Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
544 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
|---|---|---|
| 8. #11716863 | C4 | semidirect |
| 11. C52×M32 | C4 | semidirect |
| 12. #11716679 | C4 | semidirect |
| 55. C5×M32 | AGL(1,𝔽5) | semidirect |
| 112. M32 | #1043 | semidirect |
| 118. C52 | #1387 | semidirect |
| 163. C5 | #10598674 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13104736 | 2 |
| C2×#11716862 | 2 |
| M32×C5⋊D5 | 2 |
| #10598674 | 5 |