Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
282 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 2. C2×#87721 | C2 | semidirect |
| 3. #11716486 | C2 | semidirect |
| 4. #11716381 | C2 | semidirect |
| 5. C22⋊#6014 | C2 | semidirect |
| 11. C2×Dic50 | C22 | semidirect |
| 14. C4⋊Dic25 | C22 | semidirect |
| 16. C2×#6014 | C22 | semidirect |
| 44. C22×C25 | SD16 | semidirect |
| 87. C25 | #450 | semidirect |
| 138. C22 | #87721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×C25 | 2 |
| C2×#87721 | 2 |
| #11716486 | 2 |
| #11716381 | 2 |
| C22⋊#6014 | 2 |
| #65507 | 5 |