Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
418 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 418 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×#87871 | C2 | semidirect |
| 2. #11717258 | C2 | semidirect |
| 3. C2×C5×#687 | C2 | semidirect |
| 4. C2×C5×#686 | C2 | semidirect |
| 5. #11716607 | C2 | semidirect |
| 6. #11716604 | C2 | semidirect |
| 7. #11716598 | C2 | semidirect |
| 38. C5×D20 | D4 | semidirect |
| 40. C5×Dic10 | D4 | semidirect |
| 52. C2×#687 | D5 | semidirect |
| 53. C2×#686 | D5 | semidirect |
| 153. D20 | C22⋊D5 | semidirect |
| 162. Dic10 | C22⋊D5 | semidirect |
| 174. C52 | #449 | semidirect |
| 269. C5 | #65447 | semidirect |
| 270. C5 | #65461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87871 | 2 |
| #11717258 | 2 |
| C2×C5×#687 | 2 |
| C2×C5×#686 | 2 |
| #11716607 | 2 |
| #11716604 | 2 |
| #11716598 | 2 |
| #65461 | 5 |
| #65447 | 5 |