Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
426 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 7. #11716891 | C4 | semidirect |
| 12. C5×#3944 | C4 | semidirect |
| 63. #3944 | AGL(1,𝔽5) | semidirect |
| 151. C52 | #1377 | semidirect |
| 208. C5 | #10598671 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13104853 | 2 |
| C2×#11716860 | 2 |
| #13100806 | 2 |
| #10598671 | 5 |