Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
205 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 205 conjugacy classes of subgroups — too many to draw. Only its 84 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×#4004 | C2 | semidirect |
| 5. C5×#4002 | C2 | semidirect |
| 6. C5×C4⋊#170 | C2 | semidirect |
| 7. C4×C5×#170 | C2 | semidirect |
| 19. #65706 | C5 | direct (N × H) |
| 36. #4004 | C2×C5 | semidirect |
| 39. #4002 | C2×C5 | semidirect |
| 40. C4⋊#170 | C2×C5 | semidirect |
| 41. C4×#170 | C2×C5 | semidirect |
| 123. C52 | #433 | semidirect |
| 186. C5 | C5×#433 | semidirect |
| 187. C5 | #65706 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4038 | 2 |
| C5×#4004 | 2 |
| C5×#4003 | 2 |
| C5×#4002 | 2 |
| C5×C4⋊#170 | 2 |
| C4×C5×#170 | 2 |
| #65706 | 5 |
| C5×#433 | 5 |