Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
270 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 270 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. #11717221 | C2 | semidirect |
| 2. C5×#4047 | C2 | semidirect |
| 4. C5×#3947 | C2 | semidirect |
| 5. #11716618 | C2 | semidirect |
| 6. #11716611 | C2 | semidirect |
| 7. #11716610 | C2 | semidirect |
| 19. #87776 | C4 | semidirect |
| 20. #87774 | C4 | semidirect |
| 21. #87773 | C4 | semidirect |
| 22. #87771 | C4 | semidirect |
| 47. #4047 | D5 | semidirect |
| 53. #3947 | D5 | semidirect |
| 151. C52 | #444 | semidirect |
| 216. C5 | #65006 | semidirect |
| 217. C5 | #65434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717221 | 2 |
| C5×#4047 | 2 |
| #11716947 | 2 |
| C5×#3947 | 2 |
| #11716618 | 2 |
| #11716611 | 2 |
| #11716610 | 2 |
| #65434 | 5 |
| #65006 | 5 |