Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
298 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 1. C5×#3383 | C2 | semidirect |
| 5. #10598292 | C2 | semidirect |
| 6. Q8⋊#672 | C2 | semidirect |
| 7. #10598256 | C2 | semidirect |
| 54. #3383 | D5 | semidirect |
| 68. C5×Q16 | SD16 | semidirect |
| 183. Q16 | #688 | semidirect |
| 236. C5 | #12353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3383 | 2 |
| #10602174 | 2 |
| #10601732 | 2 |
| #10601707 | 2 |
| #10598292 | 2 |
| Q8⋊#672 | 2 |
| #10598256 | 2 |
| #12353 | 5 |