Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
294 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 88 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 |
|---|---|---|
| 3. Dic5×Dic10 | C2 | semidirect |
| 5. #11716614 | C2 | semidirect |
| 6. #11716606 | C2 | semidirect |
| 7. Dic5×#168 | C2 | semidirect |
| 14. C5×#687 | C4 | semidirect |
| 33. C5×Dic10 | C2×C4 | semidirect |
| 35. C5×#168 | C2×C4 | semidirect |
| 61. C5×Dic5 | SD16 | semidirect |
| 75. #687 | Dic5 | direct (N × H) |
| 122. Dic10 | C2×Dic5 | semidirect |
| 127. #168 | C2×Dic5 | semidirect |
| 135. C52 | C4×SD16 | semidirect |
| 164. Dic5 | #687 | direct (N × H) |
| 204. C5 | C4×#687 | semidirect |
| 205. C5 | SD16×Dic5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×Dic5 | 2 |
| C2×C5×#687 | 2 |
| Dic5×Dic10 | 2 |
| #11716699 | 2 |
| #11716614 | 2 |
| #11716606 | 2 |
| Dic5×#168 | 2 |
| SD16×Dic5 | 5 |
| C4×#687 | 5 |