Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
343 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 343 conjugacy classes of subgroups — too many to draw. Only its 104 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×C5×#700 | C2 | semidirect |
| 3. C2×C5×D5⋊C8 | C2 | semidirect |
| 4. C5×C22⋊#170 | C2 | semidirect |
| 16. #65776 | C5 | direct (N × H) |
| 34. C2×#700 | C2×C5 | semidirect |
| 35. C2×D5⋊C8 | C2×C5 | semidirect |
| 38. C22⋊#170 | C2×C5 | semidirect |
| 112. C52 | #408 | semidirect |
| 172. C5 | C5×#408 | semidirect |
| 173. C5 | #65776 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#711 | 2 |
| C2×C5×#700 | 2 |
| C2×C5×D5⋊C8 | 2 |
| C5×C22⋊#170 | 2 |
| #65776 | 5 |
| C5×#408 | 5 |