Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
159 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 159 conjugacy classes of subgroups — too many to draw. Only its 47 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. #11716550 | C2 | semidirect |
| 3. #11716423 | C2 | semidirect |
| 4. C8×#1035 | C2 | semidirect |
| 5. #11716408 | C2 | semidirect |
| 12. D8×C25 | C4 | semidirect |
| 13. #87721 | C4 | semidirect |
| 15. Dic100 | C4 | semidirect |
| 69. C25 | #443 | semidirect |
| 79. D8 | #1035 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11716550 | 2 |
| #11716474 | 2 |
| #11716423 | 2 |
| C8×#1035 | 2 |
| #11716408 | 2 |
| #65732 | 5 |