Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
488 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 104 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×C4⋊Dic5 | C2 | semidirect |
| 3. C2×C5×#681 | C2 | semidirect |
| 4. #11716608 | C2 | semidirect |
| 5. #11716605 | C2 | semidirect |
| 9. #87900 | C4 | semidirect |
| 29. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 32. #6045 | C2×C4 | semidirect |
| 41. C2×C4⋊Dic5 | D5 | semidirect |
| 42. C2×#681 | D5 | semidirect |
| 146. C52 | #417 | semidirect |
| 226. C5 | #65255 | semidirect |
| 227. C5 | #65422 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87900 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C2×C5×#681 | 2 |
| #11716608 | 2 |
| #11716605 | 2 |
| #65422 | 5 |
| #65255 | 5 |