Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
12000 conjugacy classes of subgroups; only the 3243 normal subgroups are shown.
This group has 12000 conjugacy classes of subgroups — too many to draw. Only its 3243 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C42 | C5⋊D5 |
| commutator, hypocenter | C52 | C23×C42 |
| Frattini | C22 | C24×C5⋊D5 |
| Fitting | C22×C42×C52 | C2 |
| socle | C24×C52 | C23 |
| prime radical | C24×C5⋊D5 | C22 |
| cosocle | C22×C52 | C25 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C42×C52 | C2 | semidirect |
| 3. C22×C4×#1039 | C2 | semidirect |
| 4. C2×C42×C5⋊D5 | C2 | direct (N × H) |
| 8. C22×C4×C5⋊D5 | C4 | direct (N × H) |
| 10. C2×C42×C52 | C22 | semidirect |
| 11. C2×C4×#1039 | C22 | semidirect |
| 12. C42×C5⋊D5 | C22 | direct (N × H) |
| 17. C22×C4×C52 | C2×C4 | semidirect |
| 19. C22×#1039 | C2×C4 | semidirect |
| 21. C2×C4×C5⋊D5 | C2×C4 | direct (N × H) |
| 23. C42×C52 | C23 | semidirect |
| 24. C4×#1039 | C23 | semidirect |
| 26. C22×C42×C5 | D5 | semidirect |
| 31. C22×C5⋊D5 | C42 | direct (N × H) |
| 34. C2×C4×C52 | C22×C4 | semidirect |
| 36. C2×#1039 | C22×C4 | semidirect |
| 38. C4×C5⋊D5 | C22×C4 | direct (N × H) |
| 44. C2×C42×C5 | C2×D5 | semidirect |
| 48. C22×C52 | C2×C42 | semidirect |
| 51. C2×C5⋊D5 | C2×C42 | direct (N × H) |
| 53. C4×C52 | C23×C4 | semidirect |
| 54. #1039 | C23×C4 | semidirect |
| 58. C22×C4×C5 | C4×D5 | semidirect |
| 64. C42×C5 | C22×D5 | semidirect |
| 69. C22×C42 | C5⋊D5 | direct (N × H) |
| 70. C2×C52 | C22×C42 | semidirect |
| 72. C5⋊D5 | C22×C42 | direct (N × H) |
| 78. C2×C4×C5 | C2×C4×D5 | semidirect |
| 90. C2×C42 | C2×C5⋊D5 | direct (N × H) |
| 91. C52 | C23×C42 | semidirect |
| 92. C22×C5 | C42×D5 | semidirect |
| 97. C4×C5 | C22×C4×D5 | semidirect |
| 106. C22×C4 | C4×C5⋊D5 | direct (N × H) |
| 109. C42 | C22×C5⋊D5 | direct (N × H) |
| 110. C2×C5 | C2×C42×D5 | semidirect |
| 121. C2×C4 | C2×C4×C5⋊D5 | direct (N × H) |
| 123. C5 | C22×C42×D5 | semidirect |
| 126. C22 | C42×C5⋊D5 | direct (N × H) |
| 130. C4 | C22×C4×C5⋊D5 | direct (N × H) |
| 132. C2 | C2×C42×C5⋊D5 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×C5⋊D5 | 2 |
| C22×C42×C52 | 2 |
| C22×C4×#1039 | 2 |
| C2×C42×C5⋊D5 | 2 |
| C22×C42×D5 | 5 |