Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
316 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 86 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×#4090 | C2 | semidirect |
| 3. C2×C5×#689 | C2 | semidirect |
| 6. C2×C5×Dic20 | C2 | semidirect |
| 7. C5×#3947 | C2 | semidirect |
| 22. #65456 | C5 | direct (N × H) |
| 47. #4090 | C2×C5 | semidirect |
| 48. C2×#689 | C2×C5 | semidirect |
| 51. C2×Dic20 | C2×C5 | semidirect |
| 53. #3947 | C2×C5 | semidirect |
| 144. C52 | #497 | semidirect |
| 208. C5 | #65456 | direct (N × H) |
| 209. C5 | C5×#497 | 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×#4090 | 2 |
| C2×C5×#689 | 2 |
| C5×#4082 | 2 |
| C2×C5×#687 | 2 |
| C2×C5×Dic20 | 2 |
| C5×#3947 | 2 |
| C5×#497 | 5 |
| #65456 | 5 |