Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
228 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 51 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. C25×#137 | C2 | semidirect |
| 3. #11716509 | C2 | semidirect |
| 4. #11716505 | C2 | semidirect |
| 5. #11716385 | C2 | semidirect |
| 6. #11716373 | C2 | semidirect |
| 7. #11716372 | C2 | semidirect |
| 9. C2×Q8×C25 | C22 | semidirect |
| 19. M16×C25 | C22 | semidirect |
| 23. C4×Dic25 | C22 | semidirect |
| 24. #87716 | C22 | semidirect |
| 114. #137 | D25 | semidirect |
| 119. C25 | #455 | semidirect |
| 136. C2×Q8 | C2×D25 | semidirect |
| 146. M16 | C2×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11716568 | 2 |
| C25×#137 | 2 |
| #11716509 | 2 |
| #11716505 | 2 |
| #11716385 | 2 |
| #11716373 | 2 |
| #11716372 | 2 |
| #65491 | 5 |