Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
702 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 702 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 |
|---|---|---|
| 1. C22×C5×#101 | C2 | semidirect |
| 3. #10602926 | C2 | semidirect |
| 4. C2×#64697 | C2 | semidirect |
| 5. #10598190 | C2 | semidirect |
| 62. C5×#101 | D4 | semidirect |
| 73. C22×#101 | D5 | semidirect |
| 260. #101 | C22⋊D5 | semidirect |
| 277. C22×C5 | #355 | semidirect |
| 428. C5 | #13092 | semidirect |
| 443. C22 | #64697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#101 | 2 |
| #10615797 | 2 |
| #10602926 | 2 |
| C2×#64697 | 2 |
| #10598190 | 2 |
| #13092 | 5 |