Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
252 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 252 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 |
|---|---|---|
| 1. #11716568 | C2 | semidirect |
| 2. C25×AGL(1,ℤ/8) | C2 | semidirect |
| 3. #11716502 | C2 | semidirect |
| 4. #11716495 | C2 | semidirect |
| 5. #11716385 | C2 | semidirect |
| 6. #11716373 | C2 | semidirect |
| 7. #11716372 | C2 | semidirect |
| 9. C2×D4×C25 | C22 | semidirect |
| 20. M16×C25 | C22 | semidirect |
| 23. C4×Dic25 | C22 | semidirect |
| 24. #87716 | C22 | semidirect |
| 29. Q8×C25 | D4 | semidirect |
| 33. D4×C25 | D4 | semidirect |
| 43. D100 | D4 | semidirect |
| 46. Dic50 | D4 | semidirect |
| 118. AGL(1,ℤ/8) | D25 | semidirect |
| 123. C25 | #453 | semidirect |
| 146. C2×D4 | C2×D25 | semidirect |
| 152. M16 | C2×D25 | semidirect |
| 164. Q8 | C22⋊D25 | semidirect |
| 175. D4 | C22⋊D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11716568 | 2 |
| C25×AGL(1,ℤ/8) | 2 |
| #11716502 | 2 |
| #11716495 | 2 |
| #11716385 | 2 |
| #11716373 | 2 |
| #11716372 | 2 |
| #65487 | 5 |