Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
384 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 96 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×C5 | D52 |
| commutator, hypocenter | C52 | C22×C4×C5 |
| Frattini | C2 | C2×C5×D52 |
| Fitting, socle | C22×C53 | C22 |
| prime radical | C22×C5×C5⋊D5 | C2 |
| cosocle | C2×C52 | C23×C5 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C22×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C52×Dic5 | C2 | semidirect |
| 3. C5×#6036 | C2 | direct (N × H) |
| 5. C2×C5×C5⋊D5 | C4 | semidirect |
| 7. C52×Dic5 | C22 | semidirect |
| 9. C2×#6036 | C5 | direct (N × H) |
| 10. C2×C53 | C2×C4 | semidirect |
| 12. C5×C5⋊D5 | C2×C4 | semidirect |
| 18. C2×C5×Dic5 | D5 | semidirect |
| 19. C2×C5×Dic5 | C2×C5 | semidirect |
| 21. #6036 | C2×C5 | direct (N × H) |
| 22. C53 | C22×C4 | semidirect |
| 28. C2×C5⋊D5 | C4×C5 | semidirect |
| 36. C5×Dic5 | C2×D5 | semidirect |
| 37. C5×Dic5 | C22×C5 | semidirect |
| 46. C2×C52 | C4×D5 | semidirect |
| 47. C2×C52 | C2×C4×C5 | semidirect |
| 50. C5⋊D5 | C2×C4×C5 | semidirect |
| 60. C2×Dic5 | C5×D5 | semidirect |
| 65. C52 | C2×C4×D5 | semidirect |
| 66. C52 | C22×C4×C5 | semidirect |
| 81. Dic5 | C2×C5×D5 | semidirect |
| 90. C2×C5 | #6036 | direct (N × H) |
| 91. C2×C5 | C4×C5×D5 | semidirect |
| 102. C5 | C2×#6036 | direct (N × H) |
| 103. C5 | C2×C4×C5×D5 | semidirect |
| 109. C2 | C5×#6036 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C5⋊D5 | 2 |
| C2×C52×Dic5 | 2 |
| C5×#6036 | 2 |
| C2×C4×C5×D5 | 5 |
| C2×#6036 | 5 |