Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
248 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 60 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×#4038 | C2 | semidirect |
| 3. #11716674 | C2 | semidirect |
| 4. C5×#3941 | C2 | semidirect |
| 5. #11716614 | C2 | semidirect |
| 6. #11716603 | C2 | semidirect |
| 7. #11716597 | C2 | semidirect |
| 38. #4038 | D5 | semidirect |
| 45. #3941 | D5 | semidirect |
| 133. C52 | #482 | semidirect |
| 204. C5 | #65068 | semidirect |
| 205. C5 | #65292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4038 | 2 |
| #11717026 | 2 |
| #11716674 | 2 |
| C5×#3941 | 2 |
| #11716614 | 2 |
| #11716603 | 2 |
| #11716597 | 2 |
| #65292 | 5 |
| #65068 | 5 |