Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
286 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 68 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. #11717036 | C2 | semidirect |
| 3. #11716699 | C2 | semidirect |
| 4. C5×#3964 | C2 | semidirect |
| 5. #11716604 | C2 | semidirect |
| 6. #11716603 | C2 | semidirect |
| 7. Dic5×#168 | C2 | semidirect |
| 47. #3964 | D5 | semidirect |
| 141. C52 | #486 | semidirect |
| 217. C5 | #65049 | semidirect |
| 218. C5 | #65359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4086 | 2 |
| #11717036 | 2 |
| #11716699 | 2 |
| C5×#3964 | 2 |
| #11716604 | 2 |
| #11716603 | 2 |
| Dic5×#168 | 2 |
| #65359 | 5 |
| #65049 | 5 |