Finite Group DatabasebetaFinite Group DatabasebetaOrder 6400.
1752 conjugacy classes of subgroups; only the 322 normal subgroups are shown.
This group has 1752 conjugacy classes of subgroups — too many to draw. Only its 322 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 |
|---|---|---|
| 15. C52×#322 | C4 | semidirect |
| 16. #13099489 | C4 | semidirect |
| 17. #13099488 | C4 | semidirect |
| 75. C5×#322 | AGL(1,𝔽5) | semidirect |
| 96. C52×C8 | #106 | semidirect |
| 98. #6029 | #106 | semidirect |
| 169. #322 | #1043 | semidirect |
| 192. C5×C8 | #3993 | semidirect |
| 214. C52 | #8819 | semidirect |
| 274. C8 | #11716861 | semidirect |
| 275. C5 | #13018810 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72223038 | 2 |
| C5⋊D5×#322 | 2 |
| #72220880 | 2 |
| #72220870 | 2 |
| #13018810 | 5 |