Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
290 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 53 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. #11717355 | C2 | semidirect |
| 5. #11716772 | C2 | semidirect |
| 6. #11716768 | C2 | semidirect |
| 7. #11716764 | C2 | semidirect |
| 18. C5×#687 | C4 | semidirect |
| 19. #87774 | C4 | semidirect |
| 32. C5×Dic10 | C2×C4 | semidirect |
| 36. C5×#168 | C2×C4 | semidirect |
| 72. #687 | AGL(1,𝔽5) | semidirect |
| 100. Dic10 | C2×AGL(1,𝔽5) | semidirect |
| 104. #168 | C2×AGL(1,𝔽5) | semidirect |
| 112. C52 | #440 | semidirect |
| 173. C5 | #65735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×#1044 | 2 |
| #11717355 | 2 |
| #11717048 | 2 |
| #11716875 | 2 |
| #11716772 | 2 |
| #11716768 | 2 |
| #11716764 | 2 |
| #65735 | 5 |