Finite Group DatabasebetaFinite Group DatabasebetaOrder 2000.
464 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 2. C2×C4×C53 | C2 | semidirect |
| 3. C2×C52×Dic5 | C2 | semidirect |
| 7. C2×C52×D5 | C4 | semidirect |
| 11. C5×#685 | C5 | direct (N × H) |
| 20. C2×C4×C52 | D5 | semidirect |
| 21. C2×C4×C52 | C2×C5 | semidirect |
| 22. C2×C5×Dic5 | C2×C5 | semidirect |
| 23. C53 | C22⋊C4 | semidirect |
| 32. C2×C5×D5 | C4×C5 | semidirect |
| 39. #685 | C52 | direct (N × H) |
| 55. C2×C4×C5 | C5×D5 | semidirect |
| 56. C2×C4×C5 | C2×C52 | semidirect |
| 57. C2×Dic5 | C2×C52 | semidirect |
| 59. C52 | #685 | direct (N × H) |
| 60. C52 | C5×C22⋊C4 | semidirect |
| 69. C2×D5 | C4×C52 | semidirect |
| 89. C2×C4 | C52×D5 | semidirect |
| 91. C5 | C5×#685 | direct (N × H) |
| 92. C5 | C52×C22⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D5 | 2 |
| C2×C4×C53 | 2 |
| C2×C52×Dic5 | 2 |
| C52×C22⋊C4 | 5 |
| C5×#685 | 5 |