Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
290 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 68 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. C5×#4092 | C2 | semidirect |
| 2. C2×C5×#688 | C2 | semidirect |
| 4. C2×D5×#168 | C2 | semidirect |
| 5. #11716702 | C2 | semidirect |
| 6. #11716614 | C2 | semidirect |
| 7. #11716603 | C2 | semidirect |
| 38. C5×#168 | D4 | semidirect |
| 41. #4092 | D5 | semidirect |
| 42. C2×#688 | D5 | semidirect |
| 60. C2×C5×D5 | SD16 | semidirect |
| 139. #168 | C22⋊D5 | semidirect |
| 147. C52 | #465 | semidirect |
| 162. C2×D5 | #688 | semidirect |
| 222. C5 | #65337 | semidirect |
| 223. C5 | #65460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4092 | 2 |
| C2×C5×#688 | 2 |
| #11717026 | 2 |
| C2×D5×#168 | 2 |
| #11716702 | 2 |
| #11716614 | 2 |
| #11716603 | 2 |
| #65460 | 5 |
| #65337 | 5 |