Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1028 conjugacy classes of subgroups.
The subgroup lattice has 992 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #20288941 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #20285532 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20285469 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20282736 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20273732 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20273731 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #20273707 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #20273706 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 9 | #20273660 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 10 | #20273659 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 11 | #20273636 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | #20273270 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 13 | #20273246 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 14 | #20273073 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 15 | C53×#1596 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 16 | #16811369 | — | 2 | 1 | no | — |
| 17 | #16811369 | — | 2 | 1 | no | — |
| 18 | #16811327 | — | 2 | 1 | no | — |
| 19 | #16811283 | — | 2 | 1 | no | — |
| 20 | #16811275 | — | 2 | 1 | no | — |
| 21 | #16811264 | — | 2 | 1 | no | — |
| 22 | #16811263 | — | 2 | 1 | no | — |
| 23 | #16811263 | — | 2 | 1 | no | — |
| 24 | #16811248 | C22 | 1 | 1 | yes | characteristic |
| 25 | #16811243 | — | 2 | 1 | no | — |
| 26 | #16811219 | — | 2 | 1 | no | — |
| 27 | #16811213 | C22 | 1 | 1 | yes | characteristic |
| 28 | #16811211 | C22 | 1 | 1 | yes | characteristic |
| 29 | #16811203 | — | 2 | 1 | no | — |
| 30 | #16811203 | — | 2 | 1 | no | — |
| 31 | #16811136 | C22 | 1 | 1 | yes | characteristic |
| 32 | C22⋊Q8×D53 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#13133190 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×#13133188 | C22 | 1 | 1 | yes | characteristic |
| 35 | #16810954 | C22 | 1 | 1 | yes | characteristic |
| 36 | #16810951 | C22 | 1 | 1 | yes | characteristic |
| 37 | #16810951 | C22 | 1 | 1 | yes | characteristic |
| 38 | #16810945 | — | 2 | 1 | no | — |
| 39 | #16810940 | — | 2 | 1 | no | — |
| 40 | #16810937 | C22 | 1 | 1 | yes | characteristic |
| 41 | #16810875 | — | 2 | 1 | no | — |
| 42 | #16810866 | — | 2 | 1 | no | — |
| 43 | #16810851 | — | 2 | 1 | no | — |
| 44 | #16810849 | — | 2 | 1 | no | — |
| 45 | #16810774 | C22 | 1 | 1 | yes | characteristic |
| 46 | #16810767 | — | 2 | 1 | no | — |
| 47 | #16810760 | — | 2 | 1 | no | — |
| 48 | #16810757 | C22 | 1 | 1 | yes | characteristic |
| 49 | #16810585 | C22 | 1 | 1 | yes | characteristic |
| 50 | C22⋊C8×D53 | C22 | 1 | 1 | yes | characteristic |
| 51 | #16810551 | — | 2 | 1 | no | — |
| 52 | #16810550 | C22 | 1 | 1 | yes | characteristic |
| 53 | #16810548 | C22 | 1 | 1 | yes | characteristic |
| 54 | #16810532 | — | 2 | 1 | no | — |
| 55 | #16810531 | — | 2 | 1 | no | — |
| 56 | #16810531 | — | 2 | 1 | no | — |
| 57 | #16810531 | C22 | 1 | 1 | yes | characteristic |
| 58 | #16810485 | C22 | 1 | 1 | yes | characteristic |
| 59 | #16810361 | C22 | 1 | 1 | yes | characteristic |
| 60 | #16810360 | C22 | 1 | 1 | yes | characteristic |
| 61 | #16810360 | C22 | 1 | 1 | yes | characteristic |
| 62 | #16810359 | C22 | 1 | 1 | yes | characteristic |
| 63 | #16810358 | C22 | 1 | 1 | yes | characteristic |
| 64 | #16810356 | C22 | 1 | 1 | yes | characteristic |
| 65 | #16810347 | C22 | 1 | 1 | yes | characteristic |
| 66 | #16810346 | C22 | 1 | 1 | yes | characteristic |
| 67 | #16810346 | C22 | 1 | 1 | yes | characteristic |
| 68 | C53×#543 | C22 | 1 | 1 | yes | characteristic |
| 69 | C53×#450 | C22 | 1 | 1 | yes | characteristic |
| 70 | C53×#450 | C22 | 1 | 1 | yes | characteristic |
| 71 | C53×#392 | C22 | 1 | 1 | yes | characteristic |
| 72 | C53×#328 | C22 | 1 | 1 | yes | characteristic |
| 73 | C53×#328 | C22 | 1 | 1 | yes | characteristic |
| 74 | C53×#323 | C22 | 1 | 1 | yes | characteristic |
| 75 | C2×#11719949 | — | 2 | 1 | no | — |
| 76 | C2×#11719949 | D4 | 1 | 1 | yes | characteristic, complemented |
| 77 | C2×#11719945 | — | 2 | 1 | no | — |
| 78 | C2×#11719945 | — | 2 | 1 | no | — |
| 79 | C2×Q8×D53 | D4 | 1 | 1 | yes | characteristic, complemented |
| 80 | C22×D212 | D4 | 1 | 1 | yes | characteristic |
| 81 | C22×C22⋊D53 | — | 2 | 1 | no | — |
| 82 | C22×C22⋊D53 | — | 2 | 1 | no | — |
| 83 | C22×C22⋊D53 | D4 | 1 | 1 | yes | characteristic |
| 84 | C22×C22⋊D53 | D4 | 1 | 1 | yes | characteristic |
| 85 | C22×C4×D53 | C23 | 1 | 1 | yes | characteristic |
| 86 | C2×#11719923 | — | 2 | 1 | no | — |
| 87 | C2×#11719922 | — | 2 | 1 | no | — |
| 88 | C2×#11719912 | — | 2 | 1 | no | — |
| 89 | C2×C8×D53 | — | 2 | 1 | no | — |
| 90 | #13133215 | — | 2 | 1 | no | — |
| 91 | #13133212 | — | 2 | 1 | no | — |
| 92 | #13133210 | — | 2 | 1 | no | — |
| 93 | #13133207 | — | 2 | 1 | no | — |
| 94 | #13133207 | — | 2 | 1 | no | — |
| 95 | #13133206 | — | 2 | 1 | no | — |
| 96 | #13133206 | — | 2 | 1 | no | — |
| 97 | #13133203 | — | 2 | 1 | no | — |
| 98 | #13133203 | — | 2 | 1 | no | — |
| 99 | #13133203 | — | 2 | 1 | no | — |
| 100 | #13133202 | — | 2 | 1 | no | — |
| 101 | #13133202 | — | 2 | 1 | no | — |
| 102 | #13133202 | — | 2 | 1 | no | — |
| 103 | #13133202 | — | 2 | 1 | no | — |
| 104 | #13133200 | — | 2 | 1 | no | — |
| 105 | #13133200 | — | 2 | 1 | no | — |
| 106 | #13133199 | — | 2 | 1 | no | — |
| 107 | #13133199 | — | 2 | 1 | no | — |
| 108 | #13133199 | — | 2 | 1 | no | — |
| 109 | #13133197 | — | 2 | 1 | no | — |
| 110 | #13133197 | D4 | 1 | 1 | yes | characteristic, complemented |
| 111 | #13133196 | C23 | 1 | 1 | yes | characteristic |
| 112 | #13133195 | — | 2 | 1 | no | — |
| 113 | #13133195 | — | 2 | 1 | no | — |
| 114 | #13133195 | — | 2 | 1 | no | — |
| 115 | #13133195 | — | 2 | 1 | no | — |
| 116 | #13133195 | — | 2 | 1 | no | — |
| 117 | #13133194 | — | 2 | 1 | no | — |
| 118 | #13133194 | — | 2 | 1 | no | — |
| 119 | #13133193 | — | 2 | 1 | no | — |
| 120 | #13133193 | — | 2 | 1 | no | — |
| 121 | #13133193 | D4 | 1 | 1 | yes | characteristic, complemented |
| 122 | #13133193 | D4 | 1 | 1 | yes | characteristic, complemented |
| 123 | #13133192 | — | 2 | 1 | no | — |
| 124 | #13133192 | — | 2 | 1 | no | — |
| 125 | #13133192 | — | 2 | 1 | no | — |
| 126 | #13133192 | — | 2 | 1 | no | — |
| 127 | #13133192 | D4 | 1 | 1 | yes | characteristic, complemented |
| 128 | #13133191 | — | 2 | 1 | no | — |
| 129 | #13133191 | — | 2 | 1 | no | — |
| 130 | #13133191 | C23 | 1 | 1 | yes | characteristic |
| 131 | #13133190 | — | 2 | 1 | no | — |
| 132 | #13133190 | — | 2 | 1 | no | — |
| 133 | #13133190 | — | 2 | 1 | no | — |
| 134 | #13133190 | — | 2 | 1 | no | — |
| 135 | #13133190 | — | 2 | 1 | no | — |
| 136 | #13133190 | — | 2 | 1 | no | — |
| 137 | #13133190 | — | 2 | 1 | no | — |
| 138 | #13133190 | — | 2 | 1 | no | — |
| 139 | #13133190 | — | 2 | 1 | no | — |
| 140 | #13133188 | — | 2 | 1 | no | — |
| 141 | #13133188 | — | 2 | 1 | no | — |
| 142 | #13133188 | — | 2 | 1 | no | — |
| 143 | #13133188 | — | 2 | 1 | no | — |
| 144 | #13133187 | — | 2 | 1 | no | — |
| 145 | #13133187 | — | 2 | 1 | no | — |
| 146 | #13133186 | — | 2 | 1 | no | — |
| 147 | #13133182 | — | 2 | 1 | no | — |
| 148 | #13133179 | — | 2 | 1 | no | — |
| 149 | #13133179 | — | 2 | 1 | no | — |
| 150 | C4×C22⋊D53 | — | 2 | 1 | no | — |
| 151 | C4×C22⋊D53 | — | 2 | 1 | no | — |
| 152 | C4×C22⋊D53 | — | 2 | 1 | no | — |
| 153 | #13133177 | — | 2 | 1 | no | — |
| 154 | #13133177 | — | 2 | 1 | no | — |
| 155 | #13133175 | D4 | 1 | 1 | yes | characteristic, complemented |
| 156 | C2×C4⋊Dic53 | C23 | 1 | 1 | yes | characteristic |
| 157 | C2×#11719919 | D4 | 1 | 1 | yes | characteristic |
| 158 | C4⋊C4×D53 | — | 2 | 1 | no | — |
| 159 | C4⋊C4×D53 | — | 2 | 1 | no | — |
| 160 | C4⋊C4×D53 | D4 | 1 | 1 | yes | characteristic, complemented |
| 161 | C2×C22⋊Dic53 | — | 2 | 1 | no | — |
| 162 | C2×C22⋊Dic53 | — | 2 | 1 | no | — |
| 163 | C2×C22⋊Dic53 | — | 2 | 1 | no | — |
| 164 | C2×#11719921 | — | 2 | 1 | no | — |
| 165 | C2×#11719921 | — | 2 | 1 | no | — |
| 166 | C2×#11719921 | C23 | 1 | 1 | yes | characteristic |
| 167 | C22⋊C4×D53 | — | 2 | 1 | no | — |
| 168 | C22⋊C4×D53 | — | 2 | 1 | no | — |
| 169 | #13133151 | — | 2 | 1 | no | — |
| 170 | #13133149 | — | 2 | 1 | no | — |
| 171 | #13133148 | — | 2 | 1 | no | — |
| 172 | #13133148 | — | 2 | 1 | no | — |
| 173 | #13133142 | — | 2 | 1 | no | — |
| 174 | #13133141 | — | 2 | 1 | no | — |
| 175 | #13133141 | — | 2 | 1 | no | — |
| 176 | #13133139 | — | 2 | 1 | no | — |
| 177 | #13133138 | — | 2 | 1 | no | — |
| 178 | #13133138 | — | 2 | 1 | no | — |
| 179 | C22⋊#88322 | C23 | 1 | 1 | yes | characteristic |
| 180 | C22⋊#88322 | C23 | 1 | 1 | yes | characteristic |
| 181 | #13133129 | — | 2 | 1 | no | — |
| 182 | #13133129 | — | 2 | 1 | no | — |
| 183 | #13133124 | — | 2 | 1 | no | — |
| 184 | #13133124 | — | 2 | 1 | no | — |
| 185 | #13133124 | — | 2 | 1 | no | — |
| 186 | #13133124 | C23 | 1 | 1 | yes | characteristic |
| 187 | C22×D4×C53 | — | 2 | 1 | no | — |
| 188 | C22×D4×C53 | C23 | 1 | 1 | yes | characteristic |
| 189 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 190 | C2×SD16×C53 | — | 2 | 1 | no | — |
| 191 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 192 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 193 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 194 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 195 | C22⋊Q8×C53 | — | 2 | 1 | no | — |
| 196 | C22⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 197 | C22⋊Q8×C53 | C23 | 1 | 1 | yes | characteristic |
| 198 | C2×C22⋊C4×C53 | — | 2 | 1 | no | — |
| 199 | C2×C22⋊C4×C53 | — | 2 | 1 | no | — |
| 200 | C2×C22⋊C4×C53 | C23 | 1 | 1 | yes | characteristic |
| 201 | #102×C53 | — | 2 | 1 | no | — |
| 202 | #102×C53 | — | 2 | 1 | no | — |
| 203 | C22⋊C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 204 | C22⋊C8×C53 | C23 | 1 | 1 | yes | characteristic |
| 205 | #95×C53 | C23 | 1 | 1 | yes | characteristic |
| 206 | C24×C53 | — | 2 | 1 | no | — |
| 207 | C24×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 208 | C23×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 209 | C23×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 210 | C2×Q8×C53 | — | 2 | 1 | no | — |
| 211 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 212 | C2×Q8×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 213 | C2×D4×C53 | — | 2 | 1 | no | — |
| 214 | C2×D4×C53 | — | 2 | 1 | no | — |
| 215 | C2×D4×C53 | — | 8 | 1 | no | — |
| 216 | C2×D4×C53 | — | 8 | 1 | no | — |
| 217 | C2×D4×C53 | — | 8 | 1 | no | — |
| 218 | C2×D4×C53 | — | 8 | 1 | no | — |
| 219 | C22×C4×C53 | — | 2 | 1 | no | — |
| 220 | C22×C4×C53 | — | 2 | 1 | no | — |
| 221 | C22×C4×C53 | — | 2 | 1 | no | — |
| 222 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 223 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 224 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 225 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 226 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 227 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 228 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 229 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 230 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 231 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 232 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 233 | C2×C22⋊D53 | — | 8 | 1 | no | — |
| 234 | C2×C22⋊D53 | — | 8 | 1 | no | — |
| 235 | C2×C22⋊D53 | — | 8 | 1 | no | — |
| 236 | C2×C22⋊D53 | — | 8 | 1 | no | — |
| 237 | C2×C22⋊D53 | — | 8 | 1 | no | — |
| 238 | C2×C22⋊D53 | — | 8 | 1 | no | — |
| 239 | C2×C22⋊D53 | — | 8 | 1 | no | — |
| 240 | C22×Dic53 | — | 2 | 1 | no | — |
| 241 | C22×Dic53 | — | 2 | 1 | no | — |
| 242 | C22×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 243 | C22×Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 244 | #11719949 | — | 8 | 1 | no | — |
| 245 | #11719949 | — | 8 | 2 | no | — |
| 246 | Q8×D53 | — | 8 | 1 | no | — |
| 247 | #11719945 | — | 8 | 2 | no | — |
| 248 | #11719945 | — | 8 | 2 | no | — |
| 249 | C2×D212 | — | 2 | 1 | no | — |
| 250 | C2×D212 | — | 2 | 1 | no | — |
| 251 | C2×D212 | — | 2 | 1 | no | — |
| 252 | C2×D212 | — | 2 | 1 | no | — |
| 253 | C2×D212 | — | 2 | 1 | no | — |
| 254 | C2×D212 | — | 2 | 1 | no | — |
| 255 | C2×D212 | — | 8 | 1 | no | — |
| 256 | C2×D212 | C2×D4 | 1 | 1 | yes | characteristic |
| 257 | C2×C4×D53 | — | 2 | 1 | no | — |
| 258 | C2×C4×D53 | — | 2 | 1 | no | — |
| 259 | C2×C4×D53 | — | 2 | 1 | no | — |
| 260 | C2×C4×D53 | — | 2 | 1 | no | — |
| 261 | C2×C4×D53 | — | 2 | 1 | no | — |
| 262 | C2×C4×D53 | — | 2 | 1 | no | — |
| 263 | C2×C4×D53 | — | 2 | 1 | no | — |
| 264 | C2×C4×D53 | — | 8 | 1 | no | — |
| 265 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 266 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 267 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 268 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 269 | C2×Dic106 | — | 2 | 1 | no | — |
| 270 | C2×Dic106 | — | 2 | 1 | no | — |
| 271 | C2×Dic106 | C2×D4 | 1 | 1 | yes | characteristic |
| 272 | SD16×C53 | — | 8 | 1 | no | — |
| 273 | SD16×C53 | — | 8 | 1 | no | — |
| 274 | C2×C8×C53 | — | 2 | 1 | no | — |
| 275 | C2×C8×C53 | — | 2 | 1 | no | — |
| 276 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 277 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 278 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 279 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 280 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 281 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 282 | C4⋊C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 283 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 284 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 285 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 286 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 287 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 288 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 289 | C22⋊C4×C53 | — | 8 | 1 | no | — |
| 290 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 291 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 292 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 293 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 294 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 295 | C22⋊Dic53 | — | 8 | 1 | no | — |
| 296 | C22⋊Dic53 | — | 8 | 1 | no | — |
| 297 | #11719923 | — | 8 | 1 | no | — |
| 298 | #11719922 | — | 8 | 1 | no | — |
| 299 | #11719921 | — | 2 | 1 | no | — |
| 300 | #11719921 | — | 2 | 1 | no | — |
| 301 | #11719921 | — | 2 | 1 | no | — |
| 302 | #11719921 | — | 2 | 1 | no | — |
| 303 | #11719921 | — | 2 | 1 | no | — |
| 304 | #11719921 | — | 2 | 1 | no | — |
| 305 | #11719921 | — | 2 | 1 | no | — |
| 306 | #11719921 | — | 2 | 1 | no | — |
| 307 | #11719921 | — | 2 | 1 | no | — |
| 308 | #11719921 | — | 2 | 1 | no | — |
| 309 | #11719921 | — | 2 | 1 | no | — |
| 310 | #11719921 | — | 2 | 1 | no | — |
| 311 | #11719921 | — | 2 | 1 | no | — |
| 312 | #11719921 | — | 2 | 1 | no | — |
| 313 | #11719921 | — | 8 | 1 | no | — |
| 314 | #11719921 | — | 8 | 1 | no | — |
| 315 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 316 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 317 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 318 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 319 | C4⋊Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 320 | C4⋊Dic53 | C2×D4 | 1 | 1 | yes | characteristic |
| 321 | #11719919 | — | 2 | 1 | no | — |
| 322 | #11719919 | — | 2 | 1 | no | — |
| 323 | #11719919 | — | 2 | 1 | no | — |
| 324 | #11719919 | — | 2 | 1 | no | — |
| 325 | #11719919 | — | 2 | 1 | no | — |
| 326 | #11719919 | — | 2 | 1 | no | — |
| 327 | #11719919 | — | 2 | 1 | no | — |
| 328 | #11719919 | — | 2 | 1 | no | — |
| 329 | #11719919 | — | 2 | 1 | no | — |
| 330 | #11719919 | — | 2 | 1 | no | — |
| 331 | C4×Dic53 | — | 2 | 1 | no | — |
| 332 | C4×Dic53 | — | 2 | 1 | no | — |
| 333 | C4×Dic53 | — | 2 | 1 | no | — |
| 334 | C2×#88322 | — | 2 | 1 | no | — |
| 335 | C2×#88322 | — | 2 | 1 | no | — |
| 336 | #11719912 | — | 8 | 1 | no | — |
| 337 | C8×D53 | — | 8 | 1 | no | — |
| 338 | C23×C53 | — | 2 | 1 | no | — |
| 339 | C23×C53 | — | 2 | 1 | no | — |
| 340 | C23×C53 | — | 2 | 1 | no | — |
| 341 | C23×C53 | — | 4 | 1 | no | — |
| 342 | C23×C53 | — | 4 | 1 | no | — |
| 343 | C23×C53 | — | 4 | 1 | no | — |
| 344 | C23×C53 | — | 4 | 1 | no | — |
| 345 | C23×C53 | — | 4 | 1 | no | — |
| 346 | C23×C53 | — | 4 | 1 | no | — |
| 347 | C23×C53 | — | 4 | 1 | no | — |
| 348 | C23×C53 | — | 4 | 1 | no | — |
| 349 | C23×C53 | — | 4 | 1 | no | — |
| 350 | C23×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 351 | C22×D53 | — | 2 | 1 | no | — |
| 352 | C22×D53 | — | 2 | 1 | no | — |
| 353 | C22×D53 | — | 2 | 1 | no | — |
| 354 | C22×D53 | — | 2 | 1 | no | — |
| 355 | C22×D53 | — | 2 | 1 | no | — |
| 356 | C22×D53 | — | 2 | 1 | no | — |
| 357 | C22×D53 | — | 4 | 1 | no | — |
| 358 | C22×D53 | — | 4 | 1 | no | — |
| 359 | C22×D53 | — | 4 | 1 | no | — |
| 360 | C22×D53 | — | 4 | 1 | no | — |
| 361 | C22×D53 | #120 | 1 | 1 | yes | characteristic |
| 362 | C22×D53 | #120 | 1 | 1 | yes | characteristic |
| 363 | Q8×C53 | — | 4 | 1 | no | — |
| 364 | Q8×C53 | — | 4 | 1 | no | — |
| 365 | Q8×C53 | — | 8 | 1 | no | — |
| 366 | D4×C53 | — | 4 | 1 | no | — |
| 367 | D4×C53 | — | 4 | 1 | no | — |
| 368 | D4×C53 | — | 4 | 1 | no | — |
| 369 | D4×C53 | — | 4 | 1 | no | — |
| 370 | D4×C53 | — | 8 | 4 | no | — |
| 371 | C2×C4×C53 | — | 2 | 1 | no | — |
| 372 | C2×C4×C53 | — | 2 | 1 | no | — |
| 373 | C2×C4×C53 | — | 2 | 1 | no | — |
| 374 | C2×C4×C53 | — | 2 | 1 | no | — |
| 375 | C2×C4×C53 | — | 2 | 1 | no | — |
| 376 | C2×C4×C53 | — | 4 | 1 | no | — |
| 377 | C2×C4×C53 | — | 4 | 1 | no | — |
| 378 | C2×C4×C53 | — | 4 | 1 | no | — |
| 379 | C2×C4×C53 | — | 4 | 1 | no | — |
| 380 | C2×C4×C53 | — | 4 | 1 | no | — |
| 381 | C2×C4×C53 | — | 8 | 1 | no | — |
| 382 | C2×C4×C53 | — | 8 | 1 | no | — |
| 383 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 384 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 385 | C22⋊D53 | — | 4 | 2 | no | — |
| 386 | C22⋊D53 | — | 4 | 2 | no | — |
| 387 | C22⋊D53 | — | 4 | 1 | no | — |
| 388 | C22⋊D53 | — | 4 | 1 | no | — |
| 389 | C22⋊D53 | — | 8 | 1 | no | — |
| 390 | C22⋊D53 | — | 8 | 1 | no | — |
| 391 | C22⋊D53 | — | 8 | 1 | no | — |
| 392 | C22⋊D53 | — | 8 | 1 | no | — |
| 393 | C22⋊D53 | — | 8 | 2 | no | — |
| 394 | C22⋊D53 | — | 8 | 2 | no | — |
| 395 | C22⋊D53 | — | 8 | 4 | no | — |
| 396 | C2×Dic53 | — | 2 | 1 | no | — |
| 397 | C2×Dic53 | — | 2 | 1 | no | — |
| 398 | C2×Dic53 | — | 2 | 1 | no | — |
| 399 | C2×Dic53 | — | 2 | 1 | no | — |
| 400 | C2×Dic53 | — | 4 | 1 | no | — |
| 401 | C2×Dic53 | — | 4 | 1 | no | — |
| 402 | C2×Dic53 | — | 4 | 1 | no | — |
| 403 | C2×Dic53 | — | 4 | 1 | no | — |
| 404 | C2×Dic53 | — | 4 | 1 | no | — |
| 405 | C2×Dic53 | — | 4 | 1 | no | — |
| 406 | C2×Dic53 | — | 4 | 1 | no | — |
| 407 | C2×Dic53 | — | 4 | 1 | no | — |
| 408 | C2×Dic53 | #120 | 1 | 1 | yes | characteristic |
| 409 | C2×Dic53 | #120 | 1 | 1 | yes | characteristic |
| 410 | D212 | — | 4 | 1 | no | — |
| 411 | D212 | — | 4 | 2 | no | — |
| 412 | D212 | — | 4 | 2 | no | — |
| 413 | D212 | — | 8 | 1 | no | — |
| 414 | D212 | — | 8 | 1 | no | — |
| 415 | D212 | — | 8 | 1 | no | — |
| 416 | D212 | — | 8 | 1 | no | — |
| 417 | C4×D53 | — | 4 | 1 | no | — |
| 418 | C4×D53 | — | 4 | 1 | no | — |
| 419 | C4×D53 | — | 4 | 1 | no | — |
| 420 | C4×D53 | — | 4 | 1 | no | — |
| 421 | C4×D53 | — | 4 | 2 | no | — |
| 422 | C4×D53 | — | 4 | 2 | no | — |
| 423 | C4×D53 | — | 8 | 1 | no | — |
| 424 | C4×D53 | — | 8 | 1 | no | — |
| 425 | C4×D53 | — | 8 | 1 | no | — |
| 426 | C4×D53 | — | 8 | 1 | no | — |
| 427 | C4×D53 | — | 8 | 1 | no | — |
| 428 | Dic106 | — | 4 | 2 | no | — |
| 429 | Dic106 | — | 4 | 1 | no | — |
| 430 | Dic106 | — | 8 | 1 | no | — |
| 431 | C8×C53 | — | 4 | 1 | no | — |
| 432 | C8×C53 | — | 4 | 1 | no | — |
| 433 | #88322 | — | 4 | 1 | no | — |
| 434 | #88322 | — | 4 | 1 | no | — |
| 435 | #18452 | — | 53 | 1 | no | maximal, Sylow |
| 436 | C22×C53 | — | 2 | 1 | no | — |
| 437 | C22×C53 | — | 2 | 1 | no | — |
| 438 | C22×C53 | — | 4 | 1 | no | — |
| 439 | C22×C53 | — | 4 | 1 | no | — |
| 440 | C22×C53 | — | 4 | 1 | no | — |
| 441 | C22×C53 | — | 8 | 1 | no | — |
| 442 | C22×C53 | — | 8 | 1 | no | — |
| 443 | C22×C53 | — | 8 | 1 | no | — |
| 444 | C22×C53 | — | 8 | 1 | no | — |
| 445 | C22×C53 | — | 8 | 1 | no | — |
| 446 | C22×C53 | — | 8 | 1 | no | — |
| 447 | C22×C53 | — | 8 | 1 | no | — |
| 448 | C22×C53 | — | 8 | 1 | no | — |
| 449 | C22×C53 | — | 8 | 1 | no | — |
| 450 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 451 | C22×C53 | #577 | 1 | 1 | yes | characteristic |
| 452 | C22×C53 | #577 | 1 | 1 | yes | characteristic |
| 453 | C2×D53 | — | 2 | 1 | no | — |
| 454 | C2×D53 | — | 2 | 1 | no | — |
| 455 | C2×D53 | — | 2 | 1 | no | — |
| 456 | C2×D53 | — | 2 | 1 | no | — |
| 457 | C2×D53 | — | 2 | 1 | no | — |
| 458 | C2×D53 | — | 2 | 1 | no | — |
| 459 | C2×D53 | — | 4 | 1 | no | — |
| 460 | C2×D53 | — | 4 | 1 | no | — |
| 461 | C2×D53 | — | 4 | 1 | no | — |
| 462 | C2×D53 | — | 4 | 1 | no | — |
| 463 | C2×D53 | — | 4 | 1 | no | — |
| 464 | C2×D53 | — | 4 | 1 | no | — |
| 465 | C2×D53 | — | 8 | 1 | no | — |
| 466 | C2×D53 | — | 8 | 1 | no | — |
| 467 | C2×D53 | — | 8 | 1 | no | — |
| 468 | C2×D53 | — | 8 | 1 | no | — |
| 469 | C4×C53 | — | 2 | 1 | no | — |
| 470 | C4×C53 | — | 2 | 1 | no | — |
| 471 | C4×C53 | — | 4 | 1 | no | — |
| 472 | C4×C53 | — | 4 | 1 | no | — |
| 473 | C4×C53 | — | 4 | 1 | no | — |
| 474 | C4×C53 | — | 4 | 1 | no | — |
| 475 | C4×C53 | — | 4 | 1 | no | — |
| 476 | C4×C53 | — | 8 | 1 | no | — |
| 477 | Dic53 | — | 2 | 1 | no | — |
| 478 | Dic53 | — | 2 | 1 | no | — |
| 479 | Dic53 | — | 4 | 1 | no | — |
| 480 | Dic53 | — | 4 | 1 | no | — |
| 481 | Dic53 | — | 4 | 1 | no | — |
| 482 | Dic53 | — | 4 | 1 | no | — |
| 483 | Dic53 | — | 8 | 1 | no | — |
| 484 | Dic53 | — | 8 | 1 | no | — |
| 485 | #3536 | — | 53 | 1 | no | — |
| 486 | #3194 | — | 53 | 1 | no | — |
| 487 | #3187 | — | 53 | 1 | no | — |
| 488 | #2815 | — | 53 | 1 | no | — |
| 489 | #1612 | — | 53 | 1 | no | — |
| 490 | #1612 | — | 53 | 1 | no | — |
| 491 | #1608 | — | 53 | 1 | no | — |
| 492 | #1608 | — | 53 | 1 | no | — |
| 493 | #1600 | — | 53 | 1 | no | — |
| 494 | #1600 | — | 53 | 1 | no | — |
| 495 | #1596 | — | 53 | 1 | no | — |
| 496 | #1596 | D53 | 1 | 1 | yes | characteristic, complemented |
| 497 | #1516 | — | 53 | 1 | no | — |
| 498 | #1511 | — | 53 | 1 | no | — |
| 499 | #1471 | — | 53 | 1 | no | — |
| 500 | C2×C53 | — | 2 | 1 | no | — |
| 501 | C2×C53 | — | 2 | 1 | no | — |
| 502 | C2×C53 | — | 8 | 1 | no | — |
| 503 | C2×C53 | — | 16 | 1 | no | — |
| 504 | C2×C53 | #3010 | 1 | 1 | yes | characteristic |
| 505 | C2×C53 | #3019 | 1 | 1 | yes | characteristic |
| 506 | C2×C53 | #3026 | 1 | 1 | yes | characteristic |
| 507 | D53 | — | 4 | 1 | no | — |
| 508 | D53 | — | 4 | 1 | no | — |
| 509 | D53 | — | 8 | 1 | no | — |
| 510 | D53 | — | 8 | 1 | no | — |
| 511 | #562 | — | 106 | 1 | no | — |
| 512 | #562 | — | 106 | 1 | no | — |
| 513 | #554 | — | 106 | 1 | no | — |
| 514 | #548 | — | 106 | 1 | no | — |
| 515 | #547 | — | 106 | 1 | no | — |
| 516 | #546 | — | 106 | 1 | no | — |
| 517 | #546 | — | 106 | 1 | no | — |
| 518 | #546 | — | 106 | 1 | no | — |
| 519 | #543 | — | 53 | 1 | no | — |
| 520 | #543 | C2×D53 | 1 | 1 | yes | characteristic |
| 521 | #542 | — | 106 | 1 | no | — |
| 522 | #539 | — | 106 | 1 | no | — |
| 523 | #538 | — | 53 | 1 | no | — |
| 524 | #538 | — | 53 | 1 | no | — |
| 525 | #537 | — | 106 | 1 | no | — |
| 526 | #537 | — | 106 | 1 | no | — |
| 527 | #525 | — | 53 | 1 | no | — |
| 528 | C2×C22⋊Q8 | — | 53 | 1 | no | — |
| 529 | C2×#121 | — | 53 | 1 | no | — |
| 530 | C2×#121 | — | 53 | 1 | no | — |
| 531 | #483 | — | 53 | 1 | no | — |
| 532 | #483 | — | 53 | 1 | no | — |
| 533 | #483 | — | 53 | 1 | no | — |
| 534 | #482 | — | 106 | 1 | no | — |
| 535 | #481 | — | 106 | 1 | no | — |
| 536 | #480 | — | 53 | 1 | no | — |
| 537 | #469 | — | 106 | 1 | no | — |
| 538 | #468 | — | 106 | 1 | no | — |
| 539 | #465 | — | 106 | 1 | no | — |
| 540 | #465 | — | 106 | 1 | no | — |
| 541 | #450 | — | 53 | 1 | no | — |
| 542 | #450 | C2×D53 | 1 | 1 | yes | characteristic |
| 543 | #450 | C2×D53 | 1 | 1 | yes | characteristic |
| 544 | #449 | — | 106 | 1 | no | — |
| 545 | #448 | — | 106 | 1 | no | — |
| 546 | #447 | — | 53 | 1 | no | — |
| 547 | #407 | — | 53 | 1 | no | — |
| 548 | C2×C22⋊C8 | — | 53 | 1 | no | — |
| 549 | #397 | — | 53 | 1 | no | — |
| 550 | #397 | — | 53 | 1 | no | — |
| 551 | #397 | — | 106 | 1 | no | — |
| 552 | #392 | — | 53 | 1 | no | — |
| 553 | #392 | — | 106 | 1 | no | — |
| 554 | #392 | — | 106 | 1 | no | — |
| 555 | #392 | — | 106 | 1 | no | — |
| 556 | #392 | C2×D53 | 1 | 1 | yes | characteristic |
| 557 | #381 | — | 53 | 1 | no | — |
| 558 | #328 | — | 53 | 1 | no | — |
| 559 | #328 | — | 53 | 1 | no | — |
| 560 | #328 | — | 53 | 1 | no | — |
| 561 | #328 | — | 53 | 1 | no | — |
| 562 | #328 | C2×D53 | 1 | 1 | yes | characteristic |
| 563 | #328 | C2×D53 | 1 | 1 | yes | characteristic |
| 564 | #327 | — | 53 | 1 | no | — |
| 565 | #327 | — | 53 | 1 | no | — |
| 566 | #323 | — | 53 | 1 | no | — |
| 567 | #323 | — | 53 | 1 | no | — |
| 568 | #323 | — | 53 | 1 | no | — |
| 569 | #323 | C2×D53 | 1 | 1 | yes | characteristic |
| 570 | C53 | #18452 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 571 | C2×#41 | — | 53 | 1 | no | — |
| 572 | C2×#41 | — | 106 | 1 | no | — |
| 573 | C2×#41 | — | 106 | 1 | no | — |
| 574 | C2×#41 | — | 106 | 1 | no | — |
| 575 | C22×Q8 | — | 53 | 1 | no | — |
| 576 | C22×D4 | — | 2 | 1 | no | — |
| 577 | C22×D4 | — | 53 | 1 | no | — |
| 578 | C22×D4 | — | 53 | 1 | no | — |
| 579 | C22×D4 | — | 53 | 1 | no | — |
| 580 | C22×D4 | — | 106 | 1 | no | — |
| 581 | C22×D4 | — | 106 | 1 | no | — |
| 582 | C22×D4 | C22×D53 | 1 | 1 | yes | characteristic |
| 583 | C23×C4 | — | 53 | 1 | no | — |
| 584 | C2×SD16 | — | 2 | 1 | no | — |
| 585 | C2×SD16 | — | 2 | 1 | no | — |
| 586 | C2×SD16 | — | 106 | 1 | no | — |
| 587 | C2×D8 | — | 106 | 1 | no | — |
| 588 | C2×M16 | — | 106 | 1 | no | — |
| 589 | C22×C8 | — | 106 | 1 | no | — |
| 590 | C4⋊Q8 | — | 106 | 1 | no | — |
| 591 | #126 | — | 106 | 1 | no | — |
| 592 | #126 | — | 106 | 1 | no | — |
| 593 | #125 | — | 106 | 1 | no | — |
| 594 | #125 | — | 106 | 1 | no | — |
| 595 | #124 | — | 106 | 1 | no | — |
| 596 | #124 | — | 106 | 1 | no | — |
| 597 | #124 | — | 106 | 1 | no | — |
| 598 | #124 | — | 106 | 1 | no | — |
| 599 | #124 | — | 106 | 1 | no | — |
| 600 | #123 | — | 106 | 1 | no | — |
| 601 | #123 | — | 106 | 1 | no | — |
| 602 | #123 | — | 106 | 1 | no | — |
| 603 | #123 | — | 106 | 1 | no | — |
| 604 | #123 | — | 106 | 1 | no | — |
| 605 | #123 | — | 106 | 1 | no | — |
| 606 | #123 | — | 106 | 1 | no | — |
| 607 | #123 | — | 106 | 1 | no | — |
| 608 | #123 | — | 106 | 1 | no | — |
| 609 | C22⋊Q8 | — | 2 | 1 | no | — |
| 610 | C22⋊Q8 | — | 2 | 1 | no | — |
| 611 | C22⋊Q8 | — | 2 | 1 | no | — |
| 612 | C22⋊Q8 | — | 2 | 1 | no | — |
| 613 | C22⋊Q8 | — | 2 | 1 | no | — |
| 614 | C22⋊Q8 | — | 53 | 1 | no | — |
| 615 | C22⋊Q8 | — | 53 | 1 | no | — |
| 616 | C22⋊Q8 | — | 53 | 1 | no | — |
| 617 | C22⋊Q8 | — | 53 | 1 | no | — |
| 618 | C22⋊Q8 | — | 106 | 1 | no | — |
| 619 | C22⋊Q8 | — | 106 | 1 | no | — |
| 620 | C22⋊Q8 | — | 106 | 1 | no | — |
| 621 | C22⋊Q8 | — | 106 | 1 | no | — |
| 622 | C22⋊Q8 | — | 106 | 1 | no | — |
| 623 | C22⋊Q8 | — | 106 | 1 | no | — |
| 624 | C22⋊Q8 | — | 106 | 1 | no | — |
| 625 | C22⋊Q8 | — | 106 | 1 | no | — |
| 626 | C22⋊Q8 | — | 106 | 1 | no | — |
| 627 | C22⋊Q8 | — | 106 | 1 | no | — |
| 628 | C22⋊Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 629 | C22⋊Q8 | C22×D53 | 1 | 1 | yes | characteristic |
| 630 | #121 | — | 53 | 1 | no | — |
| 631 | #121 | — | 53 | 1 | no | — |
| 632 | #121 | — | 106 | 1 | no | — |
| 633 | #121 | — | 106 | 1 | no | — |
| 634 | #121 | — | 106 | 1 | no | — |
| 635 | #121 | — | 106 | 1 | no | — |
| 636 | #121 | — | 106 | 1 | no | — |
| 637 | #121 | — | 106 | 1 | no | — |
| 638 | #121 | — | 106 | 1 | no | — |
| 639 | #121 | — | 106 | 1 | no | — |
| 640 | #121 | — | 106 | 1 | no | — |
| 641 | #121 | — | 106 | 1 | no | — |
| 642 | #121 | — | 106 | 1 | no | — |
| 643 | #121 | — | 106 | 1 | no | — |
| 644 | #121 | — | 106 | 1 | no | — |
| 645 | #121 | — | 106 | 1 | no | — |
| 646 | #121 | — | 106 | 1 | no | — |
| 647 | #121 | — | 106 | 1 | no | — |
| 648 | #121 | — | 106 | 1 | no | — |
| 649 | #121 | — | 106 | 1 | no | — |
| 650 | #121 | — | 106 | 1 | no | — |
| 651 | #120 | — | 106 | 1 | no | — |
| 652 | #120 | — | 106 | 1 | no | — |
| 653 | #120 | — | 106 | 1 | no | — |
| 654 | C4×Q8 | — | 106 | 1 | no | — |
| 655 | C4×D4 | — | 106 | 1 | no | — |
| 656 | C4×D4 | — | 106 | 1 | no | — |
| 657 | C4×D4 | — | 106 | 1 | no | — |
| 658 | C4×D4 | — | 106 | 1 | no | — |
| 659 | C4×D4 | — | 106 | 1 | no | — |
| 660 | C4×D4 | — | 106 | 1 | no | — |
| 661 | C4×D4 | — | 106 | 1 | no | — |
| 662 | #117 | — | 53 | 1 | no | — |
| 663 | C2×C4⋊C4 | — | 53 | 1 | no | — |
| 664 | C2×C4⋊C4 | — | 53 | 1 | no | — |
| 665 | C2×C4⋊C4 | — | 53 | 1 | no | — |
| 666 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 667 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 668 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 669 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 670 | C2×C22⋊C4 | — | 53 | 1 | no | — |
| 671 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 672 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 673 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 674 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 675 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 676 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 677 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 678 | C2×C22⋊C4 | C22×D53 | 1 | 1 | yes | characteristic |
| 679 | #107 | — | 106 | 1 | no | — |
| 680 | #106 | — | 106 | 1 | no | — |
| 681 | #106 | — | 106 | 1 | no | — |
| 682 | #106 | — | 106 | 1 | no | — |
| 683 | #103 | — | 106 | 1 | no | — |
| 684 | #103 | — | 106 | 1 | no | — |
| 685 | #103 | — | 106 | 1 | no | — |
| 686 | #102 | — | 2 | 1 | no | — |
| 687 | #102 | — | 2 | 1 | no | — |
| 688 | #102 | — | 106 | 1 | no | — |
| 689 | #102 | — | 106 | 1 | no | — |
| 690 | #102 | — | 106 | 1 | no | — |
| 691 | C22⋊C8 | — | 53 | 1 | no | — |
| 692 | C22⋊C8 | — | 53 | 1 | no | — |
| 693 | C22⋊C8 | — | 106 | 1 | no | — |
| 694 | C22⋊C8 | — | 106 | 1 | no | — |
| 695 | C22⋊C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 696 | C22⋊C8 | C22×D53 | 1 | 1 | yes | characteristic |
| 697 | #95 | — | 53 | 1 | no | — |
| 698 | #95 | — | 106 | 1 | no | — |
| 699 | #95 | — | 106 | 1 | no | — |
| 700 | #95 | — | 106 | 1 | no | — |
| 701 | #95 | C22×D53 | 1 | 1 | yes | characteristic |
| 702 | C24 | — | 2 | 1 | no | — |
| 703 | C24 | — | 53 | 1 | no | — |
| 704 | C24 | — | 53 | 1 | no | — |
| 705 | C24 | D4×D53 | 1 | 1 | yes | characteristic |
| 706 | #41 | — | 424 | 2 | no | — |
| 707 | #41 | — | 424 | 2 | no | — |
| 708 | #41 | — | 424 | 2 | no | — |
| 709 | #41 | — | 424 | 1 | no | — |
| 710 | C2×Q8 | — | 2 | 1 | no | — |
| 711 | C2×Q8 | — | 53 | 1 | no | — |
| 712 | C2×Q8 | — | 106 | 1 | no | — |
| 713 | C2×Q8 | — | 106 | 1 | no | — |
| 714 | C2×Q8 | — | 424 | 1 | no | — |
| 715 | C2×Q8 | D4×D53 | 1 | 1 | yes | characteristic |
| 716 | C2×Q8 | D4×D53 | 1 | 1 | yes | characteristic |
| 717 | C2×D4 | — | 2 | 1 | no | — |
| 718 | C2×D4 | — | 2 | 1 | no | — |
| 719 | C2×D4 | — | 8 | 1 | no | — |
| 720 | C2×D4 | — | 8 | 1 | no | — |
| 721 | C2×D4 | — | 8 | 1 | no | — |
| 722 | C2×D4 | — | 8 | 1 | no | — |
| 723 | C2×D4 | — | 53 | 1 | no | — |
| 724 | C2×D4 | — | 106 | 1 | no | — |
| 725 | C2×D4 | — | 106 | 1 | no | — |
| 726 | C2×D4 | — | 106 | 1 | no | — |
| 727 | C2×D4 | — | 106 | 1 | no | — |
| 728 | C2×D4 | — | 106 | 1 | no | — |
| 729 | C2×D4 | — | 106 | 1 | no | — |
| 730 | C2×D4 | — | 106 | 1 | no | — |
| 731 | C2×D4 | — | 106 | 1 | no | — |
| 732 | C2×D4 | — | 106 | 1 | no | — |
| 733 | C2×D4 | — | 106 | 1 | no | — |
| 734 | C2×D4 | — | 106 | 1 | no | — |
| 735 | C2×D4 | — | 106 | 1 | no | — |
| 736 | C2×D4 | — | 106 | 1 | no | — |
| 737 | C2×D4 | — | 424 | 1 | no | — |
| 738 | C2×D4 | — | 424 | 1 | no | — |
| 739 | C2×D4 | — | 424 | 1 | no | — |
| 740 | C2×D4 | — | 424 | 1 | no | — |
| 741 | C2×D4 | — | 424 | 1 | no | — |
| 742 | C2×D4 | — | 424 | 1 | no | — |
| 743 | C2×D4 | — | 424 | 1 | no | — |
| 744 | C2×D4 | — | 424 | 1 | no | — |
| 745 | C2×D4 | — | 212 | 1 | no | — |
| 746 | C2×D4 | — | 212 | 1 | no | — |
| 747 | C22×C4 | — | 2 | 1 | no | — |
| 748 | C22×C4 | — | 2 | 1 | no | — |
| 749 | C22×C4 | — | 2 | 1 | no | — |
| 750 | C22×C4 | — | 53 | 1 | no | — |
| 751 | C22×C4 | — | 53 | 1 | no | — |
| 752 | C22×C4 | — | 53 | 1 | no | — |
| 753 | C22×C4 | — | 53 | 1 | no | — |
| 754 | C22×C4 | — | 53 | 1 | no | — |
| 755 | C22×C4 | — | 53 | 1 | no | — |
| 756 | C22×C4 | — | 106 | 1 | no | — |
| 757 | C22×C4 | — | 106 | 1 | no | — |
| 758 | C22×C4 | — | 106 | 1 | no | — |
| 759 | C22×C4 | — | 106 | 1 | no | — |
| 760 | C22×C4 | — | 106 | 1 | no | — |
| 761 | C22×C4 | — | 106 | 1 | no | — |
| 762 | C22×C4 | — | 106 | 1 | no | — |
| 763 | C22×C4 | — | 106 | 1 | no | — |
| 764 | C22×C4 | — | 106 | 1 | no | — |
| 765 | C22×C4 | — | 424 | 1 | no | — |
| 766 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 767 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 768 | SD16 | — | 8 | 1 | no | — |
| 769 | SD16 | — | 8 | 1 | no | — |
| 770 | SD16 | — | 424 | 1 | no | — |
| 771 | D8 | — | 424 | 1 | no | — |
| 772 | M16 | — | 424 | 1 | no | — |
| 773 | C2×C8 | — | 2 | 1 | no | — |
| 774 | C2×C8 | — | 2 | 1 | no | — |
| 775 | C2×C8 | — | 106 | 1 | no | — |
| 776 | C2×C8 | — | 106 | 1 | no | — |
| 777 | C2×C8 | — | 424 | 1 | no | — |
| 778 | C4⋊C4 | — | 2 | 1 | no | — |
| 779 | C4⋊C4 | — | 2 | 1 | no | — |
| 780 | C4⋊C4 | — | 2 | 1 | no | — |
| 781 | C4⋊C4 | — | 2 | 1 | no | — |
| 782 | C4⋊C4 | — | 2 | 1 | no | — |
| 783 | C4⋊C4 | — | 53 | 1 | no | — |
| 784 | C4⋊C4 | — | 53 | 1 | no | — |
| 785 | C4⋊C4 | — | 106 | 1 | no | — |
| 786 | C4⋊C4 | — | 106 | 1 | no | — |
| 787 | C4⋊C4 | — | 106 | 1 | no | — |
| 788 | C4⋊C4 | — | 106 | 1 | no | — |
| 789 | C4⋊C4 | — | 106 | 1 | no | — |
| 790 | C4⋊C4 | — | 106 | 1 | no | — |
| 791 | C4⋊C4 | — | 106 | 1 | no | — |
| 792 | C4⋊C4 | — | 106 | 1 | no | — |
| 793 | C4⋊C4 | — | 106 | 1 | no | — |
| 794 | C4⋊C4 | — | 106 | 1 | no | — |
| 795 | C4⋊C4 | — | 106 | 1 | no | — |
| 796 | C4⋊C4 | — | 106 | 1 | no | — |
| 797 | C4⋊C4 | — | 106 | 1 | no | — |
| 798 | C4⋊C4 | — | 106 | 1 | no | — |
| 799 | C4⋊C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 800 | C4⋊C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 801 | C22⋊C4 | — | 2 | 1 | no | — |
| 802 | C22⋊C4 | — | 2 | 1 | no | — |
| 803 | C22⋊C4 | — | 2 | 1 | no | — |
| 804 | C22⋊C4 | — | 2 | 1 | no | — |
| 805 | C22⋊C4 | — | 2 | 1 | no | — |
| 806 | C22⋊C4 | — | 2 | 1 | no | — |
| 807 | C22⋊C4 | — | 8 | 1 | no | — |
| 808 | C22⋊C4 | — | 106 | 1 | no | — |
| 809 | C22⋊C4 | — | 106 | 1 | no | — |
| 810 | C22⋊C4 | — | 106 | 1 | no | — |
| 811 | C22⋊C4 | — | 106 | 1 | no | — |
| 812 | C22⋊C4 | — | 106 | 1 | no | — |
| 813 | C22⋊C4 | — | 106 | 1 | no | — |
| 814 | C22⋊C4 | — | 106 | 1 | no | — |
| 815 | C22⋊C4 | — | 106 | 1 | no | — |
| 816 | C22⋊C4 | — | 106 | 1 | no | — |
| 817 | C22⋊C4 | — | 106 | 1 | no | — |
| 818 | C22⋊C4 | — | 106 | 1 | no | — |
| 819 | C22⋊C4 | — | 106 | 1 | no | — |
| 820 | C22⋊C4 | — | 106 | 1 | no | — |
| 821 | C22⋊C4 | — | 106 | 1 | no | — |
| 822 | C22⋊C4 | — | 106 | 1 | no | — |
| 823 | C22⋊C4 | — | 106 | 1 | no | — |
| 824 | C22⋊C4 | — | 106 | 1 | no | — |
| 825 | C22⋊C4 | — | 424 | 1 | no | — |
| 826 | C22⋊C4 | — | 424 | 1 | no | — |
| 827 | C22⋊C4 | — | 424 | 1 | no | — |
| 828 | C22⋊C4 | — | 424 | 1 | no | — |
| 829 | C22⋊C4 | — | 212 | 1 | no | — |
| 830 | C22⋊C4 | — | 212 | 1 | no | — |
| 831 | C42 | — | 106 | 1 | no | — |
| 832 | C42 | — | 106 | 1 | no | — |
| 833 | C42 | — | 106 | 1 | no | — |
| 834 | C23 | — | 2 | 1 | no | — |
| 835 | C23 | — | 2 | 1 | no | — |
| 836 | C23 | — | 2 | 1 | no | — |
| 837 | C23 | — | 4 | 1 | no | — |
| 838 | C23 | — | 4 | 1 | no | — |
| 839 | C23 | — | 4 | 1 | no | — |
| 840 | C23 | — | 4 | 1 | no | — |
| 841 | C23 | — | 4 | 1 | no | — |
| 842 | C23 | — | 4 | 1 | no | — |
| 843 | C23 | — | 4 | 1 | no | — |
| 844 | C23 | — | 4 | 1 | no | — |
| 845 | C23 | — | 4 | 1 | no | — |
| 846 | C23 | — | 53 | 1 | no | — |
| 847 | C23 | — | 53 | 1 | no | — |
| 848 | C23 | — | 106 | 1 | no | — |
| 849 | C23 | — | 106 | 1 | no | — |
| 850 | C23 | — | 106 | 1 | no | — |
| 851 | C23 | — | 106 | 1 | no | — |
| 852 | C23 | — | 106 | 1 | no | — |
| 853 | C23 | — | 106 | 1 | no | — |
| 854 | C23 | — | 212 | 1 | no | — |
| 855 | C23 | — | 212 | 1 | no | — |
| 856 | C23 | — | 212 | 1 | no | — |
| 857 | C23 | — | 212 | 1 | no | — |
| 858 | C23 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 859 | Q8 | — | 4 | 1 | no | — |
| 860 | Q8 | — | 4 | 1 | no | — |
| 861 | Q8 | — | 8 | 1 | no | — |
| 862 | Q8 | — | 424 | 1 | no | — |
| 863 | Q8 | — | 212 | 1 | no | — |
| 864 | Q8 | — | 212 | 2 | no | — |
| 865 | D4 | — | 4 | 1 | no | — |
| 866 | D4 | — | 4 | 1 | no | — |
| 867 | D4 | — | 4 | 1 | no | — |
| 868 | D4 | — | 4 | 1 | no | — |
| 869 | D4 | — | 8 | 4 | no | — |
| 870 | D4 | — | 424 | 1 | no | — |
| 871 | D4 | — | 424 | 1 | no | — |
| 872 | D4 | — | 424 | 1 | no | — |
| 873 | D4 | — | 424 | 1 | no | — |
| 874 | D4 | — | 424 | 1 | no | — |
| 875 | D4 | — | 424 | 2 | no | — |
| 876 | D4 | — | 424 | 2 | no | — |
| 877 | D4 | — | 424 | 4 | no | — |
| 878 | D4 | — | 424 | 1 | no | — |
| 879 | D4 | — | 424 | 1 | no | — |
| 880 | D4 | — | 424 | 1 | no | — |
| 881 | D4 | — | 212 | 1 | no | — |
| 882 | D4 | — | 212 | 2 | no | — |
| 883 | D4 | — | 212 | 2 | no | — |
| 884 | D4 | — | 212 | 2 | no | — |
| 885 | D4 | — | 212 | 2 | no | — |
| 886 | D4 | — | 212 | 1 | no | — |
| 887 | D4 | — | 212 | 1 | no | — |
| 888 | C2×C4 | — | 2 | 1 | no | — |
| 889 | C2×C4 | — | 2 | 1 | no | — |
| 890 | C2×C4 | — | 2 | 1 | no | — |
| 891 | C2×C4 | — | 2 | 1 | no | — |
| 892 | C2×C4 | — | 2 | 1 | no | — |
| 893 | C2×C4 | — | 4 | 1 | no | — |
| 894 | C2×C4 | — | 4 | 1 | no | — |
| 895 | C2×C4 | — | 4 | 1 | no | — |
| 896 | C2×C4 | — | 4 | 1 | no | — |
| 897 | C2×C4 | — | 4 | 1 | no | — |
| 898 | C2×C4 | — | 8 | 1 | no | — |
| 899 | C2×C4 | — | 8 | 1 | no | — |
| 900 | C2×C4 | — | 53 | 1 | no | — |
| 901 | C2×C4 | — | 53 | 1 | no | — |
| 902 | C2×C4 | — | 106 | 1 | no | — |
| 903 | C2×C4 | — | 106 | 1 | no | — |
| 904 | C2×C4 | — | 106 | 1 | no | — |
| 905 | C2×C4 | — | 106 | 1 | no | — |
| 906 | C2×C4 | — | 424 | 1 | no | — |
| 907 | C2×C4 | — | 424 | 1 | no | — |
| 908 | C2×C4 | — | 424 | 1 | no | — |
| 909 | C2×C4 | — | 424 | 1 | no | — |
| 910 | C2×C4 | — | 424 | 1 | no | — |
| 911 | C2×C4 | — | 212 | 1 | no | — |
| 912 | C2×C4 | — | 212 | 1 | no | — |
| 913 | C2×C4 | — | 212 | 1 | no | — |
| 914 | C2×C4 | — | 212 | 1 | no | — |
| 915 | C2×C4 | — | 212 | 2 | no | — |
| 916 | C2×C4 | — | 212 | 2 | no | — |
| 917 | C2×C4 | — | 212 | 1 | no | — |
| 918 | C2×C4 | — | 212 | 1 | no | — |
| 919 | C2×C4 | — | 212 | 1 | no | — |
| 920 | C2×C4 | — | 212 | 1 | no | — |
| 921 | C2×C4 | — | 212 | 1 | no | — |
| 922 | C2×C4 | — | 212 | 1 | no | — |
| 923 | C2×C4 | — | 212 | 1 | no | — |
| 924 | C2×C4 | — | 212 | 1 | no | — |
| 925 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 926 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 927 | C8 | — | 4 | 1 | no | — |
| 928 | C8 | — | 4 | 1 | no | — |
| 929 | C8 | — | 212 | 1 | no | — |
| 930 | C8 | — | 212 | 1 | no | — |
| 931 | C22 | — | 2 | 1 | no | — |
| 932 | C22 | — | 2 | 1 | no | — |
| 933 | C22 | — | 4 | 1 | no | — |
| 934 | C22 | — | 4 | 1 | no | — |
| 935 | C22 | — | 4 | 1 | no | — |
| 936 | C22 | — | 8 | 1 | no | — |
| 937 | C22 | — | 8 | 1 | no | — |
| 938 | C22 | — | 8 | 1 | no | — |
| 939 | C22 | — | 8 | 1 | no | — |
| 940 | C22 | — | 8 | 1 | no | — |
| 941 | C22 | — | 8 | 1 | no | — |
| 942 | C22 | — | 8 | 1 | no | — |
| 943 | C22 | — | 8 | 1 | no | — |
| 944 | C22 | — | 8 | 1 | no | — |
| 945 | C22 | — | 106 | 1 | no | — |
| 946 | C22 | — | 106 | 1 | no | — |
| 947 | C22 | — | 106 | 1 | no | — |
| 948 | C22 | — | 106 | 1 | no | — |
| 949 | C22 | — | 106 | 1 | no | — |
| 950 | C22 | — | 106 | 1 | no | — |
| 951 | C22 | — | 424 | 1 | no | — |
| 952 | C22 | — | 424 | 1 | no | — |
| 953 | C22 | — | 424 | 1 | no | — |
| 954 | C22 | — | 424 | 1 | no | — |
| 955 | C22 | — | 212 | 1 | no | — |
| 956 | C22 | — | 212 | 1 | no | — |
| 957 | C22 | — | 212 | 1 | no | — |
| 958 | C22 | — | 212 | 1 | no | — |
| 959 | C22 | — | 212 | 1 | no | — |
| 960 | C22 | — | 212 | 1 | no | — |
| 961 | C22 | #120×D53 | 1 | 1 | yes | characteristic |
| 962 | C22 | #16811429 | 1 | 1 | yes | characteristic |
| 963 | C22 | #16811432 | 1 | 1 | yes | characteristic |
| 964 | C4 | — | 2 | 1 | no | — |
| 965 | C4 | — | 2 | 1 | no | — |
| 966 | C4 | — | 4 | 1 | no | — |
| 967 | C4 | — | 4 | 1 | no | — |
| 968 | C4 | — | 4 | 1 | no | — |
| 969 | C4 | — | 4 | 1 | no | — |
| 970 | C4 | — | 4 | 1 | no | — |
| 971 | C4 | — | 8 | 1 | no | — |
| 972 | C4 | — | 106 | 1 | no | — |
| 973 | C4 | — | 106 | 1 | no | — |
| 974 | C4 | — | 424 | 1 | no | — |
| 975 | C4 | — | 424 | 1 | no | — |
| 976 | C4 | — | 212 | 1 | no | — |
| 977 | C4 | — | 212 | 1 | no | — |
| 978 | C4 | — | 212 | 1 | no | — |
| 979 | C4 | — | 212 | 1 | no | — |
| 980 | C2 | — | 2 | 1 | no | — |
| 981 | C2 | — | 2 | 1 | no | — |
| 982 | C2 | — | 8 | 1 | no | — |
| 983 | C2 | — | 16 | 1 | no | — |
| 984 | C2 | — | 424 | 1 | no | — |
| 985 | C2 | — | 424 | 1 | no | — |
| 986 | C2 | — | 212 | 1 | no | — |
| 987 | C2 | — | 212 | 1 | no | — |
| 988 | C2 | #20283996 | 1 | 1 | yes | characteristic |
| 989 | C2 | #20284069 | 1 | 1 | yes | characteristic |
| 990 | C2 | #20284110 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20288941 | C2 | semidirect |
| 2. #20285532 | C2 | semidirect |
| 3. #20285469 | C2 | semidirect |
| 4. #20282736 | C2 | semidirect |
| 5. #20273732 | C2 | semidirect |
| 6. #20273731 | C2 | semidirect |
| 7. #20273707 | C2 | semidirect |
| 8. #20273706 | C2 | semidirect |
| 9. #20273660 | C2 | semidirect |
| 10. #20273659 | C2 | semidirect |
| 11. #20273636 | C2 | semidirect |
| 12. #20273270 | C2 | semidirect |
| 13. #20273246 | C2 | semidirect |
| 14. #20273073 | C2 | semidirect |
| 15. C53×#1596 | C2 | semidirect |
| 76. C2×#11719949 | D4 | semidirect |
| 79. C2×Q8×D53 | D4 | semidirect |
| 110. #13133197 | D4 | semidirect |
| 121. #13133193 | D4 | semidirect |
| 122. #13133193 | D4 | semidirect |
| 127. #13133192 | D4 | semidirect |
| 155. #13133175 | D4 | semidirect |
| 160. C4⋊C4×D53 | D4 | semidirect |
| 496. #1596 | D53 | semidirect |
| 570. C53 | #18452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20288941 | 2 |
| #20285532 | 2 |
| #20285469 | 2 |
| #20282736 | 2 |
| #20273732 | 2 |
| #20273731 | 2 |
| #20273707 | 2 |
| #20273706 | 2 |
| #20273660 | 2 |
| #20273659 | 2 |
| #20273636 | 2 |
| #20273270 | 2 |
| #20273246 | 2 |
| #20273073 | 2 |
| C53×#1596 | 2 |
| #18452 | 53 |