Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
225 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 225 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 18. #87812 | C4 | semidirect |
| 19. C5×#689 | C4 | semidirect |
| 20. #87776 | C4 | semidirect |
| 21. #87775 | C4 | semidirect |
| 87. #689 | AGL(1,𝔽5) | semidirect |
| 143. C52 | #441 | semidirect |
| 208. C5 | #65078 | semidirect |
| 209. C5 | #65739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#1042 | 2 |
| #1042⋊Q8 | 2 |
| D5×#689 | 2 |
| C5×#4009 | 2 |
| #11716742 | 2 |
| #11716737 | 2 |
| #11716733 | 2 |
| #65739 | 5 |
| #65078 | 5 |