Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
716 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 145 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×C4×D52 | C2 | semidirect |
| 3. C2×C4×#1044 | C2 | semidirect |
| 4. C2×#87836 | C2 | semidirect |
| 5. C2×#87835 | C2 | semidirect |
| 6. C4×D52⋊C2 | C2 | direct (N × H) |
| 10. C2×D52⋊C2 | C4 | direct (N × H) |
| 17. C4×D52 | C22 | semidirect |
| 18. C4×#1044 | C22 | semidirect |
| 19. #87836 | C22 | semidirect |
| 20. #87835 | C22 | semidirect |
| 25. C2×D52 | C2×C4 | semidirect |
| 28. C2×#1044 | C2×C4 | semidirect |
| 31. D52⋊C2 | C2×C4 | direct (N × H) |
| 32. C2×C4×C52 | D4 | semidirect |
| 33. C2×#1039 | D4 | semidirect |
| 34. C4×C5⋊D5 | D4 | semidirect |
| 52. D52 | C22×C4 | semidirect |
| 54. #1044 | C22×C4 | semidirect |
| 55. C4×C52 | C2×D4 | semidirect |
| 56. #1039 | C2×D4 | semidirect |
| 72. C2×C52 | C4×D4 | semidirect |
| 74. C5⋊D5 | C4×D4 | semidirect |
| 112. C52 | C2×C4×D4 | semidirect |
| 183. C2×C4 | D52⋊C2 | direct (N × H) |
| 200. C4 | C2×D52⋊C2 | direct (N × H) |
| 205. C2 | C4×D52⋊C2 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D52⋊C2 | 2 |
| C2×C4×D52 | 2 |
| C2×C4×#1044 | 2 |
| C2×#87836 | 2 |
| C2×#87835 | 2 |
| C4×D52⋊C2 | 2 |
| C2×C4×D4 | 25 |