Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
535 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 535 conjugacy classes of subgroups — too many to draw. Only its 272 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. C5×#4133 | C2 | semidirect |
| 3. C5×D5⋊M16 | C2 | semidirect |
| 10. C5×#700 | C22 | semidirect |
| 11. C5×D5⋊C8 | C22 | semidirect |
| 12. #66260 | C5 | direct (N × H) |
| 24. #4133 | C2×C5 | semidirect |
| 25. D5⋊M16 | C2×C5 | semidirect |
| 46. #700 | C22×C5 | semidirect |
| 47. D5⋊C8 | C22×C5 | semidirect |
| 76. C52 | #568 | semidirect |
| 116. C5 | C5×#568 | semidirect |
| 117. C5 | #66260 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#713 | 2 |
| C5×#4133 | 2 |
| C5×D5⋊M16 | 2 |
| #66260 | 5 |
| C5×#568 | 5 |