Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
270 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 270 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 |
|---|---|---|
| 2. #11716988 | C2 | semidirect |
| 3. #11716699 | C2 | semidirect |
| 4. C5×#3964 | C2 | semidirect |
| 5. #11716604 | C2 | semidirect |
| 6. #11716603 | C2 | semidirect |
| 7. #11716595 | C2 | semidirect |
| 46. #3964 | D5 | semidirect |
| 138. C52 | #490 | semidirect |
| 213. C5 | #65053 | semidirect |
| 214. C5 | #65360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4086 | 2 |
| #11716988 | 2 |
| #11716699 | 2 |
| C5×#3964 | 2 |
| #11716604 | 2 |
| #11716603 | 2 |
| #11716595 | 2 |
| #65360 | 5 |
| #65053 | 5 |