Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
290 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 57 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×#2236 | C2 | semidirect |
| 3. #10601419 | C2 | semidirect |
| 5. #10598268 | C2 | semidirect |
| 7. #10598016 | C2 | semidirect |
| 62. #2236 | D5 | semidirect |
| 263. C5 | #12297 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10612482 | 2 |
| C5×#2236 | 2 |
| #10601419 | 2 |
| #10601392 | 2 |
| #10598268 | 2 |
| #10598018 | 2 |
| #10598016 | 2 |
| #12297 | 5 |