Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
816 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 126 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 | D5×C5⋊D5 |
| commutator, hypocenter | C53 | C22×C4 |
| Frattini | C2 | C2×D5×C5⋊D5 |
| Fitting, socle | C22×C53 | C22 |
| prime radical | C22×C5⋊(C5⋊D5) | C2 |
| cosocle | C2×C53 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C5×#1039 | C2 | semidirect |
| 3. C2×C52×Dic5 | C2 | semidirect |
| 4. #11758751 | C2 | direct (N × H) |
| 6. C2×C5⋊(C5⋊D5) | C4 | semidirect |
| 8. C5×#1039 | C22 | semidirect |
| 9. C52×Dic5 | C22 | semidirect |
| 12. C2×C53 | C2×C4 | semidirect |
| 14. C5⋊(C5⋊D5) | C2×C4 | semidirect |
| 19. C2×#1039 | D5 | semidirect |
| 22. C2×C5×Dic5 | D5 | semidirect |
| 24. C53 | C22×C4 | semidirect |
| 35. #1039 | C2×D5 | semidirect |
| 37. C5×Dic5 | C2×D5 | semidirect |
| 42. C2×C52 | C4×D5 | semidirect |
| 43. C2×C52 | C4×D5 | semidirect |
| 55. C2×Dic5 | C5⋊D5 | semidirect |
| 59. C52 | C2×C4×D5 | semidirect |
| 60. C52 | C2×C4×D5 | semidirect |
| 73. Dic5 | C2×C5⋊D5 | semidirect |
| 77. C2×C5 | #6036 | semidirect |
| 78. C2×C5 | C4×C5⋊D5 | semidirect |
| 89. C5 | C2×#6036 | semidirect |
| 90. C5 | C2×C4×C5⋊D5 | semidirect |
| 97. C2 | #11758751 | 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×C5×#1039 | 2 |
| C2×C52×Dic5 | 2 |
| #11758751 | 2 |
| C2×C4×C5⋊D5 | 5 |
| C2×#6036 | 5 |