Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
490 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20284060 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #20276377 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20273447 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20272861 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20272860 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20272859 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C53×#1402 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #16811458 | C4 | 1 | 1 | yes | characteristic, complemented |
| 9 | #16811419 | — | 2 | 1 | no | — |
| 10 | #16811171 | C22 | 1 | 1 | yes | characteristic |
| 11 | #16810807 | — | 2 | 1 | no | — |
| 12 | #16810803 | C4 | 1 | 1 | yes | characteristic, complemented |
| 13 | #16810801 | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | #16810794 | — | 2 | 1 | no | — |
| 15 | #16810790 | C22 | 1 | 1 | yes | characteristic |
| 16 | #16810645 | — | 2 | 1 | no | — |
| 17 | #104×D53 | — | 2 | 1 | no | — |
| 18 | #16810604 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | #16810595 | — | 2 | 1 | no | — |
| 20 | #16810417 | — | 2 | 1 | no | — |
| 21 | #16810416 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #16810371 | — | 2 | 1 | no | — |
| 23 | #16810367 | C22 | 1 | 1 | yes | characteristic, complemented |
| 24 | C53×#453 | C22 | 1 | 1 | yes | characteristic |
| 25 | C53×#353 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | C53×#331 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | #13133264 | — | 2 | 1 | no | — |
| 28 | #13133264 | — | 4 | 1 | no | — |
| 29 | #13133262 | — | 4 | 1 | no | — |
| 30 | #13133262 | — | 4 | 1 | no | — |
| 31 | #13133262 | C2×C4 | 1 | 1 | yes | characteristic |
| 32 | C2×#11719947 | — | 4 | 1 | no | — |
| 33 | C2×#11719947 | — | 4 | 1 | no | — |
| 34 | C2×#11719947 | C2×C4 | 1 | 1 | yes | characteristic |
| 35 | C2×#11719947 | D4 | 1 | 1 | yes | characteristic |
| 36 | #41×D53 | — | 2 | 1 | no | — |
| 37 | #41×D53 | — | 4 | 1 | no | — |
| 38 | #13133250 | — | 2 | 1 | no | — |
| 39 | #13133247 | — | 2 | 1 | no | — |
| 40 | #13133246 | — | 4 | 1 | no | — |
| 41 | #13133243 | — | 2 | 1 | no | — |
| 42 | #13133241 | — | 4 | 1 | no | — |
| 43 | #13133238 | — | 4 | 1 | no | — |
| 44 | #13133236 | — | 4 | 1 | no | — |
| 45 | C2×#11719912 | — | 4 | 1 | no | — |
| 46 | M16×D53 | — | 2 | 1 | no | — |
| 47 | #13133217 | D4 | 1 | 1 | yes | characteristic |
| 48 | #13133204 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | #13133204 | D4 | 1 | 1 | yes | characteristic |
| 50 | #13133188 | — | 4 | 1 | no | — |
| 51 | D4×Dic53 | — | 4 | 1 | no | — |
| 52 | #13133173 | — | 4 | 1 | no | — |
| 53 | C42×D53 | D4 | 1 | 1 | yes | characteristic |
| 54 | C4⋊#88322 | — | 2 | 1 | no | — |
| 55 | #13133146 | — | 4 | 1 | no | — |
| 56 | #13133145 | — | 2 | 1 | no | — |
| 57 | #13133144 | — | 2 | 1 | no | — |
| 58 | #13133143 | — | 2 | 1 | no | — |
| 59 | #13133135 | — | 2 | 1 | no | — |
| 60 | #13133134 | C2×C4 | 1 | 1 | yes | characteristic |
| 61 | #13133132 | — | 2 | 1 | no | — |
| 62 | #13133131 | — | 4 | 1 | no | — |
| 63 | H(5,𝔽2)×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 64 | AGL(1,ℤ/8)×C53 | — | 2 | 1 | no | — |
| 65 | #127×C53 | C23 | 1 | 1 | yes | characteristic |
| 66 | C4⋊C8×C53 | — | 2 | 1 | no | — |
| 67 | #104×C53 | — | 2 | 1 | no | — |
| 68 | #100×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 69 | #99×C53 | — | 2 | 1 | no | — |
| 70 | #41×C53 | — | 2 | 1 | no | — |
| 71 | #41×C53 | — | 4 | 1 | no | — |
| 72 | C2×D4×C53 | — | 4 | 1 | no | — |
| 73 | C2×D4×C53 | — | 4 | 1 | no | — |
| 74 | C2×D4×C53 | — | 4 | 1 | no | — |
| 75 | C2×D4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 76 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 77 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 78 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 79 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 80 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 81 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 82 | C22×Dic53 | — | 2 | 1 | no | — |
| 83 | C22×Dic53 | — | 2 | 1 | no | — |
| 84 | C22×Dic53 | — | 4 | 1 | no | — |
| 85 | #11719949 | — | 2 | 1 | no | — |
| 86 | Q8×D53 | — | 2 | 1 | no | — |
| 87 | Q8×D53 | — | 4 | 1 | no | — |
| 88 | #11719947 | — | 2 | 1 | no | — |
| 89 | #11719947 | — | 4 | 1 | no | — |
| 90 | #11719947 | — | 4 | 1 | no | — |
| 91 | #11719947 | — | 4 | 1 | no | — |
| 92 | #11719947 | — | 4 | 1 | no | — |
| 93 | #11719947 | — | 4 | 1 | no | — |
| 94 | #11719947 | — | 4 | 2 | no | — |
| 95 | #11719947 | — | 4 | 1 | no | — |
| 96 | #11719947 | — | 4 | 2 | no | — |
| 97 | #11719947 | — | 4 | 2 | no | — |
| 98 | #11719947 | — | 4 | 2 | no | — |
| 99 | #11719947 | — | 4 | 1 | no | — |
| 100 | D4×D53 | — | 2 | 1 | no | — |
| 101 | D4×D53 | — | 4 | 1 | no | — |
| 102 | D4×D53 | — | 4 | 2 | no | — |
| 103 | D4×D53 | — | 4 | 1 | no | — |
| 104 | #11719945 | — | 2 | 1 | no | — |
| 105 | #11719945 | — | 4 | 1 | no | — |
| 106 | #11719945 | — | 4 | 1 | no | — |
| 107 | #11719945 | — | 4 | 2 | no | — |
| 108 | C2×C4×D53 | — | 2 | 1 | no | — |
| 109 | C2×C4×D53 | — | 4 | 1 | no | — |
| 110 | C2×C4×D53 | — | 4 | 1 | no | — |
| 111 | C2×C4×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 112 | C2×Dic106 | — | 4 | 1 | no | — |
| 113 | C2×Dic106 | — | 4 | 1 | no | — |
| 114 | C2×Dic106 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 115 | C2×Dic106 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 116 | SD16×C53 | — | 4 | 1 | no | — |
| 117 | D8×C53 | — | 4 | 1 | no | — |
| 118 | M16×C53 | — | 2 | 1 | no | — |
| 119 | C2×C8×C53 | — | 4 | 1 | no | — |
| 120 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 121 | C42×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 122 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 123 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 124 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 125 | #11719925 | — | 4 | 1 | no | — |
| 126 | #11719923 | — | 4 | 1 | no | — |
| 127 | #11719923 | — | 4 | 1 | no | — |
| 128 | #11719922 | — | 4 | 1 | no | — |
| 129 | C4⋊Dic53 | — | 4 | 1 | no | — |
| 130 | #11719919 | — | 8 | 1 | no | — |
| 131 | C4×Dic53 | — | 2 | 1 | no | — |
| 132 | C4×Dic53 | — | 8 | 1 | no | — |
| 133 | C4×Dic53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 134 | #11719917 | — | 2 | 1 | no | — |
| 135 | C2×#88322 | — | 4 | 1 | no | — |
| 136 | Dic212 | — | 4 | 1 | no | — |
| 137 | #11719913 | — | 4 | 1 | no | — |
| 138 | #11719912 | — | 4 | 1 | no | — |
| 139 | #11719912 | — | 8 | 2 | no | — |
| 140 | C8×D53 | — | 4 | 1 | no | — |
| 141 | C23×C53 | — | 2 | 1 | no | — |
| 142 | C23×C53 | — | 2 | 1 | no | — |
| 143 | C23×C53 | — | 4 | 1 | no | — |
| 144 | C22×D53 | — | 4 | 1 | no | — |
| 145 | C22×D53 | — | 4 | 1 | no | — |
| 146 | C22×D53 | #99 | 1 | 1 | yes | characteristic |
| 147 | Q8×C53 | — | 2 | 1 | no | — |
| 148 | D4×C53 | — | 2 | 1 | no | — |
| 149 | D4×C53 | — | 4 | 1 | no | — |
| 150 | D4×C53 | — | 4 | 1 | no | — |
| 151 | D4×C53 | — | 4 | 2 | no | — |
| 152 | D4×C53 | — | 4 | 1 | no | — |
| 153 | D4×C53 | — | 8 | 1 | no | — |
| 154 | D4×C53 | — | 8 | 1 | no | — |
| 155 | C2×C4×C53 | — | 2 | 1 | no | — |
| 156 | C2×C4×C53 | — | 4 | 1 | no | — |
| 157 | C2×C4×C53 | — | 4 | 1 | no | — |
| 158 | C2×C4×C53 | — | 8 | 1 | no | — |
| 159 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 160 | C22⋊D53 | — | 4 | 1 | no | — |
| 161 | C22⋊D53 | — | 4 | 2 | no | — |
| 162 | C22⋊D53 | — | 4 | 2 | no | — |
| 163 | C22⋊D53 | — | 4 | 2 | no | — |
| 164 | C22⋊D53 | — | 4 | 1 | no | — |
| 165 | C22⋊D53 | — | 4 | 1 | no | — |
| 166 | C22⋊D53 | — | 8 | 1 | no | — |
| 167 | C2×Dic53 | — | 2 | 1 | no | — |
| 168 | C2×Dic53 | — | 2 | 1 | no | — |
| 169 | C2×Dic53 | — | 2 | 1 | no | — |
| 170 | C2×Dic53 | — | 4 | 2 | no | — |
| 171 | C2×Dic53 | — | 4 | 1 | no | — |
| 172 | C2×Dic53 | — | 4 | 1 | no | — |
| 173 | C2×Dic53 | — | 4 | 1 | no | — |
| 174 | C2×Dic53 | — | 4 | 1 | no | — |
| 175 | C2×Dic53 | — | 4 | 1 | no | — |
| 176 | C2×Dic53 | — | 4 | 1 | no | — |
| 177 | C2×Dic53 | — | 8 | 1 | no | — |
| 178 | C2×Dic53 | #99 | 1 | 1 | yes | characteristic |
| 179 | D212 | — | 2 | 1 | no | — |
| 180 | D212 | — | 4 | 1 | no | — |
| 181 | C4×D53 | — | 2 | 1 | no | — |
| 182 | C4×D53 | — | 2 | 1 | no | — |
| 183 | C4×D53 | — | 4 | 1 | no | — |
| 184 | C4×D53 | — | 4 | 1 | no | — |
| 185 | C4×D53 | — | 4 | 1 | no | — |
| 186 | C4×D53 | — | 4 | 1 | no | — |
| 187 | C4×D53 | — | 4 | 2 | no | — |
| 188 | C4×D53 | — | 4 | 1 | no | — |
| 189 | Dic106 | — | 2 | 1 | no | — |
| 190 | Dic106 | — | 4 | 2 | no | — |
| 191 | Dic106 | — | 4 | 1 | no | — |
| 192 | Dic106 | — | 4 | 1 | no | — |
| 193 | Dic106 | — | 4 | 1 | no | — |
| 194 | C8×C53 | — | 4 | 1 | no | — |
| 195 | C8×C53 | — | 8 | 1 | no | — |
| 196 | #88322 | — | 4 | 1 | no | — |
| 197 | #88322 | — | 8 | 1 | no | — |
| 198 | #13562 | — | 53 | 1 | no | maximal, Sylow |
| 199 | C22×C53 | — | 4 | 1 | no | — |
| 200 | C22×C53 | — | 4 | 1 | no | — |
| 201 | C22×C53 | — | 4 | 1 | no | — |
| 202 | C22×C53 | — | 8 | 1 | no | — |
| 203 | C22×C53 | — | 8 | 1 | no | — |
| 204 | C22×C53 | — | 16 | 1 | no | — |
| 205 | C22×C53 | C2×#99 | 1 | 1 | yes | characteristic |
| 206 | C2×D53 | — | 2 | 1 | no | — |
| 207 | C2×D53 | — | 4 | 1 | no | — |
| 208 | C2×D53 | — | 4 | 1 | no | — |
| 209 | C2×D53 | — | 16 | 1 | no | — |
| 210 | C2×D53 | — | 16 | 1 | no | — |
| 211 | C4×C53 | — | 2 | 1 | no | — |
| 212 | C4×C53 | — | 2 | 1 | no | — |
| 213 | C4×C53 | — | 2 | 1 | no | — |
| 214 | C4×C53 | — | 4 | 1 | no | — |
| 215 | C4×C53 | — | 16 | 1 | no | — |
| 216 | Dic53 | — | 4 | 1 | no | — |
| 217 | Dic53 | — | 4 | 1 | no | — |
| 218 | Dic53 | — | 4 | 1 | no | — |
| 219 | Dic53 | — | 4 | 1 | no | — |
| 220 | Dic53 | — | 16 | 1 | no | — |
| 221 | Dic53 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 222 | Dic53 | AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 223 | #3018 | — | 53 | 1 | no | — |
| 224 | #2126 | — | 53 | 1 | no | — |
| 225 | #1560 | — | 53 | 1 | no | — |
| 226 | #1402 | — | 53 | 1 | no | — |
| 227 | #1402 | — | 53 | 1 | no | — |
| 228 | #1402 | — | 53 | 1 | no | — |
| 229 | #1402 | D53 | 1 | 1 | yes | characteristic, complemented |
| 230 | C2×C53 | — | 2 | 1 | no | — |
| 231 | C2×C53 | — | 8 | 1 | no | — |
| 232 | C2×C53 | — | 8 | 1 | no | — |
| 233 | C2×C53 | — | 8 | 1 | no | — |
| 234 | C2×C53 | C2×AΣL(1,𝔽16) | 1 | 1 | yes | characteristic |
| 235 | D53 | — | 4 | 1 | no | — |
| 236 | D53 | — | 8 | 1 | no | — |
| 237 | #585 | — | 53 | 1 | no | — |
| 238 | #575 | — | 106 | 1 | no | — |
| 239 | #532 | — | 53 | 1 | no | — |
| 240 | #456 | — | 106 | 1 | no | — |
| 241 | #455 | — | 53 | 1 | no | — |
| 242 | #455 | — | 53 | 1 | no | — |
| 243 | #454 | — | 106 | 1 | no | — |
| 244 | #453 | — | 53 | 1 | no | — |
| 245 | #453 | C2×D53 | 1 | 1 | yes | characteristic |
| 246 | #423 | — | 106 | 1 | no | — |
| 247 | C2×#104 | — | 106 | 1 | no | — |
| 248 | #413 | — | 53 | 1 | no | — |
| 249 | #410 | — | 106 | 1 | no | — |
| 250 | #354 | — | 106 | 1 | no | — |
| 251 | #353 | — | 53 | 1 | no | — |
| 252 | #353 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 253 | #333 | — | 106 | 1 | no | — |
| 254 | #331 | — | 53 | 1 | no | — |
| 255 | #331 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 256 | C53 | #13562 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 257 | 2−1+4 | — | 106 | 1 | no | — |
| 258 | 2−1+4 | — | 212 | 1 | no | — |
| 259 | H(5,𝔽2) | — | 53 | 1 | no | — |
| 260 | H(5,𝔽2) | — | 212 | 1 | no | — |
| 261 | H(5,𝔽2) | — | 212 | 1 | no | — |
| 262 | H(5,𝔽2) | C4×D53 | 1 | 1 | yes | characteristic |
| 263 | C2×#41 | — | 53 | 1 | no | — |
| 264 | C2×#41 | — | 53 | 1 | no | — |
| 265 | C2×#41 | — | 106 | 1 | no | — |
| 266 | C2×#41 | — | 212 | 1 | no | — |
| 267 | C2×#41 | — | 212 | 1 | no | — |
| 268 | C2×#41 | — | 212 | 1 | no | — |
| 269 | #137 | — | 106 | 1 | no | — |
| 270 | #137 | — | 106 | 1 | no | — |
| 271 | #137 | — | 212 | 1 | no | — |
| 272 | AGL(1,ℤ/8) | — | 2 | 1 | no | — |
| 273 | AGL(1,ℤ/8) | — | 106 | 1 | no | — |
| 274 | AGL(1,ℤ/8) | — | 212 | 1 | no | — |
| 275 | #135 | — | 212 | 1 | no | — |
| 276 | #135 | — | 212 | 1 | no | — |
| 277 | C2×M16 | — | 106 | 1 | no | — |
| 278 | C2×M16 | — | 212 | 1 | no | — |
| 279 | C4⋊Q8 | — | 53 | 1 | no | — |
| 280 | #127 | C22×D53 | 1 | 1 | yes | characteristic |
| 281 | #124 | — | 53 | 1 | no | — |
| 282 | #124 | — | 53 | 1 | no | — |
| 283 | #121 | — | 212 | 1 | no | — |
| 284 | C4×D4 | — | 212 | 1 | no | — |
| 285 | #117 | — | 212 | 1 | no | — |
| 286 | C2×C42 | — | 53 | 1 | no | — |
| 287 | C4⋊C8 | — | 2 | 1 | no | — |
| 288 | C4⋊C8 | — | 106 | 1 | no | — |
| 289 | C4⋊C8 | — | 212 | 1 | no | — |
| 290 | #104 | — | 2 | 1 | no | — |
| 291 | #104 | — | 106 | 1 | no | — |
| 292 | #104 | — | 106 | 1 | no | — |
| 293 | #104 | — | 106 | 1 | no | — |
| 294 | #101 | — | 106 | 1 | no | — |
| 295 | #100 | — | 53 | 1 | no | — |
| 296 | #100 | C4×D53 | 1 | 1 | yes | characteristic |
| 297 | #99 | — | 2 | 1 | no | — |
| 298 | #99 | — | 106 | 1 | no | — |
| 299 | #99 | — | 212 | 1 | no | — |
| 300 | #41 | — | 2 | 1 | no | — |
| 301 | #41 | — | 4 | 1 | no | — |
| 302 | #41 | — | 106 | 1 | no | — |
| 303 | #41 | — | 106 | 1 | no | — |
| 304 | #41 | — | 106 | 1 | no | — |
| 305 | #41 | — | 212 | 1 | no | — |
| 306 | #41 | — | 212 | 1 | no | — |
| 307 | #41 | — | 212 | 2 | no | — |
| 308 | #41 | — | 212 | 1 | no | — |
| 309 | #41 | — | 212 | 2 | no | — |
| 310 | #41 | — | 212 | 1 | no | — |
| 311 | #41 | — | 212 | 1 | no | — |
| 312 | #41 | — | 212 | 1 | no | — |
| 313 | #41 | — | 212 | 1 | no | — |
| 314 | #41 | — | 212 | 1 | no | — |
| 315 | #41 | — | 212 | 2 | no | — |
| 316 | #41 | — | 212 | 2 | no | — |
| 317 | #41 | — | 212 | 2 | no | — |
| 318 | #41 | — | 212 | 1 | no | — |
| 319 | C2×Q8 | — | 53 | 1 | no | — |
| 320 | C2×Q8 | — | 53 | 1 | no | — |
| 321 | C2×Q8 | — | 106 | 1 | no | — |
| 322 | C2×Q8 | — | 212 | 1 | no | — |
| 323 | C2×Q8 | — | 212 | 1 | no | — |
| 324 | C2×Q8 | — | 212 | 1 | no | — |
| 325 | C2×D4 | — | 4 | 1 | no | — |
| 326 | C2×D4 | — | 4 | 1 | no | — |
| 327 | C2×D4 | — | 4 | 1 | no | — |
| 328 | C2×D4 | — | 106 | 1 | no | — |
| 329 | C2×D4 | — | 106 | 1 | no | — |
| 330 | C2×D4 | — | 106 | 1 | no | — |
| 331 | C2×D4 | — | 212 | 1 | no | — |
| 332 | C2×D4 | — | 212 | 1 | no | — |
| 333 | C2×D4 | — | 212 | 2 | no | — |
| 334 | C2×D4 | — | 212 | 2 | no | — |
| 335 | C2×D4 | — | 212 | 1 | no | — |
| 336 | C2×D4 | — | 212 | 1 | no | — |
| 337 | C2×D4 | C2×C4×D53 | 1 | 1 | yes | characteristic |
| 338 | C2×D4 | D4×D53 | 1 | 1 | yes | characteristic |
| 339 | C22×C4 | — | 53 | 1 | no | — |
| 340 | C22×C4 | — | 106 | 1 | no | — |
| 341 | C22×C4 | — | 106 | 1 | no | — |
| 342 | C22×C4 | — | 106 | 1 | no | — |
| 343 | C22×C4 | — | 212 | 1 | no | — |
| 344 | C22×C4 | — | 212 | 1 | no | — |
| 345 | C22×C4 | — | 212 | 1 | no | — |
| 346 | Q16 | — | 212 | 1 | no | — |
| 347 | Q16 | — | 212 | 1 | no | — |
| 348 | SD16 | — | 4 | 1 | no | — |
| 349 | SD16 | — | 212 | 1 | no | — |
| 350 | SD16 | — | 212 | 1 | no | — |
| 351 | SD16 | — | 212 | 1 | no | — |
| 352 | D8 | — | 4 | 1 | no | — |
| 353 | D8 | — | 212 | 1 | no | — |
| 354 | M16 | — | 2 | 1 | no | — |
| 355 | M16 | — | 106 | 1 | no | — |
| 356 | M16 | — | 424 | 2 | no | — |
| 357 | M16 | — | 212 | 1 | no | — |
| 358 | C2×C8 | — | 4 | 1 | no | — |
| 359 | C2×C8 | — | 212 | 1 | no | — |
| 360 | C2×C8 | — | 212 | 1 | no | — |
| 361 | C4⋊C4 | — | 424 | 1 | no | — |
| 362 | C4⋊C4 | — | 212 | 1 | no | — |
| 363 | C22⋊C4 | — | 4 | 1 | no | — |
| 364 | C22⋊C4 | — | 212 | 1 | no | — |
| 365 | C22⋊C4 | — | 212 | 1 | no | — |
| 366 | C22⋊C4 | — | 212 | 1 | no | — |
| 367 | C42 | — | 53 | 1 | no | — |
| 368 | C42 | — | 106 | 1 | no | — |
| 369 | C42 | — | 424 | 1 | no | — |
| 370 | C42 | D4×D53 | 1 | 1 | yes | characteristic |
| 371 | C23 | — | 2 | 1 | no | — |
| 372 | C23 | — | 2 | 1 | no | — |
| 373 | C23 | — | 4 | 1 | no | — |
| 374 | C23 | — | 53 | 1 | no | — |
| 375 | C23 | — | 212 | 1 | no | — |
| 376 | C23 | — | 212 | 1 | no | — |
| 377 | Q8 | — | 2 | 1 | no | — |
| 378 | Q8 | — | 106 | 1 | no | — |
| 379 | Q8 | — | 212 | 1 | no | — |
| 380 | Q8 | — | 212 | 1 | no | — |
| 381 | Q8 | — | 212 | 1 | no | — |
| 382 | Q8 | — | 212 | 2 | no | — |
| 383 | D4 | — | 2 | 1 | no | — |
| 384 | D4 | — | 4 | 1 | no | — |
| 385 | D4 | — | 4 | 1 | no | — |
| 386 | D4 | — | 4 | 2 | no | — |
| 387 | D4 | — | 4 | 1 | no | — |
| 388 | D4 | — | 8 | 1 | no | — |
| 389 | D4 | — | 8 | 1 | no | — |
| 390 | D4 | — | 106 | 1 | no | — |
| 391 | D4 | — | 424 | 1 | no | — |
| 392 | D4 | — | 212 | 1 | no | — |
| 393 | D4 | — | 212 | 1 | no | — |
| 394 | D4 | — | 212 | 2 | no | — |
| 395 | D4 | — | 212 | 1 | no | — |
| 396 | D4 | — | 212 | 2 | no | — |
| 397 | D4 | — | 212 | 2 | no | — |
| 398 | D4 | — | 212 | 1 | no | — |
| 399 | C2×C4 | — | 2 | 1 | no | — |
| 400 | C2×C4 | — | 4 | 1 | no | — |
| 401 | C2×C4 | — | 4 | 1 | no | — |
| 402 | C2×C4 | — | 8 | 1 | no | — |
| 403 | C2×C4 | — | 53 | 1 | no | — |
| 404 | C2×C4 | — | 106 | 1 | no | — |
| 405 | C2×C4 | — | 106 | 1 | no | — |
| 406 | C2×C4 | — | 106 | 1 | no | — |
| 407 | C2×C4 | — | 106 | 1 | no | — |
| 408 | C2×C4 | — | 106 | 1 | no | — |
| 409 | C2×C4 | — | 424 | 1 | no | — |
| 410 | C2×C4 | — | 212 | 1 | no | — |
| 411 | C2×C4 | — | 212 | 1 | no | — |
| 412 | C2×C4 | — | 212 | 1 | no | — |
| 413 | C2×C4 | — | 212 | 1 | no | — |
| 414 | C2×C4 | — | 212 | 1 | no | — |
| 415 | C2×C4 | — | 212 | 2 | no | — |
| 416 | C2×C4 | — | 212 | 1 | no | — |
| 417 | C2×C4 | — | 212 | 1 | no | — |
| 418 | C2×C4 | — | 212 | 1 | no | — |
| 419 | C2×C4 | — | 212 | 1 | no | — |
| 420 | C2×C4 | — | 212 | 1 | no | — |
| 421 | C2×C4 | — | 212 | 2 | no | — |
| 422 | C2×C4 | — | 212 | 1 | no | — |
| 423 | C2×C4 | C22⋊C4×D53 | 1 | 1 | yes | characteristic |
| 424 | C8 | — | 4 | 1 | no | — |
| 425 | C8 | — | 8 | 1 | no | — |
| 426 | C8 | — | 424 | 1 | no | — |
| 427 | C8 | — | 212 | 1 | no | — |
| 428 | C22 | — | 4 | 1 | no | — |
| 429 | C22 | — | 4 | 1 | no | — |
| 430 | C22 | — | 4 | 1 | no | — |
| 431 | C22 | — | 8 | 1 | no | — |
| 432 | C22 | — | 8 | 1 | no | — |
| 433 | C22 | — | 16 | 1 | no | — |
| 434 | C22 | — | 848 | 1 | no | — |
| 435 | C22 | — | 848 | 1 | no | — |
| 436 | C22 | — | 106 | 1 | no | — |
| 437 | C22 | — | 212 | 1 | no | — |
| 438 | C22 | — | 212 | 1 | no | — |
| 439 | C22 | #99×D53 | 1 | 1 | yes | characteristic |
| 440 | C4 | — | 2 | 1 | no | — |
| 441 | C4 | — | 2 | 1 | no | — |
| 442 | C4 | — | 2 | 1 | no | — |
| 443 | C4 | — | 4 | 1 | no | — |
| 444 | C4 | — | 16 | 1 | no | — |
| 445 | C4 | — | 53 | 1 | no | — |
| 446 | C4 | — | 53 | 1 | no | — |
| 447 | C4 | — | 848 | 1 | no | — |
| 448 | C4 | — | 212 | 1 | no | — |
| 449 | C4 | — | 212 | 1 | no | — |
| 450 | C4 | — | 212 | 1 | no | — |
| 451 | C4 | — | 212 | 1 | no | — |
| 452 | C2 | — | 2 | 1 | no | — |
| 453 | C2 | — | 8 | 1 | no | — |
| 454 | C2 | — | 8 | 1 | no | — |
| 455 | C2 | — | 8 | 1 | no | — |
| 456 | C2 | — | 424 | 1 | no | — |
| 457 | C2 | — | 212 | 1 | no | — |
| 458 | C2 | AΣL(1,𝔽16)×D53 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20276377 | C2 | semidirect |
| 3. #20273447 | C2 | semidirect |
| 4. #20272861 | C2 | semidirect |
| 5. #20272860 | C2 | semidirect |
| 6. #20272859 | C2 | semidirect |
| 7. C53×#1402 | C2 | semidirect |
| 8. #16811458 | C4 | semidirect |
| 12. #16810803 | C4 | semidirect |
| 13. #16810801 | C4 | semidirect |
| 18. #16810604 | C4 | semidirect |
| 21. #16810416 | C22 | semidirect |
| 23. #16810367 | C22 | semidirect |
| 25. C53×#353 | C22 | semidirect |
| 26. C53×#331 | C22 | semidirect |
| 229. #1402 | D53 | semidirect |
| 252. #353 | C2×D53 | semidirect |
| 255. #331 | C2×D53 | semidirect |
| 256. C53 | #13562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284060 | 2 |
| #20276377 | 2 |
| #20273447 | 2 |
| #20272861 | 2 |
| #20272860 | 2 |
| #20272859 | 2 |
| C53×#1402 | 2 |
| #13562 | 53 |