Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
392 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 2. #11717451 | C2 | semidirect |
| 3. C2×#87855 | C2 | semidirect |
| 4. #11716768 | C2 | semidirect |
| 5. #11716766 | C2 | semidirect |
| 7. C5×#709 | C4 | semidirect |
| 14. #87871 | C4 | semidirect |
| 67. #709 | AGL(1,𝔽5) | semidirect |
| 124. C52 | #416 | semidirect |
| 192. C5 | #65794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717471 | 2 |
| #11717451 | 2 |
| C2×#87855 | 2 |
| #11716768 | 2 |
| #11716766 | 2 |
| #65794 | 5 |