Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
568 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 110 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×#3963 | C2 | semidirect |
| 5. #11716620 | C2 | semidirect |
| 13. C2×#6036 | C4 | semidirect |
| 41. #3963 | D5 | semidirect |
| 121. C52 | #381 | semidirect |
| 196. C5 | #64953 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6036 | 2 |
| C2×#87808 | 2 |
| C2×#87779 | 2 |
| C5×#3963 | 2 |
| #11716620 | 2 |
| #64953 | 5 |