Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
352 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 88 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. #11716885 | C2 | semidirect |
| 5. C8×#1044 | C2 | semidirect |
| 8. #87867 | C4 | semidirect |
| 12. #87863 | C4 | semidirect |
| 14. C52×M16 | C4 | semidirect |
| 15. #87804 | C4 | semidirect |
| 16. #87799 | C4 | semidirect |
| 29. #6034 | C2×C4 | semidirect |
| 30. C52×C8 | C2×C4 | semidirect |
| 31. #6029 | C2×C4 | semidirect |
| 43. #1044 | M16 | direct (N × H) |
| 58. C5×M16 | AGL(1,𝔽5) | semidirect |
| 89. C5×C8 | C2×AGL(1,𝔽5) | semidirect |
| 97. C52 | C4×M16 | semidirect |
| 122. M16 | #1044 | direct (N × H) |
| 148. C8 | C2×#1044 | semidirect |
| 150. 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 |
| #11717448 | 2 |
| M16×C5⋊D5 | 2 |
| #11716885 | 2 |
| C8×#1044 | 2 |
| M16×AGL(1,𝔽5) | 5 |