Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
522 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 17. C5×#3951 | C4 | semidirect |
| 18. #11716619 | C4 | semidirect |
| 78. #3951 | AGL(1,𝔽5) | semidirect |
| 172. C52 | #1951 | semidirect |
| 236. C5 | #10604087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13104856 | 2 |
| C2×#11716861 | 2 |
| #13103962 | 2 |
| #13101043 | 2 |
| #13099912 | 2 |
| #10604087 | 5 |