Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
528 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 109 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×#3165 | C2 | semidirect |
| 4. #10602628 | C2 | semidirect |
| 5. #10602571 | C2 | semidirect |
| 7. #10598159 | C2 | semidirect |
| 80. #3165 | D5 | semidirect |
| 105. C5×M16 | SD16 | semidirect |
| 282. M16 | #688 | semidirect |
| 354. C5 | #10201 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#3165 | 2 |
| #10615094 | 2 |
| #10614947 | 2 |
| #10602628 | 2 |
| #10602571 | 2 |
| #10600660 | 2 |
| #10598159 | 2 |
| #10201 | 5 |