Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
333 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 333 conjugacy classes of subgroups — too many to draw. Only its 133 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. Q8×Dic25 | C2 | semidirect |
| 3. #11716506 | C2 | semidirect |
| 6. #11716451 | C2 | semidirect |
| 7. #11716450 | C2 | semidirect |
| 8. #11716449 | C2 | semidirect |
| 9. #11716449 | C2 | semidirect |
| 44. C2×Dic25 | Q8 | semidirect |
| 134. C25 | #533 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C22⋊Q8 | 2 |
| Q8×Dic25 | 2 |
| #11716506 | 2 |
| #11716486 | 2 |
| C2×C4×Dic25 | 2 |
| #11716451 | 2 |
| #11716450 | 2 |
| #11716449 | 2 |
| #11716440 | 2 |
| #11716439 | 2 |
| #65956 | 5 |