Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
256 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 70 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×#4050 | C2 | semidirect |
| 3. C5×#3959 | C2 | semidirect |
| 4. C5×#3958 | C2 | semidirect |
| 5. C5×#3944 | C2 | semidirect |
| 11. C5×Dic20 | C22 | semidirect |
| 12. C5×D40 | C22 | semidirect |
| 14. C5×#672 | C22 | semidirect |
| 16. #65436 | C5 | direct (N × H) |
| 29. C2×C5×D8 | D5 | semidirect |
| 30. C2×C5×D8 | C2×C5 | semidirect |
| 31. #4050 | C2×C5 | semidirect |
| 35. #3959 | C2×C5 | semidirect |
| 36. #3958 | C2×C5 | semidirect |
| 37. #3944 | C2×C5 | semidirect |
| 62. Dic20 | C22×C5 | semidirect |
| 63. D40 | C22×C5 | semidirect |
| 66. #672 | C22×C5 | semidirect |
| 99. C2×D8 | C5×D5 | semidirect |
| 103. C52 | #509 | semidirect |
| 154. C5 | #65436 | direct (N × H) |
| 155. C5 | C5×#509 | 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×#4050 | 2 |
| C5×#3959 | 2 |
| C5×#3958 | 2 |
| C5×#3944 | 2 |
| C5×#509 | 5 |
| #65436 | 5 |