Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
480 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 104 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. C5×#4072 | C2 | semidirect |
| 3. C22×C5×#168 | C2 | semidirect |
| 4. #11716608 | C2 | semidirect |
| 5. #11716605 | C2 | semidirect |
| 9. #87900 | C4 | semidirect |
| 40. #4072 | D5 | semidirect |
| 41. C22×#168 | D5 | semidirect |
| 140. C52 | #416 | semidirect |
| 210. C5 | #65291 | semidirect |
| 211. C5 | #65402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| C5×#4072 | 2 |
| C22×C5×#168 | 2 |
| #11716608 | 2 |
| #11716605 | 2 |
| #65402 | 5 |
| #65291 | 5 |