Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
492 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 83 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. #10607911 | C2 | semidirect |
| 5. C5×#1271 | C2 | semidirect |
| 6. #10597971 | C2 | semidirect |
| 7. #10597969 | C2 | semidirect |
| 70. #1271 | D5 | semidirect |
| 113. C5×C4⋊C4 | SD16 | semidirect |
| 318. C4⋊C4 | #677 | semidirect |
| 384. C5 | #7747 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10607911 | 2 |
| #10600420 | 2 |
| #10599469 | 2 |
| #10599422 | 2 |
| C5×#1271 | 2 |
| #10597971 | 2 |
| #10597969 | 2 |
| #7747 | 5 |