Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
318 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 71 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. #10601646 | C2 | semidirect |
| 3. #10600083 | C2 | semidirect |
| 4. #10599839 | C2 | semidirect |
| 5. C5×D4⋊C16 | C2 | semidirect |
| 6. #10598055 | C2 | semidirect |
| 7. #10597995 | C2 | semidirect |
| 59. D4⋊C16 | D5 | semidirect |
| 241. C5 | #12396 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10611142 | 2 |
| #10601646 | 2 |
| #10600083 | 2 |
| #10599839 | 2 |
| C5×D4⋊C16 | 2 |
| #10598055 | 2 |
| #10597995 | 2 |
| #12396 | 5 |