Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
354 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×C5×Dic20 | C2 | semidirect |
| 3. #11716990 | C2 | semidirect |
| 4. C2×#87772 | C2 | semidirect |
| 5. #11716687 | C2 | semidirect |
| 6. C5×#3953 | C2 | semidirect |
| 7. #11716606 | C2 | semidirect |
| 50. C2×Dic20 | D5 | semidirect |
| 54. #3953 | D5 | semidirect |
| 163. C52 | #452 | semidirect |
| 246. C5 | #65072 | semidirect |
| 247. C5 | #65476 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87871 | 2 |
| C2×C5×Dic20 | 2 |
| #11716990 | 2 |
| C2×#87772 | 2 |
| #11716687 | 2 |
| C5×#3953 | 2 |
| #11716606 | 2 |
| #65476 | 5 |
| #65072 | 5 |