Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
993 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 993 conjugacy classes of subgroups — too many to draw. Only its 181 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. C24×D25 | C2 | semidirect |
| 2. C22×C22⋊D25 | C2 | semidirect |
| 3. C22×D100 | C2 | semidirect |
| 4. C2×C22⋊C4×C25 | C2 | semidirect |
| 5. C2×#87720 | C2 | semidirect |
| 6. #11716444 | C2 | direct (N × H) |
| 11. C23×D25 | C22 | semidirect |
| 12. C23×D25 | C22 | semidirect |
| 13. C22×C4×C25 | C22 | semidirect |
| 15. C2×C22⋊D25 | C22 | semidirect |
| 16. C22×Dic25 | C22 | semidirect |
| 18. C2×D100 | C22 | semidirect |
| 19. C22⋊C4×C25 | C22 | semidirect |
| 20. #87720 | C22 | semidirect |
| 23. C23×C25 | D4 | semidirect |
| 33. C22×D25 | D4 | semidirect |
| 35. C22×D25 | C23 | semidirect |
| 37. C2×C4×C25 | C23 | semidirect |
| 40. C2×Dic25 | C23 | semidirect |
| 52. C22×C25 | C2×D4 | semidirect |
| 61. C2×D25 | C2×D4 | semidirect |
| 80. C2×C25 | #120 | semidirect |
| 110. C2×C22⋊C4 | D25 | semidirect |
| 111. C25 | C2×#120 | semidirect |
| 139. C22×C4 | C2×D25 | semidirect |
| 141. C22⋊C4 | C2×D25 | semidirect |
| 159. C23 | D100 | semidirect |
| 167. C2×C4 | C22×D25 | semidirect |
| 180. C22 | C2×D100 | semidirect |
| 188. C2 | #11716444 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×D25 | 2 |
| C22×C22⋊D25 | 2 |
| C22×D100 | 2 |
| C2×C22⋊C4×C25 | 2 |
| C2×#87720 | 2 |
| #11716444 | 2 |
| C2×#4028 | 5 |