Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
394 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 77 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. #10599899 | C2 | semidirect |
| 3. #10599732 | C2 | semidirect |
| 4. C5×#1350 | C2 | semidirect |
| 5. #10598268 | C2 | semidirect |
| 6. #10598018 | C2 | semidirect |
| 7. #10597978 | C2 | semidirect |
| 69. #1350 | D5 | semidirect |
| 327. C5 | #11894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10612489 | 2 |
| #10599899 | 2 |
| #10599732 | 2 |
| C5×#1350 | 2 |
| #10598268 | 2 |
| #10598018 | 2 |
| #10597978 | 2 |
| #11894 | 5 |