Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
234 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 1. #11716988 | C2 | semidirect |
| 3. #11716683 | C2 | semidirect |
| 5. C5×C8×Dic5 | C2 | semidirect |
| 6. #11716608 | C2 | semidirect |
| 47. C8×Dic5 | D5 | semidirect |
| 129. C52 | #488 | semidirect |
| 193. C5 | #64986 | semidirect |
| 194. C5 | #65057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11716988 | 2 |
| #11716979 | 2 |
| #11716683 | 2 |
| C5×#3953 | 2 |
| C5×C8×Dic5 | 2 |
| #11716608 | 2 |
| #11716604 | 2 |
| #65057 | 5 |
| #64986 | 5 |