Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
420 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. C5×#1537 | C2 | semidirect |
| 4. #10602617 | C2 | semidirect |
| 6. #10598248 | C2 | semidirect |
| 7. #10598246 | C2 | semidirect |
| 74. #1537 | D5 | semidirect |
| 304. C5 | #9373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615089 | 2 |
| #10611069 | 2 |
| C5×#1537 | 2 |
| #10602617 | 2 |
| #10601609 | 2 |
| #10598248 | 2 |
| #10598246 | 2 |
| #9373 | 5 |