Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
336 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 4. C5×#3935 | C2 | semidirect |
| 5. C4×C5×#168 | C2 | semidirect |
| 6. #11716596 | C2 | semidirect |
| 7. #11716594 | C2 | semidirect |
| 17. #87769 | C4 | semidirect |
| 18. #87767 | C4 | semidirect |
| 45. #3935 | D5 | semidirect |
| 46. C4×#168 | D5 | semidirect |
| 122. C52 | #405 | semidirect |
| 179. C5 | #64978 | semidirect |
| 180. C5 | #64997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717192 | 2 |
| C2×#87769 | 2 |
| C2×#87767 | 2 |
| C5×#3935 | 2 |
| C4×C5×#168 | 2 |
| #11716596 | 2 |
| #11716594 | 2 |
| #64997 | 5 |
| #64978 | 5 |