Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
356 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 86 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×D8 | C2 | semidirect |
| 2. C5×#4086 | C2 | semidirect |
| 3. C5×D4×Dic5 | C2 | semidirect |
| 4. C2×C5×#686 | C2 | semidirect |
| 5. C5×#3964 | C2 | semidirect |
| 6. C5×#3953 | C2 | semidirect |
| 7. C5×#3946 | C2 | semidirect |
| 22. #65439 | C5 | direct (N × H) |
| 29. C52×D4 | D4 | semidirect |
| 43. C2×C5×D8 | D5 | semidirect |
| 44. C2×C5×D8 | C2×C5 | semidirect |
| 47. #4086 | C2×C5 | semidirect |
| 48. D4×Dic5 | C2×C5 | semidirect |
| 49. C2×#686 | C2×C5 | semidirect |
| 53. #3964 | C2×C5 | semidirect |
| 54. #3953 | C2×C5 | semidirect |
| 55. #3946 | C2×C5 | semidirect |
| 70. C5×Dic5 | D8 | semidirect |
| 130. C5×D4 | C22⋊D5 | semidirect |
| 131. C5×D4 | C5×D4 | semidirect |
| 153. C2×D8 | C5×D5 | semidirect |
| 159. C52 | #459 | semidirect |
| 198. Dic5 | C5×D8 | semidirect |
| 239. D4 | C5×C22⋊D5 | semidirect |
| 248. C5 | #65439 | direct (N × H) |
| 249. C5 | C5×#459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×D8 | 2 |
| C5×#4086 | 2 |
| C5×D4×Dic5 | 2 |
| C2×C5×#686 | 2 |
| C5×#3964 | 2 |
| C5×#3953 | 2 |
| C5×#3946 | 2 |
| C5×#459 | 5 |
| #65439 | 5 |