Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
540 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 102 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. M16×#1035 | C2 | semidirect |
| 5. #13097886 | C2 | semidirect |
| 15. #11716428 | C4 | semidirect |
| 18. C25×#100 | C4 | semidirect |
| 19. #11716380 | C4 | semidirect |
| 20. #11716372 | C4 | semidirect |
| 36. #87739 | C2×C4 | semidirect |
| 42. M16×C25 | C2×C4 | semidirect |
| 43. #87716 | C2×C4 | semidirect |
| 108. #1035 | #100 | direct (N × H) |
| 185. #100 | #1035 | direct (N × H) |
| 188. C25 | C4×#100 | semidirect |
| 224. M16 | C2×#1035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×#1035 | 2 |
| D25⋊#100 | 2 |
| M16×#1035 | 2 |
| #100×D25 | 2 |
| #13097886 | 2 |
| AGL(1,𝔽5)×#100 | 5 |