Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
206 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 56 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×#4050 | C2 | semidirect |
| 2. C2×C5×D40 | C2 | semidirect |
| 3. #11716679 | C2 | semidirect |
| 4. #11716588 | C2 | semidirect |
| 5. #11716586 | C2 | semidirect |
| 9. C5×Dic20 | C22 | semidirect |
| 12. C5×D40 | C22 | semidirect |
| 14. #87756 | C22 | semidirect |
| 29. #4050 | D5 | semidirect |
| 30. C2×D40 | D5 | semidirect |
| 57. Dic20 | C2×D5 | semidirect |
| 60. D40 | C2×D5 | semidirect |
| 98. C52 | #509 | semidirect |
| 146. C5 | #65436 | semidirect |
| 147. C5 | #65482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4050 | 2 |
| C2×C5×D40 | 2 |
| #11716679 | 2 |
| #11716588 | 2 |
| #11716586 | 2 |
| #65482 | 5 |
| #65436 | 5 |