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. #11716563 | C2 | semidirect |
| 2. C25×#127 | C2 | semidirect |
| 3. #11716495 | C2 | semidirect |
| 4. #11716380 | C2 | semidirect |
| 5. #11716353 | C2 | semidirect |
| 8. C2×D4×C25 | C22 | semidirect |
| 13. C42×C25 | C22 | semidirect |
| 16. #87716 | C22 | semidirect |
| 29. D100 | D4 | semidirect |
| 31. Dic50 | D4 | semidirect |
| 82. #127 | D25 | semidirect |
| 85. C25 | #453 | semidirect |
| 102. C2×D4 | C2×D25 | semidirect |
| 106. C42 | C2×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11716563 | 2 |
| C25×#127 | 2 |
| #11716495 | 2 |
| #11716380 | 2 |
| #11716353 | 2 |
| #65366 | 5 |