Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
508 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×#672 | C2 | semidirect |
| 3. C5×#2112 | C2 | semidirect |
| 4. C2×#64735 | C2 | semidirect |
| 5. #10598306 | C2 | semidirect |
| 53. C2×#672 | D4 | semidirect |
| 57. #2112 | D5 | semidirect |
| 176. C22×C5 | #350 | semidirect |
| 258. C5 | #12983 | semidirect |
| 265. C22 | #64735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615465 | 2 |
| C23×#672 | 2 |
| C5×#2112 | 2 |
| C2×#64735 | 2 |
| #10598306 | 2 |
| #12983 | 5 |