Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
392 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 126 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. C2×C52×M16 | C2 | semidirect |
| 3. C2×C5×C4⋊Dic5 | C2 | semidirect |
| 4. C5×#3953 | C2 | semidirect |
| 5. C5×#3948 | C2 | semidirect |
| 10. C5×#709 | C4 | semidirect |
| 19. #65422 | C5 | direct (N × H) |
| 31. C5×D20 | C2×C4 | semidirect |
| 34. C5×Dic10 | C2×C4 | semidirect |
| 39. C2×C5×M16 | D5 | semidirect |
| 40. C2×C5×M16 | C2×C5 | semidirect |
| 42. C2×C4⋊Dic5 | C2×C5 | semidirect |
| 45. #3953 | C2×C5 | semidirect |
| 46. #3948 | C2×C5 | semidirect |
| 72. #709 | C4×C5 | semidirect |
| 123. D20 | C2×C4×C5 | semidirect |
| 126. Dic10 | C2×C4×C5 | semidirect |
| 131. C2×M16 | C5×D5 | semidirect |
| 135. C52 | #417 | semidirect |
| 210. C5 | #65422 | direct (N × H) |
| 211. C5 | C5×#417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#709 | 2 |
| C2×C52×M16 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C5×#3953 | 2 |
| C5×#3948 | 2 |
| C5×#417 | 5 |
| #65422 | 5 |