Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
296 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 62 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×#4041 | C2 | semidirect |
| 2. #11717026 | C2 | semidirect |
| 3. C2×#87770 | C2 | semidirect |
| 4. C2×#87768 | C2 | semidirect |
| 5. #11716675 | C2 | semidirect |
| 6. C5×#3941 | C2 | semidirect |
| 7. #11716604 | C2 | semidirect |
| 38. #6029 | D4 | semidirect |
| 47. #4041 | D5 | semidirect |
| 51. #3941 | D5 | semidirect |
| 151. C52 | #469 | semidirect |
| 233. C5 | #65071 | semidirect |
| 234. C5 | #65328 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4041 | 2 |
| #11717026 | 2 |
| C2×#87770 | 2 |
| C2×#87768 | 2 |
| #11716675 | 2 |
| C5×#3941 | 2 |
| #11716604 | 2 |
| #65328 | 5 |
| #65071 | 5 |