Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
186 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 186 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 |
|---|---|---|
| 1. C2×SD16×C25 | C2 | semidirect |
| 2. #11716508 | C2 | semidirect |
| 4. C2×C8×D25 | C2 | semidirect |
| 5. #11716384 | C2 | semidirect |
| 6. #11716381 | C2 | semidirect |
| 7. #11716366 | C2 | semidirect |
| 36. C8×C25 | D4 | semidirect |
| 51. C2×D25 | SD16 | semidirect |
| 93. C2×SD16 | D25 | semidirect |
| 100. C25 | #465 | semidirect |
| 147. C8 | C22⋊D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD16×C25 | 2 |
| #11716508 | 2 |
| #11716500 | 2 |
| C2×C8×D25 | 2 |
| #11716384 | 2 |
| #11716381 | 2 |
| #11716366 | 2 |
| #65460 | 5 |