Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
498 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 103 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×#2992 | C2 | semidirect |
| 3. #10602548 | C2 | semidirect |
| 4. #10601611 | C2 | semidirect |
| 5. #10601250 | C2 | semidirect |
| 6. #10598241 | C2 | semidirect |
| 7. #10598199 | C2 | semidirect |
| 20. #65356 | C4 | semidirect |
| 21. #65347 | C4 | semidirect |
| 84. #2992 | D5 | semidirect |
| 397. C5 | #9378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2992 | 2 |
| #10614877 | 2 |
| #10602548 | 2 |
| #10601611 | 2 |
| #10601250 | 2 |
| #10598241 | 2 |
| #10598199 | 2 |
| #9378 | 5 |