Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
362 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 64 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. #11717215 | C2 | semidirect |
| 2. #11717034 | C2 | semidirect |
| 3. C2×#87771 | C2 | semidirect |
| 4. C2×#87767 | C2 | semidirect |
| 5. C5×#3941 | C2 | semidirect |
| 6. C5×#3939 | C2 | semidirect |
| 7. #11716605 | C2 | semidirect |
| 39. C5×#168 | D4 | semidirect |
| 53. #3941 | D5 | semidirect |
| 54. #3939 | D5 | semidirect |
| 61. C2×C5⋊D5 | D8 | semidirect |
| 151. #168 | D20 | semidirect |
| 159. C52 | #466 | semidirect |
| 249. C5 | #65064 | semidirect |
| 250. C5 | #65172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717215 | 2 |
| #11717034 | 2 |
| C2×#87771 | 2 |
| C2×#87767 | 2 |
| C5×#3941 | 2 |
| C5×#3939 | 2 |
| #11716605 | 2 |
| #65172 | 5 |
| #65064 | 5 |