Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
384 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 70 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×D5×Dic10 | C2 | semidirect |
| 2. C2×#87810 | C2 | semidirect |
| 4. C2×C5×#687 | C2 | semidirect |
| 5. #11716608 | C2 | semidirect |
| 6. #11716606 | C2 | semidirect |
| 7. #11716597 | C2 | semidirect |
| 32. #6045 | D4 | semidirect |
| 40. C5×Dic10 | D4 | semidirect |
| 53. C2×#687 | D5 | semidirect |
| 66. C2×C5×D5 | SD16 | semidirect |
| 155. Dic10 | C22⋊D5 | semidirect |
| 168. C52 | #448 | semidirect |
| 186. C2×D5 | #687 | semidirect |
| 252. C5 | #65329 | semidirect |
| 253. C5 | #65459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Dic10 | 2 |
| C2×#87810 | 2 |
| C5×#4084 | 2 |
| C2×C5×#687 | 2 |
| #11716608 | 2 |
| #11716606 | 2 |
| #11716597 | 2 |
| #65459 | 5 |
| #65329 | 5 |