Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
492 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 492 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. C5×#2112 | C2 | semidirect |
| 3. C2×#64772 | C2 | semidirect |
| 4. #10598018 | C2 | semidirect |
| 17. C5×C22⋊C16 | C22 | semidirect |
| 19. #64772 | C22 | semidirect |
| 52. #2112 | D5 | semidirect |
| 107. C22⋊C16 | C2×D5 | semidirect |
| 278. C5 | #11711 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#65404 | 2 |
| C5×#2112 | 2 |
| C2×#64772 | 2 |
| #10598018 | 2 |
| #11711 | 5 |