Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
318 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 318 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. C2×C5×D40 | C2 | semidirect |
| 2. C5×#4020 | C2 | semidirect |
| 3. C4×C5×D20 | C2 | semidirect |
| 4. C52×C4⋊C8 | C2 | semidirect |
| 5. C5×#3953 | C2 | semidirect |
| 17. #65132 | C5 | direct (N × H) |
| 29. C5×D20 | D4 | semidirect |
| 35. C2×D40 | C2×C5 | semidirect |
| 36. #4020 | C2×C5 | semidirect |
| 37. C4×D20 | C2×C5 | semidirect |
| 39. C5×C4⋊C8 | D5 | semidirect |
| 40. C5×C4⋊C8 | C2×C5 | semidirect |
| 42. #3953 | C2×C5 | semidirect |
| 51. C4×C52 | D8 | semidirect |
| 110. D20 | C5×D4 | semidirect |
| 118. C4⋊C8 | C5×D5 | semidirect |
| 120. C52 | #459 | semidirect |
| 143. C4×C5 | D40 | semidirect |
| 144. C4×C5 | C5×D8 | semidirect |
| 188. C5 | #65132 | direct (N × H) |
| 189. C5 | C5×#459 | semidirect |
| 199. C4 | C5×D40 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D40 | 2 |
| C5×#4020 | 2 |
| C4×C5×D20 | 2 |
| C52×C4⋊C8 | 2 |
| C5×#3953 | 2 |
| C5×#459 | 5 |
| #65132 | 5 |