Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
277 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 277 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 4. C5×#4002 | C2 | semidirect |
| 5. C4×C5×#170 | C2 | semidirect |
| 7. C5×#704 | C4 | semidirect |
| 8. C2×C5×#170 | C4 | semidirect |
| 16. #65691 | C5 | direct (N × H) |
| 34. #4002 | C2×C5 | semidirect |
| 35. C4×#170 | C2×C5 | semidirect |
| 48. #704 | C4×C5 | semidirect |
| 49. C2×#170 | C4×C5 | semidirect |
| 98. C52 | #405 | semidirect |
| 149. C5 | C5×#405 | semidirect |
| 150. C5 | #65691 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#704 | 2 |
| C22×C5×#170 | 2 |
| C5×#4023 | 2 |
| C5×#4002 | 2 |
| C4×C5×#170 | 2 |
| #65691 | 5 |
| C5×#405 | 5 |