Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 1. C5×#4043 | C2 | semidirect |
| 3. C2×#87772 | C2 | semidirect |
| 4. C2×D5×#168 | C2 | semidirect |
| 5. #11716675 | C2 | semidirect |
| 6. C5×#3941 | C2 | semidirect |
| 7. #11716607 | C2 | semidirect |
| 37. #6029 | D4 | semidirect |
| 46. #4043 | D5 | semidirect |
| 50. #3941 | D5 | semidirect |
| 60. C2×C5×D5 | SD16 | semidirect |
| 145. C52 | #465 | semidirect |
| 160. C2×D5 | #688 | semidirect |
| 220. C5 | #65067 | semidirect |
| 221. C5 | #65337 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4043 | 2 |
| #11717026 | 2 |
| C2×#87772 | 2 |
| C2×D5×#168 | 2 |
| #11716675 | 2 |
| C5×#3941 | 2 |
| #11716607 | 2 |
| #65337 | 5 |
| #65067 | 5 |