Finite Group DatabasebetaFinite Group DatabasebetaOrder 6400.
828 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 10. #13100361 | C4 | semidirect |
| 13. C52×C82 | C4 | semidirect |
| 15. C8×#6029 | C4 | semidirect |
| 24. #11716889 | C8 | semidirect |
| 26. #11716887 | C8 | semidirect |
| 82. C5×C82 | AGL(1,𝔽5) | semidirect |
| 215. C82 | #1044 | semidirect |
| 284. C52 | #7179 | semidirect |
| 364. C5 | #13013598 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72220909 | 2 |
| #72220906 | 2 |
| C82×C5⋊D5 | 2 |
| #13013598 | 5 |