Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
372 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 73 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. #10599912 | C2 | semidirect |
| 3. #10599517 | C2 | semidirect |
| 4. C5×#1342 | C2 | semidirect |
| 5. #10598272 | C2 | semidirect |
| 6. #10598026 | C2 | semidirect |
| 7. #10597974 | C2 | semidirect |
| 73. #1342 | D5 | semidirect |
| 338. C5 | #11872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10612637 | 2 |
| #10599912 | 2 |
| #10599517 | 2 |
| C5×#1342 | 2 |
| #10598272 | 2 |
| #10598026 | 2 |
| #10597974 | 2 |
| #11872 | 5 |