Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
234 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 65 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. #10602155 | C2 | semidirect |
| 5. C5×#1365 | C2 | semidirect |
| 6. #10598046 | C2 | semidirect |
| 7. #10597967 | C2 | semidirect |
| 51. #1365 | D5 | semidirect |
| 71. D40 | Q16 | semidirect |
| 190. C5 | #12447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10602181 | 2 |
| #10602155 | 2 |
| #10600083 | 2 |
| #10599349 | 2 |
| C5×#1365 | 2 |
| #10598046 | 2 |
| #10597967 | 2 |
| #12447 | 5 |