Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
316 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 316 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 |
|---|---|---|
| 1. C2×C52×SD16 | C2 | semidirect |
| 2. C5×#4093 | C2 | semidirect |
| 3. C5×D4×Dic5 | C2 | semidirect |
| 5. C5×#3967 | C2 | semidirect |
| 6. C5×#3953 | C2 | semidirect |
| 7. C5×#3946 | C2 | semidirect |
| 22. #65454 | C5 | direct (N × H) |
| 40. C2×C5×SD16 | D5 | semidirect |
| 41. C2×C5×SD16 | C2×C5 | semidirect |
| 45. #4093 | C2×C5 | semidirect |
| 46. D4×Dic5 | C2×C5 | semidirect |
| 51. #3967 | C2×C5 | semidirect |
| 52. #3953 | C2×C5 | semidirect |
| 53. #3946 | C2×C5 | semidirect |
| 143. C2×SD16 | C5×D5 | semidirect |
| 150. C52 | #463 | semidirect |
| 228. C5 | #65454 | direct (N × H) |
| 229. C5 | C5×#463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×SD16 | 2 |
| C5×#4093 | 2 |
| C5×D4×Dic5 | 2 |
| C2×C5×#686 | 2 |
| C5×#3967 | 2 |
| C5×#3953 | 2 |
| C5×#3946 | 2 |
| C5×#463 | 5 |
| #65454 | 5 |