Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
299 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 299 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 3. #11717302 | C2 | semidirect |
| 4. #11717300 | C2 | semidirect |
| 10. #87849 | C4 | semidirect |
| 11. C5×#700 | C4 | semidirect |
| 14. #87828 | C4 | semidirect |
| 28. #6032 | C2×C4 | semidirect |
| 29. C5×#170 | C2×C4 | semidirect |
| 40. #1044 | M16 | semidirect |
| 42. #1043 | M16 | semidirect |
| 56. #700 | AGL(1,𝔽5) | semidirect |
| 84. #170 | C2×AGL(1,𝔽5) | semidirect |
| 91. C52 | C4×M16 | semidirect |
| 143. 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 |
|---|---|
| C4×D5⋊AGL(1,𝔽5) | 2 |
| #11717331 | 2 |
| #11717302 | 2 |
| #11717300 | 2 |
| M16×AGL(1,𝔽5) | 5 |