Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
242 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 94 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. C5×#3947 | C2 | semidirect |
| 5. C5×#3946 | C2 | semidirect |
| 6. C5×#3946 | C2 | semidirect |
| 7. C5×C8×Dic5 | C2 | semidirect |
| 20. #65009 | C5 | direct (N × H) |
| 45. #3947 | C2×C5 | semidirect |
| 46. #3946 | C2×C5 | semidirect |
| 47. #3946 | C2×C5 | semidirect |
| 48. C8×Dic5 | C2×C5 | semidirect |
| 130. C52 | #433 | semidirect |
| 197. C5 | #65009 | direct (N × H) |
| 198. C5 | C5×#433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4072 | 2 |
| C52×C22⋊C8 | 2 |
| C5×C22⋊#168 | 2 |
| C5×#3947 | 2 |
| C5×#3946 | 2 |
| C5×C8×Dic5 | 2 |
| C5×#433 | 5 |
| #65009 | 5 |