Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
228 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 71 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×#2183 | C2 | semidirect |
| 2. #10601735 | C2 | semidirect |
| 5. #10598052 | C2 | semidirect |
| 7. #10597991 | C2 | semidirect |
| 47. #2183 | D5 | semidirect |
| 78. C5×C16 | SD16 | semidirect |
| 175. C16 | #688 | semidirect |
| 202. C5 | #12444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2183 | 2 |
| #10601735 | 2 |
| #10601732 | 2 |
| #10599854 | 2 |
| #10598052 | 2 |
| #10598051 | 2 |
| #10597991 | 2 |
| #12444 | 5 |