Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
364 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 81 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. #10601309 | C2 | semidirect |
| 3. #10601304 | C2 | semidirect |
| 5. #10601294 | C2 | semidirect |
| 7. C5×#1309 | C2 | semidirect |
| 70. #1309 | D5 | semidirect |
| 302. C5 | #10533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10610796 | 2 |
| #10601309 | 2 |
| #10601304 | 2 |
| #10601298 | 2 |
| #10601294 | 2 |
| #10601291 | 2 |
| C5×#1309 | 2 |
| #10533 | 5 |