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×#704 | C2 | semidirect |
| 3. C22×C5×#170 | C2 | semidirect |
| 4. C5×C22⋊#170 | C2 | semidirect |
| 5. C5×#4003 | C2 | semidirect |
| 19. #65775 | C5 | direct (N × H) |
| 42. C2×#704 | C2×C5 | semidirect |
| 43. C22×#170 | C2×C5 | semidirect |
| 46. C22⋊#170 | C2×C5 | semidirect |
| 47. #4003 | C2×C5 | semidirect |
| 142. C52 | #408 | semidirect |
| 220. C5 | C5×#408 | semidirect |
| 221. C5 | #65775 | 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×#704 | 2 |
| C22×C5×#170 | 2 |
| C5×C22⋊#170 | 2 |
| C5×#4003 | 2 |
| #65775 | 5 |
| C5×#408 | 5 |