Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
464 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 134 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×#681 | C2 | semidirect |
| 3. C5×#3968 | C2 | semidirect |
| 4. C5×#3965 | C2 | semidirect |
| 16. #65526 | C5 | direct (N × H) |
| 34. C2×#681 | C2×C5 | semidirect |
| 37. #3968 | C2×C5 | semidirect |
| 38. #3965 | C2×C5 | semidirect |
| 122. C52 | #413 | semidirect |
| 186. C5 | #65526 | direct (N × H) |
| 187. C5 | C5×#413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×#41 | 2 |
| C2×C5×#681 | 2 |
| C5×#3968 | 2 |
| C5×#3965 | 2 |
| C5×#413 | 5 |
| #65526 | 5 |