Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
368 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 81 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. #10599885 | C2 | semidirect |
| 3. #10599709 | C2 | semidirect |
| 4. C5×#1349 | C2 | semidirect |
| 5. #10598266 | C2 | semidirect |
| 6. #10598018 | C2 | semidirect |
| 7. #10597978 | C2 | semidirect |
| 68. #1349 | D5 | semidirect |
| 293. C5 | #11747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10612428 | 2 |
| #10599885 | 2 |
| #10599709 | 2 |
| C5×#1349 | 2 |
| #10598266 | 2 |
| #10598018 | 2 |
| #10597978 | 2 |
| #11747 | 5 |