Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
508 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 99 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. C5×#1965 | C2 | semidirect |
| 3. #10602554 | C2 | semidirect |
| 4. #10601296 | C2 | semidirect |
| 5. #10600660 | C2 | semidirect |
| 6. #10600643 | C2 | semidirect |
| 7. #10598206 | C2 | semidirect |
| 75. #1965 | D5 | semidirect |
| 112. C5×M16 | D8 | semidirect |
| 306. M16 | #686 | semidirect |
| 383. C5 | #10500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10614897 | 2 |
| C5×#1965 | 2 |
| #10602554 | 2 |
| #10601296 | 2 |
| #10600660 | 2 |
| #10600643 | 2 |
| #10598206 | 2 |
| #10500 | 5 |