Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
416 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 80 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, cosocle | C2×C52 | C23×C5 |
| Frattini | C2 | C2×C5×D52 |
| Fitting, socle | C22×C53 | C22 |
| hypocenter | C52 | C2×C5×D4 |
| LCS | G ▷ C2×C52 ▷ C52 | |
| UCS | C1 ◁ C22×C5 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C52×D5 | C2 | semidirect |
| 2. C2×C5×#1039 | C2 | semidirect |
| 3. C5×#6037 | C2 | direct (N × H) |
| 6. C2×C52×D5 | C22 | semidirect |
| 7. C5×#1039 | C22 | semidirect |
| 9. C2×#6037 | C5 | direct (N × H) |
| 10. C2×C53 | D4 | semidirect |
| 15. C22×C5×D5 | D5 | semidirect |
| 16. C22×C5×D5 | C2×C5 | semidirect |
| 17. C2×#1039 | C2×C5 | semidirect |
| 21. #6037 | C2×C5 | direct (N × H) |
| 22. C53 | C2×D4 | semidirect |
| 34. C2×C5×D5 | C2×D5 | semidirect |
| 35. C2×C5×D5 | C22×C5 | semidirect |
| 36. #1039 | C22×C5 | semidirect |
| 48. C2×C52 | C22⋊D5 | semidirect |
| 49. C2×C52 | C5×D4 | semidirect |
| 58. C22×D5 | C5×D5 | semidirect |
| 67. C52 | C2×C22⋊D5 | semidirect |
| 68. C52 | C2×C5×D4 | semidirect |
| 81. C2×D5 | C2×C5×D5 | semidirect |
| 95. C2×C5 | #6037 | direct (N × H) |
| 96. C2×C5 | C5×C22⋊D5 | semidirect |
| 106. C5 | C2×#6037 | direct (N × H) |
| 107. C5 | C2×C5×C22⋊D5 | semidirect |
| 113. C2 | C5×#6037 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D5 | 2 |
| C2×C5×#1039 | 2 |
| C5×#6037 | 2 |
| C2×C5×C22⋊D5 | 5 |
| C2×#6037 | 5 |