Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
356 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 72 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×#87809 | C2 | semidirect |
| 2. C5×D4×Dic5 | C2 | semidirect |
| 3. C2×C5×#686 | C2 | semidirect |
| 4. #11717029 | C2 | semidirect |
| 5. #11716612 | C2 | semidirect |
| 6. #11716605 | C2 | semidirect |
| 7. #11716603 | C2 | semidirect |
| 27. C52×D4 | D4 | semidirect |
| 44. D4×Dic5 | D5 | semidirect |
| 48. C2×#686 | D5 | semidirect |
| 70. C5×Dic5 | D8 | semidirect |
| 122. C5×D4 | D20 | semidirect |
| 123. C5×D4 | C22⋊D5 | semidirect |
| 159. C52 | #459 | semidirect |
| 198. Dic5 | #686 | semidirect |
| 239. D4 | #6038 | semidirect |
| 248. C5 | #65304 | semidirect |
| 249. C5 | #65439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87809 | 2 |
| C5×D4×Dic5 | 2 |
| C2×C5×#686 | 2 |
| #11717029 | 2 |
| #11716612 | 2 |
| #11716605 | 2 |
| #11716603 | 2 |
| #65439 | 5 |
| #65304 | 5 |