Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
159 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 159 conjugacy classes of subgroups — too many to draw. Only its 57 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. #11716510 | C2 | semidirect |
| 3. #11716469 | C2 | semidirect |
| 4. C25×#104 | C2 | semidirect |
| 5. #11716370 | C2 | semidirect |
| 6. #11716353 | C2 | semidirect |
| 7. C4×#6014 | C2 | semidirect |
| 12. #87724 | C4 | semidirect |
| 13. #87723 | C4 | semidirect |
| 14. #87722 | C4 | semidirect |
| 15. #87721 | C4 | semidirect |
| 96. #104 | 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 |
|---|---|
| #11716513 | 2 |
| #11716510 | 2 |
| #11716469 | 2 |
| C25×#104 | 2 |
| #11716370 | 2 |
| #11716353 | 2 |
| C4×#6014 | 2 |
| #65113 | 5 |