Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
602 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 240 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×#1039 | C2 | semidirect |
| 3. C5×Q8×Dic5 | C2 | semidirect |
| 5. #11716961 | C2 | semidirect |
| 6. Dic5×Dic10 | C2 | semidirect |
| 9. C5×Q8×D5 | C4 | semidirect |
| 41. Q8×Dic5 | D5 | semidirect |
| 64. Q8×D5 | Dic5 | semidirect |
| 123. C52 | #519 | semidirect |
| 183. C5 | #65906 | semidirect |
| 184. C5 | #66146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×D5 | 2 |
| Q8×#1039 | 2 |
| C5×Q8×Dic5 | 2 |
| #11716973 | 2 |
| #11716961 | 2 |
| Dic5×Dic10 | 2 |
| #11716959 | 2 |
| #66146 | 5 |
| #65906 | 5 |