Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
262 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
| 5. C52×#103 | C2 | semidirect |
| 6. C5×#3948 | C2 | semidirect |
| 7. C5×#3940 | C2 | semidirect |
| 22. #65105 | C5 | direct (N × H) |
| 43. C2×#689 | C2×C5 | semidirect |
| 49. C5×#103 | D5 | semidirect |
| 50. C5×#103 | C2×C5 | semidirect |
| 51. #3948 | C2×C5 | semidirect |
| 52. #3940 | C2×C5 | semidirect |
| 140. #103 | C5×D5 | semidirect |
| 141. C52 | #470 | semidirect |
| 209. C5 | #65105 | direct (N × H) |
| 210. C5 | C5×#470 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4092 | 2 |
| C2×C5×#689 | 2 |
| C2×C5×#676 | 2 |
| C5×#4043 | 2 |
| C52×#103 | 2 |
| C5×#3948 | 2 |
| C5×#3940 | 2 |
| C5×#470 | 5 |
| #65105 | 5 |