Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
358 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 96 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. #11716959 | C2 | semidirect |
| 3. C2×D5×#168 | C2 | semidirect |
| 4. #11716702 | C2 | semidirect |
| 5. C5×#3967 | C2 | semidirect |
| 6. #11716604 | C2 | semidirect |
| 7. #11716603 | C2 | semidirect |
| 10. C5×#713 | C4 | semidirect |
| 51. #3967 | D5 | semidirect |
| 79. #713 | Dic5 | semidirect |
| 153. C52 | #416 | semidirect |
| 230. C5 | #65093 | semidirect |
| 231. C5 | #65522 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#713 | 2 |
| #11716959 | 2 |
| C2×D5×#168 | 2 |
| #11716702 | 2 |
| C5×#3967 | 2 |
| #11716604 | 2 |
| #11716603 | 2 |
| #65522 | 5 |
| #65093 | 5 |