Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
513 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 513 conjugacy classes of subgroups — too many to draw. Only its 165 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. C23×Dic25 | C2 | semidirect |
| 3. C2×C22⋊C4×C25 | C2 | semidirect |
| 4. C2×#87720 | C2 | semidirect |
| 5. C2×C4⋊Dic25 | C2 | semidirect |
| 6. #11716448 | C2 | direct (N × H) |
| 15. C22×Dic25 | C22 | semidirect |
| 16. C22⋊C4×C25 | C22 | semidirect |
| 17. #87720 | C22 | semidirect |
| 18. C4⋊Dic25 | C22 | semidirect |
| 67. C2×C25 | #123 | semidirect |
| 91. C2×C22⋊C4 | D25 | semidirect |
| 92. C25 | C2×#123 | semidirect |
| 116. C22⋊C4 | C2×D25 | semidirect |
| 152. C2 | #11716448 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊D25 | 2 |
| C23×Dic25 | 2 |
| C2×C22⋊C4×C25 | 2 |
| C2×#87720 | 2 |
| C2×C4⋊Dic25 | 2 |
| #11716448 | 2 |
| C2×#4032 | 5 |