Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
180 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 79 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. Q8×Dic25 | C2 | semidirect |
| 4. #11716384 | C2 | semidirect |
| 6. #11716367 | C2 | semidirect |
| 7. #11716364 | C2 | semidirect |
| 11. SD16×C25 | C4 | semidirect |
| 23. Q8×C25 | C2×C4 | semidirect |
| 33. C8×C25 | C2×C4 | semidirect |
| 91. C25 | #440 | semidirect |
| 106. SD16 | Dic25 | semidirect |
| 121. Q8 | C2×Dic25 | semidirect |
| 132. C8 | C2×Dic25 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD16×C25 | 2 |
| Q8×Dic25 | 2 |
| D4×Dic25 | 2 |
| #11716384 | 2 |
| #11716381 | 2 |
| #11716367 | 2 |
| #11716364 | 2 |
| #65453 | 5 |