Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
286 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 286 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. C2×C5×#677 | C2 | semidirect |
| 3. C5×#4021 | C2 | semidirect |
| 4. C4×C5×D20 | C2 | semidirect |
| 5. C52×C4⋊C8 | C2 | semidirect |
| 6. C5×#3953 | C2 | semidirect |
| 7. C5×#3948 | C2 | semidirect |
| 22. #65133 | C5 | direct (N × H) |
| 44. C2×#677 | C2×C5 | semidirect |
| 45. #4021 | C2×C5 | semidirect |
| 46. C4×D20 | C2×C5 | semidirect |
| 48. C5×C4⋊C8 | D5 | semidirect |
| 49. C5×C4⋊C8 | C2×C5 | semidirect |
| 52. #3953 | C2×C5 | semidirect |
| 53. #3948 | C2×C5 | semidirect |
| 143. C4⋊C8 | C5×D5 | semidirect |
| 146. C52 | #463 | semidirect |
| 221. C5 | #65133 | direct (N × H) |
| 222. C5 | C5×#463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D40 | 2 |
| C2×C5×#677 | 2 |
| C5×#4021 | 2 |
| C4×C5×D20 | 2 |
| C52×C4⋊C8 | 2 |
| C5×#3953 | 2 |
| C5×#3948 | 2 |
| C5×#463 | 5 |
| #65133 | 5 |