Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
322 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 90 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. C52×C22⋊Q8 | C2 | semidirect |
| 2. C2×C5×#688 | C2 | semidirect |
| 4. C22×C5×#168 | C2 | semidirect |
| 5. C5×#3967 | C2 | semidirect |
| 6. C5×#3941 | C2 | semidirect |
| 7. C5×#3940 | C2 | semidirect |
| 22. #65337 | C5 | direct (N × H) |
| 38. C5×#168 | D4 | semidirect |
| 42. C5×C22⋊Q8 | D5 | semidirect |
| 43. C5×C22⋊Q8 | C2×C5 | semidirect |
| 45. C2×#688 | C2×C5 | semidirect |
| 47. C22×#168 | C2×C5 | semidirect |
| 51. #3967 | C2×C5 | semidirect |
| 52. #3941 | C2×C5 | semidirect |
| 53. #3940 | C2×C5 | semidirect |
| 56. C22×C52 | SD16 | semidirect |
| 144. #168 | C5×D4 | semidirect |
| 147. C22⋊Q8 | C5×D5 | semidirect |
| 152. C52 | #465 | semidirect |
| 164. C22×C5 | #688 | semidirect |
| 165. C22×C5 | C5×SD16 | semidirect |
| 232. C5 | #65337 | direct (N × H) |
| 233. C5 | C5×#465 | semidirect |
| 239. C22 | C5×#688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×C22⋊Q8 | 2 |
| C2×C5×#688 | 2 |
| C5×#4076 | 2 |
| C22×C5×#168 | 2 |
| C5×#3967 | 2 |
| C5×#3941 | 2 |
| C5×#3940 | 2 |
| C5×#465 | 5 |
| #65337 | 5 |