Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
159 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 159 conjugacy classes of subgroups — too many to draw. Only its 61 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. C25×#131 | C2 | semidirect |
| 3. #11716464 | C2 | semidirect |
| 4. #11716385 | C2 | semidirect |
| 5. #11716373 | C2 | semidirect |
| 6. #11716370 | C2 | semidirect |
| 7. C8×Dic25 | C2 | semidirect |
| 14. #87724 | C4 | semidirect |
| 15. #87723 | C4 | semidirect |
| 16. #87722 | C4 | semidirect |
| 17. #87721 | C4 | semidirect |
| 93. #131 | D25 | semidirect |
| 98. C25 | #443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#131 | 2 |
| #11716513 | 2 |
| #11716464 | 2 |
| #11716385 | 2 |
| #11716373 | 2 |
| #11716370 | 2 |
| C8×Dic25 | 2 |
| #65433 | 5 |