | — |
| 36 | #135×D53 | C22 | 1 | 1 | yes | characteristic |
| 37 | #131×D53 | C22 | 1 | 1 | yes | characteristic |
| 38 | C53×#576 | C4 | 1 | 1 | yes | characteristic, complemented |
| 39 | D53⋊M16 | — | 2 | 1 | no | — |
| 40 | C2×C4⋊#6157 | — | 2 | 1 | no | — |
| 41 | #13133292 | — | 2 | 1 | no | — |
| 42 | #13133292 | — | 2 | 1 | no | — |
| 43 | #13133292 | — | 2 | 1 | no | — |
| 44 | #13133291 | — | 2 | 1 | no | — |
| 45 | D53⋊C16 | — | 2 | 1 | no | — |
| 46 | C2×#11719910 | — | 2 | 1 | no | — |
| 47 | #13133288 | — | 2 | 1 | no | — |
| 48 | #13133287 | — | 2 | 1 | no | — |
| 49 | #13133285 | — | 2 | 1 | no | — |
| 50 | #13133285 | — | 2 | 1 | no | — |
| 51 | #13133280 | — | 4 | 1 | no | — |
| 52 | #13133279 | — | 4 | 1 | no | — |
| 53 | #13133264 | — | 2 | 1 | no | — |
| 54 | #13133264 | — | 2 | 2 | no | — |
| 55 | #13133264 | — | 2 | 1 | no | — |
| 56 | #13133264 | — | 4 | 1 | no | — |
| 57 | #13133262 | — | 2 | 2 | no | — |
| 58 | #13133262 | — | 2 | 1 | no | — |
| 59 | #13133262 | — | 4 | 2 | no | — |
| 60 | #13133262 | — | 4 | 1 | no | — |
| 61 | C2×#11719947 | — | 2 | 2 | no | — |
| 62 | C2×#11719947 | — | 2 | 1 | no | — |
| 63 | C2×#11719947 | — | 4 | 2 | no | — |
| 64 | C2×#11719947 | — | 4 | 1 | no | — |
| 65 | #41×D53 | — | 2 | 2 | no | — |
| 66 | #41×D53 | — | 2 | 1 | no | — |
| 67 | #41×D53 | — | 4 | 1 | no | — |
| 68 | #41×D53 | D4 | 1 | 1 | yes | characteristic |
| 69 | #13133250 | — | 2 | 1 | no | — |
| 70 | #13133250 | — | 2 | 2 | no | — |
| 71 | #13133247 | — | 2 | 2 | no | — |
| 72 | #13133247 | — | 2 | 1 | no | — |
| 73 | #13133246 | — | 2 | 2 | no | — |
| 74 | #13133246 | — | 2 | 2 | no | — |
| 75 | #13133246 | — | 2 | 2 | no | — |
| 76 | #13133243 | — | 2 | 2 | no | — |
| 77 | #13133243 | — | 2 | 1 | no | — |
| 78 | #13133241 | — | 2 | 2 | no | — |
| 79 | #13133241 | — | 2 | 2 | no | — |
| 80 | #13133241 | — | 2 | 2 | no | — |
| 81 | #13133240 | D4 | 1 | 1 | yes | characteristic |
| 82 | #13133239 | — | 2 | 1 | no | — |
| 83 | #13133239 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | #13133238 | — | 2 | 2 | no | — |
| 85 | #13133238 | — | 2 | 1 | no | — |
| 86 | #13133237 | — | 2 | 2 | no | — |
| 87 | #13133237 | — | 2 | 1 | no | — |
| 88 | #13133236 | — | 2 | 2 | no | — |
| 89 | #13133236 | — | 2 | 2 | no | — |
| 90 | #13133236 | — | 2 | 1 | no | — |
| 91 | #13133236 | — | 2 | 1 | no | — |
| 92 | #13133236 | — | 2 | 1 | no | — |
| 93 | #13133236 | — | 2 | 1 | no | — |
| 94 | #13133236 | D4 | 1 | 2 | yes | — |
| 95 | #13133236 | D4 | 1 | 1 | yes | characteristic |
| 96 | #13133236 | D4 | 1 | 2 | yes | — |
| 97 | C2×Dic212 | — | 2 | 1 | no | — |
| 98 | C2×Dic212 | C2×C4 | 1 | 1 | yes | characteristic |
| 99 | Q16×D53 | — | 2 | 1 | no | — |
| 100 | Q16×D53 | D4 | 1 | 1 | yes | characteristic |
| 101 | C2×#11719923 | — | 2 | 2 | no | — |
| 102 | C2×#11719923 | — | 2 | 1 | no | — |
| 103 | SD16×D53 | — | 2 | 2 | no | — |
| 104 | SD16×D53 | — | 2 | 1 | no | — |
| 105 | D8×D53 | — | 2 | 1 | no | — |
| 106 | D8×D53 | D4 | 1 | 1 | yes | characteristic |
| 107 | #13133225 | — | 2 | 1 | no | — |
| 108 | #13133225 | D4 | 1 | 1 | yes | characteristic |
| 109 | #13133224 | D4 | 1 | 1 | yes | characteristic |
| 110 | #13133223 | — | 2 | 1 | no | — |
| 111 | #13133223 | C2×C4 | 1 | 1 | yes | characteristic |
| 112 | M16×D53 | — | 2 | 1 | no | — |
| 113 | M16×D53 | D4 | 1 | 1 | yes | characteristic |
| 114 | C2×C8×D53 | — | 2 | 1 | no | — |
| 115 | C2×C8×D53 | C23 | 1 | 1 | yes | characteristic |
| 116 | H(5,𝔽2)×C53 | — | 2 | 1 | no | — |
| 117 | AGL(1,ℤ/8)×C53 | — | 2 | 2 | no | — |
| 118 | AGL(1,ℤ/8)×C53 | — | 2 | 1 | no | — |
| 119 | #135×C53 | — | 2 | 1 | no | — |
| 120 | #135×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 121 | C2×D8×C53 | — | 2 | 1 | no | — |
| 122 | C2×D8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 123 | #131×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 124 | C22×#6157 | — | 4 | 1 | no | — |
| 125 | #41×C53 | — | 2 | 2 | no | — |
| 126 | #41×C53 | — | 2 | 1 | no | — |
| 127 | #41×C53 | — | 4 | 1 | no | — |
| 128 | #41×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 129 | C2×D4×C53 | — | 2 | 2 | no | — |
| 130 | C2×D4×C53 | — | 2 | 1 | no | — |
| 131 | C2×D4×C53 | — | 4 | 2 | no | — |
| 132 | C2×D4×C53 | — | 4 | 1 | no | — |
| 133 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 134 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 135 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 136 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 137 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 138 | C22×Dic53 | — | 4 | 2 | no | — |
| 139 | C22×Dic53 | — | 4 | 1 | no | — |
| 140 | #11719949 | — | 2 | 1 | no | — |
| 141 | #11719949 | SD16 | 1 | 1 | yes | characteristic |
| 142 | Q8×D53 | — | 2 | 2 | no | — |
| 143 | Q8×D53 | — | 2 | 1 | no | — |
| 144 | Q8×D53 | — | 4 | 1 | no | — |
| 145 | Q8×D53 | D8 | 1 | 1 | yes | characteristic |
| 146 | #11719947 | — | 2 | 1 | no | — |
| 147 | #11719947 | — | 2 | 2 | no | — |
| 148 | #11719947 | — | 2 | 2 | no | — |
| 149 | #11719947 | — | 2 | 1 | no | — |
| 150 | #11719947 | — | 2 | 2 | no | — |
| 151 | #11719947 | — | 2 | 2 | no | — |
| 152 | #11719947 | — | 4 | 2 | no | — |
| 153 | #11719947 | — | 4 | 2 | no | — |
| 154 | #11719947 | — | 4 | 2 | no | — |
| 155 | #11719947 | — | 4 | 2 | no | — |
| 156 | #11719947 | — | 4 | 2 | no | — |
| 157 | #11719947 | — | 4 | 2 | no | — |
| 158 | #11719947 | — | 4 | 2 | no | — |
| 159 | #11719947 | — | 4 | 2 | no | — |
| 160 | #11719947 | — | 4 | 1 | no | — |
| 161 | #11719947 | — | 4 | 1 | no | — |
| 162 | #11719947 | — | 4 | 1 | no | — |
| 163 | #11719947 | — | 4 | 1 | no | — |
| 164 | #11719947 | — | 4 | 1 | no | — |
| 165 | #11719947 | SD16 | 1 | 1 | yes | characteristic |
| 166 | D4×D53 | — | 2 | 1 | no | — |
| 167 | D4×D53 | — | 2 | 2 | no | — |
| 168 | D4×D53 | — | 2 | 1 | no | — |
| 169 | D4×D53 | — | 4 | 2 | no | — |
| 170 | D4×D53 | — | 4 | 2 | no | — |
| 171 | D4×D53 | — | 4 | 1 | no | — |
| 172 | D4×D53 | — | 4 | 1 | no | — |
| 173 | D4×D53 | D8 | 1 | 1 | yes | characteristic |
| 174 | #11719945 | — | 2 | 1 | no | — |
| 175 | #11719945 | — | 2 | 2 | no | — |
| 176 | #11719945 | — | 2 | 1 | no | — |
| 177 | #11719945 | — | 4 | 2 | no | — |
| 178 | #11719945 | — | 4 | 2 | no | — |
| 179 | #11719945 | — | 4 | 1 | no | — |
| 180 | #11719945 | — | 4 | 1 | no | — |
| 181 | #11719945 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 182 | C2×C4×D53 | — | 2 | 1 | no | — |
| 183 | C2×C4×D53 | — | 4 | 2 | no | — |
| 184 | C2×C4×D53 | — | 4 | 1 | no | — |
| 185 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 186 | C2×Dic106 | — | 2 | 2 | no | — |
| 187 | C2×Dic106 | — | 2 | 1 | no | — |
| 188 | C2×Dic106 | — | 4 | 2 | no | — |
| 189 | C2×Dic106 | — | 4 | 1 | no | — |
| 190 | #11719940 | — | 4 | 1 | no | — |
| 191 | C4⋊#6157 | — | 4 | 1 | no | — |
| 192 | C4⋊#6157 | — | 4 | 1 | no | — |
| 193 | #11719936 | — | 4 | 1 | no | — |
| 194 | D53⋊C8 | — | 4 | 1 | no | — |
| 195 | Q16×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 196 | SD16×C53 | — | 2 | 2 | no | — |
| 197 | SD16×C53 | — | 2 | 1 | no | — |
| 198 | D8×C53 | — | 2 | 2 | no | — |
| 199 | D8×C53 | — | 2 | 1 | no | — |
| 200 | D8×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 201 | D8×C53 | C22⋊C4 | 1 | 2 | yes | — |
| 202 | M16×C53 | — | 2 | 1 | no | — |
| 203 | M16×C53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 204 | C2×C8×C53 | — | 2 | 1 | no | — |
| 205 | C2×C8×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 206 | #11719925 | — | 2 | 2 | no | — |
| 207 | #11719925 | — | 2 | 1 | no | — |
| 208 | #11719924 | — | 2 | 1 | no | — |
| 209 | #11719923 | — | 2 | 2 | no | — |
| 210 | #11719923 | — | 2 | 2 | no | — |
| 211 | #11719923 | — | 2 | 2 | no | — |
| 212 | #11719923 | — | 2 | 1 | no | — |
| 213 | #11719923 | — | 2 | 2 | no | — |
| 214 | #11719922 | — | 2 | 2 | no | — |
| 215 | #11719922 | — | 2 | 1 | no | — |
| 216 | #11719917 | — | 2 | 1 | no | — |
| 217 | #11719917 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 218 | C2×#88322 | — | 2 | 1 | no | — |
| 219 | C2×#88322 | C2×D4 | 1 | 1 | yes | characteristic |
| 220 | Dic212 | — | 2 | 2 | no | — |
| 221 | Dic212 | — | 2 | 1 | no | — |
| 222 | Dic212 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 223 | Dic212 | C22⋊C4 | 1 | 2 | yes | — |
| 224 | D424 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 225 | #11719913 | — | 2 | 2 | no | — |
| 226 | #11719913 | — | 2 | 1 | no | — |
| 227 | #11719912 | — | 2 | 1 | no | — |
| 228 | #11719912 | — | 2 | 1 | no | — |
| 229 | #11719912 | — | 2 | 1 | no | — |
| 230 | C8×D53 | — | 2 | 1 | no | — |
| 231 | C8×D53 | — | 2 | 1 | no | — |
| 232 | C8×D53 | — | 2 | 1 | no | — |
| 233 | C8×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 234 | C8×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 235 | C8×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 236 | C8×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 237 | #11719910 | — | 4 | 1 | no | — |
| 238 | #11719910 | — | 4 | 1 | no | — |
| 239 | C23×C53 | — | 4 | 2 | no | — |
| 240 | C23×C53 | — | 4 | 1 | no | — |
| 241 | C22×D53 | — | 2 | 1 | no | — |
| 242 | C22×D53 | — | 4 | 2 | no | — |
| 243 | C22×D53 | — | 4 | 1 | no | — |
| 244 | C22×D53 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 245 | C2×#6157 | — | 8 | 1 | no | — |
| 246 | C2×#6157 | — | 16 | 1 | no | — |
| 247 | Q8×C53 | — | 2 | 1 | no | — |
| 248 | Q8×C53 | #102 | 1 | 1 | yes | characteristic |
| 249 | D4×C53 | — | 2 | 1 | no | — |
| 250 | D4×C53 | — | 2 | 2 | no | — |
| 251 | D4×C53 | — | 2 | 1 | no | — |
| 252 | D4×C53 | — | 4 | 2 | no | — |
| 253 | D4×C53 | — | 4 | 2 | no | — |
| 254 | D4×C53 | — | 4 | 1 | no | — |
| 255 | D4×C53 | — | 4 | 1 | no | — |
| 256 | D4×C53 | #102 | 1 | 1 | yes | characteristic |
| 257 | C2×C4×C53 | — | 2 | 1 | no | — |
| 258 | C2×C4×C53 | — | 4 | 2 | no | — |
| 259 | C2×C4×C53 | — | 4 | 1 | no | — |
| 260 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 261 | C22⋊D53 | — | 2 | 1 | no | — |
| 262 | C22⋊D53 | — | 2 | 1 | no | — |
| 263 | C22⋊D53 | — | 2 | 1 | no | — |
| 264 | C22⋊D53 | — | 4 | 2 | no | — |
| 265 | C22⋊D53 | — | 4 | 2 | no | — |
| 266 | C22⋊D53 | — | 4 | 2 | no | — |
| 267 | C22⋊D53 | — | 4 | 2 | no | — |
| 268 | C22⋊D53 | — | 4 | 1 | no | — |
| 269 | C22⋊D53 | — | 4 | 2 | no | — |
| 270 | C22⋊D53 | — | 4 | 1 | no | — |
| 271 | C22⋊D53 | — | 4 | 2 | no | — |
| 272 | C22⋊D53 | — | 4 | 1 | no | — |
| 273 | C2×Dic53 | — | 2 | 1 | no | — |
| 274 | C2×Dic53 | — | 4 | 2 | no | — |
| 275 | C2×Dic53 | — | 4 | 2 | no | — |
| 276 | C2×Dic53 | — | 4 | 2 | no | — |
| 277 | C2×Dic53 | — | 4 | 1 | no | — |
| 278 | C2×Dic53 | — | 4 | 2 | no | — |
| 279 | C2×Dic53 | — | 4 | 2 | no | — |
| 280 | C2×Dic53 | — | 4 | 1 | no | — |
| 281 | C2×Dic53 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 282 | D212 | — | 2 | 1 | no | — |
| 283 | D212 | — | 2 | 1 | no | — |
| 284 | D212 | — | 4 | 1 | no | — |
| 285 | D212 | #102 | 1 | 1 | yes | characteristic |
| 286 | C4×D53 | — | 2 | 1 | no | — |
| 287 | C4×D53 | — | 2 | 1 | no | — |
| 288 | C4×D53 | — | 2 | 1 | no | — |
| 289 | C4×D53 | — | 4 | 2 | no | — |
| 290 | C4×D53 | — | 4 | 2 | no | — |
| 291 | C4×D53 | — | 4 | 1 | no | — |
| 292 | C4×D53 | — | 4 | 1 | no | — |
| 293 | C4×D53 | — | 4 | 1 | no | — |
| 294 | C4×D53 | #120 | 1 | 1 | yes | characteristic |
| 295 | C4×D53 | #120 | 1 | 1 | yes | characteristic |
| 296 | C4×D53 | C2×D8 | 1 | 1 | yes | characteristic |
| 297 | C4×D53 | C2×SD16 | 1 | 1 | yes | characteristic |
| 298 | Dic106 | — | 2 | 1 | no | — |
| 299 | Dic106 | — | 2 | 1 | no | — |
| 300 | Dic106 | — | 2 | 2 | no | — |
| 301 | Dic106 | — | 4 | 2 | no | — |
| 302 | Dic106 | — | 4 | 2 | no | — |
| 303 | Dic106 | — | 4 | 1 | no | — |
| 304 | Dic106 | — | 4 | 1 | no | — |
| 305 | Dic106 | #102 | 1 | 1 | yes | characteristic |
| 306 | #88324 | — | 8 | 1 | no | — |
| 307 | C8×C53 | — | 2 | 1 | no | — |
| 308 | C8×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 309 | C8×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 310 | #88322 | — | 2 | 1 | no | — |
| 311 | #88322 | #120 | 1 | 1 | yes | characteristic |
| 312 | #88322 | #120 | 1 | 1 | yes | characteristic |
| 313 | #12752 | — | 53 | 1 | no | maximal, Sylow |
| 314 | C22×C53 | — | 2 | 1 | no | — |
| 315 | C22×C53 | — | 4 | 1 | no | — |
| 316 | C22×C53 | — | 4 | 2 | no | — |
| 317 | C22×C53 | — | 16 | 1 | no | — |
| 318 | C22×C53 | — | 16 | 2 | no | — |
| 319 | C22×C53 | #418 | 1 | 1 | yes | characteristic |
| 320 | C2×D53 | — | 2 | 1 | no | — |
| 321 | C2×D53 | — | 4 | 1 | no | — |
| 322 | C2×D53 | — | 4 | 1 | no | — |
| 323 | C2×D53 | — | 8 | 1 | no | — |
| 324 | C2×D53 | — | 16 | 1 | no | — |
| 325 | C2×D53 | — | 16 | 2 | no | — |
| 326 | C2×D53 | #447 | 1 | 1 | yes | characteristic |
| 327 | C2×D53 | #450 | 1 | 1 | yes | characteristic |
| 328 | #6157 | — | 16 | 1 | no | — |
| 329 | C4×C53 | — | 2 | 1 | no | — |
| 330 | C4×C53 | — | 4 | 1 | no | — |
| 331 | C4×C53 | #379 | 1 | 1 | yes | characteristic |
| 332 | C4×C53 | C2×#102 | 1 | 1 | yes | characteristic |
| 333 | Dic53 | — | 2 | 1 | no | — |
| 334 | Dic53 | — | 4 | 2 | no | — |
| 335 | Dic53 | — | 4 | 1 | no | — |
| 336 | Dic53 | #447 | 1 | 1 | yes | characteristic |
| 337 | Dic53 | #450 | 1 | 1 | yes | characteristic |
| 338 | #3584 | — | 53 | 1 | no | — |
| 339 | #2148 | — | 53 | 1 | no | — |
| 340 | C2×#360 | — | 53 | 1 | no | — |
| 341 | C2×#360 | — | 53 | 1 | no | — |
| 342 | #2143 | — | 53 | 1 | no | — |
| 343 | #2117 | — | 53 | 1 | no | — |
| 344 | #1815 | — | 53 | 1 | no | — |
| 345 | C2×C53 | — | 2 | 1 | no | — |
| 346 | C2×C53 | — | 4 | 1 | no | — |
| 347 | C2×C53 | — | 8 | 1 | no | — |
| 348 | C2×C53 | — | 8 | 2 | no | — |
| 349 | C2×C53 | #1786 | 1 | 1 | yes | characteristic |
| 350 | D53 | — | 2 | 1 | no | — |
| 351 | D53 | — | 2 | 1 | no | — |
| 352 | D53 | — | 4 | 1 | no | — |
| 353 | D53 | — | 8 | 1 | no | — |
| 354 | #585 | — | 106 | 1 | no | — |
| 355 | #578 | — | 53 | 1 | no | — |
| 356 | #578 | — | 53 | 1 | no | — |
| 357 | #578 | — | 106 | 1 | no | — |
| 358 | #577 | — | 106 | 1 | no | — |
| 359 | #577 | — | 106 | 1 | no | — |
| 360 | #577 | — | 106 | 2 | no | — |
| 361 | #576 | — | 53 | 1 | no | — |
| 362 | #576 | — | 106 | 1 | no | — |
| 363 | #576 | #6157 | 1 | 1 | yes | characteristic, complemented |
| 364 | #575 | — | 106 | 1 | no | — |
| 365 | #575 | — | 106 | 2 | no | — |
| 366 | C2×#135 | — | 53 | 1 | no | — |
| 367 | C2×#135 | — | 53 | 1 | no | — |
| 368 | C2×#135 | — | 106 | 1 | no | — |
| 369 | C2×#135 | — | 106 | 1 | no | — |
| 370 | C2×#131 | — | 53 | 1 | no | — |
| 371 | C2×M32 | — | 53 | 1 | no | — |
| 372 | C2×M32 | — | 53 | 1 | no | — |
| 373 | C2×#108 | — | 53 | 1 | no | — |
| 374 | C2×#106 | — | 53 | 1 | no | — |
| 375 | #417 | — | 106 | 1 | no | — |
| 376 | #362 | — | 106 | 1 | no | — |
| 377 | #361 | — | 106 | 1 | no | — |
| 378 | #360 | — | 106 | 1 | no | — |
| 379 | #360 | — | 106 | 2 | no | — |
| 380 | #360 | — | 106 | 1 | no | — |
| 381 | #359 | — | 106 | 2 | no | — |
| 382 | #350 | — | 106 | 1 | no | — |
| 383 | #350 | — | 106 | 1 | no | — |
| 384 | #343 | — | 106 | 1 | no | — |
| 385 | C53 | #12752 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 386 | 2−1+4 | — | 106 | 1 | no | — |
| 387 | 2−1+4 | — | 106 | 2 | no | — |
| 388 | 2−1+4 | — | 106 | 1 | no | — |
| 389 | 2−1+4 | — | 212 | 1 | no | — |
| 390 | H(5,𝔽2) | — | 2 | 1 | no | — |
| 391 | H(5,𝔽2) | — | 106 | 1 | no | — |
| 392 | H(5,𝔽2) | — | 106 | 2 | no | — |
| 393 | H(5,𝔽2) | — | 212 | 1 | no | — |
| 394 | H(5,𝔽2) | — | 212 | 2 | no | — |
| 395 | C2×#41 | — | 53 | 1 | no | — |
| 396 | C2×#41 | — | 106 | 1 | no | — |
| 397 | C2×#41 | — | 106 | 1 | no | — |
| 398 | C2×#41 | — | 106 | 2 | no | — |
| 399 | C2×#41 | — | 106 | 2 | no | — |
| 400 | C2×#41 | — | 212 | 1 | no | — |
| 401 | C2×#41 | — | 212 | 2 | no | — |
| 402 | C2×#41 | — | 212 | 1 | no | — |
| 403 | #137 | — | 106 | 2 | no | — |
| 404 | #137 | — | 106 | 1 | no | — |
| 405 | #137 | — | 106 | 2 | no | — |
| 406 | #137 | — | 106 | 2 | no | — |
| 407 | #137 | — | 106 | 2 | no | — |
| 408 | #137 | — | 106 | 2 | no | — |
| 409 | #137 | — | 106 | 1 | no | — |
| 410 | AGL(1,ℤ/8) | — | 2 | 2 | no | — |
| 411 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 412 | AGL(1,ℤ/8) | — | 106 | 1 | no | — |
| 413 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 414 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 415 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 416 | AGL(1,ℤ/8) | — | 106 | 2 | no | — |
| 417 | #135 | — | 2 | 1 | no | — |
| 418 | #135 | — | 53 | 1 | no | — |
| 419 | #135 | — | 53 | 1 | no | — |
| 420 | #135 | — | 53 | 2 | no | — |
| 421 | #135 | — | 53 | 2 | no | — |
| 422 | #135 | — | 53 | 1 | no | — |
| 423 | #135 | — | 106 | 1 | no | — |
| 424 | #135 | — | 106 | 1 | no | — |
| 425 | #135 | — | 106 | 1 | no | — |
| 426 | #135 | — | 106 | 1 | no | — |
| 427 | #135 | — | 106 | 1 | no | — |
| 428 | #135 | — | 106 | 1 | no | — |
| 429 | #135 | — | 106 | 2 | no | — |
| 430 | #135 | — | 106 | 2 | no | — |
| 431 | #135 | — | 106 | 2 | no | — |
| 432 | #135 | — | 106 | 2 | no | — |
| 433 | #135 | — | 106 | 1 | no | — |
| 434 | #135 | C2×#6157 | 1 | 1 | yes | characteristic |
| 435 | C2×Q16 | — | 53 | 1 | no | — |
| 436 | C2×Q16 | — | 53 | 1 | no | — |
| 437 | C2×Q16 | — | 106 | 1 | no | — |
| 438 | C2×Q16 | — | 106 | 1 | no | — |
| 439 | C2×SD16 | — | 106 | 1 | no | — |
| 440 | C2×SD16 | — | 106 | 1 | no | — |
| 441 | C2×SD16 | — | 106 | 2 | no | — |
| 442 | C2×SD16 | — | 106 | 2 | no | — |
| 443 | C2×D8 | — | 2 | 1 | no | — |
| 444 | C2×D8 | — | 53 | 1 | no | — |
| 445 | C2×D8 | — | 106 | 1 | no | — |
| 446 | C2×D8 | C2×#6157 | 1 | 1 | yes | characteristic |
| 447 | #131 | — | 53 | 1 | no | — |
| 448 | #131 | — | 53 | 1 | no | — |
| 449 | #131 | — | 53 | 1 | no | — |
| 450 | #131 | — | 106 | 1 | no | — |
| 451 | #131 | — | 106 | 1 | no | — |
| 452 | #131 | C2×#6157 | 1 | 1 | yes | characteristic |
| 453 | C2×M16 | — | 53 | 1 | no | — |
| 454 | C2×M16 | — | 106 | 1 | no | — |
| 455 | C2×M16 | — | 106 | 1 | no | — |
| 456 | C22×C8 | — | 53 | 1 | no | — |
| 457 | C22×C8 | — | 106 | 1 | no | — |
| 458 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 459 | M32 | — | 106 | 1 | no | — |
| 460 | M32 | — | 106 | 1 | no | — |
| 461 | M32 | — | 106 | 1 | no | — |
| 462 | M32 | — | 106 | 1 | no | — |
| 463 | C2×C16 | — | 106 | 1 | no | — |
| 464 | C2×C16 | — | 106 | 1 | no | — |
| 465 | #108 | — | 106 | 1 | no | — |
| 466 | #108 | — | 106 | 1 | no | — |
| 467 | #106 | — | 106 | 1 | no | — |
| 468 | #106 | — | 106 | 1 | no | — |
| 469 | #103 | — | 212 | 1 | no | — |
| 470 | #102 | — | 212 | 1 | no | — |
| 471 | #41 | — | 2 | 2 | no | — |
| 472 | #41 | — | 2 | 1 | no | — |
| 473 | #41 | — | 4 | 1 | no | — |
| 474 | #41 | — | 53 | 1 | no | — |
| 475 | #41 | — | 53 | 1 | no | — |
| 476 | #41 | — | 53 | 1 | no | — |
| 477 | #41 | — | 106 | 1 | no | — |
| 478 | #41 | — | 106 | 2 | no | — |
| 479 | #41 | — | 106 | 1 | no | — |
| 480 | #41 | — | 106 | 1 | no | — |
| 481 | #41 | — | 106 | 2 | no | — |
| 482 | #41 | — | 106 | 2 | no | — |
| 483 | #41 | — | 106 | 1 | no | — |
| 484 | #41 | — | 106 | 2 | no | — |
| 485 | #41 | — | 106 | 2 | no | — |
| 486 | #41 | — | 106 | 1 | no | — |
| 487 | #41 | — | 212 | 1 | no | — |
| 488 | #41 | — | 212 | 2 | no | — |
| 489 | #41 | — | 212 | 1 | no | — |
| 490 | #41 | — | 212 | 2 | no | — |
| 491 | #41 | — | 212 | 1 | no | — |
| 492 | #41 | — | 212 | 1 | no | — |
| 493 | #41 | — | 212 | 1 | no | — |
| 494 | #41 | — | 212 | 2 | no | — |
| 495 | #41 | — | 212 | 2 | no | — |
| 496 | #41 | — | 212 | 2 | no | — |
| 497 | #41 | — | 212 | 2 | no | — |
| 498 | #41 | — | 212 | 2 | no | — |
| 499 | #41 | — | 212 | 2 | no | — |
| 500 | #41 | — | 212 | 2 | no | — |
| 501 | #41 | — | 212 | 1 | no | — |
| 502 | #41 | — | 212 | 2 | no | — |
| 503 | #41 | — | 212 | 1 | no | — |
| 504 | #41 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 505 | C2×Q8 | — | 53 | 1 | no | — |
| 506 | C2×Q8 | — | 106 | 2 | no | — |
| 507 | C2×Q8 | — | 106 | 1 | no | — |
| 508 | C2×Q8 | — | 106 | 2 | no | — |
| 509 | C2×Q8 | — | 106 | 1 | no | — |
| 510 | C2×Q8 | — | 212 | 1 | no | — |
| 511 | C2×Q8 | — | 212 | 2 | no | — |
| 512 | C2×Q8 | — | 212 | 1 | no | — |
| 513 | C2×D4 | — | 2 | 2 | no | — |
| 514 | C2×D4 | — | 2 | 1 | no | — |
| 515 | C2×D4 | — | 4 | 2 | no | — |
| 516 | C2×D4 | — | 4 | 1 | no | — |
| 517 | C2×D4 | — | 53 | 1 | no | — |
| 518 | C2×D4 | — | 106 | 1 | no | — |
| 519 | C2×D4 | — | 106 | 1 | no | — |
| 520 | C2×D4 | — | 106 | 2 | no | — |
| 521 | C2×D4 | — | 212 | 1 | no | — |
| 522 | C2×D4 | — | 212 | 2 | no | — |
| 523 | C2×D4 | — | 212 | 1 | no | — |
| 524 | C2×D4 | — | 212 | 2 | no | — |
| 525 | C2×D4 | — | 212 | 2 | no | — |
| 526 | C2×D4 | — | 212 | 2 | no | — |
| 527 | C2×D4 | — | 212 | 2 | no | — |
| 528 | C2×D4 | — | 212 | 1 | no | — |
| 529 | C2×D4 | — | 212 | 2 | no | — |
| 530 | C22×C4 | — | 53 | 1 | no | — |
| 531 | C22×C4 | — | 106 | 1 | no | — |
| 532 | C22×C4 | — | 212 | 1 | no | — |
| 533 | C22×C4 | — | 212 | 2 | no | — |
| 534 | C22×C4 | — | 212 | 1 | no | — |
| 535 | C22×C4 | — | 212 | 1 | no | — |
| 536 | C22×C4 | — | 212 | 2 | no | — |
| 537 | Q16 | — | 53 | 1 | no | — |
| 538 | Q16 | — | 53 | 2 | no | — |
| 539 | Q16 | — | 106 | 2 | no | — |
| 540 | Q16 | — | 106 | 1 | no | — |
| 541 | Q16 | — | 106 | 2 | no | — |
| 542 | Q16 | — | 106 | 1 | no | — |
| 543 | Q16 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 544 | SD16 | — | 2 | 2 | no | — |
| 545 | SD16 | — | 2 | 1 | no | — |
| 546 | SD16 | — | 106 | 2 | no | — |
| 547 | SD16 | — | 106 | 1 | no | — |
| 548 | SD16 | — | 106 | 2 | no | — |
| 549 | SD16 | — | 106 | 2 | no | — |
| 550 | SD16 | — | 106 | 1 | no | — |
| 551 | SD16 | — | 106 | 2 | no | — |
| 552 | SD16 | — | 106 | 2 | no | — |
| 553 | SD16 | — | 106 | 1 | no | — |
| 554 | D8 | — | 2 | 2 | no | — |
| 555 | D8 | — | 2 | 1 | no | — |
| 556 | D8 | — | 53 | 1 | no | — |
| 557 | D8 | — | 106 | 1 | no | — |
| 558 | D8 | — | 106 | 2 | no | — |
| 559 | D8 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 560 | D8 | C22⋊#6157 | 1 | 2 | yes | — |
| 561 | M16 | — | 2 | 1 | no | — |
| 562 | M16 | — | 53 | 1 | no | — |
| 563 | M16 | — | 106 | 1 | no | — |
| 564 | M16 | — | 106 | 1 | no | — |
| 565 | M16 | — | 106 | 1 | no | — |
| 566 | M16 | — | 106 | 1 | no | — |
| 567 | M16 | — | 212 | 1 | no | — |
| 568 | M16 | — | 212 | 1 | no | — |
| 569 | M16 | C22⋊#6157 | 1 | 1 | yes | characteristic |
| 570 | C2×C8 | — | 2 | 1 | no | — |
| 571 | C2×C8 | — | 53 | 1 | no | — |
| 572 | C2×C8 | — | 53 | 1 | no | — |
| 573 | C2×C8 | — | 53 | 1 | no | — |
| 574 | C2×C8 | — | 53 | 1 | no | — |
| 575 | C2×C8 | — | 53 | 1 | no | — |
| 576 | C2×C8 | — | 106 | 1 | no | — |
| 577 | C2×C8 | — | 106 | 1 | no | — |
| 578 | C2×C8 | — | 106 | 1 | no | — |
| 579 | C2×C8 | — | 106 | 1 | no | — |
| 580 | C2×C8 | — | 212 | 1 | no | — |
| 581 | C2×C8 | C22×#6157 | 1 | 1 | yes | characteristic |
| 582 | C4⋊C4 | — | 212 | 1 | no | — |
| 583 | C4⋊C4 | — | 212 | 1 | no | — |
| 584 | C16 | — | 212 | 1 | no | — |
| 585 | C16 | — | 212 | 1 | no | — |
| 586 | C23 | — | 4 | 2 | no | — |
| 587 | C23 | — | 4 | 1 | no | — |
| 588 | C23 | — | 53 | 1 | no | — |
| 589 | C23 | — | 106 | 1 | no | — |
| 590 | C23 | — | 212 | 1 | no | — |
| 591 | C23 | — | 212 | 2 | no | — |
| 592 | Q8 | — | 2 | 1 | no | — |
| 593 | Q8 | — | 53 | 1 | no | — |
| 594 | Q8 | — | 106 | 1 | no | — |
| 595 | Q8 | — | 106 | 2 | no | — |
| 596 | Q8 | — | 106 | 1 | no | — |
| 597 | Q8 | — | 212 | 2 | no | — |
| 598 | Q8 | — | 212 | 1 | no | — |
| 599 | Q8 | — | 212 | 2 | no | — |
| 600 | Q8 | — | 212 | 1 | no | — |
| 601 | Q8 | #13133279 | 1 | 1 | yes | characteristic |
| 602 | D4 | — | 2 | 1 | no | — |
| 603 | D4 | — | 2 | 1 | no | — |
| 604 | D4 | — | 2 | 2 | no | — |
| 605 | D4 | — | 4 | 2 | no | — |
| 606 | D4 | — | 4 | 2 | no | — |
| 607 | D4 | — | 4 | 1 | no | — |
| 608 | D4 | — | 4 | 1 | no | — |
| 609 | D4 | — | 53 | 1 | no | — |
| 610 | D4 | — | 106 | 1 | no | — |
| 611 | D4 | — | 106 | 1 | no | — |
| 612 | D4 | — | 106 | 1 | no | — |
| 613 | D4 | — | 106 | 1 | no | — |
| 614 | D4 | — | 106 | 1 | no | — |
| 615 | D4 | — | 212 | 1 | no | — |
| 616 | D4 | — | 212 | 1 | no | — |
| 617 | D4 | — | 212 | 2 | no | — |
| 618 | D4 | — | 212 | 2 | no | — |
| 619 | D4 | — | 212 | 1 | no | — |
| 620 | D4 | — | 212 | 2 | no | — |
| 621 | D4 | — | 212 | 2 | no | — |
| 622 | D4 | — | 212 | 2 | no | — |
| 623 | D4 | — | 212 | 2 | no | — |
| 624 | D4 | — | 212 | 1 | no | — |
| 625 | D4 | #13133279 | 1 | 1 | yes | characteristic |
| 626 | C2×C4 | — | 2 | 1 | no | — |
| 627 | C2×C4 | — | 4 | 2 | no | — |
| 628 | C2×C4 | — | 4 | 1 | no | — |
| 629 | C2×C4 | — | 53 | 1 | no | — |
| 630 | C2×C4 | — | 53 | 1 | no | — |
| 631 | C2×C4 | — | 53 | 1 | no | — |
| 632 | C2×C4 | — | 53 | 1 | no | — |
| 633 | C2×C4 | — | 53 | 1 | no | — |
| 634 | C2×C4 | — | 848 | 1 | no | — |
| 635 | C2×C4 | — | 106 | 1 | no | — |
| 636 | C2×C4 | — | 106 | 1 | no | — |
| 637 | C2×C4 | — | 106 | 1 | no | — |
| 638 | C2×C4 | — | 106 | 1 | no | — |
| 639 | C2×C4 | — | 424 | 1 | no | — |
| 640 | C2×C4 | — | 212 | 2 | no | — |
| 641 | C2×C4 | — | 212 | 1 | no | — |
| 642 | C2×C4 | — | 212 | 1 | no | — |
| 643 | C2×C4 | — | 212 | 2 | no | — |
| 644 | C2×C4 | — | 212 | 1 | no | — |
| 645 | C2×C4 | — | 212 | 2 | no | — |
| 646 | C2×C4 | — | 212 | 2 | no | — |
| 647 | C2×C4 | — | 212 | 2 | no | — |
| 648 | C2×C4 | — | 212 | 2 | no | — |
| 649 | C2×C4 | — | 212 | 2 | no | — |
| 650 | C2×C4 | — | 212 | 1 | no | — |
| 651 | C2×C4 | — | 212 | 1 | no | — |
| 652 | C2×C4 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 653 | C8 | — | 2 | 1 | no | — |
| 654 | C8 | — | 53 | 1 | no | — |
| 655 | C8 | — | 53 | 1 | no | — |
| 656 | C8 | — | 106 | 1 | no | — |
| 657 | C8 | — | 424 | 1 | no | — |
| 658 | C8 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 659 | C8 | C2×C22⋊#6157 | 1 | 1 | yes | characteristic |
| 660 | C22 | — | 2 | 1 | no | — |
| 661 | C22 | — | 4 | 2 | no | — |
| 662 | C22 | — | 4 | 1 | no | — |
| 663 | C22 | — | 16 | 1 | no | — |
| 664 | C22 | — | 16 | 2 | no | — |
| 665 | C22 | — | 53 | 1 | no | — |
| 666 | C22 | — | 53 | 1 | no | — |
| 667 | C22 | — | 848 | 1 | no | — |
| 668 | C22 | — | 848 | 2 | no | — |
| 669 | C22 | — | 106 | 1 | no | — |
| 670 | C22 | — | 424 | 1 | no | — |
| 671 | C22 | — | 212 | 1 | no | — |
| 672 | C22 | — | 212 | 1 | no | — |
| 673 | C22 | #16811615 | 1 | 1 | yes | characteristic |
| 674 | C4 | — | 2 | 1 | no | — |
| 675 | C4 | — | 4 | 1 | no | — |
| 676 | C4 | — | 53 | 1 | no | — |
| 677 | C4 | — | 53 | 1 | no | — |
| 678 | C4 | — | 848 | 1 | no | — |
| 679 | C4 | — | 106 | 1 | no | — |
| 680 | C4 | — | 212 | 2 | no | — |
| 681 | C4 | — | 212 | 1 | no | — |
| 682 | C4 | #16811564 | 1 | 1 | yes | characteristic |
| 683 | C4 | C2×#13133279 | 1 | 1 | yes | characteristic |
| 684 | C2 | — | 2 | 1 | no | — |
| 685 | C2 | — | 4 | 1 | no | — |
| 686 | C2 | — | 8 | 2 | no | — |
| 687 | C2 | — | 8 | 1 | no | — |
| 688 | C2 | — | 106 | 1 | no | — |
| 689 | C2 | — | 106 | 1 | no | — |
| 690 | C2 | — | 424 | 1 | no | — |
| 691 | C2 | — | 212 | 1 | no | — |
| 692 | C2 | #20290553 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20291042 | C2 | semidirect |
| 2. D53⋊#360 | C2 | semidirect |
| 3. C2×#16811539 | C2 | semidirect |
| 4. #20291030 | C2 | semidirect |
| 5. #20290958 | C2 | semidirect |
| 6. #20290603 | C2 | semidirect |
| 8. C2×#13133292 | C22 | semidirect |
| 9. D53⋊M32 | C22 | semidirect |
| 10. D53⋊#108 | C22 | semidirect |
| 11. C2×#13133285 | C22 | semidirect |
| 23. #16811440 | C4 | semidirect |
| 25. #16811437 | C4 | semidirect |
| 30. #16811424 | C4 | semidirect |
| 38. C53×#576 | C4 | semidirect |
| 363. #576 | #6157 | semidirect |
| 385. C53 | #12752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291042 | 2 |
| D53⋊#360 | 2 |
| C2×#16811539 | 2 |
| #20291030 | 2 |
| #20290958 | 2 |
| #20290603 | 2 |
| #20289483 | 2 |
| #12752 | 53 |