Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
260 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 74 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 |
|---|---|---|
| 4. C2×C5×#689 | C2 | semidirect |
| 5. C5×#3968 | C2 | semidirect |
| 6. C5×#3956 | C2 | semidirect |
| 7. C5×#3954 | C2 | semidirect |
| 24. #65493 | C5 | direct (N × H) |
| 49. C2×#689 | C2×C5 | semidirect |
| 53. #3968 | C2×C5 | semidirect |
| 54. #3956 | C2×C5 | semidirect |
| 55. #3954 | C2×C5 | semidirect |
| 150. C52 | #473 | semidirect |
| 212. C5 | #65493 | direct (N × H) |
| 213. C5 | C5×#473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#137 | 2 |
| C5×#4097 | 2 |
| C5×#4094 | 2 |
| C2×C5×#689 | 2 |
| C5×#3968 | 2 |
| C5×#3956 | 2 |
| C5×#3954 | 2 |
| C5×#473 | 5 |
| #65493 | 5 |