Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
4360 conjugacy classes of subgroups; only the 319 normal subgroups are shown.
This group has 4360 conjugacy classes of subgroups — too many to draw. Only its 319 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×#16810810 | C2 | 1 | 4 | yes | maximal, complemented |
| 2 | #20278025 | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | #20274663 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #20274630 | C2 | 1 | 3 | yes | maximal, complemented |
| 5 | C22×H(5,𝔽2)×C53 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | C23×C22⋊D53 | C22 | 1 | 1 | yes | characteristic, complemented |
| 7 | C2×#13133186 | — | 2 | 3 | no | — |
| 8 | C2×#13133185 | C22 | 1 | 6 | yes | complemented |
| 9 | #16810810 | — | 2 | 16 | no | — |
| 10 | C2×#13133132 | C22 | 1 | 12 | yes | complemented |
| 11 | #16810531 | — | 2 | 6 | no | — |
| 12 | #16810503 | C22 | 1 | 6 | yes | complemented |
| 13 | #16810502 | — | 2 | 3 | no | — |
| 14 | #16810479 | C22 | 1 | 3 | yes | complemented |
| 15 | C2×H(5,𝔽2)×C53 | — | 2 | 16 | no | — |
| 16 | C2×H(5,𝔽2)×C53 | — | 2 | 6 | no | — |
| 17 | C2×H(5,𝔽2)×C53 | C22 | 1 | 4 | yes | — |
| 18 | C22×#41×C53 | — | 2 | 3 | no | — |
| 19 | C23×D4×C53 | — | 2 | 3 | no | — |
| 20 | C23×D4×C53 | C22 | 1 | 3 | yes | — |
| 21 | C24×D53 | C23 | 1 | 1 | yes | characteristic, complemented |
| 22 | C22×C22⋊D53 | — | 2 | 3 | no | — |
| 23 | C22×C22⋊D53 | — | 2 | 3 | no | — |
| 24 | C22×C22⋊D53 | — | 2 | 6 | no | — |
| 25 | C22×C22⋊D53 | — | 4 | 4 | no | — |
| 26 | C23×Dic53 | C23 | 1 | 1 | yes | characteristic, complemented |
| 27 | #13133186 | — | 4 | 12 | no | — |
| 28 | #13133185 | — | 2 | 24 | no | — |
| 29 | C2×C22⋊Dic53 | — | 2 | 3 | no | — |
| 30 | C2×C22⋊Dic53 | — | 2 | 6 | no | — |
| 31 | C2×C22⋊Dic53 | — | 2 | 3 | no | — |
| 32 | C2×C22⋊Dic53 | C23 | 1 | 6 | yes | complemented |
| 33 | C2×#11719921 | — | 2 | 6 | no | — |
| 34 | #13133132 | — | 2 | 24 | no | — |
| 35 | #13133124 | — | 2 | 6 | no | — |
| 36 | C25×C53 | — | 2 | 1 | no | — |
| 37 | C25×C53 | D4 | 1 | 3 | yes | complemented |
| 38 | C25×C53 | C23 | 1 | 1 | yes | characteristic |
| 39 | H(5,𝔽2)×C53 | — | 2 | 48 | no | — |
| 40 | H(5,𝔽2)×C53 | — | 2 | 48 | no | — |
| 41 | H(5,𝔽2)×C53 | — | 2 | 24 | no | — |
| 42 | H(5,𝔽2)×C53 | D4 | 1 | 16 | yes | complemented |
| 43 | C2×#41×C53 | — | 2 | 12 | no | — |
| 44 | C2×#41×C53 | — | 2 | 48 | no | — |
| 45 | C2×#41×C53 | — | 2 | 12 | no | — |
| 46 | C22×Q8×C53 | — | 2 | 1 | no | — |
| 47 | C22×D4×C53 | — | 2 | 3 | no | — |
| 48 | C22×D4×C53 | — | 2 | 48 | no | — |
| 49 | C22×D4×C53 | — | 2 | 12 | no | — |
| 50 | C22×D4×C53 | — | 2 | 6 | no | — |
| 51 | C22×D4×C53 | — | 2 | 12 | no | — |
| 52 | C22×D4×C53 | — | 2 | 6 | no | — |
| 53 | C22×D4×C53 | — | 2 | 24 | no | — |
| 54 | C22×D4×C53 | D4 | 1 | 6 | yes | complemented |
| 55 | C22×D4×C53 | C23 | 1 | 6 | yes | — |
| 56 | C23×C4×C53 | — | 2 | 3 | no | — |
| 57 | C23×C4×C53 | D4 | 1 | 3 | yes | complemented |
| 58 | C24×C53 | — | 2 | 8 | no | — |
| 59 | C24×C53 | — | 2 | 4 | no | — |
| 60 | C24×C53 | — | 2 | 3 | no | — |
| 61 | C24×C53 | — | 2 | 3 | no | — |
| 62 | C24×C53 | — | 2 | 12 | no | — |
| 63 | C24×C53 | — | 2 | 4 | no | — |
| 64 | C24×C53 | — | 4 | 2 | no | — |
| 65 | C24×C53 | — | 4 | 6 | no | — |
| 66 | C24×C53 | — | 8 | 1 | no | — |
| 67 | C24×C53 | — | 8 | 3 | no | — |
| 68 | C24×C53 | — | 8 | 2 | no | — |
| 69 | C24×C53 | — | 8 | 2 | no | — |
| 70 | C24×C53 | C2×D4 | 1 | 3 | yes | — |
| 71 | C24×C53 | C2×D4 | 1 | 3 | yes | — |
| 72 | C24×C53 | C2×D4 | 1 | 6 | yes | — |
| 73 | C24×C53 | C24 | 1 | 1 | yes | characteristic |
| 74 | C23×D53 | — | 2 | 3 | no | — |
| 75 | C23×D53 | — | 2 | 4 | no | — |
| 76 | C23×D53 | — | 4 | 2 | no | — |
| 77 | C23×D53 | — | 8 | 1 | no | — |
| 78 | #41×C53 | — | 2 | 96 | no | — |
| 79 | #41×C53 | — | 2 | 48 | no | — |
| 80 | #41×C53 | — | 2 | 48 | no | — |
| 81 | C2×Q8×C53 | — | 2 | 8 | no | — |
| 82 | C2×Q8×C53 | — | 2 | 4 | no | — |
| 83 | C2×D4×C53 | — | 2 | 24 | no | — |
| 84 | C2×D4×C53 | — | 2 | 48 | no | — |
| 85 | C2×D4×C53 | — | 2 | 12 | no | — |
| 86 | C2×D4×C53 | — | 2 | 96 | no | — |
| 87 | C2×D4×C53 | — | 2 | 48 | no | — |
| 88 | C2×D4×C53 | — | 2 | 48 | no | — |
| 89 | C2×D4×C53 | — | 2 | 12 | no | — |
| 90 | C2×D4×C53 | — | 2 | 48 | no | — |
| 91 | C2×D4×C53 | — | 2 | 12 | no | — |
| 92 | C2×D4×C53 | — | 2 | 12 | no | — |
| 93 | C2×D4×C53 | — | 2 | 12 | no | — |
| 94 | C2×D4×C53 | — | 2 | 12 | no | — |
| 95 | C2×D4×C53 | C2×D4 | 1 | 24 | yes | — |
| 96 | C22×C4×C53 | — | 2 | 24 | no | — |
| 97 | C22×C4×C53 | — | 2 | 12 | no | — |
| 98 | C22×C4×C53 | — | 2 | 3 | no | — |
| 99 | C22×C4×C53 | — | 2 | 3 | no | — |
| 100 | C22×C4×C53 | — | 2 | 12 | no | — |
| 101 | C22×C4×C53 | C2×D4 | 1 | 6 | yes | — |
| 102 | C2×C22⋊D53 | — | 2 | 12 | no | — |
| 103 | C2×C22⋊D53 | — | 4 | 6 | no | — |
| 104 | C2×C22⋊D53 | — | 4 | 6 | no | — |
| 105 | C2×C22⋊D53 | — | 4 | 6 | no | — |
| 106 | C2×C22⋊D53 | — | 4 | 3 | no | — |
| 107 | C2×C22⋊D53 | — | 4 | 1 | no | — |
| 108 | C2×C22⋊D53 | — | 4 | 12 | no | — |
| 109 | C2×C22⋊D53 | — | 4 | 12 | no | — |
| 110 | C2×C22⋊D53 | — | 8 | 6 | no | — |
| 111 | C22×Dic53 | — | 2 | 3 | no | — |
| 112 | C22×Dic53 | — | 2 | 6 | no | — |
| 113 | C22×Dic53 | — | 4 | 2 | no | — |
| 114 | C22⋊Dic53 | — | 2 | 12 | no | — |
| 115 | C22⋊Dic53 | — | 4 | 12 | no | — |
| 116 | C22⋊Dic53 | — | 4 | 6 | no | — |
| 117 | C22⋊Dic53 | — | 8 | 3 | no | — |
| 118 | #11719921 | — | 4 | 12 | no | — |
| 119 | C23×C53 | — | 2 | 12 | no | — |
| 120 | C23×C53 | — | 2 | 12 | no | — |
| 121 | C23×C53 | — | 2 | 16 | no | — |
| 122 | C23×C53 | — | 2 | 6 | no | — |
| 123 | C23×C53 | — | 2 | 6 | no | — |
| 124 | C23×C53 | — | 2 | 6 | no | — |
| 125 | C23×C53 | — | 2 | 6 | no | — |
| 126 | C23×C53 | — | 2 | 6 | no | — |
| 127 | C23×C53 | — | 4 | 1 | no | — |
| 128 | C23×C53 | — | 4 | 1 | no | — |
| 129 | C23×C53 | — | 4 | 3 | no | — |
| 130 | C23×C53 | — | 4 | 3 | no | — |
| 131 | C23×C53 | — | 4 | 3 | no | — |
| 132 | C23×C53 | — | 4 | 6 | no | — |
| 133 | C23×C53 | — | 4 | 6 | no | — |
| 134 | C23×C53 | — | 4 | 6 | no | — |
| 135 | C23×C53 | — | 4 | 6 | no | — |
| 136 | C23×C53 | — | 8 | 3 | no | — |
| 137 | C23×C53 | — | 8 | 3 | no | — |
| 138 | C23×C53 | — | 8 | 8 | no | — |
| 139 | C23×C53 | — | 8 | 24 | no | — |
| 140 | C23×C53 | — | 8 | 16 | no | — |
| 141 | C23×C53 | — | 8 | 4 | no | — |
| 142 | C23×C53 | — | 8 | 4 | no | — |
| 143 | C23×C53 | #120 | 1 | 3 | yes | — |
| 144 | C23×C53 | #120 | 1 | 1 | yes | characteristic |
| 145 | C23×C53 | #120 | 1 | 12 | yes | complemented |
| 146 | C23×C53 | C22×D4 | 1 | 3 | yes | — |
| 147 | C23×C53 | C22×D4 | 1 | 4 | yes | — |
| 148 | C22×D53 | — | 2 | 6 | no | — |
| 149 | C22×D53 | — | 4 | 3 | no | — |
| 150 | C22×D53 | — | 4 | 6 | no | — |
| 151 | C22×D53 | — | 4 | 1 | no | — |
| 152 | C22×D53 | — | 4 | 6 | no | — |
| 153 | C22×D53 | — | 8 | 8 | no | — |
| 154 | Q8×C53 | — | 2 | 16 | no | — |
| 155 | D4×C53 | — | 2 | 48 | no | — |
| 156 | D4×C53 | — | 2 | 48 | no | — |
| 157 | D4×C53 | — | 2 | 48 | no | — |
| 158 | C2×C4×C53 | — | 2 | 12 | no | — |
| 159 | C2×C4×C53 | — | 2 | 12 | no | — |
| 160 | C2×C4×C53 | — | 2 | 48 | no | — |
| 161 | C2×C4×C53 | — | 2 | 6 | no | — |
| 162 | C2×C4×C53 | — | 2 | 6 | no | — |
| 163 | C2×C4×C53 | #120 | 1 | 12 | yes | complemented |
| 164 | C22⋊D53 | — | 4 | 12 | no | — |
| 165 | C22⋊D53 | — | 4 | 4 | no | — |
| 166 | C22⋊D53 | — | 8 | 24 | no | — |
| 167 | C2×Dic53 | — | 2 | 6 | no | — |
| 168 | C2×Dic53 | — | 4 | 3 | no | — |
| 169 | C2×Dic53 | — | 4 | 1 | no | — |
| 170 | C2×Dic53 | — | 4 | 6 | no | — |
| 171 | C2×Dic53 | — | 4 | 6 | no | — |
| 172 | C2×Dic53 | — | 4 | 6 | no | — |
| 173 | #32898 | — | 53 | 1 | no | maximal, Sylow |
| 174 | C22×C53 | — | 2 | 1 | no | — |
| 175 | C22×C53 | — | 2 | 3 | no | — |
| 176 | C22×C53 | — | 2 | 3 | no | — |
| 177 | C22×C53 | — | 2 | 1 | no | — |
| 178 | C22×C53 | — | 2 | 3 | no | — |
| 179 | C22×C53 | — | 2 | 12 | no | — |
| 180 | C22×C53 | — | 2 | 3 | no | — |
| 181 | C22×C53 | — | 2 | 3 | no | — |
| 182 | C22×C53 | — | 4 | 4 | no | — |
| 183 | C22×C53 | — | 4 | 12 | no | — |
| 184 | C22×C53 | — | 4 | 12 | no | — |
| 185 | C22×C53 | — | 4 | 24 | no | — |
| 186 | C22×C53 | — | 4 | 6 | no | — |
| 187 | C22×C53 | — | 4 | 6 | no | — |
| 188 | C22×C53 | — | 8 | 6 | no | — |
| 189 | C22×C53 | — | 8 | 6 | no | — |
| 190 | C22×C53 | — | 8 | 12 | no | — |
| 191 | C22×C53 | — | 8 | 16 | no | — |
| 192 | C22×C53 | B(4,𝔽2) | 1 | 2 | yes | complemented |
| 193 | C22×C53 | C2×#120 | 1 | 6 | yes | — |
| 194 | C22×C53 | C2×#120 | 1 | 1 | yes | characteristic |
| 195 | C2×D53 | — | 4 | 12 | no | — |
| 196 | C2×D53 | — | 4 | 2 | no | — |
| 197 | C2×D53 | — | 8 | 6 | no | — |
| 198 | C2×D53 | — | 8 | 1 | no | — |
| 199 | C2×D53 | — | 8 | 1 | no | — |
| 200 | C4×C53 | — | 2 | 12 | no | — |
| 201 | Dic53 | — | 4 | 2 | no | — |
| 202 | Dic53 | — | 8 | 6 | no | — |
| 203 | C22×H(5,𝔽2) | D53 | 1 | 1 | yes | characteristic, complemented |
| 204 | C2×B(4,𝔽2) | — | 53 | 4 | no | — |
| 205 | #2403 | — | 53 | 3 | no | — |
| 206 | #1790 | — | 53 | 4 | no | — |
| 207 | #1781 | — | 53 | 3 | no | — |
| 208 | C2×C53 | — | 2 | 6 | no | — |
| 209 | C2×C53 | — | 2 | 2 | no | — |
| 210 | C2×C53 | — | 4 | 3 | no | — |
| 211 | C2×C53 | — | 4 | 12 | no | — |
| 212 | C2×C53 | #2846 | 1 | 1 | yes | characteristic |
| 213 | C2×C53 | C2×B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 214 | C2×C53 | #3026 | 1 | 1 | yes | characteristic |
| 215 | D53 | — | 8 | 2 | no | — |
| 216 | C2×H(5,𝔽2) | — | 2 | 16 | no | — |
| 217 | C2×H(5,𝔽2) | — | 2 | 6 | no | — |
| 218 | C2×H(5,𝔽2) | C2×D53 | 1 | 4 | yes | — |
| 219 | C22×#41 | — | 2 | 3 | no | — |
| 220 | C23×D4 | — | 2 | 3 | no | — |
| 221 | C23×D4 | — | 53 | 1 | no | — |
| 222 | C23×D4 | C2×D53 | 1 | 3 | yes | — |
| 223 | C2×#120 | — | 53 | 6 | no | — |
| 224 | C2×#120 | — | 106 | 3 | no | — |
| 225 | B(4,𝔽2) | — | 106 | 16 | no | — |
| 226 | C2×#99 | — | 53 | 12 | no | — |
| 227 | #392 | — | 106 | 6 | no | — |
| 228 | #386 | — | 53 | 6 | no | — |
| 229 | #386 | — | 106 | 3 | no | — |
| 230 | #379 | — | 53 | 3 | no | — |
| 231 | C53 | #32898 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 232 | C25 | — | 2 | 1 | no | — |
| 233 | C25 | — | 53 | 1 | no | — |
| 234 | C25 | C22⋊D53 | 1 | 3 | yes | complemented |
| 235 | C25 | C22×D53 | 1 | 1 | yes | characteristic |
| 236 | H(5,𝔽2) | — | 2 | 48 | no | — |
| 237 | H(5,𝔽2) | — | 2 | 48 | no | — |
| 238 | H(5,𝔽2) | — | 2 | 24 | no | — |
| 239 | H(5,𝔽2) | C22⋊D53 | 1 | 16 | yes | complemented |
| 240 | C2×#41 | — | 2 | 12 | no | — |
| 241 | C2×#41 | — | 2 | 48 | no | — |
| 242 | C2×#41 | — | 2 | 12 | no | — |
| 243 | C22×Q8 | — | 2 | 1 | no | — |
| 244 | C22×D4 | — | 2 | 3 | no | — |
| 245 | C22×D4 | — | 2 | 48 | no | — |
| 246 | C22×D4 | — | 2 | 12 | no | — |
| 247 | C22×D4 | — | 2 | 6 | no | — |
| 248 | C22×D4 | — | 2 | 12 | no | — |
| 249 | C22×D4 | — | 2 | 6 | no | — |
| 250 | C22×D4 | — | 2 | 24 | no | — |
| 251 | C22×D4 | — | 106 | 3 | no | — |
| 252 | C22×D4 | — | 106 | 6 | no | — |
| 253 | C22×D4 | — | 106 | 3 | no | — |
| 254 | C22×D4 | — | 212 | 4 | no | — |
| 255 | C22×D4 | C22⋊D53 | 1 | 6 | yes | complemented |
| 256 | C22×D4 | C22×D53 | 1 | 6 | yes | — |
| 257 | C23×C4 | — | 2 | 3 | no | — |
| 258 | C23×C4 | — | 53 | 1 | no | — |
| 259 | C23×C4 | C22⋊D53 | 1 | 3 | yes | complemented |
| 260 | #120 | — | 106 | 24 | no | — |
| 261 | #120 | — | 212 | 12 | no | — |
| 262 | C2×C22⋊C4 | — | 53 | 6 | no | — |
| 263 | C2×C22⋊C4 | — | 106 | 3 | no | — |
| 264 | C2×C22⋊C4 | — | 106 | 3 | no | — |
| 265 | C2×C22⋊C4 | — | 106 | 6 | no | — |
| 266 | C2×C22⋊C4 | — | 106 | 6 | no | — |
| 267 | #99 | — | 106 | 24 | no | — |
| 268 | #95 | — | 106 | 6 | no | — |
| 269 | C24 | — | 2 | 8 | no | — |
| 270 | C24 | — | 2 | 4 | no | — |
| 271 | C24 | — | 2 | 3 | no | — |
| 272 | C24 | — | 2 | 3 | no | — |
| 273 | C24 | — | 2 | 12 | no | — |
| 274 | C24 | — | 2 | 4 | no | — |
| 275 | C24 | — | 4 | 2 | no | — |
| 276 | C24 | — | 4 | 6 | no | — |
| 277 | C24 | — | 8 | 1 | no | — |
| 278 | C24 | — | 8 | 3 | no | — |
| 279 | C24 | — | 8 | 2 | no | — |
| 280 | C24 | — | 8 | 2 | no | — |
| 281 | C24 | — | 106 | 3 | no | — |
| 282 | C24 | — | 106 | 4 | no | — |
| 283 | C24 | — | 424 | 1 | no | — |
| 284 | C24 | — | 212 | 2 | no | — |
| 285 | C24 | C2×C22⋊D53 | 1 | 3 | yes | — |
| 286 | C24 | C2×C22⋊D53 | 1 | 3 | yes | — |
| 287 | C24 | C2×C22⋊D53 | 1 | 6 | yes | — |
| 288 | C24 | C23×D53 | 1 | 1 | yes | characteristic |
| 289 | #41 | — | 2 | 96 | no | — |
| 290 | #41 | — | 2 | 48 | no | — |
| 291 | #41 | — | 2 | 48 | no | — |
| 292 | C2×Q8 | — | 2 | 8 | no | — |
| 293 | C2×Q8 | — | 2 | 4 | no | — |
| 294 | C2×D4 | — | 2 | 24 | no | — |
| 295 | C2×D4 | — | 2 | 48 | no | — |
| 296 | C2×D4 | — | 2 | 12 | no | — |
| 297 | C2×D4 | — | 2 | 96 | no | — |
| 298 | C2×D4 | — | 2 | 48 | no | — |
| 299 | C2×D4 | — | 2 | 48 | no | — |
| 300 | C2×D4 | — | 2 | 12 | no | — |
| 301 | C2×D4 | — | 2 | 48 | no | — |
| 302 | C2×D4 | — | 2 | 12 | no | — |
| 303 | C2×D4 | — | 2 | 12 | no | — |
| 304 | C2×D4 | — | 2 | 12 | no | — |
| 305 | C2×D4 | — | 2 | 12 | no | — |
| 306 | C2×D4 | — | 106 | 12 | no | — |
| 307 | C2×D4 | — | 424 | 6 | no | — |
| 308 | C2×D4 | — | 212 | 6 | no | — |
| 309 | C2×D4 | — | 212 | 12 | no | — |
| 310 | C2×D4 | — | 212 | 12 | no | — |
| 311 | C2×D4 | — | 212 | 6 | no | — |
| 312 | C2×D4 | — | 212 | 6 | no | — |
| 313 | C2×D4 | — | 212 | 3 | no | — |
| 314 | C2×D4 | — | 212 | 1 | no | — |
| 315 | C2×D4 | C2×C22⋊D53 | 1 | 24 | yes | — |
| 316 | C22×C4 | — | 2 | 24 | no | — |
| 317 | C22×C4 | — | 2 | 12 | no | — |
| 318 | C22×C4 | — | 2 | 3 | no | — |
| 319 | C22×C4 | — | 2 | 3 | no | — |
| 320 | C22×C4 | — | 2 | 12 | no | — |
| 321 | C22×C4 | — | 106 | 3 | no | — |
| 322 | C22×C4 | — | 106 | 6 | no | — |
| 323 | C22×C4 | — | 212 | 2 | no | — |
| 324 | C22×C4 | C2×C22⋊D53 | 1 | 6 | yes | — |
| 325 | C22⋊C4 | — | 106 | 12 | no | — |
| 326 | C22⋊C4 | — | 424 | 3 | no | — |
| 327 | C22⋊C4 | — | 212 | 12 | no | — |
| 328 | C22⋊C4 | — | 212 | 6 | no | — |
| 329 | C22⋊C4 | — | 212 | 12 | no | — |
| 330 | C23 | — | 2 | 12 | no | — |
| 331 | C23 | — | 2 | 12 | no | — |
| 332 | C23 | — | 2 | 16 | no | — |
| 333 | C23 | — | 2 | 6 | no | — |
| 334 | C23 | — | 2 | 6 | no | — |
| 335 | C23 | — | 2 | 6 | no | — |
| 336 | C23 | — | 2 | 6 | no | — |
| 337 | C23 | — | 2 | 6 | no | — |
| 338 | C23 | — | 4 | 1 | no | — |
| 339 | C23 | — | 4 | 3 | no | — |
| 340 | C23 | — | 4 | 1 | no | — |
| 341 | C23 | — | 4 | 3 | no | — |
| 342 | C23 | — | 4 | 3 | no | — |
| 343 | C23 | — | 4 | 6 | no | — |
| 344 | C23 | — | 4 | 6 | no | — |
| 345 | C23 | — | 4 | 6 | no | — |
| 346 | C23 | — | 4 | 6 | no | — |
| 347 | C23 | — | 8 | 3 | no | — |
| 348 | C23 | — | 8 | 3 | no | — |
| 349 | C23 | — | 8 | 8 | no | — |
| 350 | C23 | — | 8 | 24 | no | — |
| 351 | C23 | — | 8 | 16 | no | — |
| 352 | C23 | — | 8 | 4 | no | — |
| 353 | C23 | — | 8 | 4 | no | — |
| 354 | C23 | — | 106 | 6 | no | — |
| 355 | C23 | — | 424 | 8 | no | — |
| 356 | C23 | — | 212 | 6 | no | — |
| 357 | C23 | — | 212 | 3 | no | — |
| 358 | C23 | — | 212 | 6 | no | — |
| 359 | C23 | — | 212 | 1 | no | — |
| 360 | C23 | #13133186 | 1 | 3 | yes | — |
| 361 | C23 | #13133186 | 1 | 1 | yes | characteristic |
| 362 | C23 | #13133186 | 1 | 12 | yes | complemented |
| 363 | C23 | C22×C22⋊D53 | 1 | 3 | yes | — |
| 364 | C23 | C22×C22⋊D53 | 1 | 4 | yes | — |
| 365 | Q8 | — | 2 | 16 | no | — |
| 366 | D4 | — | 2 | 48 | no | — |
| 367 | D4 | — | 2 | 48 | no | — |
| 368 | D4 | — | 2 | 48 | no | — |
| 369 | D4 | — | 424 | 24 | no | — |
| 370 | D4 | — | 212 | 12 | no | — |
| 371 | D4 | — | 212 | 4 | no | — |
| 372 | C2×C4 | — | 2 | 12 | no | — |
| 373 | C2×C4 | — | 2 | 12 | no | — |
| 374 | C2×C4 | — | 2 | 48 | no | — |
| 375 | C2×C4 | — | 2 | 6 | no | — |
| 376 | C2×C4 | — | 2 | 6 | no | — |
| 377 | C2×C4 | — | 106 | 6 | no | — |
| 378 | C2×C4 | — | 212 | 6 | no | — |
| 379 | C2×C4 | — | 212 | 6 | no | — |
| 380 | C2×C4 | — | 212 | 6 | no | — |
| 381 | C2×C4 | — | 212 | 3 | no | — |
| 382 | C2×C4 | — | 212 | 1 | no | — |
| 383 | C2×C4 | #13133186 | 1 | 12 | yes | complemented |
| 384 | C22 | — | 2 | 1 | no | — |
| 385 | C22 | — | 2 | 3 | no | — |
| 386 | C22 | — | 2 | 3 | no | — |
| 387 | C22 | — | 2 | 1 | no | — |
| 388 | C22 | — | 2 | 3 | no | — |
| 389 | C22 | — | 2 | 12 | no | — |
| 390 | C22 | — | 2 | 3 | no | — |
| 391 | C22 | — | 2 | 3 | no | — |
| 392 | C22 | — | 4 | 4 | no | — |
| 393 | C22 | — | 4 | 12 | no | — |
| 394 | C22 | — | 4 | 12 | no | — |
| 395 | C22 | — | 4 | 24 | no | — |
| 396 | C22 | — | 4 | 6 | no | — |
| 397 | C22 | — | 4 | 6 | no | — |
| 398 | C22 | — | 8 | 6 | no | — |
| 399 | C22 | — | 8 | 6 | no | — |
| 400 | C22 | — | 8 | 12 | no | — |
| 401 | C22 | — | 8 | 16 | no | — |
| 402 | C22 | — | 424 | 6 | no | — |
| 403 | C22 | — | 424 | 1 | no | — |
| 404 | C22 | — | 424 | 1 | no | — |
| 405 | C22 | — | 212 | 12 | no | — |
| 406 | C22 | — | 212 | 2 | no | — |
| 407 | C22 | #16810810 | 1 | 2 | yes | complemented |
| 408 | C22 | C2×#13133186 | 1 | 6 | yes | — |
| 409 | C22 | C2×#13133186 | 1 | 1 | yes | characteristic |
| 410 | C4 | — | 2 | 12 | no | — |
| 411 | C4 | — | 424 | 6 | no | — |
| 412 | C4 | — | 212 | 2 | no | — |
| 413 | C2 | — | 2 | 6 | no | — |
| 414 | C2 | — | 2 | 2 | no | — |
| 415 | C2 | — | 4 | 3 | no | — |
| 416 | C2 | — | 4 | 12 | no | — |
| 417 | C2 | — | 424 | 2 | no | — |
| 418 | C2 | #20282992 | 1 | 1 | yes | characteristic |
| 419 | C2 | C2×#16810810 | 1 | 1 | yes | characteristic |
| 420 | C2 | #20284112 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16810810 | C2 | semidirect |
| 2. #20278025 | C2 | semidirect |
| 3. #20274663 | C2 | semidirect |
| 4. #20274630 | C2 | semidirect |
| 5. C22×H(5,𝔽2)×C53 | C2 | semidirect |
| 6. C23×C22⋊D53 | C22 | semidirect |
| 8. C2×#13133185 | C22 | semidirect |
| 10. C2×#13133132 | C22 | semidirect |
| 12. #16810503 | C22 | semidirect |
| 14. #16810479 | C22 | semidirect |
| 21. C24×D53 | C23 | semidirect |
| 26. C23×Dic53 | C23 | semidirect |
| 32. C2×C22⋊Dic53 | C23 | semidirect |
| 37. C25×C53 | D4 | semidirect |
| 42. H(5,𝔽2)×C53 | D4 | semidirect |
| 54. C22×D4×C53 | D4 | semidirect |
| 57. C23×C4×C53 | D4 | semidirect |
| 145. C23×C53 | #120 | semidirect |
| 163. C2×C4×C53 | #120 | semidirect |
| 192. C22×C53 | B(4,𝔽2) | semidirect |
| 203. C22×H(5,𝔽2) | D53 | semidirect |
| 231. C53 | #32898 | semidirect |
| 234. C25 | C22⋊D53 | semidirect |
| 239. H(5,𝔽2) | C22⋊D53 | semidirect |
| 255. C22×D4 | C22⋊D53 | semidirect |
| 259. C23×C4 | C22⋊D53 | semidirect |
| 362. C23 | #13133186 | semidirect |
| 383. C2×C4 | #13133186 | semidirect |
| 407. C22 | #16810810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810810 | 2 |
| #20278025 | 2 |
| #20274663 | 2 |
| #20274630 | 2 |
| C22×H(5,𝔽2)×C53 | 2 |
| #32898 | 53 |