Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
352 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #11716764 | C2 | semidirect |
| 5. #11716762 | C2 | semidirect |
| 11. #87860 | C4 | semidirect |
| 12. #87856 | C4 | semidirect |
| 14. C5×#681 | C4 | semidirect |
| 15. #87769 | C4 | semidirect |
| 28. #6033 | C2×C4 | semidirect |
| 29. C5×#168 | C2×C4 | semidirect |
| 41. #1044 | M16 | semidirect |
| 59. #681 | AGL(1,𝔽5) | semidirect |
| 87. #168 | C2×AGL(1,𝔽5) | semidirect |
| 93. C52 | C4×M16 | semidirect |
| 144. C5 | M16×AGL(1,𝔽5) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1044 | 2 |
| #11717435 | 2 |
| #11716936 | 2 |
| #11716764 | 2 |
| #11716762 | 2 |
| M16×AGL(1,𝔽5) | 5 |