Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
368 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 79 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. #10602105 | C2 | semidirect |
| 3. #10601709 | C2 | semidirect |
| 5. #10598284 | C2 | semidirect |
| 6. #10598256 | C2 | semidirect |
| 126. C5×D4 | Q32 | semidirect |
| 241. D4 | #3961 | semidirect |
| 258. C5 | #12322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×Q16 | 2 |
| #10602105 | 2 |
| #10601709 | 2 |
| #10601643 | 2 |
| #10598284 | 2 |
| #10598256 | 2 |
| D4⋊#672 | 2 |
| #12322 | 5 |