Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
236 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 70 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. C8×#1039 | C2 | semidirect |
| 4. C5×#3946 | C2 | semidirect |
| 5. #11716612 | C2 | semidirect |
| 7. #11716596 | C2 | semidirect |
| 44. #3946 | D5 | semidirect |
| 128. C52 | #433 | semidirect |
| 192. C5 | #65009 | semidirect |
| 193. C5 | #65129 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11716973 | 2 |
| C8×#1039 | 2 |
| C5×#3952 | 2 |
| C5×#3946 | 2 |
| #11716612 | 2 |
| #11716597 | 2 |
| #11716596 | 2 |
| #65129 | 5 |
| #65009 | 5 |