Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
456 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 108 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. C2×#87781 | C2 | semidirect |
| 5. C2×Dic52 | C2 | semidirect |
| 6. #11716698 | C2 | semidirect |
| 7. C5×#3963 | C2 | semidirect |
| 18. #87778 | C4 | semidirect |
| 62. #3963 | D5 | semidirect |
| 188. C52 | #388 | semidirect |
| 301. C5 | #64958 | semidirect |
| 302. C5 | #65234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#685 | 2 |
| C2×#87781 | 2 |
| C2×#87778 | 2 |
| C2×Dic52 | 2 |
| #11716698 | 2 |
| C5×#3963 | 2 |
| #65234 | 5 |
| #64958 | 5 |