Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
288 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 288 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 |
|---|---|---|
| 1. #11717246 | C2 | semidirect |
| 3. C5×C22⋊#168 | C2 | semidirect |
| 4. #11716616 | C2 | semidirect |
| 5. #11716614 | C2 | semidirect |
| 6. #11716604 | C2 | semidirect |
| 7. #11716604 | C2 | semidirect |
| 43. C22⋊#168 | D5 | semidirect |
| 138. C52 | #482 | semidirect |
| 214. C5 | #65026 | semidirect |
| 215. C5 | #65324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717246 | 2 |
| C5×#4076 | 2 |
| C5×C22⋊#168 | 2 |
| #11716616 | 2 |
| #11716614 | 2 |
| #11716604 | 2 |
| #65324 | 5 |
| #65026 | 5 |