Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
336 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 336 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. C52×#124 | C2 | semidirect |
| 2. C2×C5×#689 | C2 | semidirect |
| 3. C2×C5×#688 | C2 | semidirect |
| 4. C2×C5×#687 | C2 | semidirect |
| 6. C5×#4021 | C2 | semidirect |
| 7. C4×C5×#168 | C2 | semidirect |
| 22. #65348 | C5 | direct (N × H) |
| 45. C5×#124 | D5 | semidirect |
| 46. C5×#124 | C2×C5 | semidirect |
| 47. C2×#689 | C2×C5 | semidirect |
| 48. C2×#688 | C2×C5 | semidirect |
| 49. C2×#687 | C2×C5 | semidirect |
| 51. #4021 | C2×C5 | semidirect |
| 53. C4×#168 | C2×C5 | semidirect |
| 144. #124 | C5×D5 | semidirect |
| 146. C52 | #495 | semidirect |
| 215. C5 | #65348 | direct (N × H) |
| 216. C5 | C5×#495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#124 | 2 |
| C2×C5×#689 | 2 |
| C2×C5×#688 | 2 |
| C2×C5×#687 | 2 |
| C2×C5×#686 | 2 |
| C5×#4021 | 2 |
| C4×C5×#168 | 2 |
| C5×#495 | 5 |
| #65348 | 5 |