Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
504 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×C5×#349 | C2 | semidirect |
| 3. C2×#64773 | C2 | semidirect |
| 4. #10598022 | C2 | semidirect |
| 17. C5×#349 | C22 | semidirect |
| 19. #64773 | C22 | semidirect |
| 59. C2×#349 | D5 | semidirect |
| 133. #349 | C2×D5 | semidirect |
| 347. C5 | #11438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10615493 | 2 |
| C2×C5×#349 | 2 |
| C2×#64773 | 2 |
| #10598022 | 2 |
| #11438 | 5 |