Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
168 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 55 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. C2×#87723 | C2 | semidirect |
| 6. #11716365 | C2 | semidirect |
| 7. #11716363 | C2 | semidirect |
| 95. C25 | #464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD16×C25 | 2 |
| Q8×Dic25 | 2 |
| C2×#87723 | 2 |
| #11716498 | 2 |
| #11716381 | 2 |
| #11716365 | 2 |
| #11716363 | 2 |
| #65455 | 5 |