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 |
|---|---|---|
| 2. C5×#4082 | C2 | semidirect |
| 3. C2×C5×#687 | C2 | semidirect |
| 4. C2×C5×Dic20 | C2 | semidirect |
| 5. C5×C8×Dic5 | C2 | semidirect |
| 16. #65444 | C5 | direct (N × H) |
| 33. #4082 | C2×C5 | semidirect |
| 34. C2×#687 | C2×C5 | semidirect |
| 35. C2×Dic20 | C2×C5 | semidirect |
| 37. C8×Dic5 | C2×C5 | semidirect |
| 100. C52 | #495 | semidirect |
| 149. C5 | #65444 | direct (N × H) |
| 150. C5 | C5×#495 | 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×#4082 | 2 |
| C2×C5×#687 | 2 |
| C2×C5×Dic20 | 2 |
| C5×C8×Dic5 | 2 |
| C5×#495 | 5 |
| #65444 | 5 |