Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
830 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 830 conjugacy classes of subgroups — too many to draw. Only its 149 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 | #564×D53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #501×D53 | C2 | 1 | 2 | yes | maximal |
| 3 | #491×D53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | #20274045 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #20274044 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20274043 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #20274042 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | #20274041 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #330×D53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #330×D53 | C2 | 1 | 2 | yes | maximal |
| 11 | C53×#1663 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C53⋊#564 | — | 2 | 2 | no | — |
| 13 | C53⋊#564 | — | 2 | 2 | no | — |
| 14 | C53⋊#564 | — | 2 | 2 | no | — |
| 15 | C53⋊#564 | C22 | 1 | 1 | yes | characteristic |
| 16 | C53⋊#564 | C22 | 1 | 2 | yes | — |
| 17 | C4⋊Q8×D53 | C22 | 1 | 1 | yes | characteristic |
| 18 | #125×D53 | — | 2 | 2 | no | — |
| 19 | #125×D53 | — | 2 | 2 | no | — |
| 20 | #125×D53 | — | 2 | 2 | no | — |
| 21 | #125×D53 | C22 | 1 | 2 | yes | — |
| 22 | #125×D53 | C22 | 1 | 1 | yes | characteristic |
| 23 | #16811033 | C22 | 1 | 2 | yes | — |
| 24 | #16811032 | C22 | 1 | 2 | yes | — |
| 25 | #16811031 | — | 2 | 2 | no | — |
| 26 | #16811030 | — | 2 | 2 | no | — |
| 27 | #16811029 | C22 | 1 | 2 | yes | — |
| 28 | #16810993 | C22 | 1 | 1 | yes | characteristic |
| 29 | #16810992 | C22 | 1 | 1 | yes | characteristic |
| 30 | #16810991 | C22 | 1 | 1 | yes | characteristic |
| 31 | #16810990 | — | 2 | 2 | no | — |
| 32 | #107×D53 | — | 2 | 2 | no | — |
| 33 | #106×D53 | — | 2 | 2 | no | — |
| 34 | #103×D53 | — | 2 | 2 | no | — |
| 35 | #97×D53 | C22 | 1 | 2 | yes | — |
| 36 | #97×D53 | C22 | 1 | 1 | yes | characteristic |
| 37 | #16810365 | C22 | 1 | 1 | yes | characteristic |
| 38 | #16810365 | C22 | 1 | 2 | yes | — |
| 39 | #16810364 | C22 | 1 | 2 | yes | — |
| 40 | #16810364 | C22 | 1 | 2 | yes | — |
| 41 | #16810364 | C22 | 1 | 2 | yes | — |
| 42 | C53×#564 | C22 | 1 | 1 | yes | characteristic |
| 43 | C53×#501 | C22 | 1 | 2 | yes | — |
| 44 | C53×#491 | C22 | 1 | 1 | yes | characteristic |
| 45 | C53×#330 | C22 | 1 | 1 | yes | characteristic |
| 46 | C53×#330 | C22 | 1 | 2 | yes | — |
| 47 | C2×Q8×D53 | — | 2 | 1 | no | — |
| 48 | C2×C8×D53 | — | 2 | 2 | no | — |
| 49 | C2×C8×D53 | — | 2 | 1 | no | — |
| 50 | #13133217 | C23 | 1 | 1 | yes | characteristic |
| 51 | #13133216 | — | 2 | 2 | no | — |
| 52 | #13133215 | — | 2 | 1 | no | — |
| 53 | #13133209 | — | 2 | 2 | no | — |
| 54 | #13133209 | — | 2 | 2 | no | — |
| 55 | #13133209 | — | 2 | 2 | no | — |
| 56 | #13133209 | C23 | 1 | 2 | yes | — |
| 57 | #13133209 | C23 | 1 | 1 | yes | characteristic |
| 58 | #13133208 | — | 2 | 2 | no | — |
| 59 | #13133208 | — | 2 | 2 | no | — |
| 60 | #13133208 | — | 2 | 2 | no | — |
| 61 | #13133208 | — | 2 | 2 | no | — |
| 62 | #13133208 | — | 2 | 2 | no | — |
| 63 | #13133208 | — | 2 | 2 | no | — |
| 64 | #13133208 | D4 | 1 | 2 | yes | — |
| 65 | #13133208 | D4 | 1 | 2 | yes | — |
| 66 | #13133208 | D4 | 1 | 2 | yes | — |
| 67 | #13133207 | — | 2 | 2 | no | — |
| 68 | #13133207 | — | 2 | 2 | no | — |
| 69 | #13133207 | — | 2 | 2 | no | — |
| 70 | #13133207 | — | 2 | 2 | no | — |
| 71 | #13133207 | — | 2 | 2 | no | — |
| 72 | #13133207 | — | 2 | 2 | no | — |
| 73 | #13133207 | — | 2 | 2 | no | — |
| 74 | #13133207 | — | 2 | 2 | no | — |
| 75 | #13133207 | — | 2 | 2 | no | — |
| 76 | #13133207 | — | 2 | 2 | no | — |
| 77 | #13133207 | — | 2 | 2 | no | — |
| 78 | #13133207 | — | 2 | 2 | no | — |
| 79 | #13133207 | — | 2 | 2 | no | — |
| 80 | #13133207 | — | 2 | 2 | no | — |
| 81 | #13133207 | — | 2 | 2 | no | — |
| 82 | C4⋊C4×D53 | — | 2 | 2 | no | — |
| 83 | C4⋊C4×D53 | — | 2 | 2 | no | — |
| 84 | C4⋊C4×D53 | — | 2 | 2 | no | — |
| 85 | C4⋊C4×D53 | — | 2 | 2 | no | — |
| 86 | C4⋊C4×D53 | — | 2 | 2 | no | — |
| 87 | C4⋊C4×D53 | — | 2 | 2 | no | — |
| 88 | C4⋊C4×D53 | — | 2 | 2 | no | — |
| 89 | C4⋊C4×D53 | D4 | 1 | 2 | yes | — |
| 90 | C4⋊C4×D53 | D4 | 1 | 2 | yes | — |
| 91 | C4⋊C4×D53 | D4 | 1 | 2 | yes | — |
| 92 | C42×D53 | — | 2 | 2 | no | — |
| 93 | C42×D53 | C23 | 1 | 1 | yes | characteristic |
| 94 | #13133151 | — | 2 | 2 | no | — |
| 95 | #13133150 | — | 2 | 2 | no | — |
| 96 | #13133150 | — | 2 | 2 | no | — |
| 97 | #13133149 | — | 2 | 2 | no | — |
| 98 | #13133148 | — | 2 | 2 | no | — |
| 99 | #13133148 | — | 2 | 2 | no | — |
| 100 | #13133142 | — | 2 | 2 | no | — |
| 101 | #13133141 | — | 2 | 2 | no | — |
| 102 | #13133140 | — | 2 | 2 | no | — |
| 103 | #13133128 | C23 | 1 | 2 | yes | — |
| 104 | #13133128 | C23 | 1 | 1 | yes | characteristic |
| 105 | #13133127 | — | 2 | 2 | no | — |
| 106 | #13133127 | — | 2 | 1 | no | — |
| 107 | C4⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 108 | #125×C53 | — | 2 | 2 | no | — |
| 109 | #125×C53 | — | 2 | 2 | no | — |
| 110 | #125×C53 | — | 2 | 2 | no | — |
| 111 | #125×C53 | C23 | 1 | 1 | yes | characteristic |
| 112 | #125×C53 | C23 | 1 | 2 | yes | — |
| 113 | #107×C53 | — | 2 | 2 | no | — |
| 114 | #106×C53 | — | 2 | 2 | no | — |
| 115 | #103×C53 | — | 2 | 2 | no | — |
| 116 | #97×C53 | C23 | 1 | 1 | yes | characteristic |
| 117 | #97×C53 | C23 | 1 | 2 | yes | — |
| 118 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 119 | Q8×D53 | — | 4 | 4 | no | — |
| 120 | C2×C4×D53 | — | 2 | 2 | no | — |
| 121 | C2×C4×D53 | — | 2 | 2 | no | — |
| 122 | C2×C4×D53 | — | 2 | 2 | no | — |
| 123 | C2×C4×D53 | — | 4 | 1 | no | — |
| 124 | C2×C4×D53 | C2×D4 | 1 | 2 | yes | — |
| 125 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 126 | C2×Dic106 | — | 2 | 1 | no | — |
| 127 | C2×Dic106 | — | 4 | 1 | no | — |
| 128 | C2×C8×C53 | — | 2 | 2 | no | — |
| 129 | C2×C8×C53 | — | 2 | 1 | no | — |
| 130 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 131 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 132 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 133 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 134 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 135 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 136 | C4⋊C4×C53 | — | 2 | 2 | no | — |
| 137 | C4⋊C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 138 | C4⋊C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 139 | C4⋊C4×C53 | C2×D4 | 1 | 2 | yes | — |
| 140 | C42×C53 | — | 2 | 2 | no | — |
| 141 | C42×C53 | C24 | 1 | 1 | yes | characteristic |
| 142 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 143 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 144 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 145 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 146 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 147 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 148 | C4⋊Dic53 | — | 2 | 2 | no | — |
| 149 | C4⋊Dic53 | C2×D4 | 1 | 2 | yes | — |
| 150 | C4⋊Dic53 | C2×D4 | 1 | 2 | yes | — |
| 151 | C4⋊Dic53 | C2×D4 | 1 | 2 | yes | — |
| 152 | #11719919 | — | 2 | 2 | no | — |
| 153 | #11719919 | — | 2 | 2 | no | — |
| 154 | #11719919 | — | 2 | 2 | no | — |
| 155 | #11719919 | — | 2 | 2 | no | — |
| 156 | #11719919 | — | 2 | 2 | no | — |
| 157 | #11719919 | — | 2 | 2 | no | — |
| 158 | #11719919 | — | 2 | 2 | no | — |
| 159 | #11719919 | — | 2 | 2 | no | — |
| 160 | #11719919 | — | 2 | 2 | no | — |
| 161 | #11719919 | — | 2 | 2 | no | — |
| 162 | #11719919 | — | 2 | 2 | no | — |
| 163 | #11719919 | — | 2 | 2 | no | — |
| 164 | #11719919 | — | 2 | 2 | no | — |
| 165 | #11719919 | — | 2 | 2 | no | — |
| 166 | #11719919 | — | 2 | 2 | no | — |
| 167 | #11719919 | — | 4 | 2 | no | — |
| 168 | C4×Dic53 | — | 2 | 2 | no | — |
| 169 | C4×Dic53 | — | 2 | 2 | no | — |
| 170 | C4×Dic53 | — | 2 | 2 | no | — |
| 171 | C4×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | C4×Dic53 | C2×D4 | 1 | 2 | yes | — |
| 173 | C2×#88322 | — | 2 | 2 | no | — |
| 174 | C2×#88322 | — | 2 | 1 | no | — |
| 175 | C8×D53 | — | 2 | 8 | no | — |
| 176 | C8×D53 | — | 4 | 2 | no | — |
| 177 | C22×D53 | #120 | 1 | 1 | yes | characteristic |
| 178 | Q8×C53 | — | 4 | 2 | no | — |
| 179 | C2×C4×C53 | — | 2 | 2 | no | — |
| 180 | C2×C4×C53 | — | 2 | 2 | no | — |
| 181 | C2×C4×C53 | — | 2 | 2 | no | — |
| 182 | C2×C4×C53 | — | 4 | 1 | no | — |
| 183 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 184 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 185 | C2×Dic53 | — | 2 | 2 | no | — |
| 186 | C2×Dic53 | — | 2 | 2 | no | — |
| 187 | C2×Dic53 | — | 2 | 2 | no | — |
| 188 | C2×Dic53 | — | 4 | 1 | no | — |
| 189 | C2×Dic53 | #120 | 1 | 1 | yes | characteristic |
| 190 | C2×Dic53 | #120 | 1 | 2 | yes | — |
| 191 | C4×D53 | — | 2 | 2 | no | — |
| 192 | C4×D53 | — | 2 | 4 | no | — |
| 193 | C4×D53 | — | 4 | 4 | no | — |
| 194 | C4×D53 | — | 4 | 4 | no | — |
| 195 | C4×D53 | — | 4 | 4 | no | — |
| 196 | C4×D53 | — | 8 | 2 | no | — |
| 197 | Dic106 | — | 4 | 2 | no | — |
| 198 | Dic106 | — | 8 | 2 | no | — |
| 199 | C8×C53 | — | 2 | 4 | no | — |
| 200 | C8×C53 | — | 4 | 1 | no | — |
| 201 | #88322 | — | 2 | 4 | no | — |
| 202 | #88322 | — | 4 | 1 | no | — |
| 203 | C2×#1663 | — | 53 | 1 | no | maximal, Sylow |
| 204 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 205 | C2×D53 | #454 | 1 | 2 | yes | — |
| 206 | C2×D53 | #456 | 1 | 4 | yes | — |
| 207 | C4×C53 | — | 2 | 1 | no | — |
| 208 | C4×C53 | — | 2 | 2 | no | — |
| 209 | C4×C53 | — | 4 | 2 | no | — |
| 210 | C4×C53 | — | 4 | 2 | no | — |
| 211 | C4×C53 | — | 4 | 2 | no | — |
| 212 | C4×C53 | — | 8 | 1 | no | — |
| 213 | Dic53 | — | 2 | 1 | no | — |
| 214 | Dic53 | — | 2 | 2 | no | — |
| 215 | Dic53 | — | 4 | 2 | no | — |
| 216 | Dic53 | — | 4 | 2 | no | — |
| 217 | Dic53 | — | 4 | 2 | no | — |
| 218 | Dic53 | — | 8 | 1 | no | — |
| 219 | C2×#564 | — | 53 | 1 | no | — |
| 220 | C2×#501 | — | 53 | 2 | no | — |
| 221 | C2×#491 | — | 53 | 1 | no | — |
| 222 | #1663 | — | 53 | 2 | no | — |
| 223 | #1663 | — | 53 | 1 | no | — |
| 224 | #1663 | — | 53 | 1 | no | — |
| 225 | #1663 | — | 53 | 2 | no | — |
| 226 | #1663 | — | 53 | 1 | no | — |
| 227 | #1663 | D53 | 1 | 1 | yes | characteristic, direct product factor |
| 228 | C2×#330 | — | 53 | 1 | no | — |
| 229 | C2×#330 | — | 53 | 2 | no | — |
| 230 | C2×C53 | C2×#454 | 1 | 1 | yes | characteristic |
| 231 | C2×C53 | C2×#456 | 1 | 2 | yes | — |
| 232 | D53 | #1663 | 1 | 4 | yes | direct product factor |
| 233 | #564 | — | 53 | 2 | no | — |
| 234 | #564 | — | 53 | 1 | no | — |
| 235 | #564 | — | 106 | 2 | no | — |
| 236 | #564 | — | 106 | 2 | no | — |
| 237 | #564 | — | 106 | 2 | no | — |
| 238 | #564 | C2×D53 | 1 | 1 | yes | characteristic |
| 239 | C2×C4⋊Q8 | — | 53 | 1 | no | — |
| 240 | C2×#125 | — | 53 | 1 | no | — |
| 241 | C2×#125 | — | 53 | 2 | no | — |
| 242 | C2×#125 | — | 106 | 2 | no | — |
| 243 | C2×#125 | — | 106 | 2 | no | — |
| 244 | C2×#125 | — | 106 | 2 | no | — |
| 245 | #501 | — | 53 | 2 | no | — |
| 246 | #501 | — | 53 | 2 | no | — |
| 247 | #501 | — | 53 | 2 | no | — |
| 248 | #501 | — | 106 | 2 | no | — |
| 249 | #501 | — | 106 | 2 | no | — |
| 250 | #501 | C2×D53 | 1 | 2 | yes | — |
| 251 | #491 | — | 53 | 1 | no | — |
| 252 | #491 | — | 53 | 1 | no | — |
| 253 | #491 | — | 53 | 1 | no | — |
| 254 | #491 | — | 106 | 2 | no | — |
| 255 | #491 | C2×D53 | 1 | 1 | yes | characteristic |
| 256 | C2×#107 | — | 106 | 2 | no | — |
| 257 | C2×#106 | — | 106 | 2 | no | — |
| 258 | C2×#103 | — | 106 | 2 | no | — |
| 259 | C2×#97 | — | 53 | 1 | no | — |
| 260 | C2×#97 | — | 53 | 2 | no | — |
| 261 | #330 | — | 53 | 2 | no | — |
| 262 | #330 | — | 53 | 1 | no | — |
| 263 | #330 | — | 53 | 2 | no | — |
| 264 | #330 | — | 53 | 2 | no | — |
| 265 | #330 | — | 53 | 2 | no | — |
| 266 | #330 | C2×D53 | 1 | 2 | yes | — |
| 267 | #330 | C2×D53 | 1 | 1 | yes | characteristic |
| 268 | C53 | C2×#1663 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 269 | C22×Q8 | — | 106 | 1 | no | — |
| 270 | C22×C8 | — | 106 | 2 | no | — |
| 271 | C22×C8 | — | 106 | 1 | no | — |
| 272 | C4⋊Q8 | — | 53 | 1 | no | — |
| 273 | C4⋊Q8 | — | 106 | 2 | no | — |
| 274 | C4⋊Q8 | — | 106 | 1 | no | — |
| 275 | C4⋊Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 276 | #125 | — | 2 | 2 | no | — |
| 277 | #125 | — | 2 | 2 | no | — |
| 278 | #125 | — | 2 | 2 | no | — |
| 279 | #125 | — | 53 | 2 | no | — |
| 280 | #125 | — | 53 | 2 | no | — |
| 281 | #125 | — | 53 | 2 | no | — |
| 282 | #125 | — | 53 | 1 | no | — |
| 283 | #125 | — | 53 | 2 | no | — |
| 284 | #125 | — | 106 | 2 | no | — |
| 285 | #125 | — | 106 | 2 | no | — |
| 286 | #125 | — | 106 | 2 | no | — |
| 287 | #125 | — | 106 | 2 | no | — |
| 288 | #125 | — | 106 | 2 | no | — |
| 289 | #125 | — | 106 | 2 | no | — |
| 290 | #125 | — | 106 | 2 | no | — |
| 291 | #125 | — | 106 | 2 | no | — |
| 292 | #125 | — | 106 | 2 | no | — |
| 293 | #125 | — | 106 | 2 | no | — |
| 294 | #125 | — | 106 | 2 | no | — |
| 295 | #125 | — | 106 | 2 | no | — |
| 296 | #125 | — | 106 | 2 | no | — |
| 297 | #125 | — | 106 | 2 | no | — |
| 298 | #125 | — | 106 | 2 | no | — |
| 299 | #125 | — | 106 | 2 | no | — |
| 300 | #125 | — | 106 | 2 | no | — |
| 301 | #125 | — | 106 | 2 | no | — |
| 302 | #125 | — | 106 | 2 | no | — |
| 303 | #125 | — | 106 | 2 | no | — |
| 304 | #125 | — | 106 | 2 | no | — |
| 305 | #125 | — | 106 | 2 | no | — |
| 306 | #125 | — | 106 | 2 | no | — |
| 307 | #125 | — | 106 | 2 | no | — |
| 308 | #125 | C22×D53 | 1 | 1 | yes | characteristic |
| 309 | #125 | C22×D53 | 1 | 2 | yes | — |
| 310 | C2×C4⋊C4 | — | 53 | 2 | no | — |
| 311 | C2×C4⋊C4 | — | 53 | 2 | no | — |
| 312 | C2×C4⋊C4 | — | 53 | 2 | no | — |
| 313 | C2×C4⋊C4 | — | 106 | 2 | no | — |
| 314 | C2×C4⋊C4 | — | 106 | 2 | no | — |
| 315 | C2×C4⋊C4 | — | 106 | 2 | no | — |
| 316 | C2×C4⋊C4 | — | 106 | 2 | no | — |
| 317 | C2×C4⋊C4 | — | 106 | 2 | no | — |
| 318 | C2×C4⋊C4 | — | 106 | 2 | no | — |
| 319 | C2×C4⋊C4 | — | 106 | 2 | no | — |
| 320 | C2×C42 | — | 53 | 1 | no | — |
| 321 | C2×C42 | — | 106 | 2 | no | — |
| 322 | #107 | — | 2 | 2 | no | — |
| 323 | #107 | — | 106 | 2 | no | — |
| 324 | #107 | — | 106 | 2 | no | — |
| 325 | #107 | — | 106 | 2 | no | — |
| 326 | #106 | — | 2 | 2 | no | — |
| 327 | #106 | — | 106 | 2 | no | — |
| 328 | #106 | — | 106 | 2 | no | — |
| 329 | #106 | — | 106 | 2 | no | — |
| 330 | #103 | — | 2 | 2 | no | — |
| 331 | #103 | — | 106 | 2 | no | — |
| 332 | #103 | — | 106 | 2 | no | — |
| 333 | #103 | — | 106 | 2 | no | — |
| 334 | #97 | — | 53 | 1 | no | — |
| 335 | #97 | — | 53 | 2 | no | — |
| 336 | #97 | — | 106 | 1 | no | — |
| 337 | #97 | — | 106 | 2 | no | — |
| 338 | #97 | C22×D53 | 1 | 1 | yes | characteristic |
| 339 | #97 | C22×D53 | 1 | 2 | yes | — |
| 340 | C2×Q8 | — | 2 | 1 | no | — |
| 341 | C2×Q8 | — | 106 | 1 | no | — |
| 342 | C2×Q8 | — | 212 | 1 | no | — |
| 343 | C2×Q8 | — | 212 | 4 | no | — |
| 344 | C22×C4 | — | 53 | 2 | no | — |
| 345 | C22×C4 | — | 53 | 1 | no | — |
| 346 | C22×C4 | — | 106 | 2 | no | — |
| 347 | C22×C4 | — | 106 | 2 | no | — |
| 348 | C22×C4 | — | 106 | 2 | no | — |
| 349 | C22×C4 | — | 212 | 1 | no | — |
| 350 | C2×C8 | — | 2 | 2 | no | — |
| 351 | C2×C8 | — | 2 | 1 | no | — |
| 352 | C2×C8 | — | 106 | 8 | no | — |
| 353 | C2×C8 | — | 106 | 2 | no | — |
| 354 | C2×C8 | — | 106 | 1 | no | — |
| 355 | C2×C8 | — | 212 | 2 | no | — |
| 356 | C4⋊C4 | — | 2 | 2 | no | — |
| 357 | C4⋊C4 | — | 2 | 2 | no | — |
| 358 | C4⋊C4 | — | 2 | 2 | no | — |
| 359 | C4⋊C4 | — | 2 | 2 | no | — |
| 360 | C4⋊C4 | — | 2 | 2 | no | — |
| 361 | C4⋊C4 | — | 2 | 2 | no | — |
| 362 | C4⋊C4 | — | 2 | 2 | no | — |
| 363 | C4⋊C4 | — | 53 | 2 | no | — |
| 364 | C4⋊C4 | — | 53 | 2 | no | — |
| 365 | C4⋊C4 | — | 53 | 2 | no | — |
| 366 | C4⋊C4 | — | 106 | 2 | no | — |
| 367 | C4⋊C4 | — | 106 | 2 | no | — |
| 368 | C4⋊C4 | — | 106 | 2 | no | — |
| 369 | C4⋊C4 | — | 106 | 2 | no | — |
| 370 | C4⋊C4 | — | 106 | 2 | no | — |
| 371 | C4⋊C4 | — | 106 | 2 | no | — |
| 372 | C4⋊C4 | — | 106 | 2 | no | — |
| 373 | C4⋊C4 | — | 106 | 2 | no | — |
| 374 | C4⋊C4 | — | 106 | 2 | no | — |
| 375 | C4⋊C4 | — | 106 | 2 | no | — |
| 376 | C4⋊C4 | — | 106 | 2 | no | — |
| 377 | C4⋊C4 | — | 106 | 2 | no | — |
| 378 | C4⋊C4 | — | 106 | 2 | no | — |
| 379 | C4⋊C4 | — | 106 | 2 | no | — |
| 380 | C4⋊C4 | — | 106 | 2 | no | — |
| 381 | C4⋊C4 | — | 106 | 2 | no | — |
| 382 | C4⋊C4 | — | 106 | 2 | no | — |
| 383 | C4⋊C4 | — | 106 | 2 | no | — |
| 384 | C4⋊C4 | — | 106 | 2 | no | — |
| 385 | C4⋊C4 | — | 106 | 2 | no | — |
| 386 | C4⋊C4 | — | 106 | 2 | no | — |
| 387 | C4⋊C4 | — | 106 | 2 | no | — |
| 388 | C4⋊C4 | — | 212 | 2 | no | — |
| 389 | C4⋊C4 | D4×D53 | 1 | 2 | yes | — |
| 390 | C4⋊C4 | D4×D53 | 1 | 2 | yes | — |
| 391 | C4⋊C4 | D4×D53 | 1 | 2 | yes | — |
| 392 | C42 | — | 2 | 2 | no | — |
| 393 | C42 | — | 53 | 1 | no | — |
| 394 | C42 | — | 53 | 2 | no | — |
| 395 | C42 | — | 106 | 2 | no | — |
| 396 | C42 | — | 106 | 2 | no | — |
| 397 | C42 | — | 106 | 2 | no | — |
| 398 | C42 | C23×D53 | 1 | 1 | yes | characteristic |
| 399 | C23 | — | 53 | 1 | no | — |
| 400 | Q8 | — | 4 | 2 | no | — |
| 401 | Q8 | — | 424 | 2 | no | — |
| 402 | Q8 | — | 212 | 2 | no | — |
| 403 | C2×C4 | — | 2 | 2 | no | — |
| 404 | C2×C4 | — | 2 | 2 | no | — |
| 405 | C2×C4 | — | 2 | 2 | no | — |
| 406 | C2×C4 | — | 4 | 1 | no | — |
| 407 | C2×C4 | — | 53 | 2 | no | — |
| 408 | C2×C4 | — | 53 | 1 | no | — |
| 409 | C2×C4 | — | 106 | 4 | no | — |
| 410 | C2×C4 | — | 106 | 2 | no | — |
| 411 | C2×C4 | — | 106 | 2 | no | — |
| 412 | C2×C4 | — | 106 | 2 | no | — |
| 413 | C2×C4 | — | 106 | 2 | no | — |
| 414 | C2×C4 | — | 424 | 2 | no | — |
| 415 | C2×C4 | — | 212 | 4 | no | — |
| 416 | C2×C4 | — | 212 | 4 | no | — |
| 417 | C2×C4 | — | 212 | 4 | no | — |
| 418 | C2×C4 | — | 212 | 1 | no | — |
| 419 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 420 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 421 | C8 | — | 2 | 4 | no | — |
| 422 | C8 | — | 4 | 1 | no | — |
| 423 | C8 | — | 106 | 4 | no | — |
| 424 | C8 | — | 212 | 1 | no | — |
| 425 | C22 | — | 53 | 2 | no | — |
| 426 | C22 | — | 53 | 4 | no | — |
| 427 | C22 | #120×D53 | 1 | 1 | yes | characteristic |
| 428 | C4 | — | 2 | 1 | no | — |
| 429 | C4 | — | 2 | 2 | no | — |
| 430 | C4 | — | 4 | 2 | no | — |
| 431 | C4 | — | 4 | 2 | no | — |
| 432 | C4 | — | 4 | 2 | no | — |
| 433 | C4 | — | 8 | 1 | no | — |
| 434 | C4 | — | 106 | 1 | no | — |
| 435 | C4 | — | 106 | 2 | no | — |
| 436 | C4 | — | 424 | 1 | no | — |
| 437 | C4 | — | 212 | 2 | no | — |
| 438 | C4 | — | 212 | 2 | no | — |
| 439 | C4 | — | 212 | 2 | no | — |
| 440 | C2 | — | 53 | 4 | no | — |
| 441 | C2 | #454×D53 | 1 | 1 | yes | characteristic |
| 442 | C2 | #456×D53 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #20274045 | C2 | semidirect |
| 5. #20274044 | C2 | semidirect |
| 6. #20274043 | C2 | semidirect |
| 7. #20274042 | C2 | semidirect |
| 8. #20274041 | C2 | semidirect |
| 11. C53×#1663 | C2 | semidirect |
| 227. #1663 | D53 | direct (N × H) |
| 232. D53 | #1663 | direct (N × H) |
| 268. C53 | C2×#1663 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #564×D53 | 2 |
| #501×D53 | 2 |
| #491×D53 | 2 |
| #20274045 | 2 |
| #20274044 | 2 |
| #20274043 | 2 |
| #20274042 | 2 |
| #20274041 | 2 |
| #330×D53 | 2 |
| C53×#1663 | 2 |
| C2×#1663 | 53 |