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. #11716895 | C4 | semidirect |
| 13. #11716763 | C4 | semidirect |
| 14. #11716761 | C4 | semidirect |
| 15. C4×C5×#168 | C4 | semidirect |
| 16. #11716594 | C4 | semidirect |
| 67. C4×#168 | AGL(1,𝔽5) | semidirect |
| 147. C52 | #1726 | semidirect |
| 201. C5 | #10603838 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13104814 | 2 |
| #13104698 | 2 |
| C2×#11716763 | 2 |
| C2×#11716761 | 2 |
| C4×#87767 | 2 |
| #10603838 | 5 |