Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
250 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 62 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. AGL(1,𝔽5)×Dic10 | C2 | semidirect |
| 5. #11716743 | C2 | semidirect |
| 6. #11716736 | C2 | semidirect |
| 7. #11716732 | C2 | semidirect |
| 18. #87810 | C4 | semidirect |
| 19. C5×#687 | C4 | semidirect |
| 20. #87773 | C4 | semidirect |
| 21. #87772 | C4 | semidirect |
| 32. #6045 | C2×C4 | semidirect |
| 36. C5×Dic10 | C2×C4 | semidirect |
| 40. #6029 | C2×C4 | semidirect |
| 41. C5×#168 | C2×C4 | semidirect |
| 92. #687 | AGL(1,𝔽5) | semidirect |
| 135. Dic10 | C2×AGL(1,𝔽5) | semidirect |
| 142. #168 | C2×AGL(1,𝔽5) | semidirect |
| 150. C52 | #440 | semidirect |
| 225. C5 | #65307 | semidirect |
| 226. C5 | #65735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D4×AGL(1,𝔽5) | 2 |
| AGL(1,𝔽5)×Dic10 | 2 |
| D5×#687 | 2 |
| #11716850 | 2 |
| #11716743 | 2 |
| #11716736 | 2 |
| #11716732 | 2 |
| #65735 | 5 |
| #65307 | 5 |