Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
222 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 58 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×#4131 | C2 | semidirect |
| 2. #11717327 | C2 | semidirect |
| 4. #11716851 | C2 | semidirect |
| 5. #11716745 | C2 | semidirect |
| 6. #11716738 | C2 | semidirect |
| 7. #11716731 | C2 | semidirect |
| 18. #87810 | C4 | semidirect |
| 19. C5×#686 | C4 | semidirect |
| 20. #87776 | C4 | semidirect |
| 21. #87772 | C4 | semidirect |
| 42. #4131 | D5 | semidirect |
| 86. #686 | AGL(1,𝔽5) | semidirect |
| 141. C52 | #443 | semidirect |
| 203. C5 | #65433 | semidirect |
| 204. C5 | #65732 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4131 | 2 |
| #11717327 | 2 |
| #11717051 | 2 |
| #11716851 | 2 |
| #11716745 | 2 |
| #11716738 | 2 |
| #11716731 | 2 |
| #65732 | 5 |
| #65433 | 5 |