Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
170 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 61 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×#2253 | C2 | semidirect |
| 5. #10598067 | C2 | semidirect |
| 6. #10598066 | C2 | semidirect |
| 7. C4⋊#3926 | C2 | semidirect |
| 35. #2253 | D5 | semidirect |
| 141. C5 | #13707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2253 | 2 |
| C4×D80 | 2 |
| #10598068 | 2 |
| #10598067 | 2 |
| #10598066 | 2 |
| C4⋊#3926 | 2 |
| #13707 | 5 |