Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
242 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 242 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 |
|---|---|---|
| 2. #11717036 | C2 | semidirect |
| 3. #11716702 | C2 | semidirect |
| 4. C5×#3967 | C2 | semidirect |
| 7. #11716595 | C2 | semidirect |
| 43. #3967 | D5 | semidirect |
| 132. C52 | #489 | semidirect |
| 197. C5 | #65084 | semidirect |
| 198. C5 | #65344 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4093 | 2 |
| #11717036 | 2 |
| #11716702 | 2 |
| C5×#3967 | 2 |
| #11716604 | 2 |
| #11716603 | 2 |
| #11716595 | 2 |
| #65344 | 5 |
| #65084 | 5 |