Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
306 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 306 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 |
|---|---|---|
| 2. C5×#4072 | C2 | semidirect |
| 3. C5×C22⋊#168 | C2 | semidirect |
| 4. #11716616 | C2 | semidirect |
| 5. #11716614 | C2 | semidirect |
| 6. #11716605 | C2 | semidirect |
| 7. #11716605 | C2 | semidirect |
| 39. #4072 | D5 | semidirect |
| 41. C22⋊#168 | D5 | semidirect |
| 141. C52 | #482 | semidirect |
| 220. C5 | #65026 | semidirect |
| 221. C5 | #65292 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717250 | 2 |
| C5×#4072 | 2 |
| C5×C22⋊#168 | 2 |
| #11716616 | 2 |
| #11716614 | 2 |
| #11716605 | 2 |
| #65292 | 5 |
| #65026 | 5 |