← C3×#10601760 #14293360
Subgroups — C3×#10601760 #14293360
Order 1920.
280 conjugacy classes of subgroups.
The subgroup lattice has 280 nodes — too large to display as a diagram.
Conjugacy classes of subgroups
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|
| 1 | C3×C5×#446 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C3×#65310 | C2 | 1 | 1 | yes | maximal, characteristic |
| 3 | C3×#65309 | C2 | 1 | 1 | yes | maximal, characteristic |
| 4 | C3×#64970 | C2 | 1 | 1 | yes | maximal, characteristic |
| 5 | C3×#64702 | C2 | 1 | 1 | yes | maximal, characteristic |
| 6 | C3×#64701 | C2 | 1 | 1 | yes | maximal, characteristic |
| 7 | C3×#64677 | C2 | 1 | 1 | yes | maximal, characteristic |
| 8 | #10601760 | C3 | 1 | 1 | yes | maximal, characteristic, direct product factor, Hall |
| 9 | C3×C4×C5×Q8 | C22 | 1 | 1 | yes | characteristic |
| 10 | C3×#4015 | C22 | 1 | 1 | yes | characteristic |
| 11 | C3×#4015 | C22 | 1 | 1 | yes | characteristic |
| 12 | C3×C5×C4⋊C8 | — | 2 | 1 | no | — |
| 13 | C3×C5×C4⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 14 | C3×C5×#97 | — | 2 | 1 | no | — |
| 15 | C3×C4×C5×C8 | C22 | 1 | 1 | yes | characteristic |
| 16 | C3×#3967 | — | 2 | 1 | no | — |
| 17 | C3×#3967 | — | 2 | 1 | no | — |
| 18 | C3×#3948 | — | 2 | 1 | no | — |
| 19 | C3×#3948 | — | 2 | 1 | no | — |
| 20 | C3×#3940 | — | 2 | 1 | no | — |
| 21 | C3×#3939 | — | 2 | 1 | no | — |
| 22 | C3×C4⋊#168 | C22 | 1 | 1 | yes | characteristic |
| 23 | C3×C4⋊#168 | C22 | 1 | 1 | yes | characteristic |
| 24 | C3×#1704 | — | 5 | 1 | no | maximal, Hall |
| 25 | C5×#446 | C2×C3 | 1 | 1 | yes | characteristic |
| 26 | #65310 | C2×C3 | 1 | 1 | yes | characteristic |
| 27 | #65309 | C2×C3 | 1 | 1 | yes | characteristic |
| 28 | #64970 | C2×C3 | 1 | 1 | yes | characteristic |
| 29 | #64702 | C2×C3 | 1 | 1 | yes | characteristic |
| 30 | #64701 | C2×C3 | 1 | 1 | yes | characteristic |
| 31 | #64677 | C2×C3 | 1 | 1 | yes | characteristic |
| 32 | C2×C3×C5×Q8 | D4 | 1 | 1 | yes | characteristic |
| 33 | C2×C3×Dic10 | — | 2 | 1 | no | — |
| 34 | C2×C3×Dic10 | — | 2 | 1 | no | — |
| 35 | C2×C3×C5×C8 | — | 2 | 1 | no | — |
| 36 | C2×C3×C5×C8 | D4 | 1 | 1 | yes | characteristic |
| 37 | C2×C3×C5×C8 | D4 | 1 | 1 | yes | characteristic |
| 38 | C3×C5×C4⋊C4 | — | 2 | 1 | no | — |
| 39 | C3×C5×C4⋊C4 | D4 | 1 | 1 | yes | characteristic |
| 40 | C3×C42×C5 | — | 2 | 1 | no | — |
| 41 | C3×C42×C5 | C23 | 1 | 1 | yes | characteristic |
| 42 | C3×C4⋊Dic5 | — | 2 | 1 | no | — |
| 43 | C3×C4⋊Dic5 | — | 2 | 1 | no | — |
| 44 | C3×C4⋊Dic5 | — | 2 | 1 | no | — |
| 45 | C3×C4⋊Dic5 | — | 2 | 1 | no | — |
| 46 | C2×C3×#168 | — | 2 | 1 | no | — |
| 47 | C2×C3×#168 | — | 2 | 1 | no | — |
| 48 | C3×#487 | — | 5 | 1 | no | — |
| 49 | C3×#477 | — | 5 | 1 | no | — |
| 50 | C3×#475 | — | 5 | 1 | no | — |
| 51 | C3×#446 | D5 | 1 | 1 | yes | characteristic |
| 52 | C3×#334 | — | 5 | 1 | no | — |
| 53 | C3×#333 | — | 5 | 1 | no | — |
| 54 | C3×#332 | — | 5 | 1 | no | — |
| 55 | C4×C5×Q8 | C22×C3 | 1 | 1 | yes | characteristic |
| 56 | #4015 | C22×C3 | 1 | 1 | yes | characteristic |
| 57 | #4015 | C22×C3 | 1 | 1 | yes | characteristic |
| 58 | C5×C4⋊C8 | — | 2 | 1 | no | — |
| 59 | C5×C4⋊C8 | C22×C3 | 1 | 1 | yes | characteristic |
| 60 | C5×#97 | — | 2 | 1 | no | — |
| 61 | C4×C5×C8 | C22×C3 | 1 | 1 | yes | characteristic |
| 62 | #3967 | — | 2 | 1 | no | — |
| 63 | #3967 | — | 2 | 1 | no | — |
| 64 | #3948 | — | 2 | 1 | no | — |
| 65 | #3948 | — | 2 | 1 | no | — |
| 66 | #3940 | — | 2 | 1 | no | — |
| 67 | #3939 | — | 2 | 1 | no | — |
| 68 | C4⋊#168 | C22×C3 | 1 | 1 | yes | characteristic |
| 69 | C4⋊#168 | C22×C3 | 1 | 1 | yes | characteristic |
| 70 | #1704 | — | 5 | 1 | no | Sylow |
| 71 | C3×C5×Q8 | — | 2 | 1 | no | — |
| 72 | C3×C5×Q8 | — | 2 | 1 | no | — |
| 73 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 74 | C2×C3×C4×C5 | — | 2 | 1 | no | — |
| 75 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 76 | C2×C3×C4×C5 | C2×D4 | 1 | 1 | yes | characteristic |
| 77 | C2×C3×C4×C5 | #41 | 1 | 1 | yes | characteristic |
| 78 | C2×C3×Dic5 | — | 4 | 1 | no | — |
| 79 | C2×C3×Dic5 | — | 4 | 1 | no | — |
| 80 | C3×Dic10 | — | 4 | 1 | no | — |
| 81 | C3×Dic10 | — | 4 | 1 | no | — |
| 82 | C3×Dic10 | — | 8 | 1 | no | — |
| 83 | C3×C5×C8 | — | 2 | 1 | no | — |
| 84 | C3×C5×C8 | — | 2 | 1 | no | — |
| 85 | C3×C5×C8 | — | 4 | 1 | no | — |
| 86 | C3×#168 | — | 4 | 1 | no | — |
| 87 | C3×#168 | — | 4 | 1 | no | — |
| 88 | C3×C4⋊Q8 | — | 5 | 1 | no | — |
| 89 | C3×C4⋊Q8 | — | 5 | 1 | no | — |
| 90 | C3×C4×Q8 | C2×D5 | 1 | 1 | yes | characteristic |
| 91 | C3×#107 | — | 10 | 1 | no | — |
| 92 | C3×#106 | — | 10 | 1 | no | — |
| 93 | C3×C4⋊C8 | — | 2 | 1 | no | — |
| 94 | C3×C4⋊C8 | — | 5 | 1 | no | — |
| 95 | C3×C4⋊C8 | — | 5 | 1 | no | — |
| 96 | C3×C4⋊C8 | C2×D5 | 1 | 1 | yes | characteristic |
| 97 | C3×#103 | — | 10 | 1 | no | — |
| 98 | C3×#103 | — | 10 | 1 | no | — |
| 99 | C3×#103 | — | 10 | 1 | no | — |
| 100 | C3×#103 | — | 10 | 1 | no | — |
| 101 | C3×#97 | — | 2 | 1 | no | — |
| 102 | C3×C4×C8 | C2×D5 | 1 | 1 | yes | characteristic |
| 103 | C2×C5×Q8 | C3×D4 | 1 | 1 | yes | characteristic |
| 104 | C2×Dic10 | — | 2 | 1 | no | — |
| 105 | C2×Dic10 | — | 2 | 1 | no | — |
| 106 | C2×C5×C8 | — | 2 | 1 | no | — |
| 107 | C2×C5×C8 | C3×D4 | 1 | 1 | yes | characteristic |
| 108 | C2×C5×C8 | C3×D4 | 1 | 1 | yes | characteristic |
| 109 | C5×C4⋊C4 | — | 2 | 1 | no | — |
| 110 | C5×C4⋊C4 | C3×D4 | 1 | 1 | yes | characteristic |
| 111 | C42×C5 | — | 2 | 1 | no | — |
| 112 | C42×C5 | C23×C3 | 1 | 1 | yes | characteristic |
| 113 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 114 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 115 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 116 | C4⋊Dic5 | — | 2 | 1 | no | — |
| 117 | C2×#168 | — | 2 | 1 | no | — |
| 118 | C2×#168 | — | 2 | 1 | no | — |
| 119 | #487 | — | 5 | 1 | no | — |
| 120 | #477 | — | 5 | 1 | no | — |
| 121 | #475 | — | 5 | 1 | no | — |
| 122 | #446 | C3×D5 | 1 | 1 | yes | characteristic |
| 123 | #334 | — | 5 | 1 | no | — |
| 124 | #333 | — | 5 | 1 | no | — |
| 125 | #332 | — | 5 | 1 | no | — |
| 126 | C22×C3×C5 | #121 | 1 | 1 | yes | characteristic |
| 127 | C3×C4×C5 | — | 2 | 1 | no | — |
| 128 | C3×C4×C5 | — | 4 | 1 | no | — |
| 129 | C3×C4×C5 | — | 4 | 1 | no | — |
| 130 | C3×C4×C5 | #135 | 1 | 1 | yes | characteristic |
| 131 | C3×C4×C5 | #137 | 1 | 1 | yes | characteristic |
| 132 | C3×C4×C5 | #137 | 1 | 1 | yes | characteristic |
| 133 | C3×C4×C5 | #137 | 1 | 1 | yes | characteristic |
| 134 | C3×Dic5 | — | 8 | 1 | no | — |
| 135 | C3×Dic5 | — | 8 | 1 | no | — |
| 136 | C2×C3×Q8 | — | 10 | 1 | no | — |
| 137 | C2×C3×Q8 | — | 10 | 1 | no | — |
| 138 | C2×C3×Q8 | D20 | 1 | 1 | yes | characteristic |
| 139 | C2×C3×C8 | — | 2 | 1 | no | — |
| 140 | C2×C3×C8 | — | 10 | 1 | no | — |
| 141 | C2×C3×C8 | — | 10 | 1 | no | — |
| 142 | C2×C3×C8 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 143 | C2×C3×C8 | C22⋊D5 | 1 | 1 | yes | characteristic |
| 144 | C3×C4⋊C4 | — | 2 | 1 | no | — |
| 145 | C3×C4⋊C4 | — | 10 | 1 | no | — |
| 146 | C3×C4⋊C4 | — | 10 | 1 | no | — |
| 147 | C3×C4⋊C4 | — | 10 | 1 | no | — |
| 148 | C3×C4⋊C4 | — | 10 | 1 | no | — |
| 149 | C3×C4⋊C4 | D20 | 1 | 1 | yes | characteristic |
| 150 | C3×C42 | — | 2 | 1 | no | — |
| 151 | C3×C42 | C22×D5 | 1 | 1 | yes | characteristic |
| 152 | C5×Q8 | — | 2 | 1 | no | — |
| 153 | C5×Q8 | — | 2 | 1 | no | — |
| 154 | C2×C4×C5 | — | 2 | 1 | no | — |
| 155 | C2×C4×C5 | — | 2 | 1 | no | — |
| 156 | C2×C4×C5 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 157 | C2×C4×C5 | C2×C3×D4 | 1 | 1 | yes | characteristic |
| 158 | C2×C4×C5 | C3×#41 | 1 | 1 | yes | characteristic |
| 159 | C2×Dic5 | — | 4 | 1 | no | — |
| 160 | C2×Dic5 | — | 4 | 1 | no | — |
| 161 | Dic10 | — | 4 | 1 | no | — |
| 162 | Dic10 | — | 4 | 1 | no | — |
| 163 | Dic10 | — | 8 | 1 | no | — |
| 164 | C5×C8 | — | 2 | 1 | no | — |
| 165 | C5×C8 | — | 2 | 1 | no | — |
| 166 | C5×C8 | — | 4 | 1 | no | — |
| 167 | #168 | — | 4 | 1 | no | — |
| 168 | #168 | — | 4 | 1 | no | — |
| 169 | C4⋊Q8 | — | 5 | 1 | no | — |
| 170 | C4⋊Q8 | — | 5 | 1 | no | — |
| 171 | C4×Q8 | C2×C3×D5 | 1 | 1 | yes | characteristic |
| 172 | #107 | — | 10 | 1 | no | — |
| 173 | #106 | — | 10 | 1 | no | — |
| 174 | C4⋊C8 | — | 2 | 1 | no | — |
| 175 | C4⋊C8 | — | 5 | 1 | no | — |
| 176 | C4⋊C8 | — | 5 | 1 | no | — |
| 177 | C4⋊C8 | C2×C3×D5 | 1 | 1 | yes | characteristic |
| 178 | #103 | — | 10 | 1 | no | — |
| 179 | #103 | — | 10 | 1 | no | — |
| 180 | #103 | — | 10 | 1 | no | — |
| 181 | #103 | — | 10 | 1 | no | — |
| 182 | #97 | — | 2 | 1 | no | — |
| 183 | C4×C8 | C2×C3×D5 | 1 | 1 | yes | characteristic |
| 184 | C2×C3×C5 | #464 | 1 | 1 | yes | characteristic |
| 185 | C2×C3×C5 | #470 | 1 | 1 | yes | characteristic |
| 186 | C2×C3×C5 | #471 | 1 | 1 | yes | characteristic |
| 187 | C3×Q8 | — | 2 | 1 | no | — |
| 188 | C3×Q8 | — | 2 | 1 | no | — |
| 189 | C3×Q8 | — | 20 | 1 | no | — |
| 190 | C3×Q8 | — | 20 | 1 | no | — |
| 191 | C3×Q8 | — | 40 | 1 | no | — |
| 192 | C2×C3×C4 | — | 2 | 1 | no | — |
| 193 | C2×C3×C4 | — | 2 | 1 | no | — |
| 194 | C2×C3×C4 | — | 20 | 1 | no | — |
| 195 | C2×C3×C4 | — | 20 | 1 | no | — |
| 196 | C2×C3×C4 | C2×D20 | 1 | 1 | yes | characteristic |
| 197 | C2×C3×C4 | #709 | 1 | 1 | yes | characteristic |
| 198 | C2×C3×C4 | C2×C22⋊D5 | 1 | 1 | yes | characteristic |
| 199 | C3×C8 | — | 2 | 1 | no | — |
| 200 | C3×C8 | — | 2 | 1 | no | — |
| 201 | C3×C8 | — | 4 | 1 | no | — |
| 202 | C3×C8 | — | 20 | 1 | no | — |
| 203 | C3×C8 | — | 20 | 1 | no | — |
| 204 | C22×C5 | C3×#121 | 1 | 1 | yes | characteristic |
| 205 | C4×C5 | — | 2 | 1 | no | — |
| 206 | C4×C5 | — | 4 | 1 | no | — |
| 207 | C4×C5 | — | 4 | 1 | no | — |
| 208 | C4×C5 | C3×#135 | 1 | 1 | yes | characteristic |
| 209 | C4×C5 | C3×#137 | 1 | 1 | yes | characteristic |
| 210 | C4×C5 | C3×#137 | 1 | 1 | yes | characteristic |
| 211 | C4×C5 | C3×#137 | 1 | 1 | yes | characteristic |
| 212 | Dic5 | — | 8 | 1 | no | — |
| 213 | Dic5 | — | 8 | 1 | no | — |
| 214 | C2×Q8 | — | 10 | 1 | no | — |
| 215 | C2×Q8 | — | 10 | 1 | no | — |
| 216 | C2×Q8 | C3×D20 | 1 | 1 | yes | characteristic |
| 217 | C2×C8 | — | 2 | 1 | no | — |
| 218 | C2×C8 | — | 10 | 1 | no | — |
| 219 | C2×C8 | — | 10 | 1 | no | — |
| 220 | C2×C8 | C3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 221 | C2×C8 | C3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 222 | C4⋊C4 | — | 2 | 1 | no | — |
| 223 | C4⋊C4 | — | 10 | 1 | no | — |
| 224 | C4⋊C4 | — | 10 | 1 | no | — |
| 225 | C4⋊C4 | — | 10 | 1 | no | — |
| 226 | C4⋊C4 | — | 10 | 1 | no | — |
| 227 | C4⋊C4 | C3×D20 | 1 | 1 | yes | characteristic |
| 228 | C42 | — | 2 | 1 | no | — |
| 229 | C42 | C22×C3×D5 | 1 | 1 | yes | characteristic |
| 230 | C3×C5 | #1704 | 1 | 1 | yes | characteristic, complemented, Hall |
| 231 | C22×C3 | #4076 | 1 | 1 | yes | characteristic |
| 232 | C3×C4 | — | 2 | 1 | no | — |
| 233 | C3×C4 | — | 4 | 1 | no | — |
| 234 | C3×C4 | — | 4 | 1 | no | — |
| 235 | C3×C4 | — | 40 | 1 | no | — |
| 236 | C3×C4 | — | 40 | 1 | no | — |
| 237 | C3×C4 | #4055 | 1 | 1 | yes | characteristic |
| 238 | C3×C4 | #4055 | 1 | 1 | yes | characteristic |
| 239 | C3×C4 | #4088 | 1 | 1 | yes | characteristic |
| 240 | C3×C4 | #4096 | 1 | 1 | yes | characteristic |
| 241 | C2×C5 | C3×#464 | 1 | 1 | yes | characteristic |
| 242 | C2×C5 | C3×#470 | 1 | 1 | yes | characteristic |
| 243 | C2×C5 | C3×#471 | 1 | 1 | yes | characteristic |
| 244 | Q8 | — | 2 | 1 | no | — |
| 245 | Q8 | — | 2 | 1 | no | — |
| 246 | Q8 | — | 20 | 1 | no | — |
| 247 | Q8 | — | 20 | 1 | no | — |
| 248 | Q8 | — | 40 | 1 | no | — |
| 249 | C2×C4 | — | 2 | 1 | no | — |
| 250 | C2×C4 | — | 2 | 1 | no | — |
| 251 | C2×C4 | — | 20 | 1 | no | — |
| 252 | C2×C4 | — | 20 | 1 | no | — |
| 253 | C2×C4 | C2×C3×D20 | 1 | 1 | yes | characteristic |
| 254 | C2×C4 | C3×#709 | 1 | 1 | yes | characteristic |
| 255 | C2×C4 | C2×C3×C22⋊D5 | 1 | 1 | yes | characteristic |
| 256 | C8 | — | 2 | 1 | no | — |
| 257 | C8 | — | 2 | 1 | no | — |
| 258 | C8 | — | 4 | 1 | no | — |
| 259 | C8 | — | 20 | 1 | no | — |
| 260 | C8 | — | 20 | 1 | no | — |
| 261 | C2×C3 | #65317 | 1 | 1 | yes | characteristic |
| 262 | C2×C3 | #65426 | 1 | 1 | yes | characteristic |
| 263 | C2×C3 | #65430 | 1 | 1 | yes | characteristic |
| 264 | C5 | C3×#1704 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 265 | C22 | C3×#4076 | 1 | 1 | yes | characteristic |
| 266 | C4 | — | 2 | 1 | no | — |
| 267 | C4 | — | 4 | 1 | no | — |
| 268 | C4 | — | 4 | 1 | no | — |
| 269 | C4 | — | 40 | 1 | no | — |
| 270 | C4 | — | 40 | 1 | no | — |
| 271 | C4 | C3×#4055 | 1 | 1 | yes | characteristic |
| 272 | C4 | C3×#4055 | 1 | 1 | yes | characteristic |
| 273 | C4 | C3×#4088 | 1 | 1 | yes | characteristic |
| 274 | C4 | C3×#4096 | 1 | 1 | yes | characteristic |
| 275 | C3 | #10601760 | 1 | 1 | yes | characteristic, direct product factor, Sylow |
| 276 | C2 | C3×#65317 | 1 | 1 | yes | characteristic |
| 277 | C2 | C3×#65426 | 1 | 1 | yes | characteristic |
| 278 | C2 | C3×#65430 | 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