Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
376 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 63 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×#87856 | C2 | semidirect |
| 4. #11716769 | C2 | semidirect |
| 6. C5×#709 | C4 | semidirect |
| 9. #87877 | C4 | semidirect |
| 12. #87872 | C4 | semidirect |
| 16. C4×#1044 | C22 | semidirect |
| 19. #87856 | C22 | semidirect |
| 66. #709 | AGL(1,𝔽5) | semidirect |
| 122. C52 | #421 | semidirect |
| 190. C5 | #65795 | 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×#87856 | 2 |
| #11716769 | 2 |
| #65795 | 5 |