Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
286 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 286 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×#4034 | C2 | semidirect |
| 3. C52×#102 | C2 | semidirect |
| 4. C5×#3964 | C2 | semidirect |
| 5. C5×#3953 | C2 | semidirect |
| 6. C5×C8×Dic5 | C2 | semidirect |
| 7. C5×#3941 | C2 | semidirect |
| 20. #65049 | C5 | direct (N × H) |
| 40. #4034 | C2×C5 | semidirect |
| 45. C5×#102 | D5 | semidirect |
| 46. C5×#102 | C2×C5 | semidirect |
| 48. #3964 | C2×C5 | semidirect |
| 49. #3953 | C2×C5 | semidirect |
| 50. C8×Dic5 | C2×C5 | semidirect |
| 51. #3941 | C2×C5 | semidirect |
| 139. #102 | C5×D5 | semidirect |
| 141. C52 | #486 | semidirect |
| 217. C5 | #65049 | direct (N × H) |
| 218. C5 | C5×#486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4086 | 2 |
| C5×#4034 | 2 |
| C52×#102 | 2 |
| C5×#3964 | 2 |
| C5×#3953 | 2 |
| C5×C8×Dic5 | 2 |
| C5×#3941 | 2 |
| C5×#486 | 5 |
| #65049 | 5 |