Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
680 conjugacy classes of subgroups; only the 374 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 374 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×#4094 | C2 | semidirect |
| 3. C2×C5×#681 | C2 | semidirect |
| 10. C5×#681 | C22 | semidirect |
| 11. C2×C5×#168 | C22 | semidirect |
| 13. #66153 | C5 | direct (N × H) |
| 27. #4094 | C2×C5 | semidirect |
| 28. C2×#681 | C2×C5 | semidirect |
| 54. #681 | C22×C5 | semidirect |
| 55. C2×#168 | C22×C5 | semidirect |
| 86. C52 | #568 | semidirect |
| 131. C5 | #66153 | direct (N × H) |
| 132. C5 | C5×#568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×#41 | 2 |
| C5×#4094 | 2 |
| C2×C5×#681 | 2 |
| C5×#568 | 5 |
| #66153 | 5 |