Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
318 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 14. #64724 | C4 | semidirect |
| 61. C5×C16 | C4⋊C4 | semidirect |
| 146. C16 | #683 | semidirect |
| 173. C5 | #13168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#367 | 2 |
| C2×#64724 | 2 |
| C2×#64722 | 2 |
| #10601404 | 2 |
| #10598213 | 2 |
| #13168 | 5 |