Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
728 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 196 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. C42×C5⋊D5 | C2 | semidirect |
| 3. C5×#4018 | C2 | semidirect |
| 4. #11717020 | C2 | semidirect |
| 5. #11716999 | C2 | semidirect |
| 6. C4×D5×Dic5 | C2 | semidirect |
| 7. #11716992 | C2 | semidirect |
| 8. #11716956 | C2 | semidirect |
| 16. #87873 | C4 | semidirect |
| 34. C4×C5⋊D5 | C2×C4 | semidirect |
| 37. C4×C5×D5 | C2×C4 | semidirect |
| 38. #6039 | C2×C4 | semidirect |
| 39. #6038 | C2×C4 | semidirect |
| 40. #6037 | C2×C4 | semidirect |
| 50. #4018 | D5 | semidirect |
| 62. #1039 | #41 | semidirect |
| 125. C4×D5 | C4×D5 | semidirect |
| 135. C52 | C4×#41 | semidirect |
| 199. C5 | #65856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87873 | 2 |
| C42×C5⋊D5 | 2 |
| C5×#4018 | 2 |
| #11717020 | 2 |
| #11716999 | 2 |
| C4×D5×Dic5 | 2 |
| #11716992 | 2 |
| #11716956 | 2 |
| #65856 | 5 |