Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
512 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 118 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C5 | C22×C5⋊D5 |
| commutator, cosocle | C2×C52 | C23×C5 |
| Frattini | C2 | C22×C5×C5⋊D5 |
| Fitting | C53×D4 | C2 |
| socle | C2×C53 | C23 |
| hypercenter | C5×D4 | C5⋊D5 |
| hypocenter | C52 | C5×#41 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C2×C5 ◁ C5×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C53×D4 | C2 | semidirect |
| 2. C5×C22⋊(C5⋊D5) | C2 | semidirect |
| 3. C2×C5×#1039 | C2 | semidirect |
| 4. C4×C5×C5⋊D5 | C2 | semidirect |
| 5. C5×#6045 | C2 | semidirect |
| 11. #87902 | C5 | direct (N × H) |
| 17. C52×D4 | D5 | semidirect |
| 18. C52×D4 | C2×C5 | semidirect |
| 19. C22⋊(C5⋊D5) | C2×C5 | semidirect |
| 20. C2×#1039 | C2×C5 | semidirect |
| 21. C4×C5⋊D5 | C2×C5 | semidirect |
| 22. #6045 | C2×C5 | semidirect |
| 27. C53 | #41 | semidirect |
| 53. C5×D4 | C5×D5 | semidirect |
| 54. C5×D4 | C5⋊D5 | semidirect |
| 62. C52 | #711 | semidirect |
| 63. C52 | C5×#41 | semidirect |
| 87. D4 | C5×C5⋊D5 | semidirect |
| 91. C5 | C5×#711 | semidirect |
| 92. C5 | #87902 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×D4 | 2 |
| C5×C22⋊(C5⋊D5) | 2 |
| C2×C5×#1039 | 2 |
| C4×C5×C5⋊D5 | 2 |
| C5×#6045 | 2 |
| #87902 | 5 |
| C5×#711 | 5 |