← #14472057
Subgroups — #14472057
Order 1920.
672 conjugacy classes of subgroups.
The subgroup lattice has 628 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | #11755265 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11753305 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11750893 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C5×#4790 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C3×#65081 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | #11749359 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | #11749262 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #11749245 | C2 | 1 | 1 | yes | maximal, characteristic |
| 9 | #11748028 | C2 | 1 | 1 | yes | maximal, characteristic |
| 10 | #11747834 | C2 | 1 | 1 | yes | maximal, characteristic |
| 11 | #11747828 | C2 | 1 | 1 | yes | maximal, characteristic |
| 12 | C8×#1204 | C2 | 1 | 1 | yes | maximal, characteristic |
| 13 | #11747421 | C2 | 1 | 1 | yes | maximal, characteristic |
| 14 | #11747303 | C2 | 1 | 1 | yes | maximal, characteristic |
| 15 | #11747285 | C2 | 1 | 1 | yes | maximal, characteristic |
| 16 | #10611430 | — | 3 | 1 | no | maximal, Hall |
| 17 | #91833 | C22 | 1 | 1 | yes | characteristic |
| 18 | #91777 | C22 | 1 | 1 | yes | characteristic |
| 19 | C5×Q8×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 20 | C2×C5×#216 | C22 | 1 | 1 | yes | characteristic |
| 21 | C5×#887 | C22 | 1 | 1 | yes | characteristic |
| 22 | C3×#4090 | C22 | 1 | 1 | yes | characteristic |
| 23 | C3×#4034 | C22 | 1 | 1 | yes | characteristic |
| 24 | #91469 | C22 | 1 | 1 | yes | characteristic |
| 25 | C4×#1204 | C22 | 1 | 1 | yes | characteristic |
| 26 | #91389 | — | 2 | 1 | no | — |
| 27 | #91389 | C22 | 1 | 1 | yes | characteristic |
| 28 | #91379 | — | 2 | 1 | no | — |
| 29 | #91344 | C22 | 1 | 1 | yes | characteristic |
| 30 | #91336 | — | 2 | 1 | no | — |
| 31 | #91335 | — | 2 | 1 | no | — |
| 32 | #91333 | C22 | 1 | 1 | yes | characteristic |
| 33 | Dic5×Dic6 | C22 | 1 | 1 | yes | characteristic |
| 34 | #91331 | C22 | 1 | 1 | yes | characteristic |
| 35 | #91328 | — | 2 | 1 | no | — |
| 36 | #91327 | — | 2 | 1 | no | — |
| 37 | #91324 | — | 2 | 1 | no | — |
| 38 | #91324 | — | 2 | 1 | no | — |
| 39 | C2×#6663 | C22 | 1 | 1 | yes | characteristic |
| 40 | C2×#6661 | C22 | 1 | 1 | yes | characteristic |
| 41 | C3×C5×#103 | C22 | 1 | 1 | yes | characteristic |
| 42 | #91119 | C22 | 1 | 1 | yes | characteristic |
| 43 | #91100 | C22 | 1 | 1 | yes | characteristic |
| 44 | C8×Dic15 | C22 | 1 | 1 | yes | characteristic |
| 45 | #91094 | C22 | 1 | 1 | yes | characteristic |
| 46 | C5×#816 | C22 | 1 | 1 | yes | characteristic |
| 47 | C5×C8×Dic3 | C22 | 1 | 1 | yes | characteristic |
| 48 | C5×#807 | C22 | 1 | 1 | yes | characteristic |
| 49 | C3×#3967 | C22 | 1 | 1 | yes | characteristic |
| 50 | C3×#3948 | C22 | 1 | 1 | yes | characteristic |
| 51 | C3×C8×Dic5 | C22 | 1 | 1 | yes | characteristic |
| 52 | C3×#3942 | C22 | 1 | 1 | yes | characteristic |
| 53 | #90989 | C22 | 1 | 1 | yes | characteristic |
| 54 | #90988 | C22 | 1 | 1 | yes | characteristic |
| 55 | Dic3⋊#168 | C22 | 1 | 1 | yes | characteristic |
| 56 | #90983 | C22 | 1 | 1 | yes | characteristic |
| 57 | #90982 | C22 | 1 | 1 | yes | characteristic |
| 58 | #90974 | C22 | 1 | 1 | yes | characteristic |
| 59 | #90971 | C22 | 1 | 1 | yes | characteristic |
| 60 | #81624 | — | 5 | 1 | no | maximal, Hall |
| 61 | #65901 | — | 3 | 1 | no | — |
| 62 | Q8×Dic10 | — | 3 | 1 | no | — |
| 63 | C4×C5×Q16 | — | 3 | 1 | no | — |
| 64 | #65471 | — | 3 | 1 | no | — |
| 65 | #65471 | — | 3 | 1 | no | — |
| 66 | #65320 | — | 3 | 1 | no | — |
| 67 | #65310 | — | 3 | 1 | no | — |
| 68 | #65164 | — | 3 | 1 | no | — |
| 69 | #65164 | — | 3 | 1 | no | — |
| 70 | #65081 | — | 3 | 1 | no | — |
| 71 | #65081 | D3 | 1 | 1 | yes | characteristic |
| 72 | #65079 | — | 3 | 1 | no | — |
| 73 | #65079 | — | 3 | 1 | no | — |
| 74 | #64970 | — | 3 | 1 | no | — |
| 75 | C8×Dic10 | — | 3 | 1 | no | — |
| 76 | C2×C3×C5×Q8 | C23 | 1 | 1 | yes | characteristic |
| 77 | C2×Dic30 | — | 2 | 1 | no | — |
| 78 | C2×Dic30 | C23 | 1 | 1 | yes | characteristic |
| 79 | C2×C5×Dic6 | C23 | 1 | 1 | yes | characteristic |
| 80 | C2×C3×Dic10 | — | 2 | 1 | no | — |
| 81 | C2×C3×Dic10 | C23 | 1 | 1 | yes | characteristic |
| 82 | C2×#1204 | — | 2 | 1 | no | — |
| 83 | C2×#1204 | D4 | 1 | 1 | yes | characteristic |
| 84 | C2×C3×C5×C8 | C23 | 1 | 1 | yes | characteristic |
| 85 | C3×C5×C4⋊C4 | C23 | 1 | 1 | yes | characteristic |
| 86 | C4⋊Dic15 | C23 | 1 | 1 | yes | characteristic |
| 87 | #6712 | — | 2 | 1 | no | — |
| 88 | #6712 | — | 2 | 1 | no | — |
| 89 | #6712 | — | 2 | 1 | no | — |
| 90 | C4×Dic15 | C23 | 1 | 1 | yes | characteristic |
| 91 | C2×C3⋊#168 | C23 | 1 | 1 | yes | characteristic |
| 92 | C5×#216 | — | 2 | 2 | no | — |
| 93 | C5×C4⋊Dic3 | — | 2 | 1 | no | — |
| 94 | C5×C4⋊Dic3 | C23 | 1 | 1 | yes | characteristic |
| 95 | C5×Dic3⋊C4 | — | 2 | 1 | no | — |
| 96 | C4×C5×Dic3 | — | 2 | 1 | no | — |
| 97 | C4×C5×Dic3 | — | 2 | 1 | no | — |
| 98 | C4×C5×Dic3 | C23 | 1 | 1 | yes | characteristic |
| 99 | C2×C5×C3⋊C8 | C23 | 1 | 1 | yes | characteristic |
| 100 | C3×C4⋊Dic5 | C23 | 1 | 1 | yes | characteristic |
| 101 | C3×#683 | — | 2 | 1 | no | — |
| 102 | C3×#683 | — | 2 | 1 | no | — |
| 103 | C3×#683 | — | 2 | 1 | no | — |
| 104 | C3×C4×Dic5 | C23 | 1 | 1 | yes | characteristic |
| 105 | C2×C3×#168 | C23 | 1 | 1 | yes | characteristic |
| 106 | Dic3⋊Dic5 | — | 2 | 1 | no | — |
| 107 | Dic3⋊Dic5 | — | 2 | 1 | no | — |
| 108 | Dic3⋊Dic5 | — | 2 | 1 | no | — |
| 109 | Dic3⋊Dic5 | — | 2 | 1 | no | — |
| 110 | Dic3⋊Dic5 | — | 2 | 1 | no | — |
| 111 | Dic3⋊Dic5 | D4 | 1 | 1 | yes | characteristic |
| 112 | #6669 | — | 2 | 1 | no | — |
| 113 | #6669 | D4 | 1 | 1 | yes | characteristic |
| 114 | #6668 | — | 2 | 1 | no | — |
| 115 | #6668 | D4 | 1 | 1 | yes | characteristic |
| 116 | Dic3×Dic5 | — | 2 | 1 | no | — |
| 117 | Dic3×Dic5 | — | 2 | 1 | no | — |
| 118 | Dic3×Dic5 | — | 2 | 1 | no | — |
| 119 | Dic3×Dic5 | — | 2 | 1 | no | — |
| 120 | #6663 | — | 2 | 2 | no | — |
| 121 | #6661 | — | 2 | 2 | no | — |
| 122 | #5722 | — | 5 | 1 | no | — |
| 123 | #5721 | — | 5 | 1 | no | — |
| 124 | C3×#487 | — | 5 | 1 | no | — |
| 125 | #5091 | — | 5 | 1 | no | — |
| 126 | #5090 | — | 5 | 1 | no | — |
| 127 | #4795 | — | 5 | 1 | no | — |
| 128 | #4795 | — | 5 | 1 | no | — |
| 129 | #4793 | — | 5 | 1 | no | — |
| 130 | #4793 | — | 5 | 1 | no | — |
| 131 | #4792 | — | 5 | 1 | no | — |
| 132 | #4792 | — | 5 | 1 | no | — |
| 133 | #4790 | — | 5 | 1 | no | — |
| 134 | #4790 | D5 | 1 | 1 | yes | characteristic |
| 135 | C4×Dic12 | — | 5 | 1 | no | — |
| 136 | C8×Dic6 | — | 5 | 1 | no | — |
| 137 | C2×C5×Q16 | — | 3 | 1 | no | — |
| 138 | C4×C5×Q8 | — | 3 | 1 | no | — |
| 139 | C4×C5×Q8 | — | 3 | 1 | no | — |
| 140 | Q8×Dic5 | — | 3 | 1 | no | — |
| 141 | Q8×Dic5 | — | 3 | 1 | no | — |
| 142 | #4090 | — | 3 | 1 | no | — |
| 143 | #4090 | C2×D3 | 1 | 1 | yes | characteristic |
| 144 | C2×#689 | — | 3 | 1 | no | — |
| 145 | C2×#689 | — | 3 | 1 | no | — |
| 146 | #4035 | — | 6 | 1 | no | — |
| 147 | #4035 | — | 6 | 1 | no | — |
| 148 | #4034 | — | 3 | 1 | no | — |
| 149 | #4034 | — | 6 | 1 | no | — |
| 150 | #4034 | — | 6 | 1 | no | — |
| 151 | #4034 | C2×D3 | 1 | 1 | yes | characteristic |
| 152 | #4033 | — | 3 | 1 | no | — |
| 153 | #4033 | — | 3 | 1 | no | — |
| 154 | #4016 | — | 6 | 1 | no | — |
| 155 | #4015 | — | 3 | 1 | no | — |
| 156 | #4015 | — | 3 | 1 | no | — |
| 157 | #4015 | — | 6 | 1 | no | — |
| 158 | C4×Dic10 | — | 3 | 1 | no | — |
| 159 | C4×Dic10 | — | 6 | 1 | no | — |
| 160 | C4×Dic10 | — | 6 | 1 | no | — |
| 161 | C5×#107 | — | 3 | 1 | no | — |
| 162 | C5×#103 | — | 3 | 1 | no | — |
| 163 | C5×#103 | C2×D3 | 1 | 1 | yes | characteristic |
| 164 | C4×C5×C8 | — | 3 | 1 | no | — |
| 165 | #3967 | — | 3 | 1 | no | — |
| 166 | #3967 | C2×D3 | 1 | 1 | yes | characteristic |
| 167 | #3948 | — | 3 | 1 | no | — |
| 168 | #3948 | — | 3 | 1 | no | — |
| 169 | #3948 | — | 3 | 1 | no | — |
| 170 | #3948 | C2×D3 | 1 | 1 | yes | characteristic |
| 171 | #3946 | — | 3 | 1 | no | — |
| 172 | #3946 | — | 3 | 1 | no | — |
| 173 | C8×Dic5 | — | 3 | 1 | no | — |
| 174 | C8×Dic5 | C2×D3 | 1 | 1 | yes | characteristic |
| 175 | #3942 | — | 3 | 1 | no | — |
| 176 | #3942 | C2×D3 | 1 | 1 | yes | characteristic |
| 177 | #3939 | — | 3 | 1 | no | — |
| 178 | #3939 | — | 3 | 1 | no | — |
| 179 | C4⋊#168 | — | 3 | 1 | no | — |
| 180 | #3363 | — | 15 | 1 | no | Sylow |
| 181 | C3×C5×Q8 | — | 2 | 1 | no | — |
| 182 | C3×C5×Q8 | — | 2 | 1 | no | — |
| 183 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 184 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 185 | C2×C3×C4×C5 | C24 | 1 | 1 | yes | characteristic |
| 186 | C2×Dic15 | — | 2 | 1 | no | — |
| 187 | C2×Dic15 | — | 2 | 1 | no | — |
| 188 | C2×Dic15 | C2×D4 | 1 | 1 | yes | characteristic |
| 189 | C2×Dic15 | C2×D4 | 1 | 1 | yes | characteristic |
| 190 | Dic30 | — | 2 | 1 | no | — |
| 191 | Dic30 | — | 2 | 1 | no | — |
| 192 | Dic30 | — | 8 | 1 | no | — |
| 193 | C2×C5×Dic3 | — | 2 | 1 | no | — |
| 194 | C2×C5×Dic3 | — | 2 | 1 | no | — |
| 195 | C2×C5×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 196 | C2×C5×Dic3 | C2×D4 | 1 | 1 | yes | characteristic |
| 197 | C5×Dic6 | — | 2 | 1 | no | — |
| 198 | C5×Dic6 | #41 | 1 | 2 | yes | — |
| 199 | C2×C3×Dic5 | — | 2 | 1 | no | — |
| 200 | C2×C3×Dic5 | — | 2 | 1 | no | — |
| 201 | C2×C3×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 202 | C2×C3×Dic5 | C2×D4 | 1 | 1 | yes | characteristic |
| 203 | C3×Dic10 | — | 2 | 1 | no | — |
| 204 | C3×Dic10 | — | 2 | 1 | no | — |
| 205 | C3×Dic10 | — | 8 | 1 | no | — |
| 206 | #1204 | — | 8 | 1 | no | — |
| 207 | #1204 | Q16 | 1 | 4 | yes | complemented |
| 208 | C3×C5×C8 | — | 2 | 1 | no | — |
| 209 | C3⋊#168 | — | 2 | 1 | no | — |
| 210 | C3×#168 | — | 2 | 1 | no | — |
| 211 | C5×C3⋊C8 | — | 2 | 1 | no | — |
| 212 | C3×C4⋊Q8 | — | 5 | 1 | no | — |
| 213 | C3×C4⋊Q8 | — | 5 | 1 | no | — |
| 214 | Q8×Dic3 | — | 5 | 1 | no | — |
| 215 | Q8×Dic3 | C2×D5 | 1 | 1 | yes | characteristic |
| 216 | #944 | — | 5 | 1 | no | — |
| 217 | #944 | — | 5 | 1 | no | — |
| 218 | #944 | — | 10 | 1 | no | — |
| 219 | #944 | — | 10 | 1 | no | — |
| 220 | C2×#216 | — | 5 | 1 | no | — |
| 221 | C2×#216 | C2×D5 | 1 | 1 | yes | characteristic |
| 222 | C2×Dic12 | — | 5 | 1 | no | — |
| 223 | #890 | — | 10 | 1 | no | — |
| 224 | #889 | — | 10 | 1 | no | — |
| 225 | #889 | — | 10 | 1 | no | — |
| 226 | #888 | — | 5 | 1 | no | — |
| 227 | #888 | — | 5 | 1 | no | — |
| 228 | #888 | — | 10 | 1 | no | — |
| 229 | #887 | — | 5 | 1 | no | — |
| 230 | #887 | — | 10 | 1 | no | — |
| 231 | #887 | — | 10 | 1 | no | — |
| 232 | #887 | C2×D5 | 1 | 1 | yes | characteristic |
| 233 | C4×Dic6 | — | 5 | 1 | no | — |
| 234 | C4×Dic6 | — | 5 | 1 | no | — |
| 235 | C4×Dic6 | — | 5 | 1 | no | — |
| 236 | C3×#103 | — | 5 | 1 | no | — |
| 237 | C3×#103 | — | 5 | 1 | no | — |
| 238 | C3×#103 | — | 5 | 1 | no | — |
| 239 | C3×#103 | C2×D5 | 1 | 1 | yes | characteristic |
| 240 | C3×C4×C8 | — | 5 | 1 | no | — |
| 241 | #835 | — | 5 | 1 | no | — |
| 242 | #835 | — | 5 | 1 | no | — |
| 243 | #818 | — | 5 | 1 | no | — |
| 244 | #816 | — | 5 | 1 | no | — |
| 245 | #816 | C2×D5 | 1 | 1 | yes | characteristic |
| 246 | Dic3⋊C8 | — | 5 | 1 | no | — |
| 247 | Dic3⋊C8 | — | 5 | 1 | no | — |
| 248 | C8×Dic3 | — | 5 | 1 | no | — |
| 249 | C8×Dic3 | C2×D5 | 1 | 1 | yes | characteristic |
| 250 | #810 | — | 5 | 1 | no | — |
| 251 | #810 | — | 5 | 1 | no | — |
| 252 | #807 | — | 5 | 1 | no | — |
| 253 | #807 | C2×D5 | 1 | 1 | yes | characteristic |
| 254 | C4⋊(C3⋊C8) | — | 5 | 1 | no | — |
| 255 | C2×C5×Q8 | — | 3 | 1 | no | — |
| 256 | C2×C5×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 257 | C2×Dic10 | — | 2 | 1 | no | — |
| 258 | C2×Dic10 | — | 3 | 1 | no | — |
| 259 | C2×Dic10 | — | 3 | 1 | no | — |
| 260 | C2×Dic10 | — | 6 | 1 | no | — |
| 261 | C2×Dic10 | — | 6 | 1 | no | — |
| 262 | C2×Dic10 | C22×D3 | 1 | 1 | yes | characteristic |
| 263 | C5×Q16 | — | 6 | 2 | no | — |
| 264 | C2×C5×C8 | — | 3 | 1 | no | — |
| 265 | C2×C5×C8 | C22×D3 | 1 | 1 | yes | characteristic |
| 266 | C5×C4⋊C4 | — | 3 | 1 | no | — |
| 267 | C5×C4⋊C4 | — | 6 | 1 | no | — |
| 268 | C5×C4⋊C4 | — | 6 | 1 | no | — |
| 269 | C5×C4⋊C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 270 | C42×C5 | — | 3 | 1 | no | — |
| 271 | C42×C5 | — | 6 | 1 | no | — |
| 272 | C42×C5 | — | 6 | 1 | no | — |
| 273 | #689 | — | 6 | 2 | no | — |
| 274 | #689 | — | 6 | 2 | no | — |
| 275 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 276 | C4⋊Dic5 | — | 3 | 1 | no | — |
| 277 | C4⋊Dic5 | — | 6 | 1 | no | — |
| 278 | C4⋊Dic5 | — | 6 | 1 | no | — |
| 279 | C4⋊Dic5 | — | 6 | 1 | no | — |
| 280 | C4⋊Dic5 | — | 6 | 1 | no | — |
| 281 | C4⋊Dic5 | — | 6 | 1 | no | — |
| 282 | C4⋊Dic5 | C22×D3 | 1 | 1 | yes | characteristic |
| 283 | #683 | — | 2 | 1 | no | — |
| 284 | #683 | — | 2 | 1 | no | — |
| 285 | #683 | — | 2 | 1 | no | — |
| 286 | #683 | — | 3 | 1 | no | — |
| 287 | #683 | — | 3 | 1 | no | — |
| 288 | #683 | — | 6 | 1 | no | — |
| 289 | #683 | — | 6 | 1 | no | — |
| 290 | #683 | — | 6 | 1 | no | — |
| 291 | #683 | — | 6 | 1 | no | — |
| 292 | #683 | — | 6 | 1 | no | — |
| 293 | C4×Dic5 | — | 3 | 1 | no | — |
| 294 | C4×Dic5 | — | 6 | 1 | no | — |
| 295 | C4×Dic5 | — | 6 | 1 | no | — |
| 296 | C4×Dic5 | — | 6 | 1 | no | — |
| 297 | C4×Dic5 | — | 6 | 1 | no | — |
| 298 | C4×Dic5 | C22×D3 | 1 | 1 | yes | characteristic |
| 299 | C2×#168 | — | 3 | 1 | no | — |
| 300 | C2×#168 | C22×D3 | 1 | 1 | yes | characteristic |
| 301 | Q82 | — | 15 | 1 | no | — |
| 302 | #557 | — | 15 | 1 | no | — |
| 303 | #487 | — | 5 | 1 | no | — |
| 304 | #487 | — | 15 | 1 | no | — |
| 305 | #487 | — | 15 | 1 | no | — |
| 306 | #477 | — | 15 | 1 | no | — |
| 307 | #477 | — | 15 | 1 | no | — |
| 308 | #477 | — | 15 | 1 | no | — |
| 309 | #462 | — | 15 | 1 | no | — |
| 310 | #462 | — | 15 | 1 | no | — |
| 311 | #462 | — | 15 | 1 | no | — |
| 312 | C8×Q8 | — | 15 | 1 | no | — |
| 313 | C4×Q16 | — | 3 | 1 | no | — |
| 314 | C4×Q16 | — | 15 | 1 | no | — |
| 315 | C4×Q16 | — | 15 | 1 | no | — |
| 316 | C22×C3×C5 | C22×D4 | 1 | 1 | yes | characteristic |
| 317 | C3×C4×C5 | — | 4 | 1 | no | — |
| 318 | C3×C4×C5 | — | 4 | 1 | no | — |
| 319 | C3×C4×C5 | C2×#41 | 1 | 1 | yes | characteristic |
| 320 | C3×C4×C5 | 2−1+4 | 1 | 1 | yes | characteristic |
| 321 | Dic15 | — | 2 | 1 | no | — |
| 322 | Dic15 | — | 4 | 1 | no | — |
| 323 | Dic15 | — | 4 | 1 | no | — |
| 324 | Dic15 | C2×Q16 | 1 | 2 | yes | — |
| 325 | C3×Dic5 | — | 2 | 1 | no | — |
| 326 | C3×Dic5 | — | 4 | 1 | no | — |
| 327 | C3×Dic5 | — | 4 | 1 | no | — |
| 328 | C3×Dic5 | C2×Q16 | 1 | 2 | yes | — |
| 329 | C5×Dic3 | — | 2 | 2 | no | — |
| 330 | C5×Dic3 | — | 2 | 1 | no | — |
| 331 | C5×Dic3 | — | 4 | 1 | no | — |
| 332 | C5×Dic3 | C2×Q16 | 1 | 2 | yes | — |
| 333 | C2×C3×Q8 | — | 5 | 1 | no | — |
| 334 | C2×C3×Q8 | — | 10 | 1 | no | — |
| 335 | C2×C3×Q8 | C22×D5 | 1 | 1 | yes | characteristic |
| 336 | C2×Dic6 | — | 5 | 1 | no | — |
| 337 | C2×Dic6 | — | 5 | 1 | no | — |
| 338 | C2×Dic6 | — | 10 | 1 | no | — |
| 339 | C2×Dic6 | — | 10 | 1 | no | — |
| 340 | C2×Dic6 | C22×D5 | 1 | 1 | yes | characteristic |
| 341 | C2×C3×C8 | — | 5 | 1 | no | — |
| 342 | C2×C3×C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 343 | C3×C4⋊C4 | — | 5 | 1 | no | — |
| 344 | C3×C4⋊C4 | — | 10 | 1 | no | — |
| 345 | C3×C4⋊C4 | — | 10 | 1 | no | — |
| 346 | C3×C4⋊C4 | — | 10 | 1 | no | — |
| 347 | C3×C4⋊C4 | C22×D5 | 1 | 1 | yes | characteristic |
| 348 | C3×C42 | — | 5 | 1 | no | — |
| 349 | #216 | — | 2 | 2 | no | — |
| 350 | #216 | — | 10 | 2 | no | — |
| 351 | C4⋊Dic3 | — | 2 | 1 | no | — |
| 352 | C4⋊Dic3 | — | 5 | 1 | no | — |
| 353 | C4⋊Dic3 | — | 5 | 1 | no | — |
| 354 | C4⋊Dic3 | — | 10 | 1 | no | — |
| 355 | C4⋊Dic3 | C22×D5 | 1 | 1 | yes | characteristic |
| 356 | Dic3⋊C4 | — | 2 | 1 | no | — |
| 357 | Dic3⋊C4 | — | 5 | 1 | no | — |
| 358 | Dic3⋊C4 | — | 5 | 1 | no | — |
| 359 | Dic3⋊C4 | — | 10 | 1 | no | — |
| 360 | Dic3⋊C4 | — | 10 | 1 | no | — |
| 361 | Dic3⋊C4 | — | 10 | 1 | no | — |
| 362 | Dic3⋊C4 | — | 10 | 1 | no | — |
| 363 | Dic3⋊C4 | — | 10 | 1 | no | — |
| 364 | Dic3⋊C4 | — | 10 | 1 | no | — |
| 365 | Dic3⋊C4 | — | 10 | 1 | no | — |
| 366 | Dic3⋊C4 | — | 10 | 1 | no | — |
| 367 | Dic3⋊C4 | — | 10 | 1 | no | — |
| 368 | C4×Dic3 | — | 2 | 1 | no | — |
| 369 | C4×Dic3 | — | 2 | 1 | no | — |
| 370 | C4×Dic3 | — | 5 | 1 | no | — |
| 371 | C4×Dic3 | — | 10 | 1 | no | — |
| 372 | C4×Dic3 | — | 10 | 1 | no | — |
| 373 | C4×Dic3 | — | 10 | 1 | no | — |
| 374 | C4×Dic3 | — | 10 | 1 | no | — |
| 375 | C4×Dic3 | C22×D5 | 1 | 1 | yes | characteristic |
| 376 | C2×C3⋊C8 | — | 5 | 1 | no | — |
| 377 | C2×C3⋊C8 | C22×D5 | 1 | 1 | yes | characteristic |
| 378 | Dic12 | — | 10 | 2 | no | — |
| 379 | C5×Q8 | — | 2 | 1 | no | — |
| 380 | C5×Q8 | — | 2 | 1 | no | — |
| 381 | C5×Q8 | — | 3 | 2 | no | — |
| 382 | C5×Q8 | — | 6 | 1 | no | — |
| 383 | C2×C4×C5 | — | 2 | 1 | no | — |
| 384 | C2×C4×C5 | — | 2 | 1 | no | — |
| 385 | C2×C4×C5 | — | 3 | 1 | no | — |
| 386 | C2×C4×C5 | — | 3 | 1 | no | — |
| 387 | C2×C4×C5 | — | 6 | 1 | no | — |
| 388 | C2×C4×C5 | — | 6 | 1 | no | — |
| 389 | C2×C4×C5 | C23×D3 | 1 | 1 | yes | characteristic |
| 390 | C2×Dic5 | — | 2 | 1 | no | — |
| 391 | C2×Dic5 | — | 2 | 1 | no | — |
| 392 | C2×Dic5 | — | 3 | 1 | no | — |
| 393 | C2×Dic5 | — | 3 | 1 | no | — |
| 394 | C2×Dic5 | — | 6 | 1 | no | — |
| 395 | C2×Dic5 | — | 6 | 1 | no | — |
| 396 | C2×Dic5 | D3×D4 | 1 | 1 | yes | characteristic |
| 397 | C2×Dic5 | D3×D4 | 1 | 1 | yes | characteristic |
| 398 | Dic10 | — | 2 | 1 | no | — |
| 399 | Dic10 | — | 2 | 1 | no | — |
| 400 | Dic10 | — | 3 | 4 | no | — |
| 401 | Dic10 | — | 6 | 1 | no | — |
| 402 | Dic10 | — | 6 | 1 | no | — |
| 403 | Dic10 | — | 8 | 1 | no | — |
| 404 | Dic10 | — | 24 | 1 | no | — |
| 405 | Dic10 | — | 24 | 1 | no | — |
| 406 | C5×C8 | — | 2 | 1 | no | — |
| 407 | C5×C8 | — | 6 | 1 | no | — |
| 408 | #168 | — | 2 | 1 | no | — |
| 409 | #168 | — | 6 | 1 | no | — |
| 410 | C2×Q16 | — | 3 | 1 | no | — |
| 411 | C2×Q16 | — | 15 | 1 | no | — |
| 412 | C2×Q16 | — | 15 | 1 | no | — |
| 413 | C4⋊Q8 | — | 5 | 1 | no | — |
| 414 | C4⋊Q8 | — | 5 | 1 | no | — |
| 415 | C4⋊Q8 | — | 15 | 1 | no | — |
| 416 | C4⋊Q8 | — | 15 | 1 | no | — |
| 417 | C4⋊Q8 | — | 15 | 1 | no | — |
| 418 | C4⋊Q8 | — | 15 | 1 | no | — |
| 419 | C4⋊Q8 | — | 30 | 1 | no | — |
| 420 | C4⋊Q8 | — | 30 | 1 | no | — |
| 421 | C4⋊Q8 | — | 30 | 1 | no | — |
| 422 | #125 | — | 30 | 1 | no | — |
| 423 | #125 | — | 30 | 1 | no | — |
| 424 | #125 | — | 30 | 1 | no | — |
| 425 | C4×Q8 | — | 3 | 1 | no | — |
| 426 | C4×Q8 | — | 3 | 1 | no | — |
| 427 | C4×Q8 | — | 15 | 1 | no | — |
| 428 | C4×Q8 | — | 15 | 1 | no | — |
| 429 | C4×Q8 | — | 15 | 1 | no | — |
| 430 | C4×Q8 | — | 15 | 1 | no | — |
| 431 | C4×Q8 | — | 15 | 1 | no | — |
| 432 | C4×Q8 | — | 30 | 1 | no | — |
| 433 | C4×Q8 | — | 30 | 1 | no | — |
| 434 | #107 | — | 3 | 1 | no | — |
| 435 | #107 | — | 15 | 1 | no | — |
| 436 | #107 | — | 15 | 1 | no | — |
| 437 | C4⋊C8 | — | 15 | 1 | no | — |
| 438 | C4⋊C8 | — | 15 | 1 | no | — |
| 439 | C4⋊C8 | — | 15 | 1 | no | — |
| 440 | #103 | — | 3 | 1 | no | — |
| 441 | #103 | — | 5 | 1 | no | — |
| 442 | #103 | — | 5 | 1 | no | — |
| 443 | #103 | — | 5 | 1 | no | — |
| 444 | #103 | — | 15 | 1 | no | — |
| 445 | #103 | — | 15 | 1 | no | — |
| 446 | #103 | — | 15 | 1 | no | — |
| 447 | #103 | — | 15 | 1 | no | — |
| 448 | #103 | — | 15 | 1 | no | — |
| 449 | #103 | D3×D5 | 1 | 1 | yes | characteristic |
| 450 | C4×C8 | — | 3 | 1 | no | — |
| 451 | C4×C8 | — | 5 | 1 | no | — |
| 452 | C4×C8 | — | 15 | 1 | no | — |
| 453 | C2×C3×C5 | #548 | 1 | 1 | yes | characteristic |
| 454 | C2×C3×C5 | C22×Q16 | 1 | 1 | yes | characteristic |
| 455 | C2×C3×C5 | #577 | 1 | 1 | yes | characteristic |
| 456 | C3×Q8 | — | 2 | 1 | no | — |
| 457 | C3×Q8 | — | 2 | 1 | no | — |
| 458 | C3×Q8 | — | 10 | 1 | no | — |
| 459 | C3×Q8 | — | 10 | 1 | no | — |
| 460 | C3×Q8 | — | 40 | 1 | no | — |
| 461 | C2×C3×C4 | — | 2 | 1 | no | — |
| 462 | C2×C3×C4 | — | 2 | 1 | no | — |
| 463 | C2×C3×C4 | — | 5 | 1 | no | — |
| 464 | C2×C3×C4 | — | 5 | 1 | no | — |
| 465 | C2×C3×C4 | — | 10 | 1 | no | — |
| 466 | C2×C3×C4 | — | 10 | 1 | no | — |
| 467 | C2×C3×C4 | C23×D5 | 1 | 1 | yes | characteristic |
| 468 | C2×Dic3 | — | 2 | 1 | no | — |
| 469 | C2×Dic3 | — | 2 | 1 | no | — |
| 470 | C2×Dic3 | — | 5 | 1 | no | — |
| 471 | C2×Dic3 | — | 5 | 1 | no | — |
| 472 | C2×Dic3 | — | 10 | 1 | no | — |
| 473 | C2×Dic3 | — | 10 | 1 | no | — |
| 474 | C2×Dic3 | D4×D5 | 1 | 1 | yes | characteristic |
| 475 | C2×Dic3 | D4×D5 | 1 | 1 | yes | characteristic |
| 476 | Dic6 | — | 2 | 1 | no | — |
| 477 | Dic6 | — | 5 | 4 | no | — |
| 478 | Dic6 | — | 10 | 1 | no | — |
| 479 | Dic6 | — | 10 | 1 | no | — |
| 480 | Dic6 | — | 40 | 1 | no | — |
| 481 | Dic6 | — | 40 | 1 | no | — |
| 482 | Dic6 | #709 | 1 | 2 | yes | — |
| 483 | C3×C8 | — | 2 | 1 | no | — |
| 484 | C3×C8 | — | 10 | 1 | no | — |
| 485 | C3⋊C8 | — | 2 | 1 | no | — |
| 486 | C3⋊C8 | — | 10 | 1 | no | — |
| 487 | C22×C5 | C2×D3×D4 | 1 | 1 | yes | characteristic |
| 488 | C4×C5 | — | 3 | 2 | no | — |
| 489 | C4×C5 | — | 4 | 1 | no | — |
| 490 | C4×C5 | — | 4 | 1 | no | — |
| 491 | C4×C5 | — | 6 | 2 | no | — |
| 492 | C4×C5 | — | 6 | 1 | no | — |
| 493 | C4×C5 | — | 12 | 1 | no | — |
| 494 | C4×C5 | D3×#41 | 1 | 1 | yes | characteristic |
| 495 | C4×C5 | #1010 | 1 | 1 | yes | characteristic |
| 496 | Dic5 | — | 2 | 1 | no | — |
| 497 | Dic5 | — | 3 | 2 | no | — |
| 498 | Dic5 | — | 4 | 1 | no | — |
| 499 | Dic5 | — | 4 | 1 | no | — |
| 500 | Dic5 | — | 6 | 1 | no | — |
| 501 | Dic5 | — | 12 | 1 | no | — |
| 502 | Dic5 | — | 12 | 1 | no | — |
| 503 | Dic5 | D3×Q16 | 1 | 2 | yes | — |
| 504 | C2×Q8 | — | 3 | 1 | no | — |
| 505 | C2×Q8 | — | 5 | 1 | no | — |
| 506 | C2×Q8 | — | 10 | 1 | no | — |
| 507 | C2×Q8 | — | 15 | 1 | no | — |
| 508 | C2×Q8 | — | 15 | 1 | no | — |
| 509 | C2×Q8 | — | 30 | 1 | no | — |
| 510 | C2×Q8 | — | 30 | 1 | no | — |
| 511 | C2×Q8 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 512 | Q16 | — | 6 | 2 | no | — |
| 513 | Q16 | — | 30 | 2 | no | — |
| 514 | Q16 | — | 30 | 2 | no | — |
| 515 | C2×C8 | — | 3 | 1 | no | — |
| 516 | C2×C8 | — | 5 | 1 | no | — |
| 517 | C2×C8 | — | 15 | 1 | no | — |
| 518 | C2×C8 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 519 | C4⋊C4 | — | 3 | 1 | no | — |
| 520 | C4⋊C4 | — | 5 | 1 | no | — |
| 521 | C4⋊C4 | — | 6 | 1 | no | — |
| 522 | C4⋊C4 | — | 6 | 1 | no | — |
| 523 | C4⋊C4 | — | 10 | 1 | no | — |
| 524 | C4⋊C4 | — | 10 | 1 | no | — |
| 525 | C4⋊C4 | — | 10 | 1 | no | — |
| 526 | C4⋊C4 | — | 15 | 1 | no | — |
| 527 | C4⋊C4 | — | 15 | 1 | no | — |
| 528 | C4⋊C4 | — | 15 | 1 | no | — |
| 529 | C4⋊C4 | — | 15 | 1 | no | — |
| 530 | C4⋊C4 | — | 30 | 1 | no | — |
| 531 | C4⋊C4 | — | 30 | 1 | no | — |
| 532 | C4⋊C4 | — | 30 | 1 | no | — |
| 533 | C4⋊C4 | — | 30 | 1 | no | — |
| 534 | C4⋊C4 | — | 30 | 1 | no | — |
| 535 | C4⋊C4 | — | 30 | 1 | no | — |
| 536 | C4⋊C4 | — | 30 | 1 | no | — |
| 537 | C4⋊C4 | — | 30 | 1 | no | — |
| 538 | C4⋊C4 | — | 30 | 1 | no | — |
| 539 | C4⋊C4 | — | 30 | 1 | no | — |
| 540 | C4⋊C4 | C2×D3×D5 | 1 | 1 | yes | characteristic |
| 541 | C42 | — | 3 | 1 | no | — |
| 542 | C42 | — | 5 | 1 | no | — |
| 543 | C42 | — | 6 | 1 | no | — |
| 544 | C42 | — | 6 | 1 | no | — |
| 545 | C42 | — | 15 | 1 | no | — |
| 546 | C42 | — | 30 | 1 | no | — |
| 547 | C42 | — | 30 | 1 | no | — |
| 548 | C42 | — | 30 | 1 | no | — |
| 549 | C42 | — | 30 | 1 | no | — |
| 550 | C3×C5 | #3363 | 1 | 1 | yes | characteristic, complemented, Hall |
| 551 | C22×C3 | C2×D4×D5 | 1 | 1 | yes | characteristic |
| 552 | C3×C4 | — | 4 | 1 | no | — |
| 553 | C3×C4 | — | 4 | 1 | no | — |
| 554 | C3×C4 | — | 5 | 2 | no | — |
| 555 | C3×C4 | — | 10 | 1 | no | — |
| 556 | C3×C4 | — | 20 | 1 | no | — |
| 557 | C3×C4 | — | 20 | 1 | no | — |
| 558 | C3×C4 | C2×#709 | 1 | 1 | yes | characteristic |
| 559 | C3×C4 | #4150 | 1 | 1 | yes | characteristic |
| 560 | Dic3 | — | 2 | 1 | no | — |
| 561 | Dic3 | — | 2 | 2 | no | — |
| 562 | Dic3 | — | 4 | 1 | no | — |
| 563 | Dic3 | — | 5 | 2 | no | — |
| 564 | Dic3 | — | 10 | 1 | no | — |
| 565 | Dic3 | — | 20 | 1 | no | — |
| 566 | Dic3 | — | 20 | 1 | no | — |
| 567 | Dic3 | D5×Q16 | 1 | 2 | yes | — |
| 568 | C2×C5 | #5677 | 1 | 1 | yes | characteristic |
| 569 | C2×C5 | #5762 | 1 | 1 | yes | characteristic |
| 570 | C2×C5 | C2×D3×Q16 | 1 | 1 | yes | characteristic |
| 571 | Q8 | — | 2 | 1 | no | — |
| 572 | Q8 | — | 2 | 1 | no | — |
| 573 | Q8 | — | 3 | 2 | no | — |
| 574 | Q8 | — | 6 | 1 | no | — |
| 575 | Q8 | — | 10 | 1 | no | — |
| 576 | Q8 | — | 10 | 1 | no | — |
| 577 | Q8 | — | 15 | 4 | no | — |
| 578 | Q8 | — | 30 | 1 | no | — |
| 579 | Q8 | — | 30 | 1 | no | — |
| 580 | Q8 | — | 40 | 1 | no | — |
| 581 | Q8 | — | 120 | 1 | no | — |
| 582 | Q8 | — | 120 | 1 | no | — |
| 583 | C2×C4 | — | 2 | 1 | no | — |
| 584 | C2×C4 | — | 2 | 1 | no | — |
| 585 | C2×C4 | — | 3 | 1 | no | — |
| 586 | C2×C4 | — | 3 | 1 | no | — |
| 587 | C2×C4 | — | 5 | 1 | no | — |
| 588 | C2×C4 | — | 5 | 1 | no | — |
| 589 | C2×C4 | — | 6 | 1 | no | — |
| 590 | C2×C4 | — | 6 | 1 | no | — |
| 591 | C2×C4 | — | 10 | 1 | no | — |
| 592 | C2×C4 | — | 10 | 1 | no | — |
| 593 | C2×C4 | — | 15 | 1 | no | — |
| 594 | C2×C4 | — | 15 | 1 | no | — |
| 595 | C2×C4 | — | 30 | 1 | no | — |
| 596 | C2×C4 | — | 30 | 1 | no | — |
| 597 | C2×C4 | C22×D3×D5 | 1 | 1 | yes | characteristic |
| 598 | C8 | — | 2 | 1 | no | — |
| 599 | C8 | — | 6 | 1 | no | — |
| 600 | C8 | — | 10 | 1 | no | — |
| 601 | C8 | — | 30 | 1 | no | — |
| 602 | C2×C3 | #65886 | 1 | 1 | yes | characteristic |
| 603 | C2×C3 | C2×D5×Q16 | 1 | 1 | yes | characteristic |
| 604 | C2×C3 | #66104 | 1 | 1 | yes | characteristic |
| 605 | C5 | #81624 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 606 | C22 | D3×D4×D5 | 1 | 1 | yes | characteristic |
| 607 | C4 | — | 3 | 2 | no | — |
| 608 | C4 | — | 4 | 1 | no | — |
| 609 | C4 | — | 4 | 1 | no | — |
| 610 | C4 | — | 5 | 2 | no | — |
| 611 | C4 | — | 6 | 1 | no | — |
| 612 | C4 | — | 6 | 2 | no | — |
| 613 | C4 | — | 10 | 1 | no | — |
| 614 | C4 | — | 12 | 1 | no | — |
| 615 | C4 | — | 15 | 2 | no | — |
| 616 | C4 | — | 20 | 1 | no | — |
| 617 | C4 | — | 20 | 1 | no | — |
| 618 | C4 | — | 30 | 1 | no | — |
| 619 | C4 | — | 60 | 1 | no | — |
| 620 | C4 | — | 60 | 1 | no | — |
| 621 | C4 | D3×#709 | 1 | 1 | yes | characteristic |
| 622 | C4 | #92020 | 1 | 1 | yes | characteristic |
| 623 | C3 | #10611430 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 624 | C2 | #11752868 | 1 | 1 | yes | characteristic |
| 625 | C2 | #11754087 | 1 | 1 | yes | characteristic |
| 626 | C2 | D3×D5×Q16 | 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