Finite Group DatabasebetaFinite Group DatabasebetaOrder 6400.
900 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 900 conjugacy classes of subgroups — too many to draw. Only its 123 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×#64683 | C4 | semidirect |
| 18. #13099305 | C4 | semidirect |
| 97. #64683 | AGL(1,𝔽5) | semidirect |
| 320. C52 | #13181 | semidirect |
| 411. C5 | #13027223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72220908 | 2 |
| #72220906 | 2 |
| #72220870 | 2 |
| #72220710 | 2 |
| #72220690 | 2 |
| #13027223 | 5 |