Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
159 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 159 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 2. #11716510 | C2 | semidirect |
| 3. #11716385 | C2 | semidirect |
| 4. C8×Dic25 | C2 | semidirect |
| 5. #11716361 | C2 | semidirect |
| 7. Q16×C25 | C4 | semidirect |
| 8. SD16×C25 | C4 | semidirect |
| 9. D8×C25 | C4 | semidirect |
| 69. C25 | #443 | semidirect |
| 77. Q16 | Dic25 | semidirect |
| 78. SD16 | Dic25 | semidirect |
| 79. D8 | Dic25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×#135 | 2 |
| #11716510 | 2 |
| #11716385 | 2 |
| C8×Dic25 | 2 |
| #11716361 | 2 |
| #65485 | 5 |