Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
213 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 213 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #11716364 | C2 | semidirect |
| 5. C8×Dic25 | C2 | semidirect |
| 8. M16×C25 | C4 | semidirect |
| 13. #87716 | C4 | semidirect |
| 24. C8×C25 | C2×C4 | semidirect |
| 25. #6014 | C2×C4 | semidirect |
| 38. Dic25 | M16 | direct (N × H) |
| 67. C25 | C4×M16 | semidirect |
| 79. M16 | Dic25 | direct (N × H) |
| 97. C8 | C2×Dic25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×C25 | 2 |
| C2×C4×Dic25 | 2 |
| C2×#87716 | 2 |
| #11716364 | 2 |
| C8×Dic25 | 2 |
| M16×Dic5 | 5 |