Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
816 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 150 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C53 | C2 | semidirect |
| 2. C22×C5×C5⋊D5 | C2 | semidirect |
| 3. C5×C22⋊(C5⋊D5) | C2 | direct (N × H) |
| 4. C2×C5×#1039 | C2 | semidirect |
| 7. C22×C53 | C22 | semidirect |
| 9. C2×C5×C5⋊D5 | C22 | semidirect |
| 10. C5×#1039 | C22 | semidirect |
| 11. C2×C22⋊(C5⋊D5) | C5 | direct (N × H) |
| 14. C2×C53 | D4 | semidirect |
| 18. C23×C52 | D5 | semidirect |
| 19. C23×C52 | C2×C5 | semidirect |
| 20. C22×C5⋊D5 | C2×C5 | semidirect |
| 22. C22⋊(C5⋊D5) | C2×C5 | direct (N × H) |
| 23. C2×#1039 | C2×C5 | semidirect |
| 26. C53 | C2×D4 | semidirect |
| 33. C22×C52 | C2×D5 | semidirect |
| 35. C22×C52 | C22×C5 | semidirect |
| 37. C2×C5⋊D5 | C22×C5 | semidirect |
| 40. #1039 | C22×C5 | semidirect |
| 49. C2×C52 | C22⋊D5 | semidirect |
| 50. C2×C52 | C5×D4 | semidirect |
| 57. C23×C5 | C5×D5 | semidirect |
| 58. C23×C5 | C5⋊D5 | semidirect |
| 65. C52 | C2×C22⋊D5 | semidirect |
| 66. C52 | C2×C5×D4 | semidirect |
| 75. C22×C5 | C2×C5×D5 | semidirect |
| 77. C22×C5 | C2×C5⋊D5 | semidirect |
| 89. C2×C5 | C5×C22⋊D5 | semidirect |
| 90. C2×C5 | C22⋊(C5⋊D5) | direct (N × H) |
| 95. C23 | C5×C5⋊D5 | semidirect |
| 99. C5 | C2×C5×C22⋊D5 | semidirect |
| 100. C5 | C2×C22⋊(C5⋊D5) | direct (N × H) |
| 105. C22 | C2×C5×C5⋊D5 | semidirect |
| 109. C2 | C5×C22⋊(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×C53 | 2 |
| C22×C5×C5⋊D5 | 2 |
| C5×C22⋊(C5⋊D5) | 2 |
| C2×C5×#1039 | 2 |
| C2×C22⋊(C5⋊D5) | 5 |
| C2×C5×C22⋊D5 | 5 |