Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
834 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 834 conjugacy classes of subgroups — too many to draw. Only its 187 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 |
|---|---|---|
| 11. C4×#6034 | C4 | semidirect |
| 13. #11716763 | C4 | semidirect |
| 14. #11716761 | C4 | semidirect |
| 15. C5×#3935 | C4 | semidirect |
| 16. #11716596 | C4 | semidirect |
| 66. #3935 | AGL(1,𝔽5) | semidirect |
| 144. C52 | #1726 | semidirect |
| 198. C5 | #10603877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#87862 | 2 |
| #13104698 | 2 |
| C2×#11716763 | 2 |
| C2×#11716761 | 2 |
| #13100501 | 2 |
| #10603877 | 5 |