Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
346 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 346 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. C5×#4043 | C2 | semidirect |
| 3. C2×#87776 | C2 | semidirect |
| 4. C2×#87772 | C2 | semidirect |
| 5. #11716677 | C2 | semidirect |
| 6. C5×#3941 | C2 | semidirect |
| 7. #11716597 | C2 | semidirect |
| 51. #4043 | D5 | semidirect |
| 58. #3941 | D5 | semidirect |
| 162. C52 | #452 | semidirect |
| 242. C5 | #65072 | semidirect |
| 243. C5 | #65336 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87870 | 2 |
| C5×#4043 | 2 |
| C2×#87776 | 2 |
| C2×#87772 | 2 |
| #11716677 | 2 |
| C5×#3941 | 2 |
| #11716597 | 2 |
| #65336 | 5 |
| #65072 | 5 |