Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
237 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 237 conjugacy classes of subgroups — too many to draw. Only its 63 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. C22×Dic50 | C2 | semidirect |
| 3. C2×#87721 | C2 | semidirect |
| 4. C22⋊#6014 | C2 | semidirect |
| 5. #11716357 | C2 | semidirect |
| 30. Dic50 | D4 | semidirect |
| 42. C22×C25 | SD16 | semidirect |
| 84. C25 | #448 | semidirect |
| 132. C22 | #87721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic50 | 2 |
| C25×#121 | 2 |
| C2×#87721 | 2 |
| C22⋊#6014 | 2 |
| #11716357 | 2 |
| #65329 | 5 |