Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
328 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 86 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×C52×SD16 | C2 | semidirect |
| 2. C5×#4093 | C2 | semidirect |
| 3. C2×C5×#689 | C2 | semidirect |
| 4. C5×#4082 | C2 | semidirect |
| 6. C2×C5×#677 | C2 | semidirect |
| 7. C5×C8×Dic5 | C2 | semidirect |
| 22. #65457 | C5 | direct (N × H) |
| 42. C2×C5×SD16 | D5 | semidirect |
| 43. C2×C5×SD16 | C2×C5 | semidirect |
| 47. #4093 | C2×C5 | semidirect |
| 48. C2×#689 | C2×C5 | semidirect |
| 49. #4082 | C2×C5 | semidirect |
| 51. C2×#677 | C2×C5 | semidirect |
| 53. C8×Dic5 | C2×C5 | semidirect |
| 141. C2×SD16 | C5×D5 | semidirect |
| 146. C52 | #495 | semidirect |
| 214. C5 | #65457 | direct (N × H) |
| 215. C5 | C5×#495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×SD16 | 2 |
| C5×#4093 | 2 |
| C2×C5×#689 | 2 |
| C5×#4082 | 2 |
| C2×C5×#686 | 2 |
| C2×C5×#677 | 2 |
| C5×C8×Dic5 | 2 |
| C5×#495 | 5 |
| #65457 | 5 |