Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
327 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 327 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 2. C2×C5×#704 | C2 | semidirect |
| 3. C5×#4013 | C2 | semidirect |
| 4. C5×#4005 | C2 | semidirect |
| 17. #65777 | C5 | direct (N × H) |
| 39. C2×#704 | C2×C5 | semidirect |
| 41. #4013 | C2×C5 | semidirect |
| 42. #4005 | C2×C5 | semidirect |
| 132. C52 | #413 | semidirect |
| 208. C5 | C5×#413 | semidirect |
| 209. C5 | #65777 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#711 | 2 |
| C2×C5×#704 | 2 |
| C5×#4013 | 2 |
| C5×#4005 | 2 |
| #65777 | 5 |
| C5×#413 | 5 |