Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
234 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 3. #11716677 | C2 | semidirect |
| 4. C5×#3939 | C2 | semidirect |
| 5. #11716615 | C2 | semidirect |
| 6. #11716608 | C2 | semidirect |
| 48. #3939 | D5 | semidirect |
| 129. C52 | #485 | semidirect |
| 193. C5 | #65177 | semidirect |
| 194. C5 | #65285 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4038 | 2 |
| #11716975 | 2 |
| #11716677 | 2 |
| C5×#3939 | 2 |
| #11716615 | 2 |
| #11716608 | 2 |
| #11716597 | 2 |
| #65285 | 5 |
| #65177 | 5 |