Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
992 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 202 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 |
|---|---|---|
| 9. C4×C52×C8 | C4 | semidirect |
| 10. C8×#1039 | C4 | semidirect |
| 11. C4×#6029 | C4 | semidirect |
| 51. C4×C5×C8 | AGL(1,𝔽5) | semidirect |
| 112. C4×C8 | #1043 | semidirect |
| 113. C52 | #1834 | semidirect |
| 161. C5 | #10603845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13104700 | 2 |
| C4×C8×C5⋊D5 | 2 |
| #13100271 | 2 |
| #10603845 | 5 |