Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
508 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 101 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×#2549 | C2 | semidirect |
| 5. #10598116 | C2 | semidirect |
| 6. #10598108 | C2 | semidirect |
| 7. #10598103 | C2 | semidirect |
| 32. C22×D20 | Q8 | semidirect |
| 52. C2×C4⋊Dic5 | Q8 | semidirect |
| 70. #2549 | D5 | semidirect |
| 414. C5 | #10374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2549 | 2 |
| #10600302 | 2 |
| #10600249 | 2 |
| C2×#64671 | 2 |
| #10598116 | 2 |
| #10598108 | 2 |
| #10598103 | 2 |
| #10374 | 5 |