Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
275 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 275 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 |
| 2. C22×C5×#170 | C2 | semidirect |
| 4. C5×C22⋊#170 | C2 | semidirect |
| 5. C5×C22⋊#170 | C2 | semidirect |
| 6. C5×#4004 | C2 | semidirect |
| 7. C5×#4002 | C2 | semidirect |
| 21. #65773 | C5 | direct (N × H) |
| 38. C5×#170 | D4 | semidirect |
| 39. C2×#704 | C2×C5 | semidirect |
| 40. C22×#170 | C2×C5 | semidirect |
| 45. C22⋊#170 | C2×C5 | semidirect |
| 46. C22⋊#170 | C2×C5 | semidirect |
| 47. #4004 | C2×C5 | semidirect |
| 48. #4002 | C2×C5 | semidirect |
| 58. C22×C52 | M16 | semidirect |
| 130. #170 | C5×D4 | semidirect |
| 142. C52 | #435 | semidirect |
| 160. C22×C5 | C5×M16 | semidirect |
| 161. C22×C5 | #704 | semidirect |
| 222. C5 | C5×#435 | semidirect |
| 223. C5 | #65773 | direct (N × H) |
| 229. C22 | 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 |
| C22×C5×#170 | 2 |
| C5×D4×Dic5 | 2 |
| C5×C22⋊#170 | 2 |
| C5×#4004 | 2 |
| C5×#4002 | 2 |
| #65773 | 5 |
| C5×#435 | 5 |