Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
231 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 231 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. #11716549 | C2 | semidirect |
| 3. C2×#87735 | C2 | semidirect |
| 4. #11716425 | C2 | semidirect |
| 5. #11716423 | C2 | semidirect |
| 6. #41×C25 | C4 | semidirect |
| 8. Q8×D25 | C4 | semidirect |
| 12. D4×D25 | C4 | semidirect |
| 14. #87744 | C4 | semidirect |
| 20. C4×#1035 | C22 | semidirect |
| 22. #87735 | C22 | semidirect |
| 122. C25 | #421 | semidirect |
| 142. #41 | #1035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D25 | 2 |
| #11716549 | 2 |
| C2×#87735 | 2 |
| #11716425 | 2 |
| #11716423 | 2 |
| #65795 | 5 |