Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
213 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 213 conjugacy classes of subgroups — too many to draw. Only its 79 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. #11716410 | C2 | semidirect |
| 5. C8×#1035 | C2 | semidirect |
| 8. #87739 | C4 | semidirect |
| 12. #87735 | C4 | semidirect |
| 14. M16×C25 | C4 | semidirect |
| 15. #87716 | C4 | semidirect |
| 16. #87712 | C4 | semidirect |
| 29. #6016 | C2×C4 | semidirect |
| 30. C8×C25 | C2×C4 | semidirect |
| 31. #6014 | C2×C4 | semidirect |
| 42. #1035 | M16 | direct (N × H) |
| 82. C25 | C4×M16 | semidirect |
| 99. M16 | #1035 | direct (N × H) |
| 121. C8 | C2×#1035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#1035 | 2 |
| D25⋊M16 | 2 |
| M16×D25 | 2 |
| #11716410 | 2 |
| C8×#1035 | 2 |
| M16×AGL(1,𝔽5) | 5 |