Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1494 conjugacy classes of subgroups.
The subgroup lattice has 1252 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #534×D53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#100×D53 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#99×D53 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #20276362 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20276361 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20276360 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | #20276359 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #20276358 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #352×D53 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | AΣL(1,𝔽16)×D53 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | C53×#2121 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C22×D4×D53 | C4 | 1 | 1 | yes | characteristic, complemented |
| 13 | C22×D4×D53 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×M16×D53 | — | 2 | 1 | no | — |
| 15 | #16811185 | C4 | 1 | 1 | yes | characteristic, complemented |
| 16 | #16811184 | — | 2 | 1 | no | — |
| 17 | #16811184 | C4 | 1 | 1 | yes | characteristic, complemented |
| 18 | #16811184 | C22 | 1 | 1 | yes | characteristic |
| 19 | #16811183 | — | 2 | 1 | no | — |
| 20 | #16811183 | C4 | 1 | 1 | yes | characteristic, complemented |
| 21 | #16811183 | C22 | 1 | 1 | yes | characteristic |
| 22 | #16811182 | C4 | 1 | 1 | yes | characteristic, complemented |
| 23 | #16811182 | C22 | 1 | 1 | yes | characteristic |
| 24 | #16811181 | — | 2 | 1 | no | — |
| 25 | #16811181 | — | 2 | 1 | no | — |
| 26 | #123×D53 | — | 2 | 1 | no | — |
| 27 | #123×D53 | C4 | 1 | 1 | yes | characteristic, complemented |
| 28 | #123×D53 | C22 | 1 | 1 | yes | characteristic |
| 29 | #121×D53 | — | 2 | 1 | no | — |
| 30 | #121×D53 | — | 2 | 1 | no | — |
| 31 | #120×D53 | — | 2 | 1 | no | — |
| 32 | #120×D53 | C4 | 1 | 1 | yes | characteristic, complemented |
| 33 | #120×D53 | C22 | 1 | 1 | yes | characteristic |
| 34 | C2×C22⋊C4×D53 | — | 2 | 1 | no | — |
| 35 | C2×C22⋊C4×D53 | C4 | 1 | 1 | yes | characteristic, complemented |
| 36 | C2×#13133134 | C22 | 1 | 1 | yes | characteristic, complemented |
| 37 | C2×#13133133 | — | 2 | 1 | no | — |
| 38 | #100×D53 | — | 2 | 1 | no | — |
| 39 | #100×D53 | — | 2 | 1 | no | — |
| 40 | #100×D53 | C22 | 1 | 2 | yes | — |
| 41 | #100×D53 | C22 | 1 | 2 | yes | complemented |
| 42 | C2×#13133132 | C22 | 1 | 1 | yes | characteristic, complemented |
| 43 | C2×#13133131 | — | 2 | 1 | no | — |
| 44 | #99×D53 | — | 2 | 1 | no | — |
| 45 | #99×D53 | — | 2 | 1 | no | — |
| 46 | #99×D53 | C22 | 1 | 2 | yes | — |
| 47 | #99×D53 | C22 | 1 | 2 | yes | complemented |
| 48 | #16810414 | C22 | 1 | 2 | yes | complemented |
| 49 | #16810413 | C22 | 1 | 2 | yes | complemented |
| 50 | #16810412 | C22 | 1 | 2 | yes | complemented |
| 51 | #16810411 | C22 | 1 | 2 | yes | complemented |
| 52 | #16810410 | C22 | 1 | 2 | yes | complemented |
| 53 | #16810409 | C22 | 1 | 2 | yes | complemented |
| 54 | C53×#534 | C22 | 1 | 1 | yes | characteristic |
| 55 | C2×#100×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 56 | C2×#99×C53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 57 | C53×#352 | C22 | 1 | 2 | yes | complemented |
| 58 | C53×AΣL(1,𝔽16) | C22 | 1 | 2 | yes | complemented |
| 59 | C24×D53 | C2×C4 | 1 | 1 | yes | characteristic |
| 60 | C24×D53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 61 | C24×D53 | D4 | 1 | 1 | yes | characteristic |
| 62 | C22×D212 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 63 | C22×D212 | D4 | 1 | 1 | yes | characteristic |
| 64 | C22×C22⋊D53 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | C22×C22⋊D53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 66 | C22×C22⋊D53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 67 | C22×C22⋊D53 | D4 | 1 | 1 | yes | characteristic |
| 68 | C2×D4×D53 | — | 2 | 1 | no | — |
| 69 | C2×D4×D53 | — | 2 | 1 | no | — |
| 70 | C2×D4×D53 | — | 2 | 1 | no | — |
| 71 | C2×D4×D53 | — | 2 | 1 | no | — |
| 72 | C2×D4×D53 | — | 2 | 1 | no | — |
| 73 | C2×D4×D53 | — | 2 | 1 | no | — |
| 74 | C2×D4×D53 | — | 4 | 1 | no | — |
| 75 | C2×D4×D53 | — | 4 | 1 | no | — |
| 76 | C2×D4×D53 | — | 4 | 1 | no | — |
| 77 | C2×D4×D53 | — | 4 | 1 | no | — |
| 78 | C2×D4×D53 | — | 4 | 1 | no | — |
| 79 | C2×D4×D53 | — | 4 | 1 | no | — |
| 80 | C2×D4×D53 | — | 4 | 1 | no | — |
| 81 | C2×D4×D53 | — | 4 | 1 | no | — |
| 82 | C2×D4×D53 | C2×C4 | 1 | 1 | yes | characteristic |
| 83 | C2×D4×D53 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | C2×D4×D53 | D4 | 1 | 1 | yes | characteristic |
| 85 | C2×D4×D53 | D4 | 1 | 1 | yes | characteristic |
| 86 | C2×D4×D53 | D4 | 1 | 1 | yes | characteristic |
| 87 | C2×D4×D53 | D4 | 1 | 1 | yes | characteristic |
| 88 | C2×D4×D53 | C23 | 1 | 1 | yes | characteristic |
| 89 | C2×D4×D53 | C23 | 1 | 1 | yes | characteristic |
| 90 | C22×C4×D53 | — | 2 | 1 | no | — |
| 91 | C22×C4×D53 | — | 4 | 1 | no | — |
| 92 | C22×C4×D53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 93 | C22×C4×D53 | D4 | 1 | 1 | yes | characteristic |
| 94 | C2×#11719917 | — | 2 | 1 | no | — |
| 95 | C2×#11719912 | — | 4 | 1 | no | — |
| 96 | M16×D53 | — | 2 | 2 | no | — |
| 97 | M16×D53 | — | 2 | 2 | no | — |
| 98 | M16×D53 | — | 4 | 1 | no | — |
| 99 | M16×D53 | — | 4 | 1 | no | — |
| 100 | C2×C8×D53 | — | 4 | 1 | no | — |
| 101 | #13133202 | — | 2 | 1 | no | — |
| 102 | #13133202 | — | 2 | 1 | no | — |
| 103 | #13133202 | — | 2 | 1 | no | — |
| 104 | #13133202 | — | 2 | 1 | no | — |
| 105 | #13133201 | — | 2 | 1 | no | — |
| 106 | #13133201 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 107 | #13133201 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 108 | #13133200 | — | 2 | 1 | no | — |
| 109 | #13133200 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 110 | #13133200 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 111 | #13133199 | — | 2 | 1 | no | — |
| 112 | #13133199 | — | 2 | 1 | no | — |
| 113 | #13133199 | — | 2 | 1 | no | — |
| 114 | #13133199 | — | 2 | 1 | no | — |
| 115 | #13133198 | — | 2 | 1 | no | — |
| 116 | #13133198 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 117 | #13133198 | C23 | 1 | 1 | yes | characteristic |
| 118 | #13133192 | — | 2 | 1 | no | — |
| 119 | #13133192 | — | 2 | 1 | no | — |
| 120 | #13133191 | — | 2 | 1 | no | — |
| 121 | #13133191 | — | 2 | 1 | no | — |
| 122 | #13133190 | — | 2 | 1 | no | — |
| 123 | #13133190 | — | 2 | 1 | no | — |
| 124 | #13133190 | — | 2 | 1 | no | — |
| 125 | #13133190 | — | 2 | 1 | no | — |
| 126 | #13133189 | — | 2 | 1 | no | — |
| 127 | #13133189 | — | 2 | 1 | no | — |
| 128 | #13133189 | — | 2 | 1 | no | — |
| 129 | #13133189 | — | 2 | 1 | no | — |
| 130 | #13133188 | — | 2 | 1 | no | — |
| 131 | #13133188 | — | 2 | 1 | no | — |
| 132 | #13133187 | — | 2 | 1 | no | — |
| 133 | #13133187 | — | 2 | 1 | no | — |
| 134 | #13133187 | — | 2 | 1 | no | — |
| 135 | #13133187 | — | 2 | 1 | no | — |
| 136 | #13133187 | — | 2 | 1 | no | — |
| 137 | #13133187 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 138 | #13133187 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 139 | #13133186 | — | 2 | 1 | no | — |
| 140 | #13133186 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 141 | #13133186 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 142 | #13133185 | — | 2 | 1 | no | — |
| 143 | #13133185 | — | 2 | 1 | no | — |
| 144 | #13133185 | — | 2 | 1 | no | — |
| 145 | #13133185 | — | 2 | 1 | no | — |
| 146 | #13133185 | — | 2 | 1 | no | — |
| 147 | #13133185 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 148 | #13133185 | C23 | 1 | 1 | yes | characteristic |
| 149 | C4⋊C4×D53 | — | 2 | 1 | no | — |
| 150 | C4⋊C4×D53 | — | 2 | 1 | no | — |
| 151 | C2×C22⋊Dic53 | — | 2 | 1 | no | — |
| 152 | C2×C22⋊Dic53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 153 | C2×#11719921 | — | 2 | 1 | no | — |
| 154 | C2×#11719921 | — | 4 | 1 | no | — |
| 155 | C22⋊C4×D53 | — | 2 | 1 | no | — |
| 156 | C22⋊C4×D53 | — | 2 | 1 | no | — |
| 157 | C22⋊C4×D53 | — | 2 | 1 | no | — |
| 158 | C22⋊C4×D53 | — | 2 | 1 | no | — |
| 159 | C22⋊C4×D53 | — | 2 | 1 | no | — |
| 160 | C22⋊C4×D53 | — | 2 | 1 | no | — |
| 161 | C22⋊C4×D53 | — | 2 | 2 | no | — |
| 162 | C22⋊C4×D53 | — | 2 | 2 | no | — |
| 163 | C22⋊C4×D53 | — | 4 | 1 | no | — |
| 164 | C22⋊C4×D53 | — | 4 | 1 | no | — |
| 165 | C22⋊C4×D53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 166 | C22⋊C4×D53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 167 | C22⋊C4×D53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 168 | C22⋊C4×D53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 169 | #13133134 | — | 2 | 1 | no | — |
| 170 | #13133134 | C23 | 1 | 2 | yes | — |
| 171 | #13133133 | — | 2 | 2 | no | — |
| 172 | #13133133 | — | 2 | 2 | no | — |
| 173 | #13133132 | — | 2 | 1 | no | — |
| 174 | #13133132 | C23 | 1 | 2 | yes | — |
| 175 | #13133131 | — | 2 | 2 | no | — |
| 176 | #13133131 | — | 2 | 2 | no | — |
| 177 | C22×D4×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 178 | C22×D4×C53 | C23 | 1 | 1 | yes | characteristic |
| 179 | C2×M16×C53 | — | 2 | 1 | no | — |
| 180 | #123×C53 | — | 2 | 1 | no | — |
| 181 | #123×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 182 | #123×C53 | C23 | 1 | 1 | yes | characteristic |
| 183 | #121×C53 | — | 2 | 1 | no | — |
| 184 | #121×C53 | — | 2 | 1 | no | — |
| 185 | #120×C53 | — | 2 | 1 | no | — |
| 186 | #120×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 187 | #120×C53 | C23 | 1 | 1 | yes | characteristic |
| 188 | C2×C22⋊C4×C53 | — | 2 | 1 | no | — |
| 189 | C2×C22⋊C4×C53 | C2×C4 | 1 | 1 | yes | characteristic, complemented |
| 190 | #100×C53 | — | 2 | 1 | no | — |
| 191 | #100×C53 | C23 | 1 | 2 | yes | — |
| 192 | #99×C53 | — | 2 | 1 | no | — |
| 193 | #99×C53 | C23 | 1 | 2 | yes | — |
| 194 | C24×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 195 | C24×C53 | C22×C4 | 1 | 1 | yes | characteristic, complemented |
| 196 | C24×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 197 | C23×D53 | — | 2 | 1 | no | — |
| 198 | C23×D53 | — | 2 | 1 | no | — |
| 199 | C23×D53 | — | 2 | 1 | no | — |
| 200 | C23×D53 | — | 2 | 1 | no | — |
| 201 | C23×D53 | — | 2 | 1 | no | — |
| 202 | C23×D53 | — | 2 | 1 | no | — |
| 203 | C23×D53 | — | 2 | 1 | no | — |
| 204 | C23×D53 | — | 2 | 1 | no | — |
| 205 | C23×D53 | — | 2 | 1 | no | — |
| 206 | C23×D53 | — | 2 | 1 | no | — |
| 207 | C23×D53 | — | 4 | 1 | no | — |
| 208 | C23×D53 | — | 4 | 1 | no | — |
| 209 | C23×D53 | — | 8 | 2 | no | — |
| 210 | C23×D53 | — | 8 | 2 | no | — |
| 211 | C23×D53 | — | 8 | 2 | no | — |
| 212 | C23×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 213 | C23×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 214 | C23×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 215 | C23×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 216 | C23×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 217 | C23×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 218 | C23×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 219 | C23×D53 | C22×C4 | 1 | 1 | yes | characteristic |
| 220 | C23×D53 | C22×C4 | 1 | 1 | yes | characteristic |
| 221 | C23×D53 | C22×C4 | 1 | 1 | yes | characteristic, complemented |
| 222 | C23×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 223 | C23×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 224 | C2×D4×C53 | — | 2 | 1 | no | — |
| 225 | C2×D4×C53 | — | 2 | 1 | no | — |
| 226 | C2×D4×C53 | — | 2 | 1 | no | — |
| 227 | C2×D4×C53 | — | 2 | 1 | no | — |
| 228 | C2×D4×C53 | — | 4 | 1 | no | — |
| 229 | C2×D4×C53 | — | 4 | 1 | no | — |
| 230 | C2×D4×C53 | — | 4 | 1 | no | — |
| 231 | C2×D4×C53 | — | 4 | 1 | no | — |
| 232 | C2×D4×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 233 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 234 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 235 | C2×D4×C53 | C24 | 1 | 1 | yes | characteristic |
| 236 | C22×C4×C53 | — | 2 | 1 | no | — |
| 237 | C22×C4×C53 | — | 4 | 1 | no | — |
| 238 | C22×C4×C53 | C22×C4 | 1 | 1 | yes | characteristic, complemented |
| 239 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 240 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 241 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 242 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 243 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 244 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 245 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 246 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 247 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 248 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 249 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 250 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 251 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 252 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 253 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 254 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 255 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 256 | C2×C22⋊D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 257 | C2×C22⋊D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 258 | C2×C22⋊D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 259 | C2×C22⋊D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 260 | C2×C22⋊D53 | C22×C4 | 1 | 1 | yes | characteristic |
| 261 | C2×C22⋊D53 | C22×C4 | 1 | 1 | yes | characteristic |
| 262 | C2×C22⋊D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 263 | C2×C22⋊D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 264 | C22×Dic53 | — | 2 | 1 | no | — |
| 265 | C22×Dic53 | — | 4 | 1 | no | — |
| 266 | C22×Dic53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 267 | C22×Dic53 | C22×C4 | 1 | 1 | yes | characteristic, complemented |
| 268 | D4×D53 | — | 4 | 1 | no | — |
| 269 | D4×D53 | — | 4 | 1 | no | — |
| 270 | D4×D53 | — | 4 | 1 | no | — |
| 271 | D4×D53 | — | 4 | 1 | no | — |
| 272 | D4×D53 | — | 4 | 1 | no | — |
| 273 | D4×D53 | — | 4 | 1 | no | — |
| 274 | D4×D53 | — | 4 | 1 | no | — |
| 275 | D4×D53 | — | 4 | 1 | no | — |
| 276 | D4×D53 | — | 4 | 1 | no | — |
| 277 | D4×D53 | — | 4 | 1 | no | — |
| 278 | D4×D53 | — | 4 | 1 | no | — |
| 279 | D4×D53 | — | 4 | 1 | no | — |
| 280 | D4×D53 | — | 4 | 1 | no | — |
| 281 | D4×D53 | — | 4 | 1 | no | — |
| 282 | D4×D53 | — | 4 | 1 | no | — |
| 283 | D4×D53 | — | 4 | 1 | no | — |
| 284 | D4×D53 | — | 4 | 2 | no | — |
| 285 | D4×D53 | — | 4 | 2 | no | — |
| 286 | D4×D53 | — | 4 | 2 | no | — |
| 287 | D4×D53 | — | 4 | 2 | no | — |
| 288 | D4×D53 | — | 4 | 2 | no | — |
| 289 | D4×D53 | — | 4 | 2 | no | — |
| 290 | D4×D53 | — | 4 | 1 | no | — |
| 291 | D4×D53 | — | 4 | 1 | no | — |
| 292 | D4×D53 | — | 4 | 1 | no | — |
| 293 | D4×D53 | — | 4 | 1 | no | — |
| 294 | D4×D53 | — | 8 | 2 | no | — |
| 295 | D4×D53 | — | 8 | 2 | no | — |
| 296 | C2×D212 | — | 2 | 1 | no | — |
| 297 | C2×D212 | — | 2 | 1 | no | — |
| 298 | C2×D212 | — | 2 | 1 | no | — |
| 299 | C2×D212 | — | 2 | 1 | no | — |
| 300 | C2×D212 | — | 4 | 1 | no | — |
| 301 | C2×D212 | — | 4 | 1 | no | — |
| 302 | C2×D212 | — | 4 | 1 | no | — |
| 303 | C2×D212 | — | 4 | 1 | no | — |
| 304 | C2×D212 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 305 | C2×D212 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 306 | C2×D212 | C2×D4 | 1 | 1 | yes | characteristic |
| 307 | C2×D212 | C2×D4 | 1 | 1 | yes | characteristic |
| 308 | C2×C4×D53 | — | 2 | 1 | no | — |
| 309 | C2×C4×D53 | — | 2 | 1 | no | — |
| 310 | C2×C4×D53 | — | 2 | 1 | no | — |
| 311 | C2×C4×D53 | — | 2 | 1 | no | — |
| 312 | C2×C4×D53 | — | 2 | 1 | no | — |
| 313 | C2×C4×D53 | — | 2 | 1 | no | — |
| 314 | C2×C4×D53 | — | 2 | 1 | no | — |
| 315 | C2×C4×D53 | — | 2 | 1 | no | — |
| 316 | C2×C4×D53 | — | 2 | 1 | no | — |
| 317 | C2×C4×D53 | — | 2 | 1 | no | — |
| 318 | C2×C4×D53 | — | 4 | 1 | no | — |
| 319 | C2×C4×D53 | — | 4 | 1 | no | — |
| 320 | C2×C4×D53 | — | 4 | 2 | no | — |
| 321 | C2×C4×D53 | — | 4 | 2 | no | — |
| 322 | C2×C4×D53 | — | 8 | 2 | no | — |
| 323 | C2×C4×D53 | — | 8 | 4 | no | — |
| 324 | C2×C4×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 325 | C2×C4×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 326 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 327 | C2×C4×D53 | C2×D4 | 1 | 1 | yes | characteristic |
| 328 | M16×C53 | — | 2 | 2 | no | — |
| 329 | M16×C53 | — | 4 | 1 | no | — |
| 330 | C2×C8×C53 | — | 4 | 1 | no | — |
| 331 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 332 | C4⋊C4×C53 | — | 2 | 1 | no | — |
| 333 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 334 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 335 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 336 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 337 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 338 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 339 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 340 | C22⋊C4×C53 | C22×C4 | 1 | 1 | yes | characteristic, complemented |
| 341 | C22⋊C4×C53 | C22×C4 | 1 | 1 | yes | characteristic, complemented |
| 342 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 343 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 344 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 345 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 346 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 347 | C22⋊Dic53 | — | 2 | 2 | no | — |
| 348 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 349 | C22⋊Dic53 | C22×C4 | 1 | 1 | yes | characteristic, complemented |
| 350 | C22⋊Dic53 | C22×C4 | 1 | 1 | yes | characteristic, complemented |
| 351 | #11719921 | — | 2 | 1 | no | — |
| 352 | #11719921 | — | 2 | 1 | no | — |
| 353 | #11719921 | — | 2 | 1 | no | — |
| 354 | #11719921 | — | 2 | 1 | no | — |
| 355 | #11719921 | — | 2 | 1 | no | — |
| 356 | #11719921 | — | 2 | 1 | no | — |
| 357 | #11719921 | — | 2 | 1 | no | — |
| 358 | #11719921 | — | 2 | 1 | no | — |
| 359 | #11719921 | — | 2 | 1 | no | — |
| 360 | #11719921 | — | 2 | 1 | no | — |
| 361 | #11719921 | — | 2 | 1 | no | — |
| 362 | #11719921 | — | 2 | 1 | no | — |
| 363 | #11719921 | — | 4 | 2 | no | — |
| 364 | #11719921 | — | 4 | 2 | no | — |
| 365 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 366 | C4⋊Dic53 | — | 2 | 1 | no | — |
| 367 | #11719919 | — | 2 | 1 | no | — |
| 368 | #11719919 | — | 2 | 1 | no | — |
| 369 | #11719919 | — | 2 | 1 | no | — |
| 370 | #11719919 | — | 2 | 1 | no | — |
| 371 | #11719917 | — | 2 | 2 | no | — |
| 372 | #11719917 | — | 4 | 1 | no | — |
| 373 | C2×#88322 | — | 4 | 1 | no | — |
| 374 | #11719912 | — | 4 | 2 | no | — |
| 375 | #11719912 | — | 4 | 2 | no | — |
| 376 | C8×D53 | — | 4 | 2 | no | — |
| 377 | C8×D53 | — | 4 | 2 | no | — |
| 378 | C23×C53 | — | 2 | 1 | no | — |
| 379 | C23×C53 | — | 2 | 1 | no | — |
| 380 | C23×C53 | — | 2 | 1 | no | — |
| 381 | C23×C53 | — | 2 | 1 | no | — |
| 382 | C23×C53 | — | 2 | 1 | no | — |
| 383 | C23×C53 | — | 4 | 1 | no | — |
| 384 | C23×C53 | — | 8 | 1 | no | — |
| 385 | C23×C53 | — | 8 | 1 | no | — |
| 386 | C23×C53 | — | 8 | 1 | no | — |
| 387 | C23×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 388 | C23×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 389 | C23×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 390 | C23×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 391 | C23×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 392 | C22×D53 | — | 2 | 1 | no | — |
| 393 | C22×D53 | — | 2 | 1 | no | — |
| 394 | C22×D53 | — | 2 | 1 | no | — |
| 395 | C22×D53 | — | 2 | 1 | no | — |
| 396 | C22×D53 | — | 2 | 1 | no | — |
| 397 | C22×D53 | — | 2 | 1 | no | — |
| 398 | C22×D53 | — | 2 | 1 | no | — |
| 399 | C22×D53 | — | 2 | 1 | no | — |
| 400 | C22×D53 | — | 2 | 1 | no | — |
| 401 | C22×D53 | — | 2 | 1 | no | — |
| 402 | C22×D53 | — | 2 | 1 | no | — |
| 403 | C22×D53 | — | 2 | 1 | no | — |
| 404 | C22×D53 | — | 2 | 1 | no | — |
| 405 | C22×D53 | — | 2 | 1 | no | — |
| 406 | C22×D53 | — | 2 | 1 | no | — |
| 407 | C22×D53 | — | 2 | 1 | no | — |
| 408 | C22×D53 | — | 2 | 1 | no | — |
| 409 | C22×D53 | — | 2 | 1 | no | — |
| 410 | C22×D53 | — | 2 | 1 | no | — |
| 411 | C22×D53 | — | 2 | 1 | no | — |
| 412 | C22×D53 | — | 2 | 1 | no | — |
| 413 | C22×D53 | — | 4 | 2 | no | — |
| 414 | C22×D53 | — | 4 | 4 | no | — |
| 415 | C22×D53 | — | 4 | 2 | no | — |
| 416 | C22×D53 | — | 4 | 2 | no | — |
| 417 | C22×D53 | — | 4 | 2 | no | — |
| 418 | C22×D53 | — | 4 | 2 | no | — |
| 419 | C22×D53 | — | 4 | 2 | no | — |
| 420 | C22×D53 | — | 4 | 2 | no | — |
| 421 | C22×D53 | — | 4 | 2 | no | — |
| 422 | C22×D53 | — | 4 | 1 | no | — |
| 423 | C22×D53 | — | 4 | 1 | no | — |
| 424 | C22×D53 | — | 4 | 1 | no | — |
| 425 | C22×D53 | — | 8 | 2 | no | — |
| 426 | C22×D53 | — | 8 | 2 | no | — |
| 427 | C22×D53 | — | 8 | 2 | no | — |
| 428 | C22×D53 | — | 8 | 1 | no | — |
| 429 | C22×D53 | — | 8 | 1 | no | — |
| 430 | C22×D53 | — | 8 | 1 | no | — |
| 431 | C22×D53 | — | 8 | 2 | no | — |
| 432 | C22×D53 | — | 8 | 2 | no | — |
| 433 | C22×D53 | — | 8 | 2 | no | — |
| 434 | C22×D53 | — | 8 | 2 | no | — |
| 435 | C22×D53 | — | 8 | 1 | no | — |
| 436 | C22×D53 | — | 8 | 1 | no | — |
| 437 | C22×D53 | — | 8 | 1 | no | — |
| 438 | C22×D53 | — | 8 | 1 | no | — |
| 439 | C22×D53 | — | 8 | 1 | no | — |
| 440 | C22×D53 | — | 8 | 1 | no | — |
| 441 | C22×D53 | — | 8 | 4 | no | — |
| 442 | C22×D53 | — | 8 | 4 | no | — |
| 443 | C22×D53 | #99 | 1 | 1 | yes | characteristic |
| 444 | C22×D53 | #99 | 1 | 1 | yes | characteristic |
| 445 | C22×D53 | #99 | 1 | 1 | yes | characteristic |
| 446 | C22×D53 | #99 | 1 | 1 | yes | characteristic |
| 447 | C22×D53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 448 | C22×D53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 449 | C22×D53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 450 | C22×D53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 451 | C22×D53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 452 | C22×D53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 453 | D4×C53 | — | 4 | 1 | no | — |
| 454 | D4×C53 | — | 4 | 1 | no | — |
| 455 | D4×C53 | — | 4 | 1 | no | — |
| 456 | D4×C53 | — | 4 | 1 | no | — |
| 457 | D4×C53 | — | 4 | 2 | no | — |
| 458 | D4×C53 | — | 4 | 1 | no | — |
| 459 | D4×C53 | — | 4 | 1 | no | — |
| 460 | D4×C53 | — | 8 | 1 | no | — |
| 461 | D4×C53 | — | 8 | 1 | no | — |
| 462 | C2×C4×C53 | — | 2 | 1 | no | — |
| 463 | C2×C4×C53 | — | 2 | 1 | no | — |
| 464 | C2×C4×C53 | — | 2 | 1 | no | — |
| 465 | C2×C4×C53 | — | 2 | 1 | no | — |
| 466 | C2×C4×C53 | — | 2 | 1 | no | — |
| 467 | C2×C4×C53 | — | 4 | 1 | no | — |
| 468 | C2×C4×C53 | — | 4 | 2 | no | — |
| 469 | C2×C4×C53 | — | 8 | 1 | no | — |
| 470 | C2×C4×C53 | — | 8 | 2 | no | — |
| 471 | C2×C4×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 472 | C2×C4×C53 | C22×D4 | 1 | 1 | yes | characteristic |
| 473 | C22⋊D53 | — | 4 | 1 | no | — |
| 474 | C22⋊D53 | — | 4 | 1 | no | — |
| 475 | C22⋊D53 | — | 4 | 1 | no | — |
| 476 | C22⋊D53 | — | 4 | 1 | no | — |
| 477 | C22⋊D53 | — | 4 | 1 | no | — |
| 478 | C22⋊D53 | — | 4 | 1 | no | — |
| 479 | C22⋊D53 | — | 4 | 1 | no | — |
| 480 | C22⋊D53 | — | 4 | 1 | no | — |
| 481 | C22⋊D53 | — | 4 | 2 | no | — |
| 482 | C22⋊D53 | — | 4 | 2 | no | — |
| 483 | C22⋊D53 | — | 4 | 1 | no | — |
| 484 | C22⋊D53 | — | 4 | 1 | no | — |
| 485 | C22⋊D53 | — | 4 | 1 | no | — |
| 486 | C22⋊D53 | — | 4 | 1 | no | — |
| 487 | C22⋊D53 | — | 8 | 1 | no | — |
| 488 | C22⋊D53 | — | 8 | 1 | no | — |
| 489 | C22⋊D53 | — | 8 | 1 | no | — |
| 490 | C22⋊D53 | — | 8 | 1 | no | — |
| 491 | C2×Dic53 | — | 2 | 1 | no | — |
| 492 | C2×Dic53 | — | 2 | 1 | no | — |
| 493 | C2×Dic53 | — | 2 | 1 | no | — |
| 494 | C2×Dic53 | — | 2 | 1 | no | — |
| 495 | C2×Dic53 | — | 2 | 1 | no | — |
| 496 | C2×Dic53 | — | 4 | 1 | no | — |
| 497 | C2×Dic53 | — | 4 | 2 | no | — |
| 498 | C2×Dic53 | — | 8 | 1 | no | — |
| 499 | C2×Dic53 | — | 8 | 2 | no | — |
| 500 | C2×Dic53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 501 | C2×Dic53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 502 | D212 | — | 4 | 1 | no | — |
| 503 | D212 | — | 4 | 1 | no | — |
| 504 | D212 | — | 4 | 1 | no | — |
| 505 | D212 | — | 4 | 1 | no | — |
| 506 | D212 | — | 4 | 2 | no | — |
| 507 | D212 | — | 4 | 1 | no | — |
| 508 | D212 | — | 4 | 1 | no | — |
| 509 | D212 | — | 8 | 1 | no | — |
| 510 | D212 | — | 8 | 1 | no | — |
| 511 | C4×D53 | — | 2 | 1 | no | — |
| 512 | C4×D53 | — | 2 | 1 | no | — |
| 513 | C4×D53 | — | 2 | 1 | no | — |
| 514 | C4×D53 | — | 2 | 1 | no | — |
| 515 | C4×D53 | — | 2 | 1 | no | — |
| 516 | C4×D53 | — | 2 | 1 | no | — |
| 517 | C4×D53 | — | 2 | 1 | no | — |
| 518 | C4×D53 | — | 2 | 1 | no | — |
| 519 | C4×D53 | — | 4 | 2 | no | — |
| 520 | C4×D53 | — | 4 | 2 | no | — |
| 521 | C4×D53 | — | 4 | 2 | no | — |
| 522 | C4×D53 | — | 4 | 1 | no | — |
| 523 | C4×D53 | — | 4 | 1 | no | — |
| 524 | C4×D53 | — | 8 | 1 | no | — |
| 525 | C4×D53 | — | 8 | 1 | no | — |
| 526 | C4×D53 | — | 8 | 4 | no | — |
| 527 | C4×D53 | — | 8 | 4 | no | — |
| 528 | C8×C53 | — | 4 | 2 | no | — |
| 529 | #88322 | — | 4 | 2 | no | — |
| 530 | C2×#2121 | — | 53 | 1 | no | maximal, Sylow |
| 531 | C22×C53 | — | 2 | 1 | no | — |
| 532 | C22×C53 | — | 2 | 1 | no | — |
| 533 | C22×C53 | — | 2 | 1 | no | — |
| 534 | C22×C53 | — | 2 | 1 | no | — |
| 535 | C22×C53 | — | 4 | 1 | no | — |
| 536 | C22×C53 | — | 4 | 1 | no | — |
| 537 | C22×C53 | — | 4 | 1 | no | — |
| 538 | C22×C53 | — | 4 | 1 | no | — |
| 539 | C22×C53 | — | 4 | 1 | no | — |
| 540 | C22×C53 | — | 4 | 2 | no | — |
| 541 | C22×C53 | — | 4 | 1 | no | — |
| 542 | C22×C53 | — | 4 | 1 | no | — |
| 543 | C22×C53 | — | 4 | 1 | no | — |
| 544 | C22×C53 | — | 8 | 1 | no | — |
| 545 | C22×C53 | — | 8 | 1 | no | — |
| 546 | C22×C53 | — | 8 | 1 | no | — |
| 547 | C22×C53 | — | 8 | 2 | no | — |
| 548 | C22×C53 | C2×#99 | 1 | 1 | yes | characteristic |
| 549 | C22×C53 | C2×#99 | 1 | 1 | yes | characteristic |
| 550 | C22×C53 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 551 | C2×D53 | — | 2 | 2 | no | — |
| 552 | C2×D53 | — | 2 | 2 | no | — |
| 553 | C2×D53 | — | 2 | 2 | no | — |
| 554 | C2×D53 | — | 2 | 1 | no | — |
| 555 | C2×D53 | — | 2 | 1 | no | — |
| 556 | C2×D53 | — | 2 | 1 | no | — |
| 557 | C2×D53 | — | 2 | 1 | no | — |
| 558 | C2×D53 | — | 4 | 1 | no | — |
| 559 | C2×D53 | — | 4 | 1 | no | — |
| 560 | C2×D53 | — | 4 | 1 | no | — |
| 561 | C2×D53 | — | 4 | 2 | no | — |
| 562 | C2×D53 | — | 4 | 2 | no | — |
| 563 | C2×D53 | — | 4 | 2 | no | — |
| 564 | C2×D53 | — | 4 | 2 | no | — |
| 565 | C2×D53 | — | 4 | 2 | no | — |
| 566 | C2×D53 | — | 4 | 2 | no | — |
| 567 | C2×D53 | — | 4 | 2 | no | — |
| 568 | C2×D53 | — | 4 | 2 | no | — |
| 569 | C2×D53 | — | 4 | 2 | no | — |
| 570 | C2×D53 | — | 4 | 1 | no | — |
| 571 | C2×D53 | — | 4 | 1 | no | — |
| 572 | C2×D53 | — | 4 | 1 | no | — |
| 573 | C2×D53 | — | 4 | 1 | no | — |
| 574 | C2×D53 | — | 4 | 1 | no | — |
| 575 | C2×D53 | — | 4 | 1 | no | — |
| 576 | C2×D53 | — | 4 | 1 | no | — |
| 577 | C2×D53 | — | 8 | 1 | no | — |
| 578 | C2×D53 | — | 8 | 1 | no | — |
| 579 | C2×D53 | — | 8 | 1 | no | — |
| 580 | C2×D53 | — | 8 | 1 | no | — |
| 581 | C2×D53 | — | 8 | 1 | no | — |
| 582 | C2×D53 | — | 8 | 1 | no | — |
| 583 | C2×D53 | — | 8 | 1 | no | — |
| 584 | C2×D53 | — | 8 | 1 | no | — |
| 585 | C2×D53 | — | 8 | 2 | no | — |
| 586 | C2×D53 | — | 8 | 1 | no | — |
| 587 | C2×D53 | — | 8 | 1 | no | — |
| 588 | C2×D53 | — | 8 | 1 | no | — |
| 589 | C2×D53 | — | 8 | 4 | no | — |
| 590 | C2×D53 | — | 8 | 2 | no | — |
| 591 | C2×D53 | — | 8 | 2 | no | — |
| 592 | C2×D53 | C2×#99 | 1 | 1 | yes | characteristic |
| 593 | C2×D53 | C2×#99 | 1 | 1 | yes | characteristic |
| 594 | C2×D53 | C2×#99 | 1 | 1 | yes | characteristic |
| 595 | C2×D53 | C2×#99 | 1 | 1 | yes | characteristic |
| 596 | C4×C53 | — | 2 | 1 | no | — |
| 597 | C4×C53 | — | 2 | 1 | no | — |
| 598 | C4×C53 | — | 4 | 1 | no | — |
| 599 | C4×C53 | — | 4 | 1 | no | — |
| 600 | C4×C53 | — | 4 | 1 | no | — |
| 601 | C4×C53 | — | 8 | 2 | no | — |
| 602 | Dic53 | — | 2 | 1 | no | — |
| 603 | Dic53 | — | 2 | 1 | no | — |
| 604 | Dic53 | — | 4 | 1 | no | — |
| 605 | Dic53 | — | 4 | 1 | no | — |
| 606 | Dic53 | — | 4 | 1 | no | — |
| 607 | Dic53 | — | 8 | 2 | no | — |
| 608 | C2×#534 | — | 53 | 1 | no | — |
| 609 | C22×#100 | — | 53 | 1 | no | — |
| 610 | C22×#99 | — | 53 | 1 | no | — |
| 611 | #2121 | — | 53 | 1 | no | — |
| 612 | #2121 | — | 53 | 1 | no | — |
| 613 | #2121 | — | 53 | 2 | no | — |
| 614 | #2121 | — | 53 | 2 | no | — |
| 615 | #2121 | — | 53 | 1 | no | — |
| 616 | #2121 | D53 | 1 | 1 | yes | characteristic, direct product factor |
| 617 | C2×#352 | — | 53 | 2 | no | — |
| 618 | C2×AΣL(1,𝔽16) | — | 53 | 2 | no | — |
| 619 | C2×C53 | — | 2 | 1 | no | — |
| 620 | C2×C53 | — | 2 | 1 | no | — |
| 621 | C2×C53 | — | 2 | 1 | no | — |
| 622 | C2×C53 | — | 4 | 1 | no | — |
| 623 | C2×C53 | — | 4 | 1 | no | — |
| 624 | C2×C53 | — | 4 | 1 | no | — |
| 625 | C2×C53 | — | 4 | 1 | no | — |
| 626 | C2×C53 | — | 8 | 1 | no | — |
| 627 | C2×C53 | C22×#99 | 1 | 1 | yes | characteristic |
| 628 | D53 | — | 2 | 1 | no | — |
| 629 | D53 | — | 2 | 1 | no | — |
| 630 | D53 | — | 2 | 1 | no | — |
| 631 | D53 | — | 4 | 1 | no | — |
| 632 | D53 | — | 4 | 1 | no | — |
| 633 | D53 | — | 4 | 1 | no | — |
| 634 | D53 | — | 4 | 1 | no | — |
| 635 | D53 | — | 8 | 1 | no | — |
| 636 | D53 | #2121 | 1 | 2 | yes | direct product factor |
| 637 | C23×D4 | — | 53 | 1 | no | — |
| 638 | C23×D4 | — | 53 | 1 | no | — |
| 639 | C22×M16 | — | 106 | 1 | no | — |
| 640 | #534 | — | 53 | 1 | no | — |
| 641 | #534 | — | 53 | 1 | no | — |
| 642 | #534 | — | 53 | 1 | no | — |
| 643 | #534 | — | 53 | 1 | no | — |
| 644 | #534 | — | 53 | 1 | no | — |
| 645 | #534 | — | 53 | 1 | no | — |
| 646 | #534 | — | 53 | 1 | no | — |
| 647 | #534 | — | 106 | 1 | no | — |
| 648 | #534 | — | 106 | 1 | no | — |
| 649 | #534 | — | 106 | 1 | no | — |
| 650 | #534 | — | 106 | 1 | no | — |
| 651 | #534 | C2×D53 | 1 | 1 | yes | characteristic |
| 652 | C2×#123 | — | 53 | 1 | no | — |
| 653 | C2×#123 | — | 53 | 1 | no | — |
| 654 | C2×#123 | — | 106 | 1 | no | — |
| 655 | C2×#121 | — | 106 | 1 | no | — |
| 656 | C2×#121 | — | 106 | 1 | no | — |
| 657 | C2×#120 | — | 53 | 1 | no | — |
| 658 | C2×#120 | — | 53 | 1 | no | — |
| 659 | C2×#120 | — | 106 | 1 | no | — |
| 660 | C22×C22⋊C4 | — | 53 | 1 | no | — |
| 661 | C22×C22⋊C4 | — | 106 | 1 | no | — |
| 662 | C2×#100 | — | 53 | 1 | no | — |
| 663 | C2×#100 | — | 53 | 2 | no | — |
| 664 | C2×#100 | — | 53 | 2 | no | — |
| 665 | C2×#100 | — | 106 | 1 | no | — |
| 666 | C2×#100 | — | 106 | 1 | no | — |
| 667 | C2×#100 | — | 106 | 1 | no | — |
| 668 | C2×#100 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 669 | C2×#99 | — | 53 | 1 | no | — |
| 670 | C2×#99 | — | 53 | 2 | no | — |
| 671 | C2×#99 | — | 53 | 2 | no | — |
| 672 | C2×#99 | — | 106 | 1 | no | — |
| 673 | C2×#99 | — | 106 | 1 | no | — |
| 674 | C2×#99 | — | 106 | 1 | no | — |
| 675 | C2×#99 | C2×D53 | 1 | 1 | yes | characteristic, complemented |
| 676 | #352 | — | 53 | 2 | no | — |
| 677 | #352 | — | 53 | 2 | no | — |
| 678 | #352 | — | 53 | 2 | no | — |
| 679 | #352 | C2×D53 | 1 | 2 | yes | complemented |
| 680 | AΣL(1,𝔽16) | — | 53 | 2 | no | — |
| 681 | AΣL(1,𝔽16) | — | 53 | 2 | no | — |
| 682 | AΣL(1,𝔽16) | — | 53 | 2 | no | — |
| 683 | AΣL(1,𝔽16) | C2×D53 | 1 | 2 | yes | complemented |
| 684 | C53 | C2×#2121 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 685 | C25 | — | 53 | 1 | no | — |
| 686 | C25 | — | 53 | 1 | no | — |
| 687 | C25 | — | 53 | 1 | no | — |
| 688 | C22×D4 | — | 53 | 1 | no | — |
| 689 | C22×D4 | — | 53 | 1 | no | — |
| 690 | C22×D4 | — | 53 | 1 | no | — |
| 691 | C22×D4 | — | 53 | 1 | no | — |
| 692 | C22×D4 | — | 53 | 1 | no | — |
| 693 | C22×D4 | — | 53 | 1 | no | — |
| 694 | C22×D4 | — | 53 | 1 | no | — |
| 695 | C22×D4 | — | 53 | 1 | no | — |
| 696 | C22×D4 | — | 53 | 1 | no | — |
| 697 | C22×D4 | — | 53 | 1 | no | — |
| 698 | C22×D4 | — | 53 | 1 | no | — |
| 699 | C22×D4 | — | 53 | 1 | no | — |
| 700 | C22×D4 | — | 53 | 1 | no | — |
| 701 | C22×D4 | — | 53 | 1 | no | — |
| 702 | C22×D4 | — | 106 | 1 | no | — |
| 703 | C22×D4 | — | 106 | 1 | no | — |
| 704 | C22×D4 | — | 106 | 1 | no | — |
| 705 | C22×D4 | — | 106 | 1 | no | — |
| 706 | C22×D4 | — | 106 | 1 | no | — |
| 707 | C22×D4 | — | 106 | 1 | no | — |
| 708 | C22×D4 | — | 212 | 1 | no | — |
| 709 | C22×D4 | — | 212 | 1 | no | — |
| 710 | C22×D4 | — | 212 | 1 | no | — |
| 711 | C22×D4 | — | 212 | 1 | no | — |
| 712 | C22×D4 | — | 212 | 1 | no | — |
| 713 | C22×D4 | — | 212 | 1 | no | — |
| 714 | C22×D4 | — | 212 | 1 | no | — |
| 715 | C22×D4 | — | 212 | 1 | no | — |
| 716 | C22×D4 | C4×D53 | 1 | 1 | yes | characteristic, complemented |
| 717 | C22×D4 | C22×D53 | 1 | 1 | yes | characteristic |
| 718 | C23×C4 | — | 53 | 1 | no | — |
| 719 | C23×C4 | — | 53 | 1 | no | — |
| 720 | C23×C4 | — | 106 | 1 | no | — |
| 721 | C23×C4 | — | 212 | 1 | no | — |
| 722 | C2×M16 | — | 2 | 1 | no | — |
| 723 | C2×M16 | — | 106 | 2 | no | — |
| 724 | C2×M16 | — | 106 | 2 | no | — |
| 725 | C2×M16 | — | 106 | 1 | no | — |
| 726 | C2×M16 | — | 212 | 1 | no | — |
| 727 | C2×M16 | — | 212 | 1 | no | — |
| 728 | C2×M16 | — | 212 | 1 | no | — |
| 729 | C22×C8 | — | 212 | 1 | no | — |
| 730 | #123 | — | 2 | 1 | no | — |
| 731 | #123 | — | 53 | 1 | no | — |
| 732 | #123 | — | 53 | 1 | no | — |
| 733 | #123 | — | 53 | 1 | no | — |
| 734 | #123 | — | 53 | 1 | no | — |
| 735 | #123 | — | 53 | 1 | no | — |
| 736 | #123 | — | 53 | 1 | no | — |
| 737 | #123 | — | 106 | 1 | no | — |
| 738 | #123 | — | 106 | 1 | no | — |
| 739 | #123 | — | 106 | 1 | no | — |
| 740 | #123 | — | 106 | 1 | no | — |
| 741 | #123 | — | 106 | 1 | no | — |
| 742 | #123 | — | 106 | 1 | no | — |
| 743 | #123 | — | 106 | 1 | no | — |
| 744 | #123 | — | 106 | 1 | no | — |
| 745 | #123 | — | 106 | 1 | no | — |
| 746 | #123 | — | 106 | 1 | no | — |
| 747 | #123 | — | 106 | 1 | no | — |
| 748 | #123 | C4×D53 | 1 | 1 | yes | characteristic, complemented |
| 749 | #123 | C22×D53 | 1 | 1 | yes | characteristic |
| 750 | #121 | — | 2 | 1 | no | — |
| 751 | #121 | — | 2 | 1 | no | — |
| 752 | #121 | — | 106 | 1 | no | — |
| 753 | #121 | — | 106 | 1 | no | — |
| 754 | #121 | — | 106 | 1 | no | — |
| 755 | #121 | — | 106 | 1 | no | — |
| 756 | #121 | — | 106 | 1 | no | — |
| 757 | #121 | — | 106 | 1 | no | — |
| 758 | #121 | — | 106 | 1 | no | — |
| 759 | #121 | — | 106 | 1 | no | — |
| 760 | #121 | — | 106 | 1 | no | — |
| 761 | #121 | — | 106 | 1 | no | — |
| 762 | #121 | — | 106 | 1 | no | — |
| 763 | #121 | — | 106 | 1 | no | — |
| 764 | #121 | — | 106 | 1 | no | — |
| 765 | #121 | — | 106 | 1 | no | — |
| 766 | #120 | — | 2 | 1 | no | — |
| 767 | #120 | — | 53 | 1 | no | — |
| 768 | #120 | — | 53 | 1 | no | — |
| 769 | #120 | — | 53 | 1 | no | — |
| 770 | #120 | — | 53 | 1 | no | — |
| 771 | #120 | — | 53 | 1 | no | — |
| 772 | #120 | — | 53 | 1 | no | — |
| 773 | #120 | — | 106 | 1 | no | — |
| 774 | #120 | — | 106 | 1 | no | — |
| 775 | #120 | — | 106 | 1 | no | — |
| 776 | #120 | — | 106 | 1 | no | — |
| 777 | #120 | — | 106 | 1 | no | — |
| 778 | #120 | — | 106 | 1 | no | — |
| 779 | #120 | — | 106 | 1 | no | — |
| 780 | #120 | — | 106 | 1 | no | — |
| 781 | #120 | — | 106 | 1 | no | — |
| 782 | #120 | — | 106 | 1 | no | — |
| 783 | #120 | — | 106 | 1 | no | — |
| 784 | #120 | C4×D53 | 1 | 1 | yes | characteristic, complemented |
| 785 | #120 | C22×D53 | 1 | 1 | yes | characteristic |
| 786 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 787 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 788 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 789 | C2×C22⋊C4 | — | 53 | 1 | no | — |
| 790 | C2×C22⋊C4 | — | 53 | 1 | no | — |
| 791 | C2×C22⋊C4 | — | 53 | 1 | no | — |
| 792 | C2×C22⋊C4 | — | 53 | 1 | no | — |
| 793 | C2×C22⋊C4 | — | 53 | 1 | no | — |
| 794 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 795 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 796 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 797 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 798 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 799 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 800 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 801 | C2×C22⋊C4 | — | 106 | 2 | no | — |
| 802 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 803 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 804 | C2×C22⋊C4 | — | 212 | 1 | no | — |
| 805 | C2×C22⋊C4 | — | 212 | 1 | no | — |
| 806 | C2×C22⋊C4 | — | 212 | 1 | no | — |
| 807 | C2×C22⋊C4 | C4×D53 | 1 | 1 | yes | characteristic, complemented |
| 808 | #100 | — | 2 | 1 | no | — |
| 809 | #100 | — | 53 | 2 | no | — |
| 810 | #100 | — | 106 | 2 | no | — |
| 811 | #100 | — | 106 | 2 | no | — |
| 812 | #100 | — | 106 | 1 | no | — |
| 813 | #100 | C22×D53 | 1 | 2 | yes | — |
| 814 | #99 | — | 2 | 1 | no | — |
| 815 | #99 | — | 53 | 2 | no | — |
| 816 | #99 | — | 106 | 2 | no | — |
| 817 | #99 | — | 106 | 2 | no | — |
| 818 | #99 | — | 106 | 1 | no | — |
| 819 | #99 | C22×D53 | 1 | 2 | yes | — |
| 820 | C24 | — | 53 | 1 | no | — |
| 821 | C24 | — | 53 | 1 | no | — |
| 822 | C24 | — | 53 | 1 | no | — |
| 823 | C24 | — | 53 | 1 | no | — |
| 824 | C24 | — | 53 | 1 | no | — |
| 825 | C24 | — | 53 | 1 | no | — |
| 826 | C24 | — | 53 | 1 | no | — |
| 827 | C24 | — | 53 | 1 | no | — |
| 828 | C24 | — | 53 | 1 | no | — |
| 829 | C24 | — | 53 | 1 | no | — |
| 830 | C24 | — | 53 | 1 | no | — |
| 831 | C24 | — | 53 | 1 | no | — |
| 832 | C24 | — | 106 | 1 | no | — |
| 833 | C24 | — | 106 | 1 | no | — |
| 834 | C24 | — | 106 | 1 | no | — |
| 835 | C24 | — | 106 | 1 | no | — |
| 836 | C24 | — | 106 | 1 | no | — |
| 837 | C24 | — | 106 | 1 | no | — |
| 838 | C24 | — | 106 | 1 | no | — |
| 839 | C24 | — | 106 | 1 | no | — |
| 840 | C24 | — | 106 | 1 | no | — |
| 841 | C24 | — | 106 | 1 | no | — |
| 842 | C24 | — | 424 | 2 | no | — |
| 843 | C24 | — | 424 | 2 | no | — |
| 844 | C24 | — | 424 | 2 | no | — |
| 845 | C24 | — | 212 | 1 | no | — |
| 846 | C24 | — | 212 | 1 | no | — |
| 847 | C24 | C2×C4×D53 | 1 | 1 | yes | characteristic |
| 848 | C24 | C2×C4×D53 | 1 | 1 | yes | characteristic, complemented |
| 849 | C24 | D4×D53 | 1 | 1 | yes | characteristic |
| 850 | C2×D4 | — | 2 | 1 | no | — |
| 851 | C2×D4 | — | 2 | 1 | no | — |
| 852 | C2×D4 | — | 2 | 1 | no | — |
| 853 | C2×D4 | — | 2 | 1 | no | — |
| 854 | C2×D4 | — | 4 | 1 | no | — |
| 855 | C2×D4 | — | 4 | 1 | no | — |
| 856 | C2×D4 | — | 4 | 1 | no | — |
| 857 | C2×D4 | — | 4 | 1 | no | — |
| 858 | C2×D4 | — | 53 | 1 | no | — |
| 859 | C2×D4 | — | 53 | 1 | no | — |
| 860 | C2×D4 | — | 53 | 1 | no | — |
| 861 | C2×D4 | — | 53 | 1 | no | — |
| 862 | C2×D4 | — | 53 | 1 | no | — |
| 863 | C2×D4 | — | 53 | 1 | no | — |
| 864 | C2×D4 | — | 53 | 1 | no | — |
| 865 | C2×D4 | — | 53 | 1 | no | — |
| 866 | C2×D4 | — | 53 | 1 | no | — |
| 867 | C2×D4 | — | 53 | 1 | no | — |
| 868 | C2×D4 | — | 53 | 1 | no | — |
| 869 | C2×D4 | — | 53 | 1 | no | — |
| 870 | C2×D4 | — | 106 | 1 | no | — |
| 871 | C2×D4 | — | 106 | 1 | no | — |
| 872 | C2×D4 | — | 106 | 1 | no | — |
| 873 | C2×D4 | — | 106 | 1 | no | — |
| 874 | C2×D4 | — | 106 | 1 | no | — |
| 875 | C2×D4 | — | 106 | 1 | no | — |
| 876 | C2×D4 | — | 106 | 1 | no | — |
| 877 | C2×D4 | — | 106 | 1 | no | — |
| 878 | C2×D4 | — | 106 | 1 | no | — |
| 879 | C2×D4 | — | 106 | 1 | no | — |
| 880 | C2×D4 | — | 106 | 1 | no | — |
| 881 | C2×D4 | — | 106 | 1 | no | — |
| 882 | C2×D4 | — | 424 | 2 | no | — |
| 883 | C2×D4 | — | 424 | 2 | no | — |
| 884 | C2×D4 | — | 212 | 1 | no | — |
| 885 | C2×D4 | — | 212 | 1 | no | — |
| 886 | C2×D4 | — | 212 | 1 | no | — |
| 887 | C2×D4 | — | 212 | 1 | no | — |
| 888 | C2×D4 | — | 212 | 1 | no | — |
| 889 | C2×D4 | — | 212 | 1 | no | — |
| 890 | C2×D4 | — | 212 | 1 | no | — |
| 891 | C2×D4 | — | 212 | 1 | no | — |
| 892 | C2×D4 | — | 212 | 1 | no | — |
| 893 | C2×D4 | — | 212 | 1 | no | — |
| 894 | C2×D4 | — | 212 | 1 | no | — |
| 895 | C2×D4 | — | 212 | 1 | no | — |
| 896 | C2×D4 | — | 212 | 1 | no | — |
| 897 | C2×D4 | — | 212 | 1 | no | — |
| 898 | C2×D4 | — | 212 | 1 | no | — |
| 899 | C2×D4 | — | 212 | 1 | no | — |
| 900 | C2×D4 | — | 212 | 1 | no | — |
| 901 | C2×D4 | — | 212 | 1 | no | — |
| 902 | C2×D4 | — | 212 | 1 | no | — |
| 903 | C2×D4 | — | 212 | 1 | no | — |
| 904 | C2×D4 | — | 212 | 1 | no | — |
| 905 | C2×D4 | — | 212 | 1 | no | — |
| 906 | C2×D4 | — | 212 | 1 | no | — |
| 907 | C2×D4 | — | 212 | 1 | no | — |
| 908 | C2×D4 | — | 212 | 1 | no | — |
| 909 | C2×D4 | — | 212 | 1 | no | — |
| 910 | C2×D4 | — | 212 | 1 | no | — |
| 911 | C2×D4 | — | 212 | 1 | no | — |
| 912 | C2×D4 | — | 212 | 2 | no | — |
| 913 | C2×D4 | — | 212 | 2 | no | — |
| 914 | C2×D4 | — | 212 | 2 | no | — |
| 915 | C2×D4 | — | 212 | 2 | no | — |
| 916 | C2×D4 | — | 212 | 2 | no | — |
| 917 | C2×D4 | — | 212 | 2 | no | — |
| 918 | C2×D4 | — | 212 | 1 | no | — |
| 919 | C2×D4 | — | 212 | 1 | no | — |
| 920 | C2×D4 | — | 212 | 1 | no | — |
| 921 | C2×D4 | — | 212 | 1 | no | — |
| 922 | C2×D4 | C2×C4×D53 | 1 | 1 | yes | characteristic |
| 923 | C2×D4 | D4×D53 | 1 | 1 | yes | characteristic |
| 924 | C2×D4 | D4×D53 | 1 | 1 | yes | characteristic |
| 925 | C2×D4 | C23×D53 | 1 | 1 | yes | characteristic |
| 926 | C22×C4 | — | 2 | 1 | no | — |
| 927 | C22×C4 | — | 4 | 1 | no | — |
| 928 | C22×C4 | — | 53 | 1 | no | — |
| 929 | C22×C4 | — | 53 | 1 | no | — |
| 930 | C22×C4 | — | 53 | 1 | no | — |
| 931 | C22×C4 | — | 53 | 1 | no | — |
| 932 | C22×C4 | — | 53 | 1 | no | — |
| 933 | C22×C4 | — | 53 | 1 | no | — |
| 934 | C22×C4 | — | 106 | 1 | no | — |
| 935 | C22×C4 | — | 106 | 1 | no | — |
| 936 | C22×C4 | — | 106 | 1 | no | — |
| 937 | C22×C4 | — | 106 | 1 | no | — |
| 938 | C22×C4 | — | 106 | 1 | no | — |
| 939 | C22×C4 | — | 106 | 1 | no | — |
| 940 | C22×C4 | — | 106 | 1 | no | — |
| 941 | C22×C4 | — | 106 | 1 | no | — |
| 942 | C22×C4 | — | 106 | 1 | no | — |
| 943 | C22×C4 | — | 106 | 1 | no | — |
| 944 | C22×C4 | — | 106 | 1 | no | — |
| 945 | C22×C4 | — | 424 | 4 | no | — |
| 946 | C22×C4 | — | 424 | 2 | no | — |
| 947 | C22×C4 | — | 212 | 2 | no | — |
| 948 | C22×C4 | — | 212 | 2 | no | — |
| 949 | C22×C4 | — | 212 | 1 | no | — |
| 950 | C22×C4 | — | 212 | 1 | no | — |
| 951 | C22×C4 | — | 212 | 1 | no | — |
| 952 | C22×C4 | C2×C4×D53 | 1 | 1 | yes | characteristic, complemented |
| 953 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 954 | M16 | — | 2 | 2 | no | — |
| 955 | M16 | — | 4 | 1 | no | — |
| 956 | M16 | — | 106 | 2 | no | — |
| 957 | M16 | — | 212 | 2 | no | — |
| 958 | M16 | — | 212 | 2 | no | — |
| 959 | M16 | — | 212 | 1 | no | — |
| 960 | C2×C8 | — | 4 | 1 | no | — |
| 961 | C2×C8 | — | 212 | 2 | no | — |
| 962 | C2×C8 | — | 212 | 2 | no | — |
| 963 | C2×C8 | — | 212 | 1 | no | — |
| 964 | C4⋊C4 | — | 2 | 1 | no | — |
| 965 | C4⋊C4 | — | 2 | 1 | no | — |
| 966 | C4⋊C4 | — | 106 | 1 | no | — |
| 967 | C4⋊C4 | — | 106 | 1 | no | — |
| 968 | C4⋊C4 | — | 106 | 1 | no | — |
| 969 | C4⋊C4 | — | 106 | 1 | no | — |
| 970 | C4⋊C4 | — | 106 | 1 | no | — |
| 971 | C4⋊C4 | — | 106 | 1 | no | — |
| 972 | C22⋊C4 | — | 2 | 1 | no | — |
| 973 | C22⋊C4 | — | 2 | 1 | no | — |
| 974 | C22⋊C4 | — | 2 | 1 | no | — |
| 975 | C22⋊C4 | — | 2 | 1 | no | — |
| 976 | C22⋊C4 | — | 2 | 1 | no | — |
| 977 | C22⋊C4 | — | 2 | 2 | no | — |
| 978 | C22⋊C4 | — | 4 | 1 | no | — |
| 979 | C22⋊C4 | — | 53 | 1 | no | — |
| 980 | C22⋊C4 | — | 53 | 1 | no | — |
| 981 | C22⋊C4 | — | 106 | 1 | no | — |
| 982 | C22⋊C4 | — | 106 | 1 | no | — |
| 983 | C22⋊C4 | — | 106 | 1 | no | — |
| 984 | C22⋊C4 | — | 106 | 1 | no | — |
| 985 | C22⋊C4 | — | 106 | 1 | no | — |
| 986 | C22⋊C4 | — | 106 | 1 | no | — |
| 987 | C22⋊C4 | — | 106 | 1 | no | — |
| 988 | C22⋊C4 | — | 106 | 1 | no | — |
| 989 | C22⋊C4 | — | 106 | 1 | no | — |
| 990 | C22⋊C4 | — | 106 | 1 | no | — |
| 991 | C22⋊C4 | — | 106 | 1 | no | — |
| 992 | C22⋊C4 | — | 106 | 1 | no | — |
| 993 | C22⋊C4 | — | 106 | 1 | no | — |
| 994 | C22⋊C4 | — | 106 | 1 | no | — |
| 995 | C22⋊C4 | — | 106 | 1 | no | — |
| 996 | C22⋊C4 | — | 106 | 1 | no | — |
| 997 | C22⋊C4 | — | 106 | 1 | no | — |
| 998 | C22⋊C4 | — | 106 | 2 | no | — |
| 999 | C22⋊C4 | — | 212 | 2 | no | — |
| 1000 | C22⋊C4 | — | 212 | 2 | no | — |
| 1001 | C22⋊C4 | — | 212 | 1 | no | — |
| 1002 | C22⋊C4 | C2×C4×D53 | 1 | 1 | yes | characteristic, complemented |
| 1003 | C22⋊C4 | C2×C4×D53 | 1 | 1 | yes | characteristic, complemented |
| 1004 | C23 | — | 2 | 1 | no | — |
| 1005 | C23 | — | 2 | 1 | no | — |
| 1006 | C23 | — | 2 | 1 | no | — |
| 1007 | C23 | — | 2 | 1 | no | — |
| 1008 | C23 | — | 2 | 1 | no | — |
| 1009 | C23 | — | 4 | 1 | no | — |
| 1010 | C23 | — | 8 | 1 | no | — |
| 1011 | C23 | — | 8 | 1 | no | — |
| 1012 | C23 | — | 8 | 1 | no | — |
| 1013 | C23 | — | 53 | 1 | no | — |
| 1014 | C23 | — | 53 | 1 | no | — |
| 1015 | C23 | — | 53 | 1 | no | — |
| 1016 | C23 | — | 53 | 1 | no | — |
| 1017 | C23 | — | 53 | 1 | no | — |
| 1018 | C23 | — | 53 | 1 | no | — |
| 1019 | C23 | — | 53 | 1 | no | — |
| 1020 | C23 | — | 53 | 1 | no | — |
| 1021 | C23 | — | 53 | 1 | no | — |
| 1022 | C23 | — | 53 | 1 | no | — |
| 1023 | C23 | — | 106 | 1 | no | — |
| 1024 | C23 | — | 106 | 1 | no | — |
| 1025 | C23 | — | 106 | 1 | no | — |
| 1026 | C23 | — | 106 | 1 | no | — |
| 1027 | C23 | — | 106 | 1 | no | — |
| 1028 | C23 | — | 106 | 1 | no | — |
| 1029 | C23 | — | 106 | 1 | no | — |
| 1030 | C23 | — | 106 | 1 | no | — |
| 1031 | C23 | — | 106 | 1 | no | — |
| 1032 | C23 | — | 106 | 1 | no | — |
| 1033 | C23 | — | 106 | 1 | no | — |
| 1034 | C23 | — | 106 | 1 | no | — |
| 1035 | C23 | — | 106 | 1 | no | — |
| 1036 | C23 | — | 106 | 1 | no | — |
| 1037 | C23 | — | 106 | 1 | no | — |
| 1038 | C23 | — | 106 | 1 | no | — |
| 1039 | C23 | — | 106 | 1 | no | — |
| 1040 | C23 | — | 106 | 1 | no | — |
| 1041 | C23 | — | 106 | 1 | no | — |
| 1042 | C23 | — | 106 | 1 | no | — |
| 1043 | C23 | — | 106 | 1 | no | — |
| 1044 | C23 | — | 424 | 2 | no | — |
| 1045 | C23 | — | 424 | 1 | no | — |
| 1046 | C23 | — | 424 | 1 | no | — |
| 1047 | C23 | — | 424 | 1 | no | — |
| 1048 | C23 | — | 424 | 1 | no | — |
| 1049 | C23 | — | 424 | 1 | no | — |
| 1050 | C23 | — | 424 | 1 | no | — |
| 1051 | C23 | — | 424 | 1 | no | — |
| 1052 | C23 | — | 424 | 1 | no | — |
| 1053 | C23 | — | 424 | 1 | no | — |
| 1054 | C23 | — | 424 | 2 | no | — |
| 1055 | C23 | — | 424 | 2 | no | — |
| 1056 | C23 | — | 424 | 2 | no | — |
| 1057 | C23 | — | 424 | 4 | no | — |
| 1058 | C23 | — | 424 | 4 | no | — |
| 1059 | C23 | — | 424 | 2 | no | — |
| 1060 | C23 | — | 424 | 2 | no | — |
| 1061 | C23 | — | 424 | 2 | no | — |
| 1062 | C23 | — | 212 | 1 | no | — |
| 1063 | C23 | — | 212 | 1 | no | — |
| 1064 | C23 | — | 212 | 1 | no | — |
| 1065 | C23 | — | 212 | 2 | no | — |
| 1066 | C23 | — | 212 | 2 | no | — |
| 1067 | C23 | — | 212 | 2 | no | — |
| 1068 | C23 | — | 212 | 2 | no | — |
| 1069 | C23 | — | 212 | 2 | no | — |
| 1070 | C23 | — | 212 | 2 | no | — |
| 1071 | C23 | — | 212 | 2 | no | — |
| 1072 | C23 | — | 212 | 2 | no | — |
| 1073 | C23 | — | 212 | 4 | no | — |
| 1074 | C23 | C22⋊C4×D53 | 1 | 1 | yes | characteristic |
| 1075 | C23 | C22⋊C4×D53 | 1 | 1 | yes | characteristic |
| 1076 | C23 | C22⋊C4×D53 | 1 | 1 | yes | characteristic |
| 1077 | C23 | C22×C4×D53 | 1 | 1 | yes | characteristic |
| 1078 | C23 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 1079 | D4 | — | 4 | 1 | no | — |
| 1080 | D4 | — | 4 | 1 | no | — |
| 1081 | D4 | — | 4 | 1 | no | — |
| 1082 | D4 | — | 4 | 1 | no | — |
| 1083 | D4 | — | 4 | 2 | no | — |
| 1084 | D4 | — | 4 | 1 | no | — |
| 1085 | D4 | — | 4 | 1 | no | — |
| 1086 | D4 | — | 8 | 1 | no | — |
| 1087 | D4 | — | 8 | 1 | no | — |
| 1088 | D4 | — | 424 | 1 | no | — |
| 1089 | D4 | — | 424 | 1 | no | — |
| 1090 | D4 | — | 424 | 1 | no | — |
| 1091 | D4 | — | 424 | 1 | no | — |
| 1092 | D4 | — | 424 | 1 | no | — |
| 1093 | D4 | — | 424 | 1 | no | — |
| 1094 | D4 | — | 212 | 1 | no | — |
| 1095 | D4 | — | 212 | 1 | no | — |
| 1096 | D4 | — | 212 | 1 | no | — |
| 1097 | D4 | — | 212 | 1 | no | — |
| 1098 | D4 | — | 212 | 1 | no | — |
| 1099 | D4 | — | 212 | 1 | no | — |
| 1100 | D4 | — | 212 | 2 | no | — |
| 1101 | D4 | — | 212 | 1 | no | — |
| 1102 | D4 | — | 212 | 1 | no | — |
| 1103 | D4 | — | 212 | 1 | no | — |
| 1104 | D4 | — | 212 | 1 | no | — |
| 1105 | D4 | — | 212 | 1 | no | — |
| 1106 | D4 | — | 212 | 1 | no | — |
| 1107 | D4 | — | 212 | 1 | no | — |
| 1108 | D4 | — | 212 | 1 | no | — |
| 1109 | D4 | — | 212 | 2 | no | — |
| 1110 | D4 | — | 212 | 1 | no | — |
| 1111 | D4 | — | 212 | 1 | no | — |
| 1112 | D4 | — | 212 | 2 | no | — |
| 1113 | D4 | — | 212 | 1 | no | — |
| 1114 | D4 | — | 212 | 1 | no | — |
| 1115 | C2×C4 | — | 2 | 1 | no | — |
| 1116 | C2×C4 | — | 2 | 1 | no | — |
| 1117 | C2×C4 | — | 2 | 1 | no | — |
| 1118 | C2×C4 | — | 2 | 1 | no | — |
| 1119 | C2×C4 | — | 2 | 1 | no | — |
| 1120 | C2×C4 | — | 4 | 1 | no | — |
| 1121 | C2×C4 | — | 4 | 2 | no | — |
| 1122 | C2×C4 | — | 8 | 1 | no | — |
| 1123 | C2×C4 | — | 8 | 2 | no | — |
| 1124 | C2×C4 | — | 53 | 1 | no | — |
| 1125 | C2×C4 | — | 53 | 1 | no | — |
| 1126 | C2×C4 | — | 106 | 1 | no | — |
| 1127 | C2×C4 | — | 106 | 1 | no | — |
| 1128 | C2×C4 | — | 106 | 1 | no | — |
| 1129 | C2×C4 | — | 106 | 1 | no | — |
| 1130 | C2×C4 | — | 106 | 1 | no | — |
| 1131 | C2×C4 | — | 106 | 1 | no | — |
| 1132 | C2×C4 | — | 106 | 1 | no | — |
| 1133 | C2×C4 | — | 106 | 1 | no | — |
| 1134 | C2×C4 | — | 106 | 1 | no | — |
| 1135 | C2×C4 | — | 106 | 1 | no | — |
| 1136 | C2×C4 | — | 106 | 1 | no | — |
| 1137 | C2×C4 | — | 106 | 1 | no | — |
| 1138 | C2×C4 | — | 106 | 1 | no | — |
| 1139 | C2×C4 | — | 424 | 1 | no | — |
| 1140 | C2×C4 | — | 424 | 1 | no | — |
| 1141 | C2×C4 | — | 424 | 4 | no | — |
| 1142 | C2×C4 | — | 424 | 4 | no | — |
| 1143 | C2×C4 | — | 424 | 2 | no | — |
| 1144 | C2×C4 | — | 424 | 1 | no | — |
| 1145 | C2×C4 | — | 212 | 1 | no | — |
| 1146 | C2×C4 | — | 212 | 1 | no | — |
| 1147 | C2×C4 | — | 212 | 2 | no | — |
| 1148 | C2×C4 | — | 212 | 2 | no | — |
| 1149 | C2×C4 | — | 212 | 2 | no | — |
| 1150 | C2×C4 | — | 212 | 2 | no | — |
| 1151 | C2×C4 | — | 212 | 1 | no | — |
| 1152 | C2×C4 | C22⋊C4×D53 | 1 | 1 | yes | characteristic |
| 1153 | C2×C4 | C2×D4×D53 | 1 | 1 | yes | characteristic |
| 1154 | C8 | — | 4 | 2 | no | — |
| 1155 | C8 | — | 212 | 2 | no | — |
| 1156 | C22 | — | 2 | 1 | no | — |
| 1157 | C22 | — | 2 | 1 | no | — |
| 1158 | C22 | — | 2 | 1 | no | — |
| 1159 | C22 | — | 2 | 1 | no | — |
| 1160 | C22 | — | 4 | 1 | no | — |
| 1161 | C22 | — | 4 | 1 | no | — |
| 1162 | C22 | — | 4 | 1 | no | — |
| 1163 | C22 | — | 4 | 1 | no | — |
| 1164 | C22 | — | 4 | 1 | no | — |
| 1165 | C22 | — | 4 | 2 | no | — |
| 1166 | C22 | — | 4 | 1 | no | — |
| 1167 | C22 | — | 4 | 1 | no | — |
| 1168 | C22 | — | 4 | 1 | no | — |
| 1169 | C22 | — | 8 | 1 | no | — |
| 1170 | C22 | — | 8 | 1 | no | — |
| 1171 | C22 | — | 8 | 1 | no | — |
| 1172 | C22 | — | 8 | 2 | no | — |
| 1173 | C22 | — | 53 | 1 | no | — |
| 1174 | C22 | — | 53 | 1 | no | — |
| 1175 | C22 | — | 53 | 1 | no | — |
| 1176 | C22 | — | 53 | 1 | no | — |
| 1177 | C22 | — | 106 | 2 | no | — |
| 1178 | C22 | — | 106 | 2 | no | — |
| 1179 | C22 | — | 106 | 2 | no | — |
| 1180 | C22 | — | 106 | 1 | no | — |
| 1181 | C22 | — | 106 | 1 | no | — |
| 1182 | C22 | — | 106 | 1 | no | — |
| 1183 | C22 | — | 106 | 1 | no | — |
| 1184 | C22 | — | 424 | 1 | no | — |
| 1185 | C22 | — | 424 | 1 | no | — |
| 1186 | C22 | — | 424 | 1 | no | — |
| 1187 | C22 | — | 424 | 1 | no | — |
| 1188 | C22 | — | 424 | 1 | no | — |
| 1189 | C22 | — | 424 | 1 | no | — |
| 1190 | C22 | — | 424 | 1 | no | — |
| 1191 | C22 | — | 424 | 1 | no | — |
| 1192 | C22 | — | 424 | 1 | no | — |
| 1193 | C22 | — | 424 | 1 | no | — |
| 1194 | C22 | — | 424 | 1 | no | — |
| 1195 | C22 | — | 424 | 2 | no | — |
| 1196 | C22 | — | 424 | 2 | no | — |
| 1197 | C22 | — | 424 | 2 | no | — |
| 1198 | C22 | — | 424 | 4 | no | — |
| 1199 | C22 | — | 212 | 1 | no | — |
| 1200 | C22 | — | 212 | 1 | no | — |
| 1201 | C22 | — | 212 | 1 | no | — |
| 1202 | C22 | — | 212 | 1 | no | — |
| 1203 | C22 | — | 212 | 1 | no | — |
| 1204 | C22 | — | 212 | 1 | no | — |
| 1205 | C22 | — | 212 | 1 | no | — |
| 1206 | C22 | — | 212 | 1 | no | — |
| 1207 | C22 | — | 212 | 1 | no | — |
| 1208 | C22 | — | 212 | 2 | no | — |
| 1209 | C22 | — | 212 | 2 | no | — |
| 1210 | C22 | — | 212 | 2 | no | — |
| 1211 | C22 | — | 212 | 2 | no | — |
| 1212 | C22 | — | 212 | 2 | no | — |
| 1213 | C22 | — | 212 | 2 | no | — |
| 1214 | C22 | — | 212 | 2 | no | — |
| 1215 | C22 | — | 212 | 2 | no | — |
| 1216 | C22 | — | 212 | 2 | no | — |
| 1217 | C22 | — | 212 | 1 | no | — |
| 1218 | C22 | #99×D53 | 1 | 1 | yes | characteristic |
| 1219 | C22 | #99×D53 | 1 | 1 | yes | characteristic |
| 1220 | C22 | C2×C22⋊C4×D53 | 1 | 1 | yes | characteristic |
| 1221 | C4 | — | 2 | 1 | no | — |
| 1222 | C4 | — | 2 | 1 | no | — |
| 1223 | C4 | — | 4 | 1 | no | — |
| 1224 | C4 | — | 4 | 1 | no | — |
| 1225 | C4 | — | 4 | 1 | no | — |
| 1226 | C4 | — | 8 | 2 | no | — |
| 1227 | C4 | — | 106 | 1 | no | — |
| 1228 | C4 | — | 106 | 1 | no | — |
| 1229 | C4 | — | 424 | 2 | no | — |
| 1230 | C4 | — | 212 | 1 | no | — |
| 1231 | C4 | — | 212 | 1 | no | — |
| 1232 | C4 | — | 212 | 1 | no | — |
| 1233 | C2 | — | 2 | 1 | no | — |
| 1234 | C2 | — | 2 | 1 | no | — |
| 1235 | C2 | — | 2 | 1 | no | — |
| 1236 | C2 | — | 4 | 1 | no | — |
| 1237 | C2 | — | 4 | 1 | no | — |
| 1238 | C2 | — | 4 | 1 | no | — |
| 1239 | C2 | — | 4 | 1 | no | — |
| 1240 | C2 | — | 8 | 1 | no | — |
| 1241 | C2 | — | 53 | 2 | no | — |
| 1242 | C2 | — | 106 | 1 | no | — |
| 1243 | C2 | — | 106 | 1 | no | — |
| 1244 | C2 | — | 106 | 1 | no | — |
| 1245 | C2 | — | 424 | 1 | no | — |
| 1246 | C2 | — | 212 | 1 | no | — |
| 1247 | C2 | — | 212 | 1 | no | — |
| 1248 | C2 | — | 212 | 1 | no | — |
| 1249 | C2 | — | 212 | 1 | no | — |
| 1250 | C2 | C2×#99×D53 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#100×D53 | C2 | semidirect |
| 3. C2×#99×D53 | C2 | semidirect |
| 4. #20276362 | C2 | semidirect |
| 5. #20276361 | C2 | semidirect |
| 6. #20276360 | C2 | semidirect |
| 7. #20276359 | C2 | semidirect |
| 8. #20276358 | C2 | semidirect |
| 9. #352×D53 | C2 | semidirect |
| 10. AΣL(1,𝔽16)×D53 | C2 | semidirect |
| 11. C53×#2121 | C2 | semidirect |
| 12. C22×D4×D53 | C4 | semidirect |
| 15. #16811185 | C4 | semidirect |
| 17. #16811184 | C4 | semidirect |
| 20. #16811183 | C4 | semidirect |
| 22. #16811182 | C4 | semidirect |
| 27. #123×D53 | C4 | semidirect |
| 32. #120×D53 | C4 | semidirect |
| 35. C2×C22⋊C4×D53 | C4 | semidirect |
| 36. C2×#13133134 | C22 | semidirect |
| 41. #100×D53 | C22 | semidirect |
| 42. C2×#13133132 | C22 | semidirect |
| 47. #99×D53 | C22 | semidirect |
| 48. #16810414 | C22 | semidirect |
| 49. #16810413 | C22 | semidirect |
| 50. #16810412 | C22 | semidirect |
| 51. #16810411 | C22 | semidirect |
| 52. #16810410 | C22 | semidirect |
| 53. #16810409 | C22 | semidirect |
| 55. C2×#100×C53 | C22 | semidirect |
| 56. C2×#99×C53 | C22 | semidirect |
| 57. C53×#352 | C22 | semidirect |
| 58. C53×AΣL(1,𝔽16) | C22 | semidirect |
| 60. C24×D53 | C2×C4 | semidirect |
| 62. C22×D212 | C2×C4 | semidirect |
| 65. C22×C22⋊D53 | C2×C4 | semidirect |
| 66. C22×C22⋊D53 | C2×C4 | semidirect |
| 92. C22×C4×D53 | C2×C4 | semidirect |
| 106. #13133201 | C2×C4 | semidirect |
| 107. #13133201 | C2×C4 | semidirect |
| 109. #13133200 | C2×C4 | semidirect |
| 110. #13133200 | C2×C4 | semidirect |
| 116. #13133198 | C2×C4 | semidirect |
| 137. #13133187 | C2×C4 | semidirect |
| 138. #13133187 | C2×C4 | semidirect |
| 140. #13133186 | C2×C4 | semidirect |
| 141. #13133186 | C2×C4 | semidirect |
| 147. #13133185 | C2×C4 | semidirect |
| 152. C2×C22⋊Dic53 | C2×C4 | semidirect |
| 165. C22⋊C4×D53 | C2×C4 | semidirect |
| 166. C22⋊C4×D53 | C2×C4 | semidirect |
| 167. C22⋊C4×D53 | C2×C4 | semidirect |
| 168. C22⋊C4×D53 | C2×C4 | semidirect |
| 177. C22×D4×C53 | C2×C4 | semidirect |
| 181. #123×C53 | C2×C4 | semidirect |
| 186. #120×C53 | C2×C4 | semidirect |
| 189. C2×C22⋊C4×C53 | C2×C4 | semidirect |
| 195. C24×C53 | C22×C4 | semidirect |
| 221. C23×D53 | C22×C4 | semidirect |
| 238. C22×C4×C53 | C22×C4 | semidirect |
| 267. C22×Dic53 | C22×C4 | semidirect |
| 340. C22⋊C4×C53 | C22×C4 | semidirect |
| 341. C22⋊C4×C53 | C22×C4 | semidirect |
| 349. C22⋊Dic53 | C22×C4 | semidirect |
| 350. C22⋊Dic53 | C22×C4 | semidirect |
| 616. #2121 | D53 | direct (N × H) |
| 636. D53 | #2121 | direct (N × H) |
| 668. C2×#100 | C2×D53 | semidirect |
| 675. C2×#99 | C2×D53 | semidirect |
| 679. #352 | C2×D53 | semidirect |
| 683. AΣL(1,𝔽16) | C2×D53 | semidirect |
| 684. C53 | C2×#2121 | semidirect |
| 716. C22×D4 | C4×D53 | semidirect |
| 748. #123 | C4×D53 | semidirect |
| 784. #120 | C4×D53 | semidirect |
| 807. C2×C22⋊C4 | C4×D53 | semidirect |
| 848. C24 | C2×C4×D53 | semidirect |
| 952. C22×C4 | C2×C4×D53 | semidirect |
| 1002. C22⋊C4 | C2×C4×D53 | semidirect |
| 1003. C22⋊C4 | C2×C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #534×D53 | 2 |
| C2×#100×D53 | 2 |
| C2×#99×D53 | 2 |
| #20276362 | 2 |
| #20276361 | 2 |
| #20276360 | 2 |
| #20276359 | 2 |
| #20276358 | 2 |
| #352×D53 | 2 |
| AΣL(1,𝔽16)×D53 | 2 |
| C53×#2121 | 2 |
| C2×#2121 | 53 |