Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
243 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 243 conjugacy classes of subgroups — too many to draw. Only its 61 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×D8×C25 | C2 | semidirect |
| 2. #11716502 | C2 | semidirect |
| 3. C2×#87722 | C2 | semidirect |
| 4. C2×D200 | C2 | semidirect |
| 5. C8×Dic25 | C2 | semidirect |
| 25. C8×C25 | D4 | semidirect |
| 26. #6014 | D4 | semidirect |
| 39. Dic25 | D8 | semidirect |
| 67. C2×D8 | D25 | semidirect |
| 70. C25 | #493 | semidirect |
| 102. C8 | C22⋊D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×C25 | 2 |
| #11716502 | 2 |
| C2×#87722 | 2 |
| C2×D200 | 2 |
| C8×Dic25 | 2 |
| #65440 | 5 |