Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
400 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 66 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×#87874 | C2 | semidirect |
| 2. C2×#87809 | C2 | semidirect |
| 3. C5×#4084 | C2 | semidirect |
| 4. C2×C5×#687 | C2 | semidirect |
| 5. #11716606 | C2 | semidirect |
| 6. #11716605 | C2 | semidirect |
| 7. #11716597 | C2 | semidirect |
| 32. C4⋊(C5⋊D5) | D4 | semidirect |
| 40. C5×Dic10 | D4 | semidirect |
| 49. #4084 | D5 | semidirect |
| 50. C2×#687 | D5 | semidirect |
| 158. Dic10 | C22⋊D5 | semidirect |
| 171. C52 | #449 | semidirect |
| 264. C5 | #65326 | semidirect |
| 265. C5 | #65461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87874 | 2 |
| C2×#87809 | 2 |
| C5×#4084 | 2 |
| C2×C5×#687 | 2 |
| #11716606 | 2 |
| #11716605 | 2 |
| #11716597 | 2 |
| #65461 | 5 |
| #65326 | 5 |