Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
392 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 78 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. #11717212 | C2 | semidirect |
| 3. C2×#87767 | C2 | semidirect |
| 4. C5×#3942 | C2 | semidirect |
| 5. C5×#3941 | C2 | semidirect |
| 6. #11716607 | C2 | semidirect |
| 7. #11716604 | C2 | semidirect |
| 14. #87871 | C4 | semidirect |
| 54. #3942 | D5 | semidirect |
| 55. #3941 | D5 | semidirect |
| 156. C52 | #416 | semidirect |
| 238. C5 | #65061 | semidirect |
| 239. C5 | #65093 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87871 | 2 |
| #11717212 | 2 |
| C2×#87767 | 2 |
| C5×#3942 | 2 |
| C5×#3941 | 2 |
| #11716607 | 2 |
| #11716604 | 2 |
| #65093 | 5 |
| #65061 | 5 |