Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
620 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 620 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 |
|---|---|---|
| 2. #10606029 | C2 | semidirect |
| 3. C5×#1514 | C2 | semidirect |
| 4. #10602606 | C2 | semidirect |
| 5. #10601611 | C2 | semidirect |
| 6. #10598243 | C2 | semidirect |
| 7. #10598124 | C2 | semidirect |
| 13. #65374 | C4 | semidirect |
| 14. #65362 | C4 | semidirect |
| 31. C5×C4⋊Q8 | C2×C4 | semidirect |
| 32. C5×#127 | C2×C4 | semidirect |
| 64. C4×#168 | C2×C4 | semidirect |
| 69. #1514 | D5 | semidirect |
| 187. C4⋊Q8 | C4×D5 | semidirect |
| 192. #127 | C4×D5 | semidirect |
| 333. C5 | #9428 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615018 | 2 |
| #10606029 | 2 |
| C5×#1514 | 2 |
| #10602606 | 2 |
| #10601611 | 2 |
| #10598243 | 2 |
| #10598124 | 2 |
| #9428 | 5 |