Finite Group DatabasebetaFinite Group DatabasebetaOrder 1280.
934 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 135 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. C5×#2972 | C2 | semidirect |
| 3. #10602412 | C2 | semidirect |
| 4. #10600752 | C2 | semidirect |
| 5. #10598167 | C2 | semidirect |
| 18. #65280 | C4 | semidirect |
| 19. #65249 | C4 | semidirect |
| 35. C22×C5×C8 | D4 | semidirect |
| 61. #2972 | D5 | semidirect |
| 144. C23×C5 | #102 | semidirect |
| 178. C2×C4×C5 | #102 | semidirect |
| 205. C22×C8 | C22⋊D5 | semidirect |
| 349. C23 | #3953 | semidirect |
| 380. C2×C4 | #3953 | semidirect |
| 385. C5 | #9468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#2972 | 2 |
| #10614134 | 2 |
| #10602412 | 2 |
| #10600752 | 2 |
| #10598167 | 2 |
| #9468 | 5 |