← #14418668
Subgroups — #14418668
Order 1920.
712 conjugacy classes of subgroups.
The subgroup lattice has 468 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #11756276 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×C5×#424 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11751220 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | M16×Dic15 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | #11751202 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C2×#91098 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #11751098 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #11750932 | C2 | 1 | 2 | yes | maximal, complemented |
| 9 | #11750931 | C2 | 1 | 2 | yes | maximal, complemented |
| 10 | #11750929 | C2 | 1 | 2 | yes | maximal, complemented |
| 11 | #11750929 | C2 | 1 | 2 | yes | maximal, complemented |
| 12 | #10610809 | — | 3 | 1 | no | maximal, Hall |
| 13 | C2×C3×C5×M16 | C22 | 1 | 1 | yes | characteristic |
| 14 | C22×C3×C5×C8 | C22 | 1 | 1 | yes | characteristic |
| 15 | C3×C5×#117 | C22 | 1 | 1 | yes | characteristic |
| 16 | #91815 | C22 | 1 | 1 | yes | characteristic |
| 17 | C2×C4×Dic15 | C22 | 1 | 1 | yes | characteristic |
| 18 | C2×#6710 | C22 | 1 | 1 | yes | characteristic |
| 19 | C22×C3⋊#168 | C22 | 1 | 1 | yes | characteristic |
| 20 | #91779 | C4 | 1 | 1 | yes | characteristic |
| 21 | #91779 | C4 | 1 | 1 | yes | characteristic |
| 22 | #91777 | C4 | 1 | 1 | yes | characteristic |
| 23 | #91777 | C4 | 1 | 1 | yes | characteristic |
| 24 | #91767 | C4 | 1 | 2 | yes | — |
| 25 | #91767 | C4 | 1 | 2 | yes | — |
| 26 | C4×Dic30 | C22 | 1 | 2 | yes | — |
| 27 | C4×Dic30 | C22 | 1 | 2 | yes | — |
| 28 | C3×C5×C4⋊C8 | C22 | 1 | 2 | yes | — |
| 29 | C3×C5×C4⋊C8 | C22 | 1 | 2 | yes | — |
| 30 | #91099 | C22 | 1 | 2 | yes | — |
| 31 | #91099 | C22 | 1 | 2 | yes | — |
| 32 | #91098 | C22 | 1 | 1 | yes | characteristic |
| 33 | #91098 | C22 | 1 | 1 | yes | characteristic |
| 34 | #91098 | C22 | 1 | 2 | yes | — |
| 35 | #91098 | C22 | 1 | 1 | yes | characteristic |
| 36 | #91098 | C22 | 1 | 2 | yes | — |
| 37 | #91098 | C22 | 1 | 1 | yes | characteristic |
| 38 | C8×Dic15 | C22 | 1 | 2 | yes | — |
| 39 | C8×Dic15 | C22 | 1 | 2 | yes | — |
| 40 | #91087 | C22 | 1 | 2 | yes | — |
| 41 | C4×C3⋊#168 | C22 | 1 | 2 | yes | — |
| 42 | #79078 | — | 5 | 1 | no | maximal, Hall |
| 43 | #65851 | — | 3 | 1 | no | — |
| 44 | C5×#424 | D3 | 1 | 1 | yes | characteristic |
| 45 | #65408 | — | 3 | 1 | no | — |
| 46 | M16×Dic5 | — | 3 | 1 | no | — |
| 47 | #65390 | — | 3 | 1 | no | — |
| 48 | C2×#3946 | — | 3 | 1 | no | — |
| 49 | #65286 | — | 3 | 1 | no | — |
| 50 | #65120 | — | 3 | 2 | no | — |
| 51 | #65119 | — | 3 | 2 | no | — |
| 52 | #65117 | — | 3 | 2 | no | — |
| 53 | #65117 | — | 3 | 2 | no | — |
| 54 | C22×C3×C4×C5 | C23 | 1 | 1 | yes | characteristic |
| 55 | C22×Dic15 | C2×C4 | 1 | 1 | yes | characteristic |
| 56 | C22×Dic15 | C2×C4 | 1 | 1 | yes | characteristic |
| 57 | C2×Dic30 | C2×C4 | 1 | 2 | yes | — |
| 58 | C2×Dic30 | C2×C4 | 1 | 2 | yes | — |
| 59 | C3×C5×M16 | — | 2 | 2 | no | — |
| 60 | C2×C3×C5×C8 | — | 2 | 2 | no | — |
| 61 | C2×C3×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 62 | C2×C3×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×C3×C5×C8 | C23 | 1 | 2 | yes | — |
| 64 | C3×C5×C4⋊C4 | C2×C4 | 1 | 1 | yes | characteristic |
| 65 | C3×C5×C4⋊C4 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | C3×C5×C22⋊C4 | C2×C4 | 1 | 2 | yes | — |
| 67 | C3×C42×C5 | C23 | 1 | 2 | yes | — |
| 68 | #6719 | C2×C4 | 1 | 2 | yes | — |
| 69 | C4⋊Dic15 | C2×C4 | 1 | 2 | yes | — |
| 70 | C4⋊Dic15 | C2×C4 | 1 | 2 | yes | — |
| 71 | C4⋊Dic15 | C2×C4 | 1 | 1 | yes | characteristic |
| 72 | C4⋊Dic15 | C2×C4 | 1 | 1 | yes | characteristic |
| 73 | #6712 | C2×C4 | 1 | 2 | yes | — |
| 74 | #6712 | C2×C4 | 1 | 2 | yes | — |
| 75 | #6712 | C2×C4 | 1 | 2 | yes | — |
| 76 | #6712 | C2×C4 | 1 | 2 | yes | — |
| 77 | C4×Dic15 | C2×C4 | 1 | 1 | yes | characteristic |
| 78 | C4×Dic15 | C2×C4 | 1 | 1 | yes | characteristic |
| 79 | C4×Dic15 | C23 | 1 | 1 | yes | characteristic |
| 80 | C4×Dic15 | C23 | 1 | 1 | yes | characteristic |
| 81 | C4×Dic15 | C23 | 1 | 2 | yes | — |
| 82 | #6710 | Q8 | 1 | 4 | yes | complemented |
| 83 | C2×C3⋊#168 | — | 2 | 2 | no | — |
| 84 | C2×C3⋊#168 | C23 | 1 | 1 | yes | characteristic |
| 85 | C2×C3⋊#168 | C23 | 1 | 1 | yes | characteristic |
| 86 | C2×C3⋊#168 | C23 | 1 | 2 | yes | — |
| 87 | #5517 | — | 5 | 1 | no | — |
| 88 | C3×#424 | D5 | 1 | 1 | yes | characteristic |
| 89 | #5119 | — | 5 | 1 | no | — |
| 90 | Dic3×M16 | — | 5 | 1 | no | — |
| 91 | #5101 | — | 5 | 1 | no | — |
| 92 | C2×Dic3⋊C8 | — | 5 | 1 | no | — |
| 93 | #4997 | — | 5 | 1 | no | — |
| 94 | #4831 | — | 5 | 2 | no | — |
| 95 | #4830 | — | 5 | 2 | no | — |
| 96 | #4828 | — | 5 | 2 | no | — |
| 97 | #4828 | — | 5 | 2 | no | — |
| 98 | C2×C5×M16 | C2×D3 | 1 | 1 | yes | characteristic |
| 99 | C22×C5×C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 100 | C5×#117 | C2×D3 | 1 | 1 | yes | characteristic |
| 101 | #4072 | — | 3 | 1 | no | — |
| 102 | C2×C4×Dic5 | — | 3 | 1 | no | — |
| 103 | C2×#681 | — | 3 | 1 | no | — |
| 104 | C22×#168 | — | 3 | 1 | no | — |
| 105 | #4036 | — | 3 | 1 | no | — |
| 106 | #4036 | — | 3 | 1 | no | — |
| 107 | #4034 | — | 3 | 1 | no | — |
| 108 | #4034 | — | 3 | 1 | no | — |
| 109 | #4024 | — | 3 | 2 | no | — |
| 110 | #4024 | — | 3 | 2 | no | — |
| 111 | C4×Dic10 | — | 3 | 2 | no | — |
| 112 | C4×Dic10 | — | 3 | 2 | no | — |
| 113 | C5×C4⋊C8 | C2×D3 | 1 | 2 | yes | — |
| 114 | C5×C4⋊C8 | C2×D3 | 1 | 2 | yes | — |
| 115 | #3947 | — | 3 | 2 | no | — |
| 116 | #3947 | — | 3 | 2 | no | — |
| 117 | #3946 | — | 3 | 1 | no | — |
| 118 | #3946 | — | 3 | 1 | no | — |
| 119 | #3946 | — | 3 | 2 | no | — |
| 120 | #3946 | — | 3 | 1 | no | — |
| 121 | #3946 | — | 3 | 2 | no | — |
| 122 | #3946 | — | 3 | 1 | no | — |
| 123 | C8×Dic5 | — | 3 | 2 | no | — |
| 124 | C8×Dic5 | — | 3 | 2 | no | — |
| 125 | #3935 | — | 3 | 2 | no | — |
| 126 | C4×#168 | — | 3 | 2 | no | — |
| 127 | #2962 | — | 15 | 1 | no | Sylow |
| 128 | C23×C3×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 129 | C2×C3×C4×C5 | C22×C4 | 1 | 2 | yes | — |
| 130 | C2×C3×C4×C5 | C22×C4 | 1 | 2 | yes | — |
| 131 | C2×C3×C4×C5 | C22×C4 | 1 | 1 | yes | characteristic |
| 132 | C2×C3×C4×C5 | C2×Q8 | 1 | 2 | yes | — |
| 133 | C2×C3×C4×C5 | #41 | 1 | 2 | yes | — |
| 134 | C2×C3×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 135 | C2×Dic15 | — | 2 | 2 | no | — |
| 136 | C2×Dic15 | — | 4 | 1 | no | — |
| 137 | C2×Dic15 | C22×C4 | 1 | 1 | yes | characteristic |
| 138 | C2×Dic15 | C22×C4 | 1 | 1 | yes | characteristic |
| 139 | C2×Dic15 | C22×C4 | 1 | 1 | yes | characteristic |
| 140 | C2×Dic15 | C22×C4 | 1 | 2 | yes | — |
| 141 | C2×Dic15 | C22×C4 | 1 | 2 | yes | — |
| 142 | C2×Dic15 | C22×C4 | 1 | 1 | yes | characteristic |
| 143 | Dic30 | — | 2 | 4 | no | — |
| 144 | Dic30 | — | 4 | 2 | no | — |
| 145 | C3×C5×C8 | — | 2 | 1 | no | — |
| 146 | C3×C5×C8 | — | 2 | 1 | no | — |
| 147 | C3×C5×C8 | — | 2 | 2 | no | — |
| 148 | C3⋊#168 | — | 2 | 1 | no | — |
| 149 | C3⋊#168 | — | 2 | 1 | no | — |
| 150 | C3⋊#168 | C2×Q8 | 1 | 4 | yes | — |
| 151 | C2×C3×M16 | C2×D5 | 1 | 1 | yes | characteristic |
| 152 | C22×C3×C8 | C2×D5 | 1 | 1 | yes | characteristic |
| 153 | C3×#117 | C2×D5 | 1 | 1 | yes | characteristic |
| 154 | #926 | — | 5 | 1 | no | — |
| 155 | C2×C4×Dic3 | — | 5 | 1 | no | — |
| 156 | C2×#208 | — | 5 | 1 | no | — |
| 157 | C22×C3⋊C8 | — | 5 | 1 | no | — |
| 158 | #890 | — | 5 | 1 | no | — |
| 159 | #890 | — | 5 | 1 | no | — |
| 160 | #888 | — | 5 | 1 | no | — |
| 161 | #888 | — | 5 | 1 | no | — |
| 162 | #878 | — | 5 | 2 | no | — |
| 163 | #878 | — | 5 | 2 | no | — |
| 164 | C4×Dic6 | — | 5 | 2 | no | — |
| 165 | C4×Dic6 | — | 5 | 2 | no | — |
| 166 | C3×C4⋊C8 | C2×D5 | 1 | 2 | yes | — |
| 167 | C3×C4⋊C8 | C2×D5 | 1 | 2 | yes | — |
| 168 | #815 | — | 5 | 2 | no | — |
| 169 | #815 | — | 5 | 2 | no | — |
| 170 | Dic3⋊C8 | — | 5 | 1 | no | — |
| 171 | Dic3⋊C8 | — | 5 | 1 | no | — |
| 172 | Dic3⋊C8 | — | 5 | 2 | no | — |
| 173 | Dic3⋊C8 | — | 5 | 1 | no | — |
| 174 | Dic3⋊C8 | — | 5 | 2 | no | — |
| 175 | Dic3⋊C8 | — | 5 | 1 | no | — |
| 176 | C8×Dic3 | — | 5 | 2 | no | — |
| 177 | C8×Dic3 | — | 5 | 2 | no | — |
| 178 | #803 | — | 5 | 2 | no | — |
| 179 | C4×C3⋊C8 | — | 5 | 2 | no | — |
| 180 | C22×C4×C5 | C22×D3 | 1 | 1 | yes | characteristic |
| 181 | C22×Dic5 | — | 3 | 1 | no | — |
| 182 | C22×Dic5 | — | 3 | 1 | no | — |
| 183 | C2×Dic10 | — | 3 | 2 | no | — |
| 184 | C2×Dic10 | — | 3 | 2 | no | — |
| 185 | C5×M16 | — | 2 | 2 | no | — |
| 186 | C2×C5×C8 | — | 2 | 2 | no | — |
| 187 | C2×C5×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 188 | C2×C5×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 189 | C2×C5×C8 | C22×D3 | 1 | 2 | yes | — |
| 190 | C5×C4⋊C4 | C4×D3 | 1 | 1 | yes | characteristic |
| 191 | C5×C4⋊C4 | C4×D3 | 1 | 1 | yes | characteristic |
| 192 | C5×C22⋊C4 | C4×D3 | 1 | 2 | yes | — |
| 193 | C42×C5 | C22×D3 | 1 | 2 | yes | — |
| 194 | C22⋊Dic5 | — | 3 | 2 | no | — |
| 195 | C4⋊Dic5 | — | 3 | 2 | no | — |
| 196 | C4⋊Dic5 | — | 3 | 2 | no | — |
| 197 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 198 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 199 | #683 | — | 3 | 2 | no | — |
| 200 | #683 | — | 3 | 2 | no | — |
| 201 | #683 | — | 3 | 2 | no | — |
| 202 | #683 | — | 3 | 2 | no | — |
| 203 | C4×Dic5 | — | 3 | 1 | no | — |
| 204 | C4×Dic5 | — | 3 | 1 | no | — |
| 205 | C4×Dic5 | — | 3 | 1 | no | — |
| 206 | C4×Dic5 | — | 3 | 2 | no | — |
| 207 | C4×Dic5 | — | 3 | 1 | no | — |
| 208 | #681 | — | 3 | 4 | no | — |
| 209 | C2×#168 | — | 3 | 2 | no | — |
| 210 | C2×#168 | — | 3 | 1 | no | — |
| 211 | C2×#168 | — | 3 | 1 | no | — |
| 212 | C2×#168 | — | 6 | 2 | no | — |
| 213 | #533 | — | 15 | 1 | no | — |
| 214 | #446 | — | 15 | 2 | no | — |
| 215 | #446 | — | 15 | 2 | no | — |
| 216 | #446 | — | 15 | 2 | no | — |
| 217 | C8×Q8 | — | 15 | 2 | no | — |
| 218 | #424 | — | 15 | 1 | no | — |
| 219 | #424 | D15 | 1 | 1 | yes | characteristic |
| 220 | C2×C4⋊C8 | — | 15 | 1 | no | — |
| 221 | #405 | — | 15 | 1 | no | — |
| 222 | #405 | — | 15 | 1 | no | — |
| 223 | C4×M16 | — | 15 | 1 | no | — |
| 224 | C22×C3×C5 | — | 2 | 1 | no | — |
| 225 | C22×C3×C5 | — | 2 | 1 | no | — |
| 226 | C22×C3×C5 | C4×Q8 | 1 | 2 | yes | — |
| 227 | C22×C3×C5 | C23×C4 | 1 | 1 | yes | characteristic |
| 228 | C3×C4×C5 | — | 2 | 2 | no | — |
| 229 | C3×C4×C5 | — | 2 | 2 | no | — |
| 230 | C3×C4×C5 | C4×Q8 | 1 | 2 | yes | — |
| 231 | C3×C4×C5 | C22×Q8 | 1 | 1 | yes | characteristic |
| 232 | C3×C4×C5 | C2×#41 | 1 | 1 | yes | characteristic |
| 233 | Dic15 | — | 2 | 2 | no | — |
| 234 | Dic15 | — | 2 | 1 | no | — |
| 235 | Dic15 | — | 2 | 1 | no | — |
| 236 | Dic15 | — | 2 | 2 | no | — |
| 237 | Dic15 | — | 2 | 1 | no | — |
| 238 | Dic15 | #131 | 1 | 2 | yes | — |
| 239 | C22×C3×C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 240 | C22×Dic3 | — | 5 | 1 | no | — |
| 241 | C22×Dic3 | — | 5 | 1 | no | — |
| 242 | C2×Dic6 | — | 5 | 2 | no | — |
| 243 | C2×Dic6 | — | 5 | 2 | no | — |
| 244 | C3×M16 | — | 2 | 2 | no | — |
| 245 | C2×C3×C8 | — | 2 | 2 | no | — |
| 246 | C2×C3×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 247 | C2×C3×C8 | C22×D5 | 1 | 2 | yes | — |
| 248 | C2×C3×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 249 | C3×C4⋊C4 | C4×D5 | 1 | 1 | yes | characteristic |
| 250 | C3×C4⋊C4 | C4×D5 | 1 | 1 | yes | characteristic |
| 251 | C3×C22⋊C4 | C4×D5 | 1 | 2 | yes | — |
| 252 | C3×C42 | C22×D5 | 1 | 2 | yes | — |
| 253 | #217 | — | 5 | 2 | no | — |
| 254 | C4⋊Dic3 | — | 5 | 2 | no | — |
| 255 | C4⋊Dic3 | — | 5 | 2 | no | — |
| 256 | C4⋊Dic3 | — | 5 | 1 | no | — |
| 257 | C4⋊Dic3 | — | 5 | 1 | no | — |
| 258 | Dic3⋊C4 | — | 5 | 2 | no | — |
| 259 | Dic3⋊C4 | — | 5 | 2 | no | — |
| 260 | Dic3⋊C4 | — | 5 | 2 | no | — |
| 261 | Dic3⋊C4 | — | 5 | 2 | no | — |
| 262 | C4×Dic3 | — | 5 | 1 | no | — |
| 263 | C4×Dic3 | — | 5 | 1 | no | — |
| 264 | C4×Dic3 | — | 5 | 1 | no | — |
| 265 | C4×Dic3 | — | 5 | 2 | no | — |
| 266 | C4×Dic3 | — | 5 | 1 | no | — |
| 267 | #208 | — | 5 | 4 | no | — |
| 268 | C2×C3⋊C8 | — | 5 | 2 | no | — |
| 269 | C2×C3⋊C8 | — | 5 | 1 | no | — |
| 270 | C2×C3⋊C8 | — | 5 | 1 | no | — |
| 271 | C2×C3⋊C8 | — | 10 | 2 | no | — |
| 272 | C23×C5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 273 | C2×C4×C5 | C2×C4×D3 | 1 | 2 | yes | — |
| 274 | C2×C4×C5 | C2×C4×D3 | 1 | 2 | yes | — |
| 275 | C2×C4×C5 | C2×C4×D3 | 1 | 1 | yes | characteristic |
| 276 | C2×C4×C5 | #237 | 1 | 2 | yes | — |
| 277 | C2×C4×C5 | D3×Q8 | 1 | 2 | yes | — |
| 278 | C2×C4×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 279 | C2×Dic5 | — | 3 | 1 | no | — |
| 280 | C2×Dic5 | — | 3 | 1 | no | — |
| 281 | C2×Dic5 | — | 3 | 1 | no | — |
| 282 | C2×Dic5 | — | 3 | 1 | no | — |
| 283 | C2×Dic5 | — | 3 | 2 | no | — |
| 284 | C2×Dic5 | — | 3 | 2 | no | — |
| 285 | C2×Dic5 | — | 6 | 2 | no | — |
| 286 | C2×Dic5 | — | 12 | 1 | no | — |
| 287 | Dic10 | — | 6 | 4 | no | — |
| 288 | Dic10 | — | 12 | 2 | no | — |
| 289 | C5×C8 | — | 2 | 1 | no | — |
| 290 | C5×C8 | — | 2 | 1 | no | — |
| 291 | C5×C8 | — | 2 | 2 | no | — |
| 292 | #168 | — | 3 | 4 | no | — |
| 293 | #168 | — | 6 | 1 | no | — |
| 294 | #168 | — | 6 | 1 | no | — |
| 295 | C2×M16 | — | 15 | 1 | no | — |
| 296 | C2×M16 | C2×D15 | 1 | 1 | yes | characteristic |
| 297 | C22×C8 | — | 15 | 1 | no | — |
| 298 | C22×C8 | C2×D15 | 1 | 1 | yes | characteristic |
| 299 | C4⋊Q8 | — | 15 | 1 | no | — |
| 300 | C4⋊Q8 | — | 15 | 1 | no | — |
| 301 | #125 | — | 15 | 1 | no | — |
| 302 | #125 | — | 15 | 1 | no | — |
| 303 | C22⋊Q8 | — | 15 | 2 | no | — |
| 304 | C22⋊Q8 | — | 15 | 2 | no | — |
| 305 | C4×Q8 | — | 15 | 2 | no | — |
| 306 | C4×Q8 | — | 15 | 2 | no | — |
| 307 | #117 | — | 15 | 1 | no | — |
| 308 | #117 | C2×D15 | 1 | 1 | yes | characteristic |
| 309 | C2×C42 | — | 15 | 1 | no | — |
| 310 | C4⋊C8 | — | 15 | 1 | no | — |
| 311 | C4⋊C8 | — | 15 | 1 | no | — |
| 312 | C4⋊C8 | — | 15 | 1 | no | — |
| 313 | C4⋊C8 | — | 15 | 1 | no | — |
| 314 | C4⋊C8 | — | 15 | 2 | no | — |
| 315 | C4⋊C8 | — | 15 | 2 | no | — |
| 316 | C4⋊C8 | C2×D15 | 1 | 2 | yes | — |
| 317 | C4⋊C8 | C2×D15 | 1 | 2 | yes | — |
| 318 | #97 | — | 15 | 2 | no | — |
| 319 | #97 | — | 15 | 2 | no | — |
| 320 | #97 | — | 15 | 2 | no | — |
| 321 | C4×C8 | — | 15 | 2 | no | — |
| 322 | C4×C8 | — | 15 | 2 | no | — |
| 323 | C4×C8 | — | 15 | 2 | no | — |
| 324 | C2×C3×C5 | — | 2 | 2 | no | — |
| 325 | C2×C3×C5 | C2×C4×Q8 | 1 | 1 | yes | characteristic |
| 326 | C2×C3×C5 | C2×#131 | 1 | 1 | yes | characteristic |
| 327 | C2×C3×C5 | #568 | 1 | 1 | yes | characteristic |
| 328 | C23×C3 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 329 | C2×C3×C4 | C2×C4×D5 | 1 | 2 | yes | — |
| 330 | C2×C3×C4 | C2×C4×D5 | 1 | 2 | yes | — |
| 331 | C2×C3×C4 | C2×C4×D5 | 1 | 1 | yes | characteristic |
| 332 | C2×C3×C4 | #711 | 1 | 2 | yes | — |
| 333 | C2×C3×C4 | Q8×D5 | 1 | 2 | yes | — |
| 334 | C2×C3×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 335 | C2×Dic3 | — | 5 | 1 | no | — |
| 336 | C2×Dic3 | — | 5 | 1 | no | — |
| 337 | C2×Dic3 | — | 5 | 1 | no | — |
| 338 | C2×Dic3 | — | 5 | 1 | no | — |
| 339 | C2×Dic3 | — | 5 | 2 | no | — |
| 340 | C2×Dic3 | — | 5 | 2 | no | — |
| 341 | C2×Dic3 | — | 10 | 2 | no | — |
| 342 | C2×Dic3 | — | 20 | 1 | no | — |
| 343 | Dic6 | — | 10 | 4 | no | — |
| 344 | Dic6 | — | 20 | 2 | no | — |
| 345 | C3×C8 | — | 2 | 1 | no | — |
| 346 | C3×C8 | — | 2 | 1 | no | — |
| 347 | C3×C8 | — | 2 | 2 | no | — |
| 348 | C3⋊C8 | — | 5 | 4 | no | — |
| 349 | C3⋊C8 | — | 10 | 1 | no | — |
| 350 | C3⋊C8 | — | 10 | 1 | no | — |
| 351 | C22×C5 | — | 2 | 1 | no | — |
| 352 | C22×C5 | — | 2 | 1 | no | — |
| 353 | C22×C5 | #887 | 1 | 2 | yes | — |
| 354 | C22×C5 | C22×C4×D3 | 1 | 1 | yes | characteristic |
| 355 | C4×C5 | — | 2 | 2 | no | — |
| 356 | C4×C5 | — | 2 | 2 | no | — |
| 357 | C4×C5 | #887 | 1 | 2 | yes | — |
| 358 | C4×C5 | C2×#237 | 1 | 1 | yes | characteristic |
| 359 | C4×C5 | C2×D3×Q8 | 1 | 1 | yes | characteristic |
| 360 | Dic5 | — | 3 | 2 | no | — |
| 361 | Dic5 | — | 6 | 2 | no | — |
| 362 | Dic5 | — | 6 | 1 | no | — |
| 363 | Dic5 | — | 6 | 1 | no | — |
| 364 | Dic5 | — | 6 | 2 | no | — |
| 365 | Dic5 | — | 6 | 1 | no | — |
| 366 | C2×Q8 | — | 15 | 2 | no | — |
| 367 | C2×Q8 | — | 15 | 2 | no | — |
| 368 | C22×C4 | — | 15 | 1 | no | — |
| 369 | C22×C4 | — | 15 | 1 | no | — |
| 370 | C22×C4 | C22×D15 | 1 | 1 | yes | characteristic |
| 371 | M16 | — | 2 | 2 | no | — |
| 372 | M16 | — | 15 | 4 | no | — |
| 373 | C2×C8 | — | 2 | 2 | no | — |
| 374 | C2×C8 | — | 15 | 2 | no | — |
| 375 | C2×C8 | — | 15 | 1 | no | — |
| 376 | C2×C8 | — | 15 | 1 | no | — |
| 377 | C2×C8 | — | 30 | 2 | no | — |
| 378 | C2×C8 | C22×D15 | 1 | 1 | yes | characteristic |
| 379 | C2×C8 | C22×D15 | 1 | 2 | yes | — |
| 380 | C2×C8 | C22×D15 | 1 | 1 | yes | characteristic |
| 381 | C4⋊C4 | — | 15 | 1 | no | — |
| 382 | C4⋊C4 | — | 15 | 1 | no | — |
| 383 | C4⋊C4 | — | 15 | 2 | no | — |
| 384 | C4⋊C4 | — | 15 | 2 | no | — |
| 385 | C4⋊C4 | — | 15 | 2 | no | — |
| 386 | C4⋊C4 | — | 15 | 2 | no | — |
| 387 | C4⋊C4 | — | 15 | 2 | no | — |
| 388 | C4⋊C4 | — | 15 | 2 | no | — |
| 389 | C4⋊C4 | C4×D15 | 1 | 1 | yes | characteristic |
| 390 | C4⋊C4 | C4×D15 | 1 | 1 | yes | characteristic |
| 391 | C22⋊C4 | — | 15 | 2 | no | — |
| 392 | C22⋊C4 | C4×D15 | 1 | 2 | yes | — |
| 393 | C42 | — | 15 | 1 | no | — |
| 394 | C42 | — | 15 | 1 | no | — |
| 395 | C42 | — | 15 | 1 | no | — |
| 396 | C42 | — | 15 | 2 | no | — |
| 397 | C42 | — | 15 | 1 | no | — |
| 398 | C42 | C22×D15 | 1 | 2 | yes | — |
| 399 | C3×C5 | #2962 | 1 | 1 | yes | characteristic, complemented, Hall |
| 400 | C22×C3 | — | 2 | 1 | no | — |
| 401 | C22×C3 | — | 2 | 1 | no | — |
| 402 | C22×C3 | #4033 | 1 | 2 | yes | — |
| 403 | C22×C3 | C22×C4×D5 | 1 | 1 | yes | characteristic |
| 404 | C3×C4 | — | 2 | 2 | no | — |
| 405 | C3×C4 | — | 2 | 2 | no | — |
| 406 | C3×C4 | #4033 | 1 | 2 | yes | — |
| 407 | C3×C4 | C2×#711 | 1 | 1 | yes | characteristic |
| 408 | C3×C4 | C2×Q8×D5 | 1 | 1 | yes | characteristic |
| 409 | Dic3 | — | 5 | 2 | no | — |
| 410 | Dic3 | — | 10 | 2 | no | — |
| 411 | Dic3 | — | 10 | 1 | no | — |
| 412 | Dic3 | — | 10 | 1 | no | — |
| 413 | Dic3 | — | 10 | 2 | no | — |
| 414 | Dic3 | — | 10 | 1 | no | — |
| 415 | C2×C5 | — | 2 | 2 | no | — |
| 416 | C2×C5 | C2×#887 | 1 | 1 | yes | characteristic |
| 417 | C2×C5 | D3×#131 | 1 | 1 | yes | characteristic |
| 418 | C2×C5 | #5750 | 1 | 1 | yes | characteristic |
| 419 | C23 | C2×C4×D15 | 1 | 1 | yes | characteristic |
| 420 | Q8 | — | 30 | 4 | no | — |
| 421 | Q8 | — | 60 | 2 | no | — |
| 422 | C2×C4 | — | 15 | 1 | no | — |
| 423 | C2×C4 | — | 15 | 1 | no | — |
| 424 | C2×C4 | — | 15 | 1 | no | — |
| 425 | C2×C4 | — | 15 | 1 | no | — |
| 426 | C2×C4 | — | 15 | 2 | no | — |
| 427 | C2×C4 | — | 15 | 2 | no | — |
| 428 | C2×C4 | — | 30 | 2 | no | — |
| 429 | C2×C4 | — | 60 | 1 | no | — |
| 430 | C2×C4 | C2×C4×D15 | 1 | 2 | yes | — |
| 431 | C2×C4 | C2×C4×D15 | 1 | 2 | yes | — |
| 432 | C2×C4 | C2×C4×D15 | 1 | 1 | yes | characteristic |
| 433 | C2×C4 | #6819 | 1 | 2 | yes | — |
| 434 | C2×C4 | Q8×D15 | 1 | 2 | yes | — |
| 435 | C2×C4 | C23×D15 | 1 | 1 | yes | characteristic |
| 436 | C8 | — | 2 | 1 | no | — |
| 437 | C8 | — | 2 | 1 | no | — |
| 438 | C8 | — | 2 | 2 | no | — |
| 439 | C8 | — | 15 | 4 | no | — |
| 440 | C8 | — | 30 | 1 | no | — |
| 441 | C8 | — | 30 | 1 | no | — |
| 442 | C2×C3 | — | 2 | 2 | no | — |
| 443 | C2×C3 | C2×#4033 | 1 | 1 | yes | characteristic |
| 444 | C2×C3 | D5×#131 | 1 | 1 | yes | characteristic |
| 445 | C2×C3 | #66084 | 1 | 1 | yes | characteristic |
| 446 | C5 | #79078 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 447 | C22 | — | 2 | 1 | no | — |
| 448 | C22 | — | 2 | 1 | no | — |
| 449 | C22 | #91776 | 1 | 2 | yes | — |
| 450 | C22 | C22×C4×D15 | 1 | 1 | yes | characteristic |
| 451 | C4 | — | 2 | 2 | no | — |
| 452 | C4 | — | 2 | 2 | no | — |
| 453 | C4 | — | 15 | 2 | no | — |
| 454 | C4 | — | 30 | 1 | no | — |
| 455 | C4 | — | 30 | 2 | no | — |
| 456 | C4 | — | 30 | 1 | no | — |
| 457 | C4 | — | 30 | 1 | no | — |
| 458 | C4 | — | 30 | 2 | no | — |
| 459 | C4 | #91776 | 1 | 2 | yes | — |
| 460 | C4 | C2×#6819 | 1 | 1 | yes | characteristic |
| 461 | C4 | C2×Q8×D15 | 1 | 1 | yes | characteristic |
| 462 | C3 | #10610809 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 463 | C2 | — | 2 | 2 | no | — |
| 464 | C2 | C2×#91776 | 1 | 1 | yes | characteristic |
| 465 | C2 | D15×#131 | 1 | 1 | yes | characteristic |
| 466 | C2 | #11756509 | 1 | 1 | yes | characteristic |
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