Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
292 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 82 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. C5×Q8×Dic5 | C2 | semidirect |
| 3. C2×C5×#689 | C2 | semidirect |
| 6. C5×#3948 | C2 | semidirect |
| 7. C5×#3946 | C2 | semidirect |
| 22. #65455 | C5 | direct (N × H) |
| 44. Q8×Dic5 | C2×C5 | semidirect |
| 45. C2×#689 | C2×C5 | semidirect |
| 51. #3948 | C2×C5 | semidirect |
| 52. #3946 | C2×C5 | semidirect |
| 144. C52 | #464 | semidirect |
| 215. C5 | #65455 | direct (N × H) |
| 216. C5 | C5×#464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×SD16 | 2 |
| C5×Q8×Dic5 | 2 |
| C2×C5×#689 | 2 |
| C5×#4082 | 2 |
| C5×#3964 | 2 |
| C5×#3948 | 2 |
| C5×#3946 | 2 |
| C5×#464 | 5 |
| #65455 | 5 |