Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
242 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 4. #11716617 | C2 | semidirect |
| 5. #11716615 | C2 | semidirect |
| 6. #11716606 | C2 | semidirect |
| 7. #11716606 | C2 | semidirect |
| 130. C52 | #485 | semidirect |
| 197. C5 | #65285 | semidirect |
| 198. C5 | #65334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4072 | 2 |
| C5×#4070 | 2 |
| C22⋊#6029 | 2 |
| #11716617 | 2 |
| #11716615 | 2 |
| #11716606 | 2 |
| #65334 | 5 |
| #65285 | 5 |