Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
150 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 53 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. #11716431 | C2 | semidirect |
| 3. C25×#97 | C2 | semidirect |
| 5. #11716365 | C2 | semidirect |
| 68. #97 | D25 | semidirect |
| 69. C25 | #489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11716437 | 2 |
| #11716431 | 2 |
| C25×#97 | 2 |
| #11716369 | 2 |
| #11716365 | 2 |
| #65003 | 5 |