Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
271 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 271 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 1. C2×C5×#704 | C2 | semidirect |
| 3. C5×C22⋊#170 | C2 | semidirect |
| 4. C5×C4⋊#170 | C2 | semidirect |
| 5. C4×C5×#170 | C2 | semidirect |
| 15. #65774 | C5 | direct (N × H) |
| 27. C5×#170 | D4 | semidirect |
| 28. C2×#704 | C2×C5 | semidirect |
| 32. C22⋊#170 | C2×C5 | semidirect |
| 33. C4⋊#170 | C2×C5 | semidirect |
| 34. C4×#170 | C2×C5 | semidirect |
| 42. C4×C52 | M16 | semidirect |
| 92. #170 | C5×D4 | semidirect |
| 101. C52 | #436 | semidirect |
| 119. C4×C5 | C5×M16 | semidirect |
| 120. C4×C5 | #704 | semidirect |
| 158. C5 | C5×#436 | semidirect |
| 159. C5 | #65774 | direct (N × H) |
| 168. C4 | C5×#704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#704 | 2 |
| C5×D4×Dic5 | 2 |
| C5×C22⋊#170 | 2 |
| C5×C4⋊#170 | 2 |
| C4×C5×#170 | 2 |
| #65774 | 5 |
| C5×#436 | 5 |