Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
240 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 51 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. C25×#123 | C2 | semidirect |
| 3. #11716491 | C2 | semidirect |
| 4. #11716382 | C2 | semidirect |
| 5. #11716354 | C2 | semidirect |
| 7. C22×C4×C25 | C22 | semidirect |
| 15. C22⋊C4×C25 | C22 | semidirect |
| 16. C22⋊Dic25 | C22 | semidirect |
| 95. #123 | D25 | semidirect |
| 98. C25 | #458 | semidirect |
| 118. C22×C4 | C2×D25 | semidirect |
| 124. C22⋊C4 | C2×D25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11716563 | 2 |
| C25×#123 | 2 |
| #11716491 | 2 |
| #11716382 | 2 |
| #11716354 | 2 |
| #65342 | 5 |