Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2598 conjugacy classes of subgroups.
The subgroup lattice has 644 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#16811439 | C2 | 1 | 2 | yes | maximal, complemented |
| 2 | C2×#16811438 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #20286516 | C2 | 1 | 16 | yes | maximal, direct product factor |
| 4 | C2×#16811002 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C2×#16810897 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | C2×#16810896 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C2×#16810807 | C2 | 1 | 2 | yes | maximal, complemented |
| 8 | C2×#16810805 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | C2×#16810737 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | C2×C53×#456 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | C2×#13133265 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×#13133264 | C22 | 1 | 2 | yes | — |
| 13 | #16811439 | — | 2 | 8 | no | — |
| 14 | #16811439 | C22 | 1 | 16 | yes | complemented |
| 15 | #16811438 | — | 2 | 8 | no | — |
| 16 | #16811438 | C22 | 1 | 16 | yes | complemented |
| 17 | C2×#13133250 | C22 | 1 | 2 | yes | — |
| 18 | C2×#13133249 | — | 2 | 2 | no | — |
| 19 | C2×#13133248 | — | 2 | 2 | no | — |
| 20 | C2×#13133248 | C22 | 1 | 2 | yes | — |
| 21 | C2×#13133247 | — | 2 | 2 | no | — |
| 22 | C2×#13133247 | C22 | 1 | 2 | yes | — |
| 23 | C2×#13133246 | — | 2 | 2 | no | — |
| 24 | C2×#13133238 | — | 2 | 2 | no | — |
| 25 | C2×#13133237 | — | 2 | 2 | no | — |
| 26 | C2×#13133237 | C22 | 1 | 2 | yes | — |
| 27 | C22×#11719925 | — | 2 | 2 | no | — |
| 28 | C22×#11719925 | C22 | 1 | 2 | yes | — |
| 29 | C22×#11719925 | C22 | 1 | 2 | yes | — |
| 30 | C2×Q16×D53 | — | 2 | 2 | no | — |
| 31 | C2×#13133225 | C22 | 1 | 2 | yes | — |
| 32 | C2×#13133224 | C22 | 1 | 2 | yes | — |
| 33 | C2×#13133217 | C22 | 1 | 1 | yes | characteristic |
| 34 | #16811002 | C22 | 1 | 8 | yes | complemented |
| 35 | #16810897 | C22 | 1 | 16 | yes | complemented |
| 36 | #16810896 | C22 | 1 | 16 | yes | complemented |
| 37 | #16810807 | C22 | 1 | 16 | yes | complemented |
| 38 | #16810805 | C22 | 1 | 8 | yes | complemented |
| 39 | #16810737 | C22 | 1 | 16 | yes | complemented |
| 40 | C2×#13133152 | C22 | 1 | 2 | yes | — |
| 41 | C2×#13133145 | C22 | 1 | 2 | yes | — |
| 42 | C2×#13133136 | C22 | 1 | 1 | yes | characteristic |
| 43 | C2×#13133135 | C22 | 1 | 2 | yes | — |
| 44 | C2×C4×#88322 | C22 | 1 | 1 | yes | characteristic |
| 45 | C2×2−1+4×C53 | C22 | 1 | 1 | yes | characteristic |
| 46 | C2×#137×C53 | C22 | 1 | 2 | yes | — |
| 47 | C2×C4⋊Q8×C53 | C22 | 1 | 1 | yes | characteristic |
| 48 | C53×#456 | C22 | 1 | 8 | yes | complemented |
| 49 | C2×#104×C53 | C22 | 1 | 2 | yes | — |
| 50 | C2×#101×C53 | C22 | 1 | 1 | yes | characteristic |
| 51 | #13133265 | — | 2 | 4 | no | — |
| 52 | #13133265 | — | 4 | 1 | no | — |
| 53 | #13133265 | C23 | 1 | 4 | yes | — |
| 54 | #13133264 | — | 2 | 4 | no | — |
| 55 | #13133264 | — | 2 | 4 | no | — |
| 56 | #13133264 | — | 4 | 2 | no | — |
| 57 | #13133264 | C23 | 1 | 8 | yes | — |
| 58 | C2×#11719949 | — | 2 | 2 | no | — |
| 59 | C2×#11719945 | — | 2 | 2 | no | — |
| 60 | C2×#11719945 | — | 4 | 1 | no | — |
| 61 | C2×#11719945 | C23 | 1 | 2 | yes | — |
| 62 | C2×#11719947 | — | 2 | 2 | no | — |
| 63 | C2×#11719947 | — | 4 | 2 | no | — |
| 64 | C22×Dic106 | — | 2 | 2 | no | — |
| 65 | C22×Dic106 | C23 | 1 | 2 | yes | — |
| 66 | C2×Q8×D53 | — | 2 | 2 | no | — |
| 67 | C2×Q8×D53 | — | 2 | 2 | no | — |
| 68 | #13133250 | — | 2 | 4 | no | — |
| 69 | #13133250 | C23 | 1 | 8 | yes | — |
| 70 | #13133249 | — | 2 | 16 | no | — |
| 71 | #13133248 | — | 2 | 16 | no | — |
| 72 | #13133248 | — | 2 | 4 | no | — |
| 73 | #13133248 | C23 | 1 | 8 | yes | — |
| 74 | #13133247 | — | 2 | 16 | no | — |
| 75 | #13133247 | — | 2 | 4 | no | — |
| 76 | #13133247 | C23 | 1 | 8 | yes | — |
| 77 | #13133246 | — | 2 | 16 | no | — |
| 78 | #13133238 | — | 2 | 16 | no | — |
| 79 | #13133237 | — | 2 | 16 | no | — |
| 80 | #13133237 | D4 | 1 | 8 | yes | — |
| 81 | #13133237 | C23 | 1 | 8 | yes | — |
| 82 | C2×Dic212 | — | 2 | 2 | no | — |
| 83 | C2×#11719925 | — | 2 | 16 | no | — |
| 84 | C2×#11719925 | — | 2 | 2 | no | — |
| 85 | C2×#11719925 | — | 2 | 2 | no | — |
| 86 | C2×#11719925 | — | 2 | 2 | no | — |
| 87 | C2×#11719925 | — | 2 | 2 | no | — |
| 88 | C2×#11719925 | — | 2 | 4 | no | — |
| 89 | C2×#11719925 | — | 2 | 4 | no | — |
| 90 | C2×#11719925 | — | 2 | 2 | no | — |
| 91 | C2×#11719925 | — | 2 | 2 | no | — |
| 92 | C2×#11719925 | D4 | 1 | 2 | yes | — |
| 93 | C2×#11719925 | C23 | 1 | 8 | yes | — |
| 94 | C2×#11719925 | C23 | 1 | 8 | yes | — |
| 95 | Q16×D53 | — | 2 | 16 | no | — |
| 96 | C2×#11719913 | — | 2 | 2 | no | — |
| 97 | C2×#11719923 | — | 2 | 2 | no | — |
| 98 | C2×#11719923 | D4 | 1 | 2 | yes | — |
| 99 | C2×#11719924 | — | 2 | 2 | no | — |
| 100 | C2×#11719924 | D4 | 1 | 2 | yes | — |
| 101 | C2×#11719922 | D4 | 1 | 2 | yes | — |
| 102 | #13133225 | — | 2 | 4 | no | — |
| 103 | #13133225 | C23 | 1 | 8 | yes | — |
| 104 | #13133224 | — | 2 | 4 | no | — |
| 105 | #13133224 | C23 | 1 | 8 | yes | — |
| 106 | C2×#11719917 | — | 2 | 2 | no | — |
| 107 | C2×#11719917 | C23 | 1 | 2 | yes | — |
| 108 | C2×#11719912 | — | 2 | 2 | no | — |
| 109 | C22×#88322 | — | 2 | 2 | no | — |
| 110 | C22×#88322 | C23 | 1 | 2 | yes | — |
| 111 | C2×C8×D53 | — | 2 | 2 | no | — |
| 112 | #13133217 | — | 4 | 1 | no | — |
| 113 | #13133217 | C23 | 1 | 4 | yes | — |
| 114 | C2×C4⋊Dic53 | — | 4 | 1 | no | — |
| 115 | #13133152 | C23 | 1 | 8 | yes | — |
| 116 | #13133145 | C23 | 1 | 8 | yes | — |
| 117 | #13133136 | C23 | 1 | 4 | yes | — |
| 118 | #13133135 | C23 | 1 | 8 | yes | — |
| 119 | C4×#88322 | C23 | 1 | 4 | yes | — |
| 120 | 2−1+4×C53 | — | 2 | 4 | no | — |
| 121 | 2−1+4×C53 | — | 4 | 1 | no | — |
| 122 | 2−1+4×C53 | C23 | 1 | 4 | yes | — |
| 123 | C2×#41×C53 | — | 2 | 2 | no | — |
| 124 | C2×#41×C53 | — | 4 | 1 | no | — |
| 125 | C2×#41×C53 | C23 | 1 | 2 | yes | — |
| 126 | C22×Q8×C53 | — | 2 | 2 | no | — |
| 127 | C22×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 128 | C22×Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 129 | #137×C53 | — | 2 | 4 | no | — |
| 130 | #137×C53 | C23 | 1 | 8 | yes | — |
| 131 | C2×Q16×C53 | — | 2 | 2 | no | — |
| 132 | C2×SD16×C53 | — | 2 | 2 | no | — |
| 133 | C2×M16×C53 | C23 | 1 | 2 | yes | — |
| 134 | C4⋊Q8×C53 | — | 4 | 1 | no | — |
| 135 | C4⋊Q8×C53 | C23 | 1 | 4 | yes | — |
| 136 | C2×C4⋊C4×C53 | — | 4 | 1 | no | — |
| 137 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 138 | #104×C53 | C23 | 1 | 8 | yes | — |
| 139 | #101×C53 | C23 | 1 | 4 | yes | — |
| 140 | #41×C53 | — | 2 | 2 | no | — |
| 141 | #41×C53 | — | 2 | 2 | no | — |
| 142 | #41×C53 | — | 2 | 8 | no | — |
| 143 | #41×C53 | — | 4 | 4 | no | — |
| 144 | #41×C53 | — | 4 | 4 | no | — |
| 145 | #41×C53 | — | 4 | 4 | no | — |
| 146 | #41×C53 | C2×D4 | 1 | 4 | yes | — |
| 147 | #41×C53 | C24 | 1 | 4 | yes | — |
| 148 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 149 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 150 | C2×Q8×C53 | — | 2 | 8 | no | — |
| 151 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 152 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 153 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 154 | C2×Q8×C53 | — | 2 | 2 | no | — |
| 155 | C2×Q8×C53 | — | 4 | 1 | no | — |
| 156 | C2×Q8×C53 | — | 4 | 4 | no | — |
| 157 | C2×Q8×C53 | C2×D4 | 1 | 2 | yes | — |
| 158 | C2×Q8×C53 | C24 | 1 | 2 | yes | — |
| 159 | C2×Q8×C53 | C24 | 1 | 2 | yes | — |
| 160 | C2×D4×C53 | — | 2 | 2 | no | — |
| 161 | C2×D4×C53 | — | 4 | 1 | no | — |
| 162 | C2×D4×C53 | C2×D4 | 1 | 2 | yes | — |
| 163 | C22×C4×C53 | — | 2 | 1 | no | — |
| 164 | C22×C4×C53 | — | 2 | 2 | no | — |
| 165 | C22×C4×C53 | — | 2 | 1 | no | — |
| 166 | C22×C4×C53 | — | 2 | 1 | no | — |
| 167 | C22×C4×C53 | — | 4 | 2 | no | — |
| 168 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 169 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 170 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 171 | C22×Dic53 | — | 2 | 2 | no | — |
| 172 | C22×Dic53 | — | 4 | 2 | no | — |
| 173 | #11719949 | — | 2 | 8 | no | — |
| 174 | #11719949 | — | 4 | 4 | no | — |
| 175 | Q8×D53 | — | 2 | 8 | no | — |
| 176 | Q8×D53 | — | 2 | 8 | no | — |
| 177 | Q8×D53 | — | 4 | 4 | no | — |
| 178 | Q8×D53 | — | 4 | 4 | no | — |
| 179 | #11719947 | — | 2 | 8 | no | — |
| 180 | #11719947 | — | 4 | 4 | no | — |
| 181 | #11719947 | — | 4 | 8 | no | — |
| 182 | #11719947 | — | 4 | 8 | no | — |
| 183 | #11719945 | — | 2 | 2 | no | — |
| 184 | #11719945 | — | 2 | 2 | no | — |
| 185 | #11719945 | — | 2 | 8 | no | — |
| 186 | #11719945 | — | 4 | 4 | no | — |
| 187 | #11719945 | — | 4 | 4 | no | — |
| 188 | #11719945 | — | 4 | 4 | no | — |
| 189 | #11719945 | C2×D4 | 1 | 4 | yes | — |
| 190 | #11719945 | C24 | 1 | 4 | yes | — |
| 191 | C2×D212 | — | 4 | 1 | no | — |
| 192 | C2×D212 | C2×D4 | 1 | 2 | yes | — |
| 193 | C2×C4×D53 | — | 2 | 2 | no | — |
| 194 | C2×C4×D53 | — | 4 | 2 | no | — |
| 195 | C2×C4×D53 | — | 4 | 2 | no | — |
| 196 | C2×Dic106 | — | 2 | 2 | no | — |
| 197 | C2×Dic106 | — | 2 | 2 | no | — |
| 198 | C2×Dic106 | — | 2 | 2 | no | — |
| 199 | C2×Dic106 | — | 2 | 2 | no | — |
| 200 | C2×Dic106 | — | 2 | 8 | no | — |
| 201 | C2×Dic106 | — | 2 | 2 | no | — |
| 202 | C2×Dic106 | — | 4 | 4 | no | — |
| 203 | C2×Dic106 | — | 4 | 1 | no | — |
| 204 | C2×Dic106 | — | 4 | 2 | no | — |
| 205 | C2×Dic106 | C2×D4 | 1 | 2 | yes | — |
| 206 | C2×Dic106 | C24 | 1 | 4 | yes | — |
| 207 | Q16×C53 | — | 2 | 8 | no | — |
| 208 | SD16×C53 | — | 2 | 8 | no | — |
| 209 | M16×C53 | — | 2 | 2 | no | — |
| 210 | M16×C53 | C24 | 1 | 4 | yes | — |
| 211 | C2×C8×C53 | — | 2 | 2 | no | — |
| 212 | C4⋊C4×C53 | — | 4 | 4 | no | — |
| 213 | C42×C53 | — | 2 | 1 | no | — |
| 214 | C42×C53 | C24 | 1 | 2 | yes | — |
| 215 | #11719925 | — | 2 | 8 | no | — |
| 216 | #11719925 | — | 2 | 8 | no | — |
| 217 | #11719925 | — | 2 | 8 | no | — |
| 218 | #11719925 | — | 2 | 8 | no | — |
| 219 | #11719925 | — | 2 | 8 | no | — |
| 220 | #11719925 | — | 2 | 8 | no | — |
| 221 | #11719925 | C2×D4 | 1 | 8 | yes | — |
| 222 | #11719924 | — | 2 | 8 | no | — |
| 223 | #11719924 | C2×D4 | 1 | 8 | yes | — |
| 224 | #11719923 | — | 2 | 8 | no | — |
| 225 | #11719923 | C2×D4 | 1 | 8 | yes | — |
| 226 | #11719922 | C2×D4 | 1 | 8 | yes | — |
| 227 | C4⋊Dic53 | — | 4 | 4 | no | — |
| 228 | #11719917 | — | 2 | 2 | no | — |
| 229 | #11719917 | — | 2 | 8 | no | — |
| 230 | #11719917 | C24 | 1 | 4 | yes | — |
| 231 | C2×#88322 | — | 2 | 2 | no | — |
| 232 | C2×#88322 | — | 2 | 8 | no | — |
| 233 | C2×#88322 | C2×D4 | 1 | 2 | yes | — |
| 234 | C2×#88322 | C2×D4 | 1 | 2 | yes | — |
| 235 | C2×#88322 | C2×D4 | 1 | 4 | yes | — |
| 236 | C2×#88322 | C24 | 1 | 4 | yes | — |
| 237 | Dic212 | — | 2 | 8 | no | — |
| 238 | #11719913 | — | 2 | 8 | no | — |
| 239 | #11719912 | — | 2 | 8 | no | — |
| 240 | C8×D53 | — | 2 | 8 | no | — |
| 241 | C23×C53 | — | 2 | 2 | no | — |
| 242 | C23×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 243 | C22×D53 | — | 2 | 2 | no | — |
| 244 | Q8×C53 | — | 2 | 2 | no | — |
| 245 | Q8×C53 | — | 2 | 4 | no | — |
| 246 | Q8×C53 | — | 2 | 4 | no | — |
| 247 | Q8×C53 | — | 4 | 4 | no | — |
| 248 | Q8×C53 | — | 4 | 2 | no | — |
| 249 | Q8×C53 | — | 4 | 2 | no | — |
| 250 | Q8×C53 | C22×D4 | 1 | 4 | yes | — |
| 251 | D4×C53 | — | 2 | 4 | no | — |
| 252 | D4×C53 | — | 2 | 4 | no | — |
| 253 | D4×C53 | — | 2 | 2 | no | — |
| 254 | D4×C53 | — | 4 | 4 | no | — |
| 255 | D4×C53 | C22×D4 | 1 | 4 | yes | — |
| 256 | C2×C4×C53 | — | 2 | 4 | no | — |
| 257 | C2×C4×C53 | — | 2 | 2 | no | — |
| 258 | C2×C4×C53 | — | 2 | 2 | no | — |
| 259 | C2×C4×C53 | — | 2 | 4 | no | — |
| 260 | C2×C4×C53 | — | 2 | 4 | no | — |
| 261 | C2×C4×C53 | — | 2 | 2 | no | — |
| 262 | C2×C4×C53 | — | 2 | 2 | no | — |
| 263 | C2×C4×C53 | — | 4 | 8 | no | — |
| 264 | C2×C4×C53 | — | 4 | 1 | no | — |
| 265 | C2×C4×C53 | — | 4 | 1 | no | — |
| 266 | C2×C4×C53 | — | 4 | 1 | no | — |
| 267 | C2×C4×C53 | — | 4 | 1 | no | — |
| 268 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 269 | C2×C4×C53 | C22×D4 | 1 | 2 | yes | — |
| 270 | C2×C4×C53 | H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 271 | C2×C4×C53 | C25 | 1 | 1 | yes | characteristic |
| 272 | C22⋊D53 | — | 2 | 4 | no | — |
| 273 | C22⋊D53 | — | 2 | 4 | no | — |
| 274 | C22⋊D53 | — | 4 | 8 | no | — |
| 275 | C2×Dic53 | — | 2 | 2 | no | — |
| 276 | C2×Dic53 | — | 2 | 4 | no | — |
| 277 | C2×Dic53 | — | 4 | 8 | no | — |
| 278 | C2×Dic53 | — | 4 | 2 | no | — |
| 279 | C2×Dic53 | — | 4 | 2 | no | — |
| 280 | D212 | — | 2 | 2 | no | — |
| 281 | D212 | — | 4 | 4 | no | — |
| 282 | D212 | C22×D4 | 1 | 4 | yes | — |
| 283 | C4×D53 | — | 2 | 4 | no | — |
| 284 | C4×D53 | — | 2 | 4 | no | — |
| 285 | C4×D53 | — | 4 | 8 | no | — |
| 286 | C4×D53 | — | 4 | 8 | no | — |
| 287 | Dic106 | — | 2 | 2 | no | — |
| 288 | Dic106 | — | 2 | 4 | no | — |
| 289 | Dic106 | — | 2 | 4 | no | — |
| 290 | Dic106 | — | 4 | 4 | no | — |
| 291 | Dic106 | — | 4 | 8 | no | — |
| 292 | Dic106 | — | 4 | 2 | no | — |
| 293 | Dic106 | — | 4 | 2 | no | — |
| 294 | Dic106 | C22×D4 | 1 | 4 | yes | — |
| 295 | C8×C53 | — | 2 | 4 | no | — |
| 296 | #88322 | — | 2 | 4 | no | — |
| 297 | #88322 | C22×D4 | 1 | 4 | yes | — |
| 298 | #88322 | C22×D4 | 1 | 4 | yes | — |
| 299 | C2×#3293 | — | 53 | 1 | no | maximal, Sylow |
| 300 | C22×C53 | — | 2 | 2 | no | — |
| 301 | C22×C53 | — | 2 | 4 | no | — |
| 302 | C22×C53 | — | 4 | 4 | no | — |
| 303 | C22×C53 | D42 | 1 | 1 | yes | characteristic |
| 304 | C22×C53 | D42 | 1 | 1 | yes | characteristic |
| 305 | C22×C53 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 306 | C2×D53 | — | 2 | 4 | no | — |
| 307 | C2×D53 | — | 4 | 4 | no | — |
| 308 | C4×C53 | — | 2 | 4 | no | — |
| 309 | C4×C53 | — | 2 | 4 | no | — |
| 310 | C4×C53 | — | 4 | 2 | no | — |
| 311 | C4×C53 | — | 4 | 2 | no | — |
| 312 | C4×C53 | D42 | 1 | 2 | yes | — |
| 313 | C4×C53 | C23×D4 | 1 | 2 | yes | — |
| 314 | Dic53 | — | 2 | 4 | no | — |
| 315 | Dic53 | — | 4 | 4 | no | — |
| 316 | C2×#578 | — | 53 | 2 | no | — |
| 317 | C2×#578 | — | 53 | 2 | no | — |
| 318 | #3293 | — | 53 | 16 | no | — |
| 319 | C2×#494 | — | 53 | 1 | no | — |
| 320 | C2×#473 | — | 53 | 2 | no | — |
| 321 | C2×#473 | — | 53 | 2 | no | — |
| 322 | C2×#456 | — | 53 | 2 | no | — |
| 323 | C2×#456 | — | 53 | 1 | no | — |
| 324 | C2×#456 | D53 | 1 | 1 | yes | characteristic, complemented |
| 325 | C2×#443 | — | 53 | 2 | no | — |
| 326 | C2×C53 | — | 2 | 1 | no | — |
| 327 | C2×C53 | — | 2 | 1 | no | — |
| 328 | C2×C53 | — | 4 | 4 | no | — |
| 329 | C2×C53 | #3293 | 1 | 2 | yes | complemented |
| 330 | C2×C53 | C2×D42 | 1 | 1 | yes | characteristic |
| 331 | D53 | — | 4 | 4 | no | — |
| 332 | C2×2−1+4 | — | 53 | 2 | no | — |
| 333 | C2×2−1+4 | — | 53 | 1 | no | — |
| 334 | C2×2−1+4 | C2×D53 | 1 | 1 | yes | characteristic |
| 335 | #578 | — | 53 | 16 | no | — |
| 336 | #578 | — | 53 | 16 | no | — |
| 337 | #578 | — | 106 | 8 | no | — |
| 338 | #578 | — | 106 | 8 | no | — |
| 339 | C2×#137 | — | 53 | 2 | no | — |
| 340 | C2×#137 | — | 53 | 2 | no | — |
| 341 | C2×#137 | — | 53 | 2 | no | — |
| 342 | C2×#137 | — | 106 | 2 | no | — |
| 343 | C2×#137 | — | 106 | 2 | no | — |
| 344 | C2×#137 | — | 106 | 2 | no | — |
| 345 | C2×#137 | — | 106 | 2 | no | — |
| 346 | C2×#137 | C2×D53 | 1 | 2 | yes | — |
| 347 | C2×#135 | — | 53 | 2 | no | — |
| 348 | C2×#135 | — | 106 | 2 | no | — |
| 349 | C2×#135 | — | 106 | 2 | no | — |
| 350 | C22×Q16 | — | 53 | 2 | no | — |
| 351 | C22×Q16 | — | 53 | 2 | no | — |
| 352 | C22×Q16 | — | 106 | 2 | no | — |
| 353 | C22×Q16 | — | 106 | 2 | no | — |
| 354 | C2×#131 | — | 53 | 2 | no | — |
| 355 | C2×#131 | — | 53 | 2 | no | — |
| 356 | C2×C4⋊Q8 | — | 53 | 1 | no | — |
| 357 | C2×C4⋊Q8 | C2×D53 | 1 | 1 | yes | characteristic |
| 358 | #494 | — | 53 | 8 | no | — |
| 359 | #473 | — | 53 | 16 | no | — |
| 360 | #473 | — | 53 | 16 | no | — |
| 361 | #456 | — | 53 | 8 | no | — |
| 362 | #456 | — | 53 | 16 | no | — |
| 363 | #456 | C2×D53 | 1 | 8 | yes | complemented |
| 364 | #443 | — | 53 | 16 | no | — |
| 365 | C2×#108 | — | 53 | 2 | no | — |
| 366 | C2×#104 | — | 53 | 2 | no | — |
| 367 | C2×#104 | C2×D53 | 1 | 2 | yes | — |
| 368 | C2×#101 | — | 53 | 1 | no | — |
| 369 | C2×#101 | — | 53 | 2 | no | — |
| 370 | C2×#101 | C2×D53 | 1 | 1 | yes | characteristic |
| 371 | C2×C4×C8 | — | 53 | 1 | no | — |
| 372 | C53 | C2×#3293 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 373 | 2−1+4 | — | 2 | 4 | no | — |
| 374 | 2−1+4 | — | 4 | 1 | no | — |
| 375 | 2−1+4 | — | 53 | 8 | no | — |
| 376 | 2−1+4 | — | 53 | 4 | no | — |
| 377 | 2−1+4 | — | 106 | 4 | no | — |
| 378 | 2−1+4 | — | 106 | 4 | no | — |
| 379 | 2−1+4 | — | 106 | 4 | no | — |
| 380 | 2−1+4 | — | 212 | 1 | no | — |
| 381 | 2−1+4 | — | 212 | 2 | no | — |
| 382 | 2−1+4 | C22×D53 | 1 | 4 | yes | — |
| 383 | C2×#41 | — | 2 | 2 | no | — |
| 384 | C2×#41 | — | 4 | 1 | no | — |
| 385 | C2×#41 | — | 53 | 2 | no | — |
| 386 | C2×#41 | — | 106 | 2 | no | — |
| 387 | C2×#41 | — | 106 | 2 | no | — |
| 388 | C2×#41 | — | 106 | 2 | no | — |
| 389 | C2×#41 | — | 212 | 1 | no | — |
| 390 | C2×#41 | — | 212 | 2 | no | — |
| 391 | C2×#41 | C22×D53 | 1 | 2 | yes | — |
| 392 | C22×Q8 | — | 2 | 2 | no | — |
| 393 | C22×Q8 | — | 53 | 2 | no | — |
| 394 | C22×Q8 | — | 106 | 2 | no | — |
| 395 | C22×Q8 | — | 106 | 2 | no | — |
| 396 | C22×Q8 | — | 106 | 2 | no | — |
| 397 | C22×Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 398 | C22×Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 399 | #137 | — | 2 | 4 | no | — |
| 400 | #137 | — | 53 | 8 | no | — |
| 401 | #137 | — | 53 | 8 | no | — |
| 402 | #137 | — | 53 | 8 | no | — |
| 403 | #137 | — | 106 | 4 | no | — |
| 404 | #137 | — | 106 | 16 | no | — |
| 405 | #137 | — | 106 | 16 | no | — |
| 406 | #137 | — | 106 | 16 | no | — |
| 407 | #137 | — | 106 | 16 | no | — |
| 408 | #137 | — | 106 | 4 | no | — |
| 409 | #137 | — | 106 | 4 | no | — |
| 410 | #137 | C22×D53 | 1 | 8 | yes | — |
| 411 | #135 | — | 53 | 8 | no | — |
| 412 | #135 | — | 53 | 8 | no | — |
| 413 | #135 | — | 106 | 16 | no | — |
| 414 | #135 | — | 106 | 16 | no | — |
| 415 | C2×Q16 | — | 2 | 2 | no | — |
| 416 | C2×Q16 | — | 53 | 2 | no | — |
| 417 | C2×Q16 | — | 53 | 8 | no | — |
| 418 | C2×Q16 | — | 53 | 8 | no | — |
| 419 | C2×Q16 | — | 106 | 2 | no | — |
| 420 | C2×Q16 | — | 106 | 2 | no | — |
| 421 | C2×Q16 | — | 106 | 2 | no | — |
| 422 | C2×Q16 | — | 106 | 2 | no | — |
| 423 | C2×Q16 | — | 106 | 2 | no | — |
| 424 | C2×Q16 | — | 106 | 4 | no | — |
| 425 | C2×Q16 | — | 106 | 4 | no | — |
| 426 | C2×Q16 | — | 106 | 16 | no | — |
| 427 | C2×Q16 | — | 106 | 16 | no | — |
| 428 | C2×Q16 | — | 106 | 2 | no | — |
| 429 | C2×Q16 | — | 106 | 2 | no | — |
| 430 | C2×SD16 | — | 2 | 2 | no | — |
| 431 | C2×SD16 | — | 53 | 2 | no | — |
| 432 | C2×SD16 | — | 53 | 2 | no | — |
| 433 | C2×SD16 | — | 106 | 2 | no | — |
| 434 | C2×SD16 | — | 106 | 2 | no | — |
| 435 | C2×SD16 | — | 106 | 2 | no | — |
| 436 | C2×D8 | — | 53 | 2 | no | — |
| 437 | #131 | — | 53 | 8 | no | — |
| 438 | #131 | — | 53 | 8 | no | — |
| 439 | #131 | — | 106 | 4 | no | — |
| 440 | #131 | — | 106 | 4 | no | — |
| 441 | C2×M16 | — | 53 | 2 | no | — |
| 442 | C2×M16 | — | 106 | 2 | no | — |
| 443 | C2×M16 | — | 106 | 2 | no | — |
| 444 | C2×M16 | C22×D53 | 1 | 2 | yes | — |
| 445 | C22×C8 | — | 53 | 2 | no | — |
| 446 | C22×C8 | — | 106 | 2 | no | — |
| 447 | C22×C8 | — | 106 | 2 | no | — |
| 448 | C4⋊Q8 | — | 4 | 1 | no | — |
| 449 | C4⋊Q8 | — | 53 | 4 | no | — |
| 450 | C4⋊Q8 | — | 212 | 1 | no | — |
| 451 | C4⋊Q8 | C22×D53 | 1 | 4 | yes | — |
| 452 | C2×C4⋊C4 | — | 4 | 1 | no | — |
| 453 | C2×C4⋊C4 | — | 212 | 1 | no | — |
| 454 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 455 | #108 | — | 53 | 8 | no | — |
| 456 | #104 | — | 53 | 8 | no | — |
| 457 | #104 | C22×D53 | 1 | 8 | yes | — |
| 458 | #101 | — | 53 | 4 | no | — |
| 459 | #101 | — | 53 | 8 | no | — |
| 460 | #101 | C22×D53 | 1 | 4 | yes | — |
| 461 | C4×C8 | — | 53 | 4 | no | — |
| 462 | #41 | — | 2 | 2 | no | — |
| 463 | #41 | — | 2 | 2 | no | — |
| 464 | #41 | — | 2 | 8 | no | — |
| 465 | #41 | — | 4 | 4 | no | — |
| 466 | #41 | — | 4 | 4 | no | — |
| 467 | #41 | — | 4 | 4 | no | — |
| 468 | #41 | — | 53 | 4 | no | — |
| 469 | #41 | — | 53 | 4 | no | — |
| 470 | #41 | — | 106 | 8 | no | — |
| 471 | #41 | — | 106 | 2 | no | — |
| 472 | #41 | — | 106 | 2 | no | — |
| 473 | #41 | — | 106 | 8 | no | — |
| 474 | #41 | — | 106 | 8 | no | — |
| 475 | #41 | — | 212 | 4 | no | — |
| 476 | #41 | — | 212 | 4 | no | — |
| 477 | #41 | — | 212 | 4 | no | — |
| 478 | #41 | — | 212 | 8 | no | — |
| 479 | #41 | — | 212 | 4 | no | — |
| 480 | #41 | — | 212 | 4 | no | — |
| 481 | #41 | — | 212 | 8 | no | — |
| 482 | #41 | D4×D53 | 1 | 4 | yes | — |
| 483 | #41 | C23×D53 | 1 | 4 | yes | — |
| 484 | C2×Q8 | — | 2 | 1 | no | — |
| 485 | C2×Q8 | — | 2 | 1 | no | — |
| 486 | C2×Q8 | — | 2 | 8 | no | — |
| 487 | C2×Q8 | — | 2 | 2 | no | — |
| 488 | C2×Q8 | — | 2 | 2 | no | — |
| 489 | C2×Q8 | — | 2 | 2 | no | — |
| 490 | C2×Q8 | — | 2 | 2 | no | — |
| 491 | C2×Q8 | — | 4 | 1 | no | — |
| 492 | C2×Q8 | — | 4 | 4 | no | — |
| 493 | C2×Q8 | — | 53 | 2 | no | — |
| 494 | C2×Q8 | — | 53 | 4 | no | — |
| 495 | C2×Q8 | — | 106 | 8 | no | — |
| 496 | C2×Q8 | — | 106 | 2 | no | — |
| 497 | C2×Q8 | — | 106 | 8 | no | — |
| 498 | C2×Q8 | — | 106 | 8 | no | — |
| 499 | C2×Q8 | — | 106 | 2 | no | — |
| 500 | C2×Q8 | — | 106 | 2 | no | — |
| 501 | C2×Q8 | — | 106 | 2 | no | — |
| 502 | C2×Q8 | — | 106 | 2 | no | — |
| 503 | C2×Q8 | — | 212 | 2 | no | — |
| 504 | C2×Q8 | — | 212 | 4 | no | — |
| 505 | C2×Q8 | — | 212 | 1 | no | — |
| 506 | C2×Q8 | — | 212 | 4 | no | — |
| 507 | C2×Q8 | — | 212 | 4 | no | — |
| 508 | C2×Q8 | D4×D53 | 1 | 2 | yes | — |
| 509 | C2×Q8 | C23×D53 | 1 | 2 | yes | — |
| 510 | C2×Q8 | C23×D53 | 1 | 2 | yes | — |
| 511 | C2×D4 | — | 2 | 2 | no | — |
| 512 | C2×D4 | — | 4 | 1 | no | — |
| 513 | C2×D4 | — | 53 | 2 | no | — |
| 514 | C2×D4 | — | 106 | 2 | no | — |
| 515 | C2×D4 | — | 212 | 1 | no | — |
| 516 | C2×D4 | — | 212 | 2 | no | — |
| 517 | C2×D4 | D4×D53 | 1 | 2 | yes | — |
| 518 | C22×C4 | — | 2 | 1 | no | — |
| 519 | C22×C4 | — | 2 | 2 | no | — |
| 520 | C22×C4 | — | 2 | 1 | no | — |
| 521 | C22×C4 | — | 2 | 1 | no | — |
| 522 | C22×C4 | — | 4 | 2 | no | — |
| 523 | C22×C4 | — | 106 | 2 | no | — |
| 524 | C22×C4 | — | 106 | 2 | no | — |
| 525 | C22×C4 | — | 212 | 2 | no | — |
| 526 | C22×C4 | — | 212 | 2 | no | — |
| 527 | C22×C4 | — | 212 | 2 | no | — |
| 528 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 529 | Q16 | — | 2 | 8 | no | — |
| 530 | Q16 | — | 53 | 8 | no | — |
| 531 | Q16 | — | 106 | 8 | no | — |
| 532 | Q16 | — | 106 | 8 | no | — |
| 533 | Q16 | — | 106 | 8 | no | — |
| 534 | Q16 | — | 106 | 8 | no | — |
| 535 | Q16 | — | 106 | 8 | no | — |
| 536 | Q16 | — | 106 | 8 | no | — |
| 537 | Q16 | — | 106 | 8 | no | — |
| 538 | SD16 | — | 2 | 8 | no | — |
| 539 | SD16 | — | 53 | 8 | no | — |
| 540 | SD16 | — | 53 | 8 | no | — |
| 541 | SD16 | — | 106 | 8 | no | — |
| 542 | SD16 | — | 106 | 8 | no | — |
| 543 | SD16 | — | 106 | 8 | no | — |
| 544 | D8 | — | 53 | 8 | no | — |
| 545 | M16 | — | 2 | 2 | no | — |
| 546 | M16 | — | 53 | 4 | no | — |
| 547 | M16 | — | 106 | 8 | no | — |
| 548 | M16 | — | 106 | 8 | no | — |
| 549 | M16 | — | 106 | 2 | no | — |
| 550 | M16 | C23×D53 | 1 | 4 | yes | — |
| 551 | C2×C8 | — | 2 | 2 | no | — |
| 552 | C2×C8 | — | 53 | 2 | no | — |
| 553 | C2×C8 | — | 53 | 2 | no | — |
| 554 | C2×C8 | — | 53 | 4 | no | — |
| 555 | C2×C8 | — | 53 | 4 | no | — |
| 556 | C2×C8 | — | 106 | 8 | no | — |
| 557 | C2×C8 | — | 106 | 8 | no | — |
| 558 | C2×C8 | — | 106 | 2 | no | — |
| 559 | C4⋊C4 | — | 4 | 4 | no | — |
| 560 | C4⋊C4 | — | 212 | 4 | no | — |
| 561 | C42 | — | 2 | 1 | no | — |
| 562 | C42 | C23×D53 | 1 | 2 | yes | — |
| 563 | C23 | — | 2 | 2 | no | — |
| 564 | C23 | — | 106 | 2 | no | — |
| 565 | C23 | #13133262 | 1 | 1 | yes | characteristic |
| 566 | Q8 | — | 2 | 2 | no | — |
| 567 | Q8 | — | 2 | 4 | no | — |
| 568 | Q8 | — | 2 | 4 | no | — |
| 569 | Q8 | — | 4 | 4 | no | — |
| 570 | Q8 | — | 4 | 2 | no | — |
| 571 | Q8 | — | 4 | 2 | no | — |
| 572 | Q8 | — | 53 | 4 | no | — |
| 573 | Q8 | — | 106 | 2 | no | — |
| 574 | Q8 | — | 106 | 4 | no | — |
| 575 | Q8 | — | 106 | 4 | no | — |
| 576 | Q8 | — | 212 | 8 | no | — |
| 577 | Q8 | — | 212 | 4 | no | — |
| 578 | Q8 | — | 212 | 2 | no | — |
| 579 | Q8 | — | 212 | 2 | no | — |
| 580 | Q8 | C2×D4×D53 | 1 | 4 | yes | — |
| 581 | D4 | — | 2 | 4 | no | — |
| 582 | D4 | — | 2 | 4 | no | — |
| 583 | D4 | — | 2 | 2 | no | — |
| 584 | D4 | — | 4 | 4 | no | — |
| 585 | D4 | — | 53 | 4 | no | — |
| 586 | D4 | — | 106 | 4 | no | — |
| 587 | D4 | — | 106 | 4 | no | — |
| 588 | D4 | — | 106 | 2 | no | — |
| 589 | D4 | — | 212 | 4 | no | — |
| 590 | D4 | — | 212 | 8 | no | — |
| 591 | D4 | C2×D4×D53 | 1 | 4 | yes | — |
| 592 | C2×C4 | — | 2 | 4 | no | — |
| 593 | C2×C4 | — | 2 | 2 | no | — |
| 594 | C2×C4 | — | 2 | 2 | no | — |
| 595 | C2×C4 | — | 2 | 4 | no | — |
| 596 | C2×C4 | — | 2 | 4 | no | — |
| 597 | C2×C4 | — | 2 | 2 | no | — |
| 598 | C2×C4 | — | 2 | 2 | no | — |
| 599 | C2×C4 | — | 4 | 8 | no | — |
| 600 | C2×C4 | — | 4 | 1 | no | — |
| 601 | C2×C4 | — | 4 | 1 | no | — |
| 602 | C2×C4 | — | 4 | 1 | no | — |
| 603 | C2×C4 | — | 4 | 1 | no | — |
| 604 | C2×C4 | — | 106 | 2 | no | — |
| 605 | C2×C4 | — | 106 | 4 | no | — |
| 606 | C2×C4 | — | 106 | 4 | no | — |
| 607 | C2×C4 | — | 106 | 4 | no | — |
| 608 | C2×C4 | — | 212 | 8 | no | — |
| 609 | C2×C4 | — | 212 | 8 | no | — |
| 610 | C2×C4 | — | 212 | 8 | no | — |
| 611 | C2×C4 | — | 212 | 2 | no | — |
| 612 | C2×C4 | — | 212 | 2 | no | — |
| 613 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 614 | C2×C4 | C2×D4×D53 | 1 | 2 | yes | — |
| 615 | C2×C4 | #13133262 | 1 | 1 | yes | characteristic |
| 616 | C2×C4 | C24×D53 | 1 | 1 | yes | characteristic |
| 617 | C8 | — | 2 | 4 | no | — |
| 618 | C8 | — | 53 | 4 | no | — |
| 619 | C8 | — | 53 | 4 | no | — |
| 620 | C8 | — | 106 | 4 | no | — |
| 621 | C22 | — | 2 | 2 | no | — |
| 622 | C22 | — | 2 | 4 | no | — |
| 623 | C22 | — | 4 | 4 | no | — |
| 624 | C22 | — | 106 | 4 | no | — |
| 625 | C22 | — | 212 | 4 | no | — |
| 626 | C22 | #16811255 | 1 | 1 | yes | characteristic |
| 627 | C22 | #16811255 | 1 | 1 | yes | characteristic |
| 628 | C22 | C2×#13133262 | 1 | 1 | yes | characteristic |
| 629 | C4 | — | 2 | 4 | no | — |
| 630 | C4 | — | 2 | 4 | no | — |
| 631 | C4 | — | 4 | 2 | no | — |
| 632 | C4 | — | 4 | 2 | no | — |
| 633 | C4 | — | 106 | 4 | no | — |
| 634 | C4 | — | 212 | 4 | no | — |
| 635 | C4 | #16811255 | 1 | 2 | yes | — |
| 636 | C4 | C22×D4×D53 | 1 | 2 | yes | — |
| 637 | C2 | — | 2 | 1 | no | — |
| 638 | C2 | — | 2 | 1 | no | — |
| 639 | C2 | — | 4 | 4 | no | — |
| 640 | C2 | — | 212 | 4 | no | — |
| 641 | C2 | #20286516 | 1 | 2 | yes | direct product factor |
| 642 | C2 | C2×#16811255 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16811439 | C2 | semidirect |
| 2. C2×#16811438 | C2 | semidirect |
| 3. #20286516 | C2 | direct (N × H) |
| 4. C2×#16811002 | C2 | semidirect |
| 5. C2×#16810897 | C2 | semidirect |
| 6. C2×#16810896 | C2 | semidirect |
| 7. C2×#16810807 | C2 | semidirect |
| 8. C2×#16810805 | C2 | semidirect |
| 9. C2×#16810737 | C2 | semidirect |
| 10. C2×C53×#456 | C2 | semidirect |
| 14. #16811439 | C22 | semidirect |
| 16. #16811438 | C22 | semidirect |
| 34. #16811002 | C22 | semidirect |
| 35. #16810897 | C22 | semidirect |
| 36. #16810896 | C22 | semidirect |
| 37. #16810807 | C22 | semidirect |
| 38. #16810805 | C22 | semidirect |
| 39. #16810737 | C22 | semidirect |
| 48. C53×#456 | C22 | semidirect |
| 324. C2×#456 | D53 | semidirect |
| 329. C2×C53 | #3293 | semidirect |
| 363. #456 | C2×D53 | semidirect |
| 372. C53 | C2×#3293 | semidirect |
| 641. C2 | #20286516 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811439 | 2 |
| C2×#16811438 | 2 |
| #20286516 | 2 |
| C2×#16811002 | 2 |
| C2×#16810897 | 2 |
| C2×#16810896 | 2 |
| C2×#16810807 | 2 |
| C2×#16810805 | 2 |
| C2×#16810737 | 2 |
| C2×C53×#456 | 2 |
| C2×#3293 | 53 |