← D53×#2979 #28248859
Subgroups — D53×#2979 #28248859
Order 13568.
2274 conjugacy classes of subgroups.
The subgroup lattice has 612 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #532×D53 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #20283782 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #20283781 | C2 | 1 | 2 | yes | maximal, complemented |
| 4 | #20283780 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #20283779 | C2 | 1 | 4 | yes | maximal, complemented |
| 6 | #20283778 | C2 | 1 | 4 | yes | maximal, complemented |
| 7 | #436×D53 | C2 | 1 | 4 | yes | maximal, complemented |
| 8 | C8×D4×D53 | C2 | 1 | 4 | yes | maximal, complemented |
| 9 | #431×D53 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #408×D53 | C2 | 1 | 4 | yes | maximal, complemented |
| 11 | C53×#2979 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 12 | C2×#41×D53 | C22 | 1 | 2 | yes | — |
| 13 | C2×M16×D53 | C22 | 1 | 4 | yes | — |
| 14 | C22×C8×D53 | C22 | 1 | 4 | yes | — |
| 15 | #16811174 | C4 | 1 | 1 | yes | characteristic |
| 16 | #16811173 | C22 | 1 | 1 | yes | characteristic |
| 17 | #16811172 | C4 | 1 | 2 | yes | — |
| 18 | #16811171 | C4 | 1 | 1 | yes | characteristic |
| 19 | #16811170 | C22 | 1 | 4 | yes | — |
| 20 | #16811169 | C22 | 1 | 2 | yes | — |
| 21 | #16811168 | C4 | 1 | 4 | yes | — |
| 22 | C4⋊Q8×D53 | C4 | 1 | 1 | yes | characteristic |
| 23 | #127×D53 | C4 | 1 | 1 | yes | characteristic |
| 24 | #124×D53 | C4 | 1 | 2 | yes | — |
| 25 | #121×D53 | C4 | 1 | 4 | yes | — |
| 26 | C4×D4×D53 | C22 | 1 | 4 | yes | — |
| 27 | C2×C42×D53 | C22 | 1 | 1 | yes | characteristic |
| 28 | #16810702 | C22 | 1 | 4 | yes | complemented |
| 29 | #16810701 | C22 | 1 | 4 | yes | complemented |
| 30 | #16810700 | C22 | 1 | 4 | yes | complemented |
| 31 | #16810699 | C22 | 1 | 8 | yes | complemented |
| 32 | #16810698 | C22 | 1 | 8 | yes | complemented |
| 33 | C8×D212 | C22 | 1 | 4 | yes | complemented |
| 34 | D4×#88322 | C22 | 1 | 4 | yes | complemented |
| 35 | #16810688 | C22 | 1 | 4 | yes | complemented |
| 36 | C8×C22⋊D53 | C22 | 1 | 8 | yes | complemented |
| 37 | #16810686 | C22 | 1 | 8 | yes | complemented |
| 38 | #16810676 | C22 | 1 | 2 | yes | complemented |
| 39 | #16810675 | C22 | 1 | 2 | yes | complemented |
| 40 | #16810675 | C22 | 1 | 2 | yes | complemented |
| 41 | #16810674 | C22 | 1 | 4 | yes | complemented |
| 42 | #16810673 | C22 | 1 | 4 | yes | complemented |
| 43 | C4⋊C8×D53 | C22 | 1 | 2 | yes | — |
| 44 | C4⋊C8×D53 | C22 | 1 | 2 | yes | — |
| 45 | #16810591 | C22 | 1 | 4 | yes | complemented |
| 46 | #16810590 | C22 | 1 | 4 | yes | complemented |
| 47 | #16810589 | C22 | 1 | 4 | yes | complemented |
| 48 | #16810588 | C22 | 1 | 8 | yes | complemented |
| 49 | #16810588 | C22 | 1 | 8 | yes | complemented |
| 50 | C22⋊C8×D53 | C22 | 1 | 8 | yes | — |
| 51 | C22⋊C8×D53 | C22 | 1 | 4 | yes | — |
| 52 | C4×C8×D53 | C22 | 1 | 4 | yes | — |
| 53 | C53×#532 | C22 | 1 | 1 | yes | characteristic |
| 54 | C53×#436 | C22 | 1 | 4 | yes | complemented |
| 55 | C8×D4×C53 | C22 | 1 | 4 | yes | complemented |
| 56 | C53×#431 | C22 | 1 | 2 | yes | complemented |
| 57 | C53×#408 | C22 | 1 | 4 | yes | complemented |
| 58 | C2×#11719949 | C2×C4 | 1 | 2 | yes | — |
| 59 | C2×#11719945 | C23 | 1 | 2 | yes | — |
| 60 | C2×#11719945 | C23 | 1 | 4 | yes | — |
| 61 | C2×#11719947 | C2×C4 | 1 | 4 | yes | — |
| 62 | C2×#11719947 | C2×C4 | 1 | 2 | yes | — |
| 63 | #41×D53 | — | 4 | 4 | no | — |
| 64 | #41×D53 | — | 4 | 4 | no | — |
| 65 | C2×Q8×D53 | C2×C4 | 1 | 2 | yes | — |
| 66 | C2×D4×D53 | C2×C4 | 1 | 4 | yes | — |
| 67 | C2×D4×D53 | C2×C4 | 1 | 4 | yes | — |
| 68 | C2×D4×D53 | C2×C4 | 1 | 2 | yes | — |
| 69 | C22×C4×D53 | C2×C4 | 1 | 2 | yes | — |
| 70 | C22×C4×D53 | C23 | 1 | 1 | yes | characteristic |
| 71 | C22×C4×D53 | C23 | 1 | 4 | yes | — |
| 72 | C2×#11719917 | C23 | 1 | 4 | yes | — |
| 73 | C2×#11719912 | C23 | 1 | 8 | yes | — |
| 74 | M16×D53 | — | 4 | 8 | no | — |
| 75 | C22×#88322 | C23 | 1 | 4 | yes | — |
| 76 | C2×C8×D53 | — | 4 | 8 | no | — |
| 77 | C2×C8×D53 | C23 | 1 | 4 | yes | — |
| 78 | C2×C8×D53 | C23 | 1 | 4 | yes | — |
| 79 | C2×C8×D53 | C23 | 1 | 8 | yes | — |
| 80 | #13133217 | C2×C4 | 1 | 1 | yes | characteristic |
| 81 | #13133216 | C2×C4 | 1 | 4 | yes | — |
| 82 | #13133215 | C2×C4 | 1 | 2 | yes | — |
| 83 | #13133214 | C2×C4 | 1 | 1 | yes | characteristic |
| 84 | #13133213 | C2×C4 | 1 | 4 | yes | — |
| 85 | #13133213 | C2×C4 | 1 | 2 | yes | — |
| 86 | #13133206 | C2×C4 | 1 | 2 | yes | — |
| 87 | #13133205 | C2×C4 | 1 | 2 | yes | — |
| 88 | #13133204 | C2×C4 | 1 | 2 | yes | — |
| 89 | #13133203 | C2×C4 | 1 | 8 | yes | — |
| 90 | #13133192 | C2×C4 | 1 | 4 | yes | — |
| 91 | #13133191 | C2×C4 | 1 | 4 | yes | — |
| 92 | #13133190 | C2×C4 | 1 | 8 | yes | — |
| 93 | #13133189 | C2×C4 | 1 | 8 | yes | — |
| 94 | #13133188 | C2×C4 | 1 | 4 | yes | — |
| 95 | C4×D212 | C23 | 1 | 4 | yes | — |
| 96 | D4×Dic53 | C2×C4 | 1 | 4 | yes | — |
| 97 | #13133179 | C2×C4 | 1 | 4 | yes | — |
| 98 | C4×C22⋊D53 | C23 | 1 | 8 | yes | — |
| 99 | #13133177 | C2×C4 | 1 | 8 | yes | — |
| 100 | C4⋊C4×D53 | C2×C4 | 1 | 4 | yes | — |
| 101 | C22⋊C4×D53 | C2×C4 | 1 | 8 | yes | — |
| 102 | C2×C4×Dic53 | C2×C4 | 1 | 2 | yes | — |
| 103 | C2×C4×Dic53 | C23 | 1 | 1 | yes | characteristic |
| 104 | C42×D53 | C2×C4 | 1 | 1 | yes | characteristic |
| 105 | C42×D53 | C2×C4 | 1 | 1 | yes | characteristic |
| 106 | C42×D53 | C2×C4 | 1 | 1 | yes | characteristic |
| 107 | C42×D53 | C2×C4 | 1 | 1 | yes | characteristic |
| 108 | C42×D53 | C23 | 1 | 2 | yes | — |
| 109 | C42×D53 | C23 | 1 | 2 | yes | — |
| 110 | C4⋊#88322 | C23 | 1 | 2 | yes | — |
| 111 | C4⋊#88322 | C23 | 1 | 2 | yes | — |
| 112 | #13133146 | C23 | 1 | 4 | yes | — |
| 113 | #13133146 | C23 | 1 | 4 | yes | — |
| 114 | C22⋊#88322 | C23 | 1 | 4 | yes | — |
| 115 | C22⋊#88322 | C23 | 1 | 8 | yes | — |
| 116 | #13133129 | C23 | 1 | 4 | yes | — |
| 117 | #13133129 | C23 | 1 | 4 | yes | — |
| 118 | #13133129 | C23 | 1 | 8 | yes | — |
| 119 | #13133129 | C23 | 1 | 8 | yes | — |
| 120 | C4×#88322 | C23 | 1 | 4 | yes | — |
| 121 | C8×Dic53 | C23 | 1 | 4 | yes | — |
| 122 | C8×Dic53 | C23 | 1 | 4 | yes | — |
| 123 | C2×#41×C53 | C23 | 1 | 2 | yes | — |
| 124 | C2×M16×C53 | C23 | 1 | 4 | yes | — |
| 125 | C22×C8×C53 | C23 | 1 | 4 | yes | — |
| 126 | C4⋊Q8×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 127 | #127×C53 | C2×C4 | 1 | 1 | yes | characteristic |
| 128 | #124×C53 | C2×C4 | 1 | 2 | yes | — |
| 129 | #121×C53 | C2×C4 | 1 | 4 | yes | — |
| 130 | C4×D4×C53 | C23 | 1 | 4 | yes | — |
| 131 | C2×C42×C53 | C23 | 1 | 1 | yes | characteristic |
| 132 | C4⋊C8×C53 | C23 | 1 | 2 | yes | — |
| 133 | C4⋊C8×C53 | C23 | 1 | 2 | yes | — |
| 134 | C22⋊C8×C53 | C23 | 1 | 4 | yes | — |
| 135 | C22⋊C8×C53 | C23 | 1 | 8 | yes | — |
| 136 | C4×C8×C53 | C23 | 1 | 4 | yes | — |
| 137 | C23×D53 | C22×C4 | 1 | 4 | yes | — |
| 138 | C23×D53 | C22×C4 | 1 | 1 | yes | characteristic |
| 139 | #41×C53 | — | 4 | 2 | no | — |
| 140 | #41×C53 | — | 4 | 2 | no | — |
| 141 | C2×Q8×C53 | C22×C4 | 1 | 2 | yes | — |
| 142 | C2×D4×C53 | C22×C4 | 1 | 4 | yes | — |
| 143 | C2×D4×C53 | C22×C4 | 1 | 4 | yes | — |
| 144 | C2×D4×C53 | C22×C4 | 1 | 2 | yes | — |
| 145 | C22×C4×C53 | C22×C4 | 1 | 2 | yes | — |
| 146 | C22×C4×C53 | C24 | 1 | 1 | yes | characteristic |
| 147 | C22×C4×C53 | C24 | 1 | 4 | yes | — |
| 148 | C2×C22⋊D53 | C22×C4 | 1 | 8 | yes | — |
| 149 | C2×C22⋊D53 | C22×C4 | 1 | 4 | yes | — |
| 150 | C2×C22⋊D53 | C22×C4 | 1 | 4 | yes | — |
| 151 | C2×C22⋊D53 | C22×C4 | 1 | 4 | yes | — |
| 152 | C22×Dic53 | C22×C4 | 1 | 1 | yes | characteristic |
| 153 | C22×Dic53 | C22×C4 | 1 | 2 | yes | — |
| 154 | C22×Dic53 | C22×C4 | 1 | 4 | yes | — |
| 155 | #11719949 | — | 4 | 4 | no | — |
| 156 | Q8×D53 | — | 4 | 4 | no | — |
| 157 | #11719947 | — | 4 | 4 | no | — |
| 158 | #11719947 | — | 4 | 8 | no | — |
| 159 | D4×D53 | — | 2 | 16 | no | — |
| 160 | D4×D53 | — | 4 | 4 | no | — |
| 161 | D4×D53 | — | 4 | 8 | no | — |
| 162 | #11719945 | — | 4 | 4 | no | — |
| 163 | #11719945 | — | 4 | 4 | no | — |
| 164 | #11719945 | — | 4 | 2 | no | — |
| 165 | #11719945 | — | 4 | 2 | no | — |
| 166 | C2×D212 | C22×C4 | 1 | 4 | yes | — |
| 167 | C2×D212 | C22×C4 | 1 | 4 | yes | — |
| 168 | C2×D212 | C22×C4 | 1 | 2 | yes | — |
| 169 | C2×C4×D53 | — | 2 | 8 | no | — |
| 170 | C2×C4×D53 | — | 2 | 8 | no | — |
| 171 | C2×C4×D53 | — | 2 | 8 | no | — |
| 172 | C2×C4×D53 | — | 2 | 2 | no | — |
| 173 | C2×C4×D53 | — | 2 | 2 | no | — |
| 174 | C2×C4×D53 | C22×C4 | 1 | 1 | yes | characteristic |
| 175 | C2×C4×D53 | C22×C4 | 1 | 1 | yes | characteristic |
| 176 | C2×C4×D53 | C22×C4 | 1 | 2 | yes | — |
| 177 | C2×C4×D53 | C22×C4 | 1 | 2 | yes | — |
| 178 | C2×C4×D53 | C22×C4 | 1 | 2 | yes | — |
| 179 | C2×C4×D53 | C22×C4 | 1 | 4 | yes | — |
| 180 | C2×C4×D53 | C22×C4 | 1 | 4 | yes | — |
| 181 | C2×C4×D53 | C22×C4 | 1 | 2 | yes | — |
| 182 | C2×C4×D53 | C24 | 1 | 1 | yes | characteristic |
| 183 | C2×C4×D53 | C24 | 1 | 4 | yes | — |
| 184 | C2×C4×D53 | C24 | 1 | 1 | yes | characteristic |
| 185 | C2×Dic106 | C22×C4 | 1 | 4 | yes | — |
| 186 | C2×Dic106 | C22×C4 | 1 | 2 | yes | — |
| 187 | M16×C53 | — | 4 | 4 | no | — |
| 188 | C2×C8×C53 | — | 4 | 4 | no | — |
| 189 | C2×C8×C53 | C24 | 1 | 4 | yes | — |
| 190 | C2×C8×C53 | C24 | 1 | 4 | yes | — |
| 191 | C4⋊C4×C53 | C22×C4 | 1 | 4 | yes | — |
| 192 | C22⋊C4×C53 | C22×C4 | 1 | 8 | yes | — |
| 193 | C42×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 194 | C42×C53 | C22×C4 | 1 | 1 | yes | characteristic |
| 195 | C42×C53 | C24 | 1 | 2 | yes | — |
| 196 | C22⋊Dic53 | C22×C4 | 1 | 8 | yes | — |
| 197 | #11719921 | C22×C4 | 1 | 8 | yes | — |
| 198 | #11719921 | C22×C4 | 1 | 8 | yes | — |
| 199 | C4⋊Dic53 | C22×C4 | 1 | 4 | yes | — |
| 200 | #11719919 | C22×C4 | 1 | 8 | yes | — |
| 201 | C4×Dic53 | C22×C4 | 1 | 1 | yes | characteristic |
| 202 | C4×Dic53 | C22×C4 | 1 | 1 | yes | characteristic |
| 203 | C4×Dic53 | C22×C4 | 1 | 2 | yes | — |
| 204 | C4×Dic53 | C22×C4 | 1 | 2 | yes | — |
| 205 | C4×Dic53 | C22×C4 | 1 | 2 | yes | — |
| 206 | C4×Dic53 | C22×C4 | 1 | 2 | yes | — |
| 207 | C4×Dic53 | C24 | 1 | 2 | yes | — |
| 208 | #11719917 | — | 4 | 4 | no | — |
| 209 | C2×#88322 | — | 4 | 4 | no | — |
| 210 | C2×#88322 | C24 | 1 | 4 | yes | — |
| 211 | C2×#88322 | C24 | 1 | 4 | yes | — |
| 212 | #11719912 | — | 4 | 8 | no | — |
| 213 | C8×D53 | — | 2 | 8 | no | — |
| 214 | C8×D53 | — | 2 | 8 | no | — |
| 215 | C8×D53 | — | 4 | 8 | no | — |
| 216 | C23×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 217 | C23×C53 | C23×C4 | 1 | 4 | yes | — |
| 218 | C22×D53 | — | 2 | 2 | no | — |
| 219 | C22×D53 | — | 2 | 8 | no | — |
| 220 | C22×D53 | — | 2 | 4 | no | — |
| 221 | C22×D53 | — | 2 | 16 | no | — |
| 222 | C22×D53 | C23×C4 | 1 | 1 | yes | characteristic |
| 223 | C22×D53 | C23×C4 | 1 | 4 | yes | — |
| 224 | C22×D53 | C23×C4 | 1 | 1 | yes | characteristic |
| 225 | Q8×C53 | — | 4 | 2 | no | — |
| 226 | D4×C53 | — | 2 | 8 | no | — |
| 227 | D4×C53 | — | 4 | 2 | no | — |
| 228 | D4×C53 | — | 4 | 4 | no | — |
| 229 | C2×C4×C53 | — | 2 | 4 | no | — |
| 230 | C2×C4×C53 | — | 2 | 1 | no | — |
| 231 | C2×C4×C53 | — | 2 | 1 | no | — |
| 232 | C2×C4×C53 | — | 2 | 4 | no | — |
| 233 | C2×C4×C53 | — | 2 | 4 | no | — |
| 234 | C2×C4×C53 | C23×C4 | 1 | 1 | yes | characteristic |
| 235 | C2×C4×C53 | C23×C4 | 1 | 4 | yes | — |
| 236 | C2×C4×C53 | C23×C4 | 1 | 2 | yes | — |
| 237 | C2×C4×C53 | C23×C4 | 1 | 2 | yes | — |
| 238 | C2×C4×C53 | C25 | 1 | 1 | yes | characteristic |
| 239 | C22⋊D53 | — | 2 | 16 | no | — |
| 240 | C22⋊D53 | — | 4 | 4 | no | — |
| 241 | C22⋊D53 | — | 4 | 4 | no | — |
| 242 | C22⋊D53 | — | 4 | 4 | no | — |
| 243 | C2×Dic53 | — | 2 | 2 | no | — |
| 244 | C2×Dic53 | — | 2 | 8 | no | — |
| 245 | C2×Dic53 | — | 2 | 4 | no | — |
| 246 | C2×Dic53 | C23×C4 | 1 | 1 | yes | characteristic |
| 247 | C2×Dic53 | C23×C4 | 1 | 4 | yes | — |
| 248 | C2×Dic53 | C23×C4 | 1 | 2 | yes | — |
| 249 | C2×Dic53 | C23×C4 | 1 | 1 | yes | characteristic |
| 250 | C2×Dic53 | C23×C4 | 1 | 2 | yes | — |
| 251 | D212 | — | 2 | 8 | no | — |
| 252 | D212 | — | 4 | 2 | no | — |
| 253 | D212 | — | 4 | 4 | no | — |
| 254 | C4×D53 | — | 2 | 2 | no | — |
| 255 | C4×D53 | — | 2 | 8 | no | — |
| 256 | C4×D53 | — | 2 | 4 | no | — |
| 257 | C4×D53 | — | 2 | 4 | no | — |
| 258 | C4×D53 | — | 2 | 1 | no | — |
| 259 | C4×D53 | — | 2 | 1 | no | — |
| 260 | C4×D53 | — | 2 | 4 | no | — |
| 261 | C4×D53 | — | 2 | 4 | no | — |
| 262 | C4×D53 | — | 2 | 2 | no | — |
| 263 | C4×D53 | — | 2 | 8 | no | — |
| 264 | C4×D53 | — | 2 | 4 | no | — |
| 265 | C4×D53 | #131 | 1 | 8 | yes | — |
| 266 | C4×D53 | H(5,𝔽2) | 1 | 2 | yes | — |
| 267 | C4×D53 | H(5,𝔽2) | 1 | 2 | yes | — |
| 268 | Dic106 | — | 4 | 4 | no | — |
| 269 | Dic106 | — | 4 | 2 | no | — |
| 270 | C8×C53 | — | 2 | 4 | no | — |
| 271 | C8×C53 | — | 2 | 4 | no | — |
| 272 | #88322 | — | 2 | 4 | no | — |
| 273 | #88322 | — | 2 | 4 | no | — |
| 274 | C2×#2979 | — | 53 | 1 | no | maximal, Sylow |
| 275 | C22×C53 | — | 2 | 1 | no | — |
| 276 | C22×C53 | — | 2 | 4 | no | — |
| 277 | C22×C53 | — | 2 | 2 | no | — |
| 278 | C22×C53 | — | 2 | 8 | no | — |
| 279 | C22×C53 | C24×C4 | 1 | 1 | yes | characteristic |
| 280 | C2×D53 | — | 2 | 1 | no | — |
| 281 | C2×D53 | — | 2 | 4 | no | — |
| 282 | C2×D53 | — | 2 | 2 | no | — |
| 283 | C2×D53 | — | 2 | 8 | no | — |
| 284 | C2×D53 | — | 4 | 4 | no | — |
| 285 | C2×D53 | — | 4 | 16 | no | — |
| 286 | C2×D53 | #518 | 1 | 2 | yes | — |
| 287 | C2×D53 | C2×#131 | 1 | 4 | yes | — |
| 288 | C4×C53 | — | 2 | 1 | no | — |
| 289 | C4×C53 | — | 2 | 4 | no | — |
| 290 | C4×C53 | — | 2 | 2 | no | — |
| 291 | C4×C53 | C2×#131 | 1 | 4 | yes | — |
| 292 | C4×C53 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 293 | C4×C53 | C2×H(5,𝔽2) | 1 | 1 | yes | characteristic |
| 294 | Dic53 | — | 2 | 1 | no | — |
| 295 | Dic53 | — | 2 | 4 | no | — |
| 296 | Dic53 | — | 2 | 2 | no | — |
| 297 | Dic53 | #518 | 1 | 2 | yes | — |
| 298 | Dic53 | C2×#131 | 1 | 4 | yes | — |
| 299 | C2×#532 | — | 53 | 1 | no | — |
| 300 | #2979 | — | 53 | 4 | no | — |
| 301 | #2979 | — | 53 | 4 | no | — |
| 302 | #2979 | — | 53 | 2 | no | — |
| 303 | #2979 | — | 53 | 4 | no | — |
| 304 | #2979 | — | 53 | 1 | no | — |
| 305 | #2979 | D53 | 1 | 1 | yes | characteristic, direct product factor |
| 306 | C2×#436 | — | 53 | 4 | no | — |
| 307 | C2×C8×D4 | — | 53 | 4 | no | — |
| 308 | C2×#431 | — | 53 | 2 | no | — |
| 309 | C2×#408 | — | 53 | 4 | no | — |
| 310 | C2×C53 | — | 4 | 1 | no | — |
| 311 | C2×C53 | — | 4 | 4 | no | — |
| 312 | C2×C53 | C2×#518 | 1 | 1 | yes | characteristic |
| 313 | C2×C53 | C22×#131 | 1 | 2 | yes | — |
| 314 | D53 | — | 4 | 1 | no | — |
| 315 | D53 | — | 4 | 4 | no | — |
| 316 | D53 | #2979 | 1 | 4 | yes | direct product factor |
| 317 | C22×#41 | — | 53 | 2 | no | — |
| 318 | C22×M16 | — | 53 | 4 | no | — |
| 319 | C23×C8 | — | 53 | 4 | no | — |
| 320 | #532 | — | 53 | 2 | no | — |
| 321 | #532 | — | 53 | 1 | no | — |
| 322 | #532 | — | 53 | 1 | no | — |
| 323 | #532 | — | 53 | 2 | no | — |
| 324 | #532 | — | 53 | 4 | no | — |
| 325 | #532 | — | 53 | 4 | no | — |
| 326 | #532 | — | 53 | 1 | no | — |
| 327 | #532 | C2×D53 | 1 | 1 | yes | characteristic |
| 328 | C2×C4⋊Q8 | — | 53 | 1 | no | — |
| 329 | C2×#127 | — | 53 | 1 | no | — |
| 330 | C2×#124 | — | 53 | 2 | no | — |
| 331 | C2×#121 | — | 53 | 4 | no | — |
| 332 | C2×C4×D4 | — | 53 | 4 | no | — |
| 333 | C22×C42 | — | 53 | 1 | no | — |
| 334 | #436 | — | 53 | 8 | no | — |
| 335 | #436 | — | 53 | 4 | no | — |
| 336 | #436 | — | 53 | 4 | no | — |
| 337 | #436 | — | 53 | 8 | no | — |
| 338 | #436 | — | 53 | 4 | no | — |
| 339 | #436 | C2×D53 | 1 | 4 | yes | complemented |
| 340 | C8×D4 | — | 53 | 8 | no | — |
| 341 | C8×D4 | — | 53 | 4 | no | — |
| 342 | C8×D4 | — | 53 | 4 | no | — |
| 343 | C8×D4 | — | 53 | 8 | no | — |
| 344 | C8×D4 | — | 53 | 4 | no | — |
| 345 | C8×D4 | C2×D53 | 1 | 4 | yes | complemented |
| 346 | #431 | — | 53 | 2 | no | — |
| 347 | #431 | — | 53 | 2 | no | — |
| 348 | #431 | — | 53 | 2 | no | — |
| 349 | #431 | — | 53 | 4 | no | — |
| 350 | #431 | — | 53 | 4 | no | — |
| 351 | #431 | C2×D53 | 1 | 2 | yes | complemented |
| 352 | C2×C4⋊C8 | — | 53 | 2 | no | — |
| 353 | C2×C4⋊C8 | — | 53 | 2 | no | — |
| 354 | #408 | — | 53 | 4 | no | — |
| 355 | #408 | — | 53 | 4 | no | — |
| 356 | #408 | — | 53 | 4 | no | — |
| 357 | #408 | — | 53 | 8 | no | — |
| 358 | #408 | — | 53 | 8 | no | — |
| 359 | #408 | C2×D53 | 1 | 4 | yes | complemented |
| 360 | C2×C22⋊C8 | — | 53 | 4 | no | — |
| 361 | C2×C22⋊C8 | — | 53 | 8 | no | — |
| 362 | C2×C4×C8 | — | 53 | 4 | no | — |
| 363 | C53 | C2×#2979 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 364 | C2×#41 | — | 53 | 2 | no | — |
| 365 | C2×#41 | — | 53 | 4 | no | — |
| 366 | C2×#41 | — | 53 | 2 | no | — |
| 367 | C2×#41 | — | 53 | 4 | no | — |
| 368 | C2×#41 | — | 53 | 2 | no | — |
| 369 | C2×#41 | — | 212 | 4 | no | — |
| 370 | C2×#41 | — | 212 | 4 | no | — |
| 371 | C2×#41 | C22×D53 | 1 | 2 | yes | — |
| 372 | C22×Q8 | — | 53 | 2 | no | — |
| 373 | C22×D4 | — | 53 | 4 | no | — |
| 374 | C22×D4 | — | 53 | 4 | no | — |
| 375 | C22×D4 | — | 53 | 2 | no | — |
| 376 | C23×C4 | — | 53 | 2 | no | — |
| 377 | C23×C4 | — | 53 | 4 | no | — |
| 378 | C23×C4 | — | 53 | 1 | no | — |
| 379 | C2×M16 | — | 53 | 4 | no | — |
| 380 | C2×M16 | — | 53 | 8 | no | — |
| 381 | C2×M16 | — | 212 | 8 | no | — |
| 382 | C2×M16 | C22×D53 | 1 | 4 | yes | — |
| 383 | C22×C8 | — | 53 | 4 | no | — |
| 384 | C22×C8 | — | 53 | 4 | no | — |
| 385 | C22×C8 | — | 53 | 4 | no | — |
| 386 | C22×C8 | — | 53 | 8 | no | — |
| 387 | C22×C8 | — | 212 | 8 | no | — |
| 388 | C22×C8 | C22×D53 | 1 | 4 | yes | — |
| 389 | C4⋊Q8 | — | 53 | 2 | no | — |
| 390 | C4⋊Q8 | — | 53 | 4 | no | — |
| 391 | C4⋊Q8 | — | 53 | 1 | no | — |
| 392 | C4⋊Q8 | C4×D53 | 1 | 1 | yes | characteristic |
| 393 | #127 | — | 53 | 2 | no | — |
| 394 | #127 | — | 53 | 4 | no | — |
| 395 | #127 | — | 53 | 1 | no | — |
| 396 | #127 | C4×D53 | 1 | 1 | yes | characteristic |
| 397 | #124 | — | 53 | 2 | no | — |
| 398 | #124 | — | 53 | 2 | no | — |
| 399 | #124 | — | 53 | 8 | no | — |
| 400 | #124 | — | 53 | 2 | no | — |
| 401 | #124 | C4×D53 | 1 | 2 | yes | — |
| 402 | #121 | — | 53 | 4 | no | — |
| 403 | #121 | — | 53 | 8 | no | — |
| 404 | #121 | — | 53 | 4 | no | — |
| 405 | #121 | — | 53 | 4 | no | — |
| 406 | #121 | — | 53 | 8 | no | — |
| 407 | #121 | C4×D53 | 1 | 4 | yes | — |
| 408 | C4×D4 | — | 53 | 4 | no | — |
| 409 | C4×D4 | — | 53 | 8 | no | — |
| 410 | C4×D4 | — | 53 | 4 | no | — |
| 411 | C4×D4 | — | 53 | 8 | no | — |
| 412 | C4×D4 | — | 53 | 4 | no | — |
| 413 | C4×D4 | C22×D53 | 1 | 4 | yes | — |
| 414 | C2×C4⋊C4 | — | 53 | 4 | no | — |
| 415 | C2×C22⋊C4 | — | 53 | 8 | no | — |
| 416 | C2×C42 | — | 53 | 2 | no | — |
| 417 | C2×C42 | — | 53 | 1 | no | — |
| 418 | C2×C42 | — | 53 | 1 | no | — |
| 419 | C2×C42 | — | 53 | 1 | no | — |
| 420 | C2×C42 | — | 53 | 1 | no | — |
| 421 | C2×C42 | — | 53 | 1 | no | — |
| 422 | C2×C42 | — | 53 | 2 | no | — |
| 423 | C2×C42 | — | 53 | 2 | no | — |
| 424 | C2×C42 | C22×D53 | 1 | 1 | yes | characteristic |
| 425 | C4⋊C8 | — | 53 | 4 | no | — |
| 426 | C4⋊C8 | — | 53 | 4 | no | — |
| 427 | C4⋊C8 | — | 53 | 2 | no | — |
| 428 | C4⋊C8 | — | 53 | 2 | no | — |
| 429 | C4⋊C8 | C22×D53 | 1 | 2 | yes | — |
| 430 | C4⋊C8 | C22×D53 | 1 | 2 | yes | — |
| 431 | C22⋊C8 | — | 53 | 4 | no | — |
| 432 | C22⋊C8 | — | 53 | 8 | no | — |
| 433 | C22⋊C8 | — | 53 | 4 | no | — |
| 434 | C22⋊C8 | — | 53 | 4 | no | — |
| 435 | C22⋊C8 | — | 53 | 8 | no | — |
| 436 | C22⋊C8 | — | 53 | 8 | no | — |
| 437 | C22⋊C8 | C22×D53 | 1 | 4 | yes | — |
| 438 | C22⋊C8 | C22×D53 | 1 | 8 | yes | — |
| 439 | C4×C8 | — | 53 | 4 | no | — |
| 440 | C4×C8 | — | 53 | 4 | no | — |
| 441 | C4×C8 | — | 53 | 4 | no | — |
| 442 | C4×C8 | C22×D53 | 1 | 4 | yes | — |
| 443 | C24 | — | 53 | 4 | no | — |
| 444 | C24 | — | 53 | 1 | no | — |
| 445 | #41 | — | 4 | 2 | no | — |
| 446 | #41 | — | 4 | 2 | no | — |
| 447 | #41 | — | 212 | 4 | no | — |
| 448 | #41 | — | 212 | 4 | no | — |
| 449 | #41 | — | 212 | 2 | no | — |
| 450 | #41 | — | 212 | 2 | no | — |
| 451 | #41 | — | 212 | 8 | no | — |
| 452 | #41 | — | 212 | 4 | no | — |
| 453 | #41 | — | 212 | 4 | no | — |
| 454 | C2×Q8 | — | 53 | 4 | no | — |
| 455 | C2×Q8 | — | 53 | 2 | no | — |
| 456 | C2×Q8 | — | 212 | 4 | no | — |
| 457 | C2×Q8 | C2×C4×D53 | 1 | 2 | yes | — |
| 458 | C2×D4 | — | 53 | 8 | no | — |
| 459 | C2×D4 | — | 53 | 4 | no | — |
| 460 | C2×D4 | — | 53 | 4 | no | — |
| 461 | C2×D4 | — | 53 | 4 | no | — |
| 462 | C2×D4 | — | 53 | 4 | no | — |
| 463 | C2×D4 | — | 53 | 4 | no | — |
| 464 | C2×D4 | — | 53 | 2 | no | — |
| 465 | C2×D4 | — | 106 | 16 | no | — |
| 466 | C2×D4 | — | 212 | 4 | no | — |
| 467 | C2×D4 | — | 212 | 8 | no | — |
| 468 | C2×D4 | C2×C4×D53 | 1 | 4 | yes | — |
| 469 | C2×D4 | C2×C4×D53 | 1 | 4 | yes | — |
| 470 | C2×D4 | C2×C4×D53 | 1 | 2 | yes | — |
| 471 | C22×C4 | — | 53 | 2 | no | — |
| 472 | C22×C4 | — | 53 | 1 | no | — |
| 473 | C22×C4 | — | 53 | 2 | no | — |
| 474 | C22×C4 | — | 53 | 1 | no | — |
| 475 | C22×C4 | — | 53 | 4 | no | — |
| 476 | C22×C4 | — | 53 | 2 | no | — |
| 477 | C22×C4 | — | 53 | 2 | no | — |
| 478 | C22×C4 | — | 53 | 2 | no | — |
| 479 | C22×C4 | — | 53 | 1 | no | — |
| 480 | C22×C4 | — | 53 | 1 | no | — |
| 481 | C22×C4 | — | 53 | 4 | no | — |
| 482 | C22×C4 | — | 53 | 4 | no | — |
| 483 | C22×C4 | — | 53 | 1 | no | — |
| 484 | C22×C4 | — | 53 | 4 | no | — |
| 485 | C22×C4 | — | 106 | 8 | no | — |
| 486 | C22×C4 | — | 106 | 8 | no | — |
| 487 | C22×C4 | — | 106 | 8 | no | — |
| 488 | C22×C4 | — | 106 | 2 | no | — |
| 489 | C22×C4 | — | 106 | 2 | no | — |
| 490 | C22×C4 | C2×C4×D53 | 1 | 2 | yes | — |
| 491 | C22×C4 | C23×D53 | 1 | 1 | yes | characteristic |
| 492 | C22×C4 | C23×D53 | 1 | 4 | yes | — |
| 493 | M16 | — | 4 | 4 | no | — |
| 494 | M16 | — | 212 | 8 | no | — |
| 495 | M16 | — | 212 | 4 | no | — |
| 496 | C2×C8 | — | 4 | 4 | no | — |
| 497 | C2×C8 | — | 53 | 4 | no | — |
| 498 | C2×C8 | — | 53 | 4 | no | — |
| 499 | C2×C8 | — | 106 | 8 | no | — |
| 500 | C2×C8 | — | 106 | 8 | no | — |
| 501 | C2×C8 | — | 212 | 8 | no | — |
| 502 | C2×C8 | — | 212 | 4 | no | — |
| 503 | C2×C8 | C23×D53 | 1 | 4 | yes | — |
| 504 | C2×C8 | C23×D53 | 1 | 4 | yes | — |
| 505 | C4⋊C4 | — | 53 | 8 | no | — |
| 506 | C4⋊C4 | — | 53 | 4 | no | — |
| 507 | C4⋊C4 | C2×C4×D53 | 1 | 4 | yes | — |
| 508 | C22⋊C4 | — | 53 | 8 | no | — |
| 509 | C22⋊C4 | — | 53 | 8 | no | — |
| 510 | C22⋊C4 | — | 53 | 8 | no | — |
| 511 | C22⋊C4 | C2×C4×D53 | 1 | 8 | yes | — |
| 512 | C42 | — | 53 | 2 | no | — |
| 513 | C42 | — | 53 | 2 | no | — |
| 514 | C42 | — | 53 | 1 | no | — |
| 515 | C42 | — | 53 | 2 | no | — |
| 516 | C42 | — | 53 | 1 | no | — |
| 517 | C42 | — | 53 | 2 | no | — |
| 518 | C42 | — | 53 | 2 | no | — |
| 519 | C42 | C2×C4×D53 | 1 | 1 | yes | characteristic |
| 520 | C42 | C2×C4×D53 | 1 | 1 | yes | characteristic |
| 521 | C42 | C23×D53 | 1 | 2 | yes | — |
| 522 | C23 | — | 53 | 1 | no | — |
| 523 | C23 | — | 53 | 4 | no | — |
| 524 | C23 | — | 53 | 1 | no | — |
| 525 | C23 | — | 106 | 2 | no | — |
| 526 | C23 | — | 106 | 8 | no | — |
| 527 | C23 | — | 106 | 4 | no | — |
| 528 | C23 | — | 106 | 16 | no | — |
| 529 | C23 | C22×C4×D53 | 1 | 4 | yes | — |
| 530 | C23 | C22×C4×D53 | 1 | 1 | yes | characteristic |
| 531 | Q8 | — | 4 | 2 | no | — |
| 532 | Q8 | — | 212 | 2 | no | — |
| 533 | Q8 | — | 212 | 4 | no | — |
| 534 | D4 | — | 2 | 8 | no | — |
| 535 | D4 | — | 4 | 2 | no | — |
| 536 | D4 | — | 4 | 4 | no | — |
| 537 | D4 | — | 106 | 16 | no | — |
| 538 | D4 | — | 106 | 8 | no | — |
| 539 | D4 | — | 212 | 2 | no | — |
| 540 | D4 | — | 212 | 4 | no | — |
| 541 | D4 | — | 212 | 4 | no | — |
| 542 | D4 | — | 212 | 4 | no | — |
| 543 | D4 | — | 212 | 4 | no | — |
| 544 | C2×C4 | — | 2 | 4 | no | — |
| 545 | C2×C4 | — | 2 | 4 | no | — |
| 546 | C2×C4 | — | 2 | 4 | no | — |
| 547 | C2×C4 | — | 2 | 1 | no | — |
| 548 | C2×C4 | — | 2 | 1 | no | — |
| 549 | C2×C4 | — | 53 | 2 | no | — |
| 550 | C2×C4 | — | 53 | 1 | no | — |
| 551 | C2×C4 | — | 53 | 8 | no | — |
| 552 | C2×C4 | — | 53 | 2 | no | — |
| 553 | C2×C4 | — | 53 | 2 | no | — |
| 554 | C2×C4 | — | 53 | 2 | no | — |
| 555 | C2×C4 | — | 53 | 1 | no | — |
| 556 | C2×C4 | — | 53 | 4 | no | — |
| 557 | C2×C4 | — | 106 | 4 | no | — |
| 558 | C2×C4 | — | 106 | 8 | no | — |
| 559 | C2×C4 | — | 106 | 2 | no | — |
| 560 | C2×C4 | — | 106 | 4 | no | — |
| 561 | C2×C4 | — | 106 | 2 | no | — |
| 562 | C2×C4 | — | 106 | 8 | no | — |
| 563 | C2×C4 | — | 106 | 4 | no | — |
| 564 | C2×C4 | — | 106 | 8 | no | — |
| 565 | C2×C4 | — | 106 | 2 | no | — |
| 566 | C2×C4 | — | 106 | 4 | no | — |
| 567 | C2×C4 | — | 106 | 4 | no | — |
| 568 | C2×C4 | — | 106 | 4 | no | — |
| 569 | C2×C4 | — | 106 | 1 | no | — |
| 570 | C2×C4 | — | 106 | 1 | no | — |
| 571 | C2×C4 | C22×C4×D53 | 1 | 1 | yes | characteristic |
| 572 | C2×C4 | C22×C4×D53 | 1 | 2 | yes | — |
| 573 | C2×C4 | C22×C4×D53 | 1 | 4 | yes | — |
| 574 | C2×C4 | C22×C4×D53 | 1 | 2 | yes | — |
| 575 | C2×C4 | C24×D53 | 1 | 1 | yes | characteristic |
| 576 | C8 | — | 2 | 4 | no | — |
| 577 | C8 | — | 2 | 4 | no | — |
| 578 | C8 | — | 106 | 4 | no | — |
| 579 | C8 | — | 106 | 4 | no | — |
| 580 | C22 | — | 2 | 2 | no | — |
| 581 | C22 | — | 2 | 8 | no | — |
| 582 | C22 | — | 2 | 1 | no | — |
| 583 | C22 | — | 2 | 4 | no | — |
| 584 | C22 | — | 53 | 4 | no | — |
| 585 | C22 | — | 53 | 2 | no | — |
| 586 | C22 | — | 106 | 2 | no | — |
| 587 | C22 | — | 106 | 8 | no | — |
| 588 | C22 | — | 106 | 1 | no | — |
| 589 | C22 | — | 106 | 4 | no | — |
| 590 | C22 | — | 212 | 4 | no | — |
| 591 | C22 | — | 212 | 16 | no | — |
| 592 | C22 | C23×C4×D53 | 1 | 1 | yes | characteristic |
| 593 | C4 | — | 2 | 2 | no | — |
| 594 | C4 | — | 2 | 1 | no | — |
| 595 | C4 | — | 2 | 4 | no | — |
| 596 | C4 | — | 53 | 4 | no | — |
| 597 | C4 | — | 53 | 2 | no | — |
| 598 | C4 | — | 106 | 2 | no | — |
| 599 | C4 | — | 106 | 1 | no | — |
| 600 | C4 | — | 106 | 4 | no | — |
| 601 | C4 | #131×D53 | 1 | 4 | yes | — |
| 602 | C4 | H(5,𝔽2)×D53 | 1 | 1 | yes | characteristic |
| 603 | C4 | H(5,𝔽2)×D53 | 1 | 1 | yes | characteristic |
| 604 | C2 | — | 4 | 1 | no | — |
| 605 | C2 | — | 4 | 4 | no | — |
| 606 | C2 | — | 53 | 4 | no | — |
| 607 | C2 | — | 212 | 1 | no | — |
| 608 | C2 | — | 212 | 4 | no | — |
| 609 | C2 | #518×D53 | 1 | 1 | yes | characteristic |
| 610 | C2 | C2×#131×D53 | 1 | 2 | yes | — |
Complements
Splittings G = N ⋊ H with N normal; H ≅ G/N.
Maximal subgroups
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
Finite Group Databasebeta