Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
562 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 97 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. #11716897 | C4 | semidirect |
| 12. C5×C4⋊#168 | C4 | semidirect |
| 74. C4⋊#168 | AGL(1,𝔽5) | semidirect |
| 190. C52 | #1296 | semidirect |
| 283. C5 | #10598586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13104816 | 2 |
| #13104700 | 2 |
| #13100510 | 2 |
| #10598586 | 5 |