Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
214 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 65 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×#2215 | C2 | semidirect |
| 2. C2×#64739 | C2 | semidirect |
| 3. #10602206 | C2 | semidirect |
| 4. C22×#3926 | C2 | semidirect |
| 5. #10598315 | C2 | semidirect |
| 6. #10598068 | C2 | semidirect |
| 7. #10598066 | C2 | semidirect |
| 40. #3926 | D4 | semidirect |
| 44. #2215 | D5 | semidirect |
| 123. C22×C5 | D32 | semidirect |
| 177. C5 | #13694 | semidirect |
| 186. C22 | #64739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2215 | 2 |
| C2×#64739 | 2 |
| #10602206 | 2 |
| C22×#3926 | 2 |
| #10598315 | 2 |
| #10598068 | 2 |
| #10598066 | 2 |
| #13694 | 5 |