Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1168 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C2×#16811188 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×#16810411 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C2×#16810410 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C2×#16810409 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #20274640 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #20274631 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C2×C53×AΣL(1,𝔽16) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×#11719947 | C22 | 1 | 1 | yes | characteristic |
| 9 | C23×C22⋊D53 | C4 | 1 | 1 | yes | characteristic, complemented |
| 10 | #16811188 | — | 2 | 2 | no | — |
| 11 | #16811188 | — | 2 | 2 | no | — |
| 12 | #16811188 | — | 2 | 2 | no | — |
| 13 | #16811188 | — | 2 | 2 | no | — |
| 14 | C2×#13133213 | — | 2 | 1 | no | — |
| 15 | C2×#13133203 | — | 2 | 1 | no | — |
| 16 | C2×#13133190 | — | 2 | 1 | no | — |
| 17 | C2×#13133189 | — | 2 | 1 | no | — |
| 18 | C2×#13133187 | C4 | 1 | 1 | yes | characteristic, complemented |
| 19 | C2×#13133186 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | C2×#13133185 | C22 | 1 | 1 | yes | characteristic |
| 21 | C2×#13133173 | C4 | 1 | 1 | yes | characteristic, complemented |
| 22 | C2×#13133135 | — | 2 | 1 | no | — |
| 23 | C2×#13133134 | C22 | 1 | 1 | yes | characteristic |
| 24 | C2×#13133132 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#13133131 | — | 2 | 1 | no | — |
| 26 | #16810586 | — | 2 | 1 | no | — |
| 27 | #16810484 | — | 2 | 1 | no | — |
| 28 | #16810411 | — | 2 | 2 | no | — |
| 29 | #16810410 | — | 2 | 2 | no | — |
| 30 | #16810409 | — | 2 | 2 | no | — |
| 31 | C2×#120×C53 | C22 | 1 | 1 | yes | characteristic |
| 32 | C2×#100×C53 | C22 | 1 | 1 | yes | characteristic |
| 33 | C2×#99×C53 | C22 | 1 | 1 | yes | characteristic |
| 34 | C53×AΣL(1,𝔽16) | — | 2 | 2 | no | — |
| 35 | C24×D53 | C2×C4 | 1 | 1 | yes | characteristic |
| 36 | C2×#11719947 | — | 2 | 1 | no | — |
| 37 | C2×#11719947 | — | 2 | 1 | no | — |
| 38 | C2×#11719947 | — | 2 | 1 | no | — |
| 39 | C2×#11719947 | — | 2 | 1 | no | — |
| 40 | C2×#11719947 | — | 4 | 2 | no | — |
| 41 | C2×#11719947 | — | 4 | 2 | no | — |
| 42 | C22×Dic106 | D4 | 1 | 1 | yes | characteristic |
| 43 | C22×D212 | — | 2 | 1 | no | — |
| 44 | C22×C22⋊D53 | — | 2 | 2 | no | — |
| 45 | C22×C22⋊D53 | — | 2 | 2 | no | — |
| 46 | C22×C22⋊D53 | — | 2 | 1 | no | — |
| 47 | C22×C22⋊D53 | — | 2 | 1 | no | — |
| 48 | C22×C22⋊D53 | — | 2 | 1 | no | — |
| 49 | C22×C22⋊D53 | — | 2 | 1 | no | — |
| 50 | C22×C22⋊D53 | — | 4 | 2 | no | — |
| 51 | C22×C22⋊D53 | — | 4 | 2 | no | — |
| 52 | C22×C22⋊D53 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | C22×C22⋊D53 | D4 | 1 | 1 | yes | characteristic |
| 54 | C23×Dic53 | C2×C4 | 1 | 1 | yes | characteristic |
| 55 | C23×Dic53 | D4 | 1 | 1 | yes | characteristic |
| 56 | C22×C4×D53 | D4 | 1 | 1 | yes | characteristic |
| 57 | C2×#11719917 | — | 2 | 1 | no | — |
| 58 | #13133213 | — | 2 | 4 | no | — |
| 59 | #13133213 | — | 2 | 4 | no | — |
| 60 | #13133203 | — | 2 | 4 | no | — |
| 61 | #13133203 | — | 2 | 4 | no | — |
| 62 | #13133190 | — | 2 | 4 | no | — |
| 63 | #13133190 | — | 2 | 4 | no | — |
| 64 | #13133189 | — | 2 | 4 | no | — |
| 65 | #13133189 | — | 2 | 4 | no | — |
| 66 | #13133187 | — | 2 | 2 | no | — |
| 67 | #13133187 | — | 2 | 2 | no | — |
| 68 | #13133186 | — | 2 | 2 | no | — |
| 69 | #13133186 | — | 2 | 2 | no | — |
| 70 | #13133185 | — | 2 | 1 | no | — |
| 71 | #13133185 | — | 2 | 1 | no | — |
| 72 | #13133185 | D4 | 1 | 2 | yes | — |
| 73 | #13133185 | D4 | 1 | 2 | yes | — |
| 74 | #13133173 | — | 2 | 2 | no | — |
| 75 | #13133173 | — | 2 | 2 | no | — |
| 76 | C2×#11719919 | — | 2 | 1 | no | — |
| 77 | C2×C22⋊Dic53 | — | 2 | 1 | no | — |
| 78 | C2×C22⋊Dic53 | — | 2 | 1 | no | — |
| 79 | C2×C22⋊Dic53 | C2×C4 | 1 | 1 | yes | characteristic |
| 80 | C2×#11719921 | — | 2 | 1 | no | — |
| 81 | C2×#11719921 | — | 2 | 1 | no | — |
| 82 | C2×C4×Dic53 | — | 2 | 1 | no | — |
| 83 | #13133135 | — | 4 | 2 | no | — |
| 84 | #13133134 | — | 2 | 1 | no | — |
| 85 | #13133134 | — | 2 | 1 | no | — |
| 86 | #13133132 | — | 2 | 1 | no | — |
| 87 | #13133132 | — | 2 | 1 | no | — |
| 88 | #13133131 | — | 4 | 2 | no | — |
| 89 | #13133129 | — | 4 | 2 | no | — |
| 90 | #13133124 | — | 4 | 2 | no | — |
| 91 | C25×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 92 | C22×D4×C53 | — | 2 | 1 | no | — |
| 93 | C22×D4×C53 | C23 | 1 | 1 | yes | characteristic |
| 94 | C2×M16×C53 | — | 2 | 1 | no | — |
| 95 | #120×C53 | — | 2 | 1 | no | — |
| 96 | #120×C53 | — | 2 | 1 | no | — |
| 97 | #120×C53 | D4 | 1 | 2 | yes | — |
| 98 | #120×C53 | D4 | 1 | 2 | yes | — |
| 99 | C2×C22⋊C4×C53 | — | 2 | 1 | no | — |
| 100 | C2×C22⋊C4×C53 | — | 2 | 1 | no | — |
| 101 | C2×C22⋊C4×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 102 | #100×C53 | — | 2 | 1 | no | — |
| 103 | #100×C53 | — | 2 | 1 | no | — |
| 104 | #99×C53 | — | 2 | 1 | no | — |
| 105 | #99×C53 | — | 2 | 1 | no | — |
| 106 | C24×C53 | — | 2 | 1 | no | — |
| 107 | C24×C53 | — | 2 | 1 | no | — |
| 108 | C24×C53 | — | 4 | 1 | no | — |
| 109 | C24×C53 | — | 4 | 1 | no | — |
| 110 | C24×C53 | — | 8 | 2 | no | — |
| 111 | C24×C53 | C22⋊C4 | 1 | 2 | yes | — |
| 112 | C24×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 113 | C24×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 114 | C23×D53 | — | 2 | 1 | no | — |
| 115 | C23×D53 | — | 2 | 1 | no | — |
| 116 | C23×D53 | — | 4 | 1 | no | — |
| 117 | C23×D53 | — | 4 | 1 | no | — |
| 118 | C23×D53 | — | 8 | 2 | no | — |
| 119 | C23×D53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 120 | C23×D53 | C22⋊C4 | 1 | 2 | yes | — |
| 121 | C2×D4×C53 | — | 2 | 2 | no | — |
| 122 | C2×D4×C53 | — | 2 | 2 | no | — |
| 123 | C2×D4×C53 | — | 4 | 1 | no | — |
| 124 | C2×D4×C53 | — | 4 | 1 | no | — |
| 125 | C2×D4×C53 | — | 8 | 2 | no | — |
| 126 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 127 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 128 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 129 | C2×D4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 130 | C22×C4×C53 | — | 2 | 1 | no | — |
| 131 | C22×C4×C53 | — | 4 | 1 | no | — |
| 132 | C22×C4×C53 | C2×D4 | 1 | 1 | yes | characteristic |
| 133 | C2×C22⋊D53 | — | 2 | 4 | no | — |
| 134 | C2×C22⋊D53 | — | 2 | 4 | no | — |
| 135 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 136 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 137 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 138 | C2×C22⋊D53 | — | 2 | 1 | no | — |
| 139 | C2×C22⋊D53 | — | 2 | 4 | no | — |
| 140 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 141 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 142 | C2×C22⋊D53 | — | 2 | 2 | no | — |
| 143 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 144 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 145 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 146 | C2×C22⋊D53 | — | 4 | 8 | no | — |
| 147 | C2×C22⋊D53 | — | 4 | 8 | no | — |
| 148 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 149 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 150 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 151 | C2×C22⋊D53 | — | 4 | 2 | no | — |
| 152 | C2×C22⋊D53 | — | 8 | 2 | no | — |
| 153 | C2×C22⋊D53 | — | 8 | 2 | no | — |
| 154 | C22×Dic53 | — | 2 | 1 | no | — |
| 155 | C22×Dic53 | — | 2 | 1 | no | — |
| 156 | C22×Dic53 | — | 2 | 2 | no | — |
| 157 | C22×Dic53 | — | 2 | 2 | no | — |
| 158 | C22×Dic53 | — | 2 | 1 | no | — |
| 159 | C22×Dic53 | — | 2 | 1 | no | — |
| 160 | C22×Dic53 | — | 2 | 1 | no | — |
| 161 | C22×Dic53 | — | 2 | 2 | no | — |
| 162 | C22×Dic53 | — | 4 | 1 | no | — |
| 163 | C22×Dic53 | — | 4 | 1 | no | — |
| 164 | C22×Dic53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 165 | C22×Dic53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 166 | C22×Dic53 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 167 | #11719947 | — | 4 | 4 | no | — |
| 168 | #11719947 | — | 4 | 4 | no | — |
| 169 | #11719947 | — | 4 | 4 | no | — |
| 170 | #11719947 | — | 4 | 4 | no | — |
| 171 | C2×D212 | — | 2 | 4 | no | — |
| 172 | C2×D212 | — | 8 | 2 | no | — |
| 173 | C2×C4×D53 | — | 2 | 1 | no | — |
| 174 | C2×C4×D53 | — | 2 | 1 | no | — |
| 175 | C2×C4×D53 | — | 2 | 2 | no | — |
| 176 | C2×C4×D53 | — | 4 | 1 | no | — |
| 177 | C2×Dic106 | — | 2 | 1 | no | — |
| 178 | C2×Dic106 | — | 2 | 1 | no | — |
| 179 | C2×Dic106 | — | 2 | 2 | no | — |
| 180 | C2×Dic106 | — | 4 | 1 | no | — |
| 181 | M16×C53 | — | 4 | 1 | no | — |
| 182 | M16×C53 | — | 4 | 1 | no | — |
| 183 | C2×C8×C53 | — | 4 | 1 | no | — |
| 184 | C22⋊C4×C53 | — | 2 | 1 | no | — |
| 185 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 186 | C22⋊C4×C53 | — | 2 | 2 | no | — |
| 187 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 188 | C22⋊C4×C53 | — | 4 | 1 | no | — |
| 189 | C22⋊C4×C53 | C22⋊C4 | 1 | 2 | yes | — |
| 190 | C22⋊Dic53 | — | 2 | 4 | no | — |
| 191 | C22⋊Dic53 | — | 2 | 1 | no | — |
| 192 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 193 | C22⋊Dic53 | — | 4 | 1 | no | — |
| 194 | C22⋊Dic53 | C22⋊C4 | 1 | 2 | yes | — |
| 195 | #11719921 | — | 2 | 4 | no | — |
| 196 | #11719921 | — | 2 | 2 | no | — |
| 197 | #11719921 | — | 2 | 2 | no | — |
| 198 | #11719919 | — | 2 | 4 | no | — |
| 199 | C4×Dic53 | — | 2 | 4 | no | — |
| 200 | #11719917 | — | 4 | 1 | no | — |
| 201 | #11719917 | — | 4 | 1 | no | — |
| 202 | C2×#88322 | — | 4 | 1 | no | — |
| 203 | C23×C53 | — | 2 | 1 | no | — |
| 204 | C23×C53 | — | 2 | 1 | no | — |
| 205 | C23×C53 | — | 2 | 1 | no | — |
| 206 | C23×C53 | — | 2 | 1 | no | — |
| 207 | C23×C53 | — | 2 | 2 | no | — |
| 208 | C23×C53 | — | 4 | 2 | no | — |
| 209 | C23×C53 | — | 4 | 2 | no | — |
| 210 | C23×C53 | — | 4 | 2 | no | — |
| 211 | C23×C53 | — | 4 | 2 | no | — |
| 212 | C23×C53 | — | 4 | 2 | no | — |
| 213 | C23×C53 | — | 4 | 2 | no | — |
| 214 | C23×C53 | — | 4 | 1 | no | — |
| 215 | C23×C53 | — | 4 | 1 | no | — |
| 216 | C23×C53 | — | 8 | 2 | no | — |
| 217 | C23×C53 | — | 8 | 2 | no | — |
| 218 | C23×C53 | — | 8 | 4 | no | — |
| 219 | C23×C53 | — | 8 | 4 | no | — |
| 220 | C23×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 221 | C23×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 222 | C23×C53 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 223 | C23×C53 | #120 | 1 | 1 | yes | characteristic |
| 224 | C23×C53 | #120 | 1 | 1 | yes | characteristic |
| 225 | C22×D53 | — | 2 | 1 | no | — |
| 226 | C22×D53 | — | 2 | 2 | no | — |
| 227 | C22×D53 | — | 2 | 1 | no | — |
| 228 | C22×D53 | — | 2 | 1 | no | — |
| 229 | C22×D53 | — | 4 | 2 | no | — |
| 230 | C22×D53 | — | 4 | 2 | no | — |
| 231 | C22×D53 | — | 4 | 2 | no | — |
| 232 | C22×D53 | — | 4 | 2 | no | — |
| 233 | C22×D53 | — | 4 | 1 | no | — |
| 234 | C22×D53 | — | 4 | 1 | no | — |
| 235 | C22×D53 | — | 4 | 2 | no | — |
| 236 | C22×D53 | — | 8 | 2 | no | — |
| 237 | C22×D53 | — | 8 | 2 | no | — |
| 238 | C22×D53 | — | 8 | 4 | no | — |
| 239 | C22×D53 | — | 8 | 4 | no | — |
| 240 | D4×C53 | — | 4 | 1 | no | — |
| 241 | D4×C53 | — | 4 | 1 | no | — |
| 242 | D4×C53 | — | 4 | 1 | no | — |
| 243 | D4×C53 | — | 4 | 1 | no | — |
| 244 | D4×C53 | — | 8 | 2 | no | — |
| 245 | D4×C53 | — | 8 | 2 | no | — |
| 246 | C2×C4×C53 | — | 2 | 1 | no | — |
| 247 | C2×C4×C53 | — | 2 | 1 | no | — |
| 248 | C2×C4×C53 | — | 2 | 2 | no | — |
| 249 | C2×C4×C53 | — | 4 | 2 | no | — |
| 250 | C2×C4×C53 | — | 8 | 1 | no | — |
| 251 | C2×C4×C53 | — | 8 | 2 | no | — |
| 252 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 253 | C2×C4×C53 | #120 | 1 | 1 | yes | characteristic |
| 254 | C22⋊D53 | — | 4 | 2 | no | — |
| 255 | C22⋊D53 | — | 4 | 2 | no | — |
| 256 | C22⋊D53 | — | 4 | 8 | no | — |
| 257 | C22⋊D53 | — | 4 | 8 | no | — |
| 258 | C22⋊D53 | — | 4 | 2 | no | — |
| 259 | C22⋊D53 | — | 4 | 2 | no | — |
| 260 | C22⋊D53 | — | 8 | 4 | no | — |
| 261 | C22⋊D53 | — | 8 | 2 | no | — |
| 262 | C22⋊D53 | — | 8 | 2 | no | — |
| 263 | C2×Dic53 | — | 2 | 4 | no | — |
| 264 | C2×Dic53 | — | 2 | 4 | no | — |
| 265 | C2×Dic53 | — | 2 | 1 | no | — |
| 266 | C2×Dic53 | — | 2 | 1 | no | — |
| 267 | C2×Dic53 | — | 2 | 1 | no | — |
| 268 | C2×Dic53 | — | 2 | 1 | no | — |
| 269 | C2×Dic53 | — | 2 | 1 | no | — |
| 270 | C2×Dic53 | — | 2 | 2 | no | — |
| 271 | C2×Dic53 | — | 2 | 1 | no | — |
| 272 | C2×Dic53 | — | 2 | 1 | no | — |
| 273 | C2×Dic53 | — | 4 | 2 | no | — |
| 274 | C2×Dic53 | — | 4 | 2 | no | — |
| 275 | C2×Dic53 | — | 4 | 2 | no | — |
| 276 | C2×Dic53 | — | 8 | 1 | no | — |
| 277 | C2×Dic53 | — | 8 | 2 | no | — |
| 278 | C2×Dic53 | #99 | 1 | 2 | yes | — |
| 279 | C2×Dic53 | #99 | 1 | 2 | yes | — |
| 280 | D212 | — | 8 | 4 | no | — |
| 281 | C4×D53 | — | 4 | 2 | no | — |
| 282 | C4×D53 | — | 4 | 2 | no | — |
| 283 | Dic106 | — | 4 | 2 | no | — |
| 284 | Dic106 | — | 4 | 2 | no | — |
| 285 | C8×C53 | — | 8 | 1 | no | — |
| 286 | #88322 | — | 8 | 1 | no | — |
| 287 | #12691 | — | 53 | 1 | no | maximal, Sylow |
| 288 | C22×C53 | — | 2 | 2 | no | — |
| 289 | C22×C53 | — | 2 | 1 | no | — |
| 290 | C22×C53 | — | 2 | 1 | no | — |
| 291 | C22×C53 | — | 2 | 1 | no | — |
| 292 | C22×C53 | — | 2 | 1 | no | — |
| 293 | C22×C53 | — | 4 | 1 | no | — |
| 294 | C22×C53 | — | 4 | 1 | no | — |
| 295 | C22×C53 | — | 4 | 1 | no | — |
| 296 | C22×C53 | — | 4 | 1 | no | — |
| 297 | C22×C53 | — | 4 | 2 | no | — |
| 298 | C22×C53 | — | 4 | 2 | no | — |
| 299 | C22×C53 | — | 4 | 2 | no | — |
| 300 | C22×C53 | — | 4 | 2 | no | — |
| 301 | C22×C53 | — | 4 | 2 | no | — |
| 302 | C22×C53 | — | 4 | 2 | no | — |
| 303 | C22×C53 | — | 8 | 1 | no | — |
| 304 | C22×C53 | — | 8 | 2 | no | — |
| 305 | C22×C53 | — | 8 | 4 | no | — |
| 306 | C22×C53 | — | 8 | 4 | no | — |
| 307 | C22×C53 | — | 8 | 2 | no | — |
| 308 | C22×C53 | #379 | 1 | 1 | yes | characteristic |
| 309 | C22×C53 | C2×#99 | 1 | 1 | yes | characteristic |
| 310 | C22×C53 | C2×#99 | 1 | 1 | yes | characteristic |
| 311 | C2×D53 | — | 4 | 2 | no | — |
| 312 | C2×D53 | — | 4 | 2 | no | — |
| 313 | C2×D53 | — | 4 | 2 | no | — |
| 314 | C2×D53 | — | 4 | 2 | no | — |
| 315 | C2×D53 | — | 4 | 1 | no | — |
| 316 | C2×D53 | — | 4 | 2 | no | — |
| 317 | C2×D53 | — | 8 | 2 | no | — |
| 318 | C2×D53 | — | 8 | 4 | no | — |
| 319 | C2×D53 | — | 8 | 2 | no | — |
| 320 | C2×D53 | — | 8 | 1 | no | — |
| 321 | C2×D53 | — | 8 | 4 | no | — |
| 322 | C4×C53 | — | 2 | 1 | no | — |
| 323 | C4×C53 | — | 2 | 1 | no | — |
| 324 | C4×C53 | — | 4 | 2 | no | — |
| 325 | C4×C53 | — | 16 | 1 | no | — |
| 326 | Dic53 | — | 2 | 2 | no | — |
| 327 | Dic53 | — | 2 | 2 | no | — |
| 328 | Dic53 | — | 4 | 2 | no | — |
| 329 | Dic53 | — | 4 | 1 | no | — |
| 330 | Dic53 | — | 16 | 1 | no | — |
| 331 | C2×#535 | — | 53 | 1 | no | — |
| 332 | C2×AΣL(1,𝔽16) | — | 53 | 1 | no | — |
| 333 | C2×AΣL(1,𝔽16) | — | 53 | 1 | no | — |
| 334 | C2×AΣL(1,𝔽16) | — | 53 | 1 | no | — |
| 335 | C2×AΣL(1,𝔽16) | D53 | 1 | 1 | yes | characteristic, complemented |
| 336 | #1785 | — | 53 | 1 | no | — |
| 337 | #1782 | — | 53 | 1 | no | — |
| 338 | C2×C53 | — | 2 | 1 | no | — |
| 339 | C2×C53 | — | 2 | 1 | no | — |
| 340 | C2×C53 | — | 4 | 1 | no | — |
| 341 | C2×C53 | — | 4 | 1 | no | — |
| 342 | C2×C53 | — | 4 | 1 | no | — |
| 343 | C2×C53 | — | 4 | 1 | no | — |
| 344 | C2×C53 | — | 8 | 2 | no | — |
| 345 | C2×C53 | #1781 | 1 | 1 | yes | characteristic |
| 346 | C2×C53 | #2122 | 1 | 2 | yes | — |
| 347 | D53 | — | 8 | 1 | no | — |
| 348 | D53 | — | 8 | 2 | no | — |
| 349 | C22×#41 | — | 53 | 1 | no | — |
| 350 | C23×D4 | — | 53 | 1 | no | — |
| 351 | #535 | — | 106 | 2 | no | — |
| 352 | #535 | — | 106 | 2 | no | — |
| 353 | #535 | — | 106 | 2 | no | — |
| 354 | #535 | — | 106 | 2 | no | — |
| 355 | C2×#127 | — | 106 | 1 | no | — |
| 356 | C2×#124 | — | 106 | 1 | no | — |
| 357 | C2×#121 | — | 106 | 1 | no | — |
| 358 | C2×#121 | — | 106 | 1 | no | — |
| 359 | C2×#120 | — | 53 | 1 | no | — |
| 360 | C2×#120 | — | 53 | 1 | no | — |
| 361 | C2×#120 | — | 53 | 1 | no | — |
| 362 | C2×#120 | C2×D53 | 1 | 1 | yes | characteristic |
| 363 | C2×#117 | — | 53 | 1 | no | — |
| 364 | C2×#101 | — | 106 | 1 | no | — |
| 365 | C2×#100 | — | 53 | 1 | no | — |
| 366 | C2×#100 | C2×D53 | 1 | 1 | yes | characteristic |
| 367 | C2×#99 | — | 53 | 1 | no | — |
| 368 | C2×#99 | — | 106 | 1 | no | — |
| 369 | C2×#99 | C2×D53 | 1 | 1 | yes | characteristic |
| 370 | #407 | — | 106 | 1 | no | — |
| 371 | #381 | — | 106 | 1 | no | — |
| 372 | AΣL(1,𝔽16) | — | 2 | 2 | no | — |
| 373 | AΣL(1,𝔽16) | — | 106 | 2 | no | — |
| 374 | AΣL(1,𝔽16) | — | 106 | 2 | no | — |
| 375 | AΣL(1,𝔽16) | — | 106 | 2 | no | — |
| 376 | C53 | #12691 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 377 | C25 | — | 53 | 1 | no | — |
| 378 | C25 | C4×D53 | 1 | 1 | yes | characteristic |
| 379 | C2×#41 | — | 106 | 1 | no | — |
| 380 | C2×#41 | — | 106 | 1 | no | — |
| 381 | C2×#41 | — | 106 | 1 | no | — |
| 382 | C2×#41 | — | 106 | 1 | no | — |
| 383 | C2×#41 | — | 212 | 2 | no | — |
| 384 | C2×#41 | — | 212 | 2 | no | — |
| 385 | C22×Q8 | — | 53 | 1 | no | — |
| 386 | C22×D4 | — | 2 | 1 | no | — |
| 387 | C22×D4 | — | 53 | 1 | no | — |
| 388 | C22×D4 | — | 53 | 1 | no | — |
| 389 | C22×D4 | — | 106 | 1 | no | — |
| 390 | C22×D4 | — | 106 | 1 | no | — |
| 391 | C22×D4 | — | 106 | 1 | no | — |
| 392 | C22×D4 | — | 106 | 1 | no | — |
| 393 | C22×D4 | — | 106 | 1 | no | — |
| 394 | C22×D4 | — | 106 | 2 | no | — |
| 395 | C22×D4 | — | 106 | 2 | no | — |
| 396 | C22×D4 | — | 212 | 2 | no | — |
| 397 | C22×D4 | — | 212 | 2 | no | — |
| 398 | C22×D4 | C22×D53 | 1 | 1 | yes | characteristic |
| 399 | C23×C4 | — | 53 | 1 | no | — |
| 400 | C23×C4 | — | 53 | 1 | no | — |
| 401 | C23×C4 | — | 53 | 1 | no | — |
| 402 | C2×M16 | — | 2 | 1 | no | — |
| 403 | C2×M16 | — | 106 | 1 | no | — |
| 404 | #127 | — | 106 | 4 | no | — |
| 405 | #127 | — | 106 | 4 | no | — |
| 406 | #124 | — | 106 | 4 | no | — |
| 407 | #124 | — | 106 | 4 | no | — |
| 408 | #121 | — | 106 | 4 | no | — |
| 409 | #121 | — | 106 | 4 | no | — |
| 410 | #121 | — | 106 | 4 | no | — |
| 411 | #121 | — | 106 | 4 | no | — |
| 412 | #120 | — | 2 | 1 | no | — |
| 413 | #120 | — | 2 | 1 | no | — |
| 414 | #120 | — | 53 | 2 | no | — |
| 415 | #120 | — | 53 | 2 | no | — |
| 416 | #120 | — | 106 | 2 | no | — |
| 417 | #120 | — | 106 | 2 | no | — |
| 418 | #120 | — | 106 | 2 | no | — |
| 419 | #120 | — | 106 | 1 | no | — |
| 420 | #120 | — | 106 | 1 | no | — |
| 421 | #120 | — | 106 | 2 | no | — |
| 422 | #120 | D212 | 1 | 2 | yes | — |
| 423 | #120 | C22⋊D53 | 1 | 2 | yes | — |
| 424 | #117 | — | 106 | 2 | no | — |
| 425 | #117 | — | 106 | 2 | no | — |
| 426 | C2×C4⋊C4 | — | 106 | 1 | no | — |
| 427 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 428 | C2×C22⋊C4 | — | 2 | 1 | no | — |
| 429 | C2×C22⋊C4 | — | 53 | 1 | no | — |
| 430 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 431 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 432 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 433 | C2×C22⋊C4 | — | 106 | 1 | no | — |
| 434 | C2×C22⋊C4 | C4×D53 | 1 | 1 | yes | characteristic |
| 435 | C2×C42 | — | 106 | 1 | no | — |
| 436 | #101 | — | 212 | 2 | no | — |
| 437 | #100 | — | 2 | 1 | no | — |
| 438 | #100 | — | 2 | 1 | no | — |
| 439 | #100 | — | 106 | 1 | no | — |
| 440 | #100 | — | 106 | 1 | no | — |
| 441 | #99 | — | 2 | 1 | no | — |
| 442 | #99 | — | 2 | 1 | no | — |
| 443 | #99 | — | 106 | 1 | no | — |
| 444 | #99 | — | 106 | 1 | no | — |
| 445 | #99 | — | 212 | 2 | no | — |
| 446 | C22⋊C8 | — | 212 | 2 | no | — |
| 447 | #95 | — | 212 | 2 | no | — |
| 448 | C24 | — | 2 | 1 | no | — |
| 449 | C24 | — | 2 | 1 | no | — |
| 450 | C24 | — | 4 | 1 | no | — |
| 451 | C24 | — | 4 | 1 | no | — |
| 452 | C24 | — | 8 | 2 | no | — |
| 453 | C24 | — | 53 | 1 | no | — |
| 454 | C24 | — | 53 | 2 | no | — |
| 455 | C24 | — | 106 | 1 | no | — |
| 456 | C24 | — | 106 | 1 | no | — |
| 457 | C24 | — | 424 | 2 | no | — |
| 458 | C24 | — | 212 | 1 | no | — |
| 459 | C24 | — | 212 | 1 | no | — |
| 460 | C24 | #11719921 | 1 | 2 | yes | — |
| 461 | C24 | C2×C4×D53 | 1 | 1 | yes | characteristic |
| 462 | C24 | D4×D53 | 1 | 1 | yes | characteristic |
| 463 | #41 | — | 212 | 4 | no | — |
| 464 | #41 | — | 212 | 4 | no | — |
| 465 | #41 | — | 212 | 4 | no | — |
| 466 | #41 | — | 212 | 4 | no | — |
| 467 | C2×Q8 | — | 106 | 2 | no | — |
| 468 | C2×Q8 | — | 106 | 1 | no | — |
| 469 | C2×Q8 | — | 106 | 1 | no | — |
| 470 | C2×Q8 | — | 212 | 1 | no | — |
| 471 | C2×D4 | — | 2 | 2 | no | — |
| 472 | C2×D4 | — | 2 | 2 | no | — |
| 473 | C2×D4 | — | 4 | 1 | no | — |
| 474 | C2×D4 | — | 4 | 1 | no | — |
| 475 | C2×D4 | — | 8 | 2 | no | — |
| 476 | C2×D4 | — | 106 | 4 | no | — |
| 477 | C2×D4 | — | 106 | 2 | no | — |
| 478 | C2×D4 | — | 106 | 4 | no | — |
| 479 | C2×D4 | — | 106 | 2 | no | — |
| 480 | C2×D4 | — | 106 | 2 | no | — |
| 481 | C2×D4 | — | 106 | 4 | no | — |
| 482 | C2×D4 | — | 106 | 4 | no | — |
| 483 | C2×D4 | — | 106 | 1 | no | — |
| 484 | C2×D4 | — | 106 | 1 | no | — |
| 485 | C2×D4 | — | 106 | 1 | no | — |
| 486 | C2×D4 | — | 106 | 1 | no | — |
| 487 | C2×D4 | — | 424 | 2 | no | — |
| 488 | C2×D4 | — | 424 | 2 | no | — |
| 489 | C2×D4 | — | 424 | 2 | no | — |
| 490 | C2×D4 | — | 212 | 2 | no | — |
| 491 | C2×D4 | — | 212 | 2 | no | — |
| 492 | C2×D4 | — | 212 | 1 | no | — |
| 493 | C2×D4 | — | 212 | 1 | no | — |
| 494 | C2×D4 | — | 212 | 1 | no | — |
| 495 | C2×D4 | — | 212 | 8 | no | — |
| 496 | C2×D4 | — | 212 | 8 | no | — |
| 497 | C2×D4 | — | 212 | 2 | no | — |
| 498 | C2×D4 | — | 212 | 2 | no | — |
| 499 | C2×D4 | C2×D212 | 1 | 1 | yes | characteristic |
| 500 | C2×D4 | D4×D53 | 1 | 1 | yes | characteristic |
| 501 | C2×D4 | D4×D53 | 1 | 1 | yes | characteristic |
| 502 | C2×D4 | C2×C22⋊D53 | 1 | 1 | yes | characteristic |
| 503 | C22×C4 | — | 2 | 1 | no | — |
| 504 | C22×C4 | — | 4 | 1 | no | — |
| 505 | C22×C4 | — | 53 | 1 | no | — |
| 506 | C22×C4 | — | 53 | 1 | no | — |
| 507 | C22×C4 | — | 53 | 1 | no | — |
| 508 | C22×C4 | — | 106 | 2 | no | — |
| 509 | C22×C4 | — | 106 | 2 | no | — |
| 510 | C22×C4 | — | 106 | 2 | no | — |
| 511 | C22×C4 | — | 106 | 2 | no | — |
| 512 | C22×C4 | — | 106 | 1 | no | — |
| 513 | C22×C4 | — | 106 | 1 | no | — |
| 514 | C22×C4 | — | 106 | 1 | no | — |
| 515 | C22×C4 | — | 106 | 1 | no | — |
| 516 | C22×C4 | — | 106 | 1 | no | — |
| 517 | C22×C4 | — | 106 | 1 | no | — |
| 518 | C22×C4 | — | 106 | 1 | no | — |
| 519 | C22×C4 | — | 212 | 1 | no | — |
| 520 | C22×C4 | — | 212 | 1 | no | — |
| 521 | C22×C4 | — | 212 | 1 | no | — |
| 522 | C22×C4 | D4×D53 | 1 | 1 | yes | characteristic |
| 523 | M16 | — | 4 | 1 | no | — |
| 524 | M16 | — | 4 | 1 | no | — |
| 525 | M16 | — | 212 | 1 | no | — |
| 526 | M16 | — | 212 | 1 | no | — |
| 527 | C2×C8 | — | 4 | 1 | no | — |
| 528 | C2×C8 | — | 212 | 1 | no | — |
| 529 | C4⋊C4 | — | 106 | 4 | no | — |
| 530 | C22⋊C4 | — | 2 | 1 | no | — |
| 531 | C22⋊C4 | — | 2 | 2 | no | — |
| 532 | C22⋊C4 | — | 2 | 2 | no | — |
| 533 | C22⋊C4 | — | 4 | 1 | no | — |
| 534 | C22⋊C4 | — | 4 | 1 | no | — |
| 535 | C22⋊C4 | — | 53 | 2 | no | — |
| 536 | C22⋊C4 | — | 106 | 4 | no | — |
| 537 | C22⋊C4 | — | 106 | 4 | no | — |
| 538 | C22⋊C4 | — | 106 | 1 | no | — |
| 539 | C22⋊C4 | — | 106 | 2 | no | — |
| 540 | C22⋊C4 | — | 106 | 2 | no | — |
| 541 | C22⋊C4 | — | 212 | 1 | no | — |
| 542 | C22⋊C4 | — | 212 | 1 | no | — |
| 543 | C22⋊C4 | #11719921 | 1 | 2 | yes | — |
| 544 | C42 | — | 106 | 4 | no | — |
| 545 | C23 | — | 2 | 1 | no | — |
| 546 | C23 | — | 2 | 1 | no | — |
| 547 | C23 | — | 2 | 1 | no | — |
| 548 | C23 | — | 2 | 1 | no | — |
| 549 | C23 | — | 2 | 2 | no | — |
| 550 | C23 | — | 4 | 2 | no | — |
| 551 | C23 | — | 4 | 2 | no | — |
| 552 | C23 | — | 4 | 2 | no | — |
| 553 | C23 | — | 4 | 2 | no | — |
| 554 | C23 | — | 4 | 2 | no | — |
| 555 | C23 | — | 4 | 2 | no | — |
| 556 | C23 | — | 4 | 1 | no | — |
| 557 | C23 | — | 4 | 1 | no | — |
| 558 | C23 | — | 8 | 2 | no | — |
| 559 | C23 | — | 8 | 2 | no | — |
| 560 | C23 | — | 8 | 4 | no | — |
| 561 | C23 | — | 8 | 4 | no | — |
| 562 | C23 | — | 106 | 1 | no | — |
| 563 | C23 | — | 106 | 1 | no | — |
| 564 | C23 | — | 106 | 2 | no | — |
| 565 | C23 | — | 106 | 1 | no | — |
| 566 | C23 | — | 424 | 4 | no | — |
| 567 | C23 | — | 424 | 4 | no | — |
| 568 | C23 | — | 424 | 2 | no | — |
| 569 | C23 | — | 424 | 2 | no | — |
| 570 | C23 | — | 212 | 2 | no | — |
| 571 | C23 | — | 212 | 2 | no | — |
| 572 | C23 | — | 212 | 2 | no | — |
| 573 | C23 | — | 212 | 2 | no | — |
| 574 | C23 | — | 212 | 2 | no | — |
| 575 | C23 | — | 212 | 1 | no | — |
| 576 | C23 | — | 212 | 1 | no | — |
| 577 | C23 | C22⋊C4×D53 | 1 | 1 | yes | characteristic |
| 578 | C23 | C22⋊C4×D53 | 1 | 1 | yes | characteristic |
| 579 | C23 | C2×#11719921 | 1 | 1 | yes | characteristic |
| 580 | C23 | #13133185 | 1 | 1 | yes | characteristic |
| 581 | C23 | #13133187 | 1 | 1 | yes | characteristic |
| 582 | Q8 | — | 212 | 2 | no | — |
| 583 | Q8 | — | 212 | 2 | no | — |
| 584 | D4 | — | 4 | 1 | no | — |
| 585 | D4 | — | 4 | 1 | no | — |
| 586 | D4 | — | 4 | 1 | no | — |
| 587 | D4 | — | 4 | 1 | no | — |
| 588 | D4 | — | 8 | 2 | no | — |
| 589 | D4 | — | 8 | 2 | no | — |
| 590 | D4 | — | 424 | 4 | no | — |
| 591 | D4 | — | 424 | 2 | no | — |
| 592 | D4 | — | 424 | 2 | no | — |
| 593 | D4 | — | 424 | 4 | no | — |
| 594 | D4 | — | 212 | 2 | no | — |
| 595 | D4 | — | 212 | 2 | no | — |
| 596 | D4 | — | 212 | 8 | no | — |
| 597 | D4 | — | 212 | 8 | no | — |
| 598 | D4 | — | 212 | 2 | no | — |
| 599 | D4 | — | 212 | 2 | no | — |
| 600 | C2×C4 | — | 2 | 1 | no | — |
| 601 | C2×C4 | — | 2 | 1 | no | — |
| 602 | C2×C4 | — | 2 | 2 | no | — |
| 603 | C2×C4 | — | 4 | 2 | no | — |
| 604 | C2×C4 | — | 8 | 1 | no | — |
| 605 | C2×C4 | — | 8 | 2 | no | — |
| 606 | C2×C4 | — | 53 | 2 | no | — |
| 607 | C2×C4 | — | 53 | 2 | no | — |
| 608 | C2×C4 | — | 106 | 4 | no | — |
| 609 | C2×C4 | — | 106 | 4 | no | — |
| 610 | C2×C4 | — | 106 | 1 | no | — |
| 611 | C2×C4 | — | 106 | 1 | no | — |
| 612 | C2×C4 | — | 106 | 1 | no | — |
| 613 | C2×C4 | — | 106 | 1 | no | — |
| 614 | C2×C4 | — | 106 | 1 | no | — |
| 615 | C2×C4 | — | 106 | 1 | no | — |
| 616 | C2×C4 | — | 106 | 2 | no | — |
| 617 | C2×C4 | — | 106 | 1 | no | — |
| 618 | C2×C4 | — | 424 | 1 | no | — |
| 619 | C2×C4 | — | 424 | 2 | no | — |
| 620 | C2×C4 | — | 212 | 2 | no | — |
| 621 | C2×C4 | — | 212 | 2 | no | — |
| 622 | C2×C4 | — | 212 | 2 | no | — |
| 623 | C2×C4 | — | 212 | 2 | no | — |
| 624 | C2×C4 | — | 212 | 2 | no | — |
| 625 | C2×C4 | #13133185 | 1 | 1 | yes | characteristic |
| 626 | C2×C4 | #13133187 | 1 | 1 | yes | characteristic |
| 627 | C8 | — | 8 | 1 | no | — |
| 628 | C8 | — | 424 | 1 | no | — |
| 629 | C22 | — | 2 | 2 | no | — |
| 630 | C22 | — | 2 | 1 | no | — |
| 631 | C22 | — | 2 | 1 | no | — |
| 632 | C22 | — | 2 | 1 | no | — |
| 633 | C22 | — | 2 | 1 | no | — |
| 634 | C22 | — | 4 | 1 | no | — |
| 635 | C22 | — | 4 | 1 | no | — |
| 636 | C22 | — | 4 | 1 | no | — |
| 637 | C22 | — | 4 | 1 | no | — |
| 638 | C22 | — | 4 | 2 | no | — |
| 639 | C22 | — | 4 | 2 | no | — |
| 640 | C22 | — | 4 | 2 | no | — |
| 641 | C22 | — | 4 | 2 | no | — |
| 642 | C22 | — | 4 | 2 | no | — |
| 643 | C22 | — | 4 | 2 | no | — |
| 644 | C22 | — | 8 | 1 | no | — |
| 645 | C22 | — | 8 | 2 | no | — |
| 646 | C22 | — | 8 | 4 | no | — |
| 647 | C22 | — | 8 | 4 | no | — |
| 648 | C22 | — | 8 | 2 | no | — |
| 649 | C22 | — | 424 | 1 | no | — |
| 650 | C22 | — | 424 | 2 | no | — |
| 651 | C22 | — | 424 | 4 | no | — |
| 652 | C22 | — | 424 | 4 | no | — |
| 653 | C22 | — | 424 | 2 | no | — |
| 654 | C22 | — | 212 | 2 | no | — |
| 655 | C22 | — | 212 | 2 | no | — |
| 656 | C22 | — | 212 | 2 | no | — |
| 657 | C22 | — | 212 | 2 | no | — |
| 658 | C22 | — | 212 | 1 | no | — |
| 659 | C22 | — | 212 | 2 | no | — |
| 660 | C22 | #16810478 | 1 | 1 | yes | characteristic |
| 661 | C22 | #99×D53 | 1 | 1 | yes | characteristic |
| 662 | C22 | #99×D53 | 1 | 1 | yes | characteristic |
| 663 | C4 | — | 2 | 1 | no | — |
| 664 | C4 | — | 2 | 1 | no | — |
| 665 | C4 | — | 4 | 2 | no | — |
| 666 | C4 | — | 16 | 1 | no | — |
| 667 | C4 | — | 848 | 1 | no | — |
| 668 | C4 | — | 106 | 2 | no | — |
| 669 | C4 | — | 106 | 2 | no | — |
| 670 | C4 | — | 212 | 2 | no | — |
| 671 | C4 | — | 212 | 1 | no | — |
| 672 | C2 | — | 2 | 1 | no | — |
| 673 | C2 | — | 2 | 1 | no | — |
| 674 | C2 | — | 4 | 1 | no | — |
| 675 | C2 | — | 4 | 1 | no | — |
| 676 | C2 | — | 4 | 1 | no | — |
| 677 | C2 | — | 4 | 1 | no | — |
| 678 | C2 | — | 8 | 2 | no | — |
| 679 | C2 | — | 424 | 2 | no | — |
| 680 | C2 | — | 424 | 1 | no | — |
| 681 | C2 | #20274628 | 1 | 1 | yes | characteristic |
| 682 | C2 | #20276363 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#16810411 | C2 | semidirect |
| 3. C2×#16810410 | C2 | semidirect |
| 4. C2×#16810409 | C2 | semidirect |
| 5. #20274640 | C2 | semidirect |
| 6. #20274631 | C2 | semidirect |
| 7. C2×C53×AΣL(1,𝔽16) | C2 | semidirect |
| 9. C23×C22⋊D53 | C4 | semidirect |
| 18. C2×#13133187 | C4 | semidirect |
| 19. C2×#13133186 | C4 | semidirect |
| 21. C2×#13133173 | C4 | semidirect |
| 335. C2×AΣL(1,𝔽16) | D53 | semidirect |
| 376. C53 | #12691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811188 | 2 |
| C2×#16810411 | 2 |
| C2×#16810410 | 2 |
| C2×#16810409 | 2 |
| #20274640 | 2 |
| #20274631 | 2 |
| C2×C53×AΣL(1,𝔽16) | 2 |
| #12691 | 53 |