Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
368 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 95 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. #10600067 | C2 | semidirect |
| 3. #10599845 | C2 | semidirect |
| 4. C5×D4⋊C16 | C2 | semidirect |
| 5. D4⋊#672 | C2 | semidirect |
| 6. #10598047 | C2 | semidirect |
| 7. #10597994 | C2 | semidirect |
| 69. D4⋊C16 | D5 | semidirect |
| 312. C5 | #11630 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611153 | 2 |
| #10600067 | 2 |
| #10599845 | 2 |
| C5×D4⋊C16 | 2 |
| D4⋊#672 | 2 |
| #10598047 | 2 |
| #10597994 | 2 |
| #11630 | 5 |