Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
300 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 300 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. C2×C5×#689 | C2 | semidirect |
| 4. C4×C5×Dic10 | C2 | semidirect |
| 5. C5×#3967 | C2 | semidirect |
| 7. C5×C4⋊#168 | C2 | semidirect |
| 22. #65343 | C5 | direct (N × H) |
| 44. C2×#689 | C2×C5 | semidirect |
| 46. C4×Dic10 | C2×C5 | semidirect |
| 50. #3967 | C2×C5 | semidirect |
| 52. C4⋊#168 | C2×C5 | semidirect |
| 146. C52 | #464 | semidirect |
| 219. C5 | #65343 | direct (N × H) |
| 220. C5 | C5×#464 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#124 | 2 |
| C2×C5×#689 | 2 |
| C2×C5×#687 | 2 |
| C4×C5×Dic10 | 2 |
| C5×#3967 | 2 |
| C5×#3964 | 2 |
| C5×C4⋊#168 | 2 |
| C5×#464 | 5 |
| #65343 | 5 |