Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
714 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 1. C22×C5×D16 | C2 | semidirect |
| 2. #10615567 | C2 | semidirect |
| 3. C2×#65190 | C2 | semidirect |
| 4. #10602826 | C2 | semidirect |
| 5. #10602263 | C2 | semidirect |
| 6. #10602262 | C2 | semidirect |
| 7. #10602197 | C2 | semidirect |
| 17. #65446 | C22 | semidirect |
| 21. C2×#3930 | C22 | semidirect |
| 22. C2×D5×C16 | C22 | semidirect |
| 23. #64782 | C22 | semidirect |
| 24. #64725 | C22 | semidirect |
| 25. #64724 | C22 | semidirect |
| 46. C2×C5×C16 | D4 | semidirect |
| 56. C22×D16 | D5 | semidirect |
| 160. C2×C16 | C22⋊D5 | semidirect |
| 240. C5 | #33607 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D16 | 2 |
| #10615567 | 2 |
| C2×#65190 | 2 |
| #10602826 | 2 |
| #10602263 | 2 |
| #10602262 | 2 |
| #10602197 | 2 |
| #33607 | 5 |