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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4×C53 | C2 | semidirect |
| 2. C5×C22⋊(C5⋊D5) | C2 | semidirect |
| 3. C5×C4⋊(C5⋊D5) | C2 | semidirect |
| 4. C4×C5×C5⋊D5 | C2 | semidirect |
| 5. C5×#6045 | C2 | semidirect |
| 11. #87900 | C5 | direct (N × H) |
| 17. C2×C4×C52 | D5 | semidirect |
| 18. C2×C4×C52 | C2×C5 | semidirect |
| 19. C22⋊(C5⋊D5) | C2×C5 | semidirect |
| 20. C4⋊(C5⋊D5) | C2×C5 | semidirect |
| 21. C4×C5⋊D5 | C2×C5 | semidirect |
| 22. #6045 | C2×C5 | semidirect |
| 27. C53 | #41 | semidirect |
| 56. C2×C4×C5 | C5×D5 | semidirect |
| 57. C2×C4×C5 | C5⋊D5 | semidirect |
| 63. C52 | #709 | semidirect |
| 64. C52 | C5×#41 | semidirect |
| 91. C2×C4 | C5×C5⋊D5 | semidirect |
| 93. C5 | C5×#709 | semidirect |
| 94. C5 | #87900 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C53 | 2 |
| C5×C22⋊(C5⋊D5) | 2 |
| C5×C4⋊(C5⋊D5) | 2 |
| C4×C5×C5⋊D5 | 2 |
| C5×#6045 | 2 |
| #87900 | 5 |
| C5×#709 | 5 |