Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
626 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 118 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. #11716889 | C4 | semidirect |
| 12. #11716888 | C4 | semidirect |
| 13. #11716887 | C4 | semidirect |
| 14. #11716886 | C4 | semidirect |
| 17. C4×C52×C8 | C4 | semidirect |
| 18. C8×#1039 | C4 | semidirect |
| 19. C8×#1039 | C4 | semidirect |
| 20. C4×#6029 | C4 | semidirect |
| 86. C4×C5×C8 | AGL(1,𝔽5) | semidirect |
| 206. C4×C8 | #1044 | semidirect |
| 207. C52 | #1772 | semidirect |
| 281. C5 | #10603851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13104862 | 2 |
| #13104859 | 2 |
| #13104856 | 2 |
| C4×C8×C5⋊D5 | 2 |
| #13100332 | 2 |
| #10603851 | 5 |