Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
242 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 2. C5×#4016 | C2 | semidirect |
| 3. C52×C4⋊C8 | C2 | semidirect |
| 6. C5×#3950 | C2 | semidirect |
| 7. C5×#3949 | C2 | semidirect |
| 20. #65136 | C5 | direct (N × H) |
| 36. #4016 | C2×C5 | semidirect |
| 40. C5×C4⋊C8 | D5 | semidirect |
| 41. C5×C4⋊C8 | C2×C5 | semidirect |
| 46. #3950 | C2×C5 | semidirect |
| 47. #3949 | C2×C5 | semidirect |
| 122. C4⋊C8 | C5×D5 | semidirect |
| 125. C52 | #478 | semidirect |
| 188. C5 | #65136 | direct (N × H) |
| 189. C5 | C5×#478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C5×D20 | 2 |
| C5×#4016 | 2 |
| C52×C4⋊C8 | 2 |
| C5×#3953 | 2 |
| C5×#3950 | 2 |
| C5×#3949 | 2 |
| C5×#478 | 5 |
| #65136 | 5 |