Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
334 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 78 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. C4×C5×Dic10 | C2 | semidirect |
| 4. C5×#3935 | C2 | semidirect |
| 5. #11716616 | C2 | semidirect |
| 6. #11716607 | C2 | semidirect |
| 19. #87774 | C4 | semidirect |
| 33. C5×Dic10 | C2×C4 | semidirect |
| 35. C5×#168 | C2×C4 | semidirect |
| 42. C4×Dic10 | D5 | semidirect |
| 50. #3935 | D5 | semidirect |
| 127. Dic10 | C4×D5 | semidirect |
| 131. #168 | C4×D5 | semidirect |
| 139. C52 | #440 | semidirect |
| 210. C5 | #64999 | semidirect |
| 211. C5 | #65315 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C4⋊(C5⋊D5) | 2 |
| C4×C5×Dic10 | 2 |
| C2×#87774 | 2 |
| C5×#3935 | 2 |
| #11716616 | 2 |
| #11716607 | 2 |
| #11716605 | 2 |
| #65315 | 5 |
| #64999 | 5 |