Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
274 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 51 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. #11717441 | C2 | semidirect |
| 2. #11717358 | C2 | semidirect |
| 4. #11716903 | C2 | semidirect |
| 5. #11716773 | C2 | semidirect |
| 6. #11716769 | C2 | semidirect |
| 7. #11716762 | C2 | semidirect |
| 18. C5×#689 | C4 | semidirect |
| 19. C5×#688 | C4 | semidirect |
| 20. #87774 | C4 | semidirect |
| 21. #87771 | C4 | semidirect |
| 91. #689 | AGL(1,𝔽5) | semidirect |
| 93. #688 | AGL(1,𝔽5) | semidirect |
| 151. C52 | #443 | semidirect |
| 216. C5 | #65736 | semidirect |
| 217. C5 | #65740 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717441 | 2 |
| #11717358 | 2 |
| #11717068 | 2 |
| #11716903 | 2 |
| #11716773 | 2 |
| #11716769 | 2 |
| #11716762 | 2 |
| #65740 | 5 |
| #65736 | 5 |