Finite Group DatabasebetaFinite Group DatabasebetaOrder 6400.
756 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 103 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. #13100331 | C4 | semidirect |
| 12. C5×#64683 | C4 | semidirect |
| 75. #64683 | AGL(1,𝔽5) | semidirect |
| 262. C52 | #7268 | semidirect |
| 337. C5 | #13013896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72220909 | 2 |
| #72220908 | 2 |
| #72220880 | 2 |
| #13013896 | 5 |