Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
234 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 63 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×#2170 | C2 | semidirect |
| 2. #10601719 | C2 | semidirect |
| 3. #10599853 | C2 | semidirect |
| 4. #10598062 | C2 | semidirect |
| 5. #10597993 | C2 | semidirect |
| 39. #2170 | D5 | semidirect |
| 156. C5 | #12436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2170 | 2 |
| #10601719 | 2 |
| #10599853 | 2 |
| #10598062 | 2 |
| #10597993 | 2 |
| #12436 | 5 |