Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
378 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 72 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. #11717244 | C2 | semidirect |
| 3. C2×#87776 | C2 | semidirect |
| 4. C2×#87773 | C2 | semidirect |
| 5. C5×C22⋊#168 | C2 | semidirect |
| 6. #11716607 | C2 | semidirect |
| 7. #11716604 | C2 | semidirect |
| 56. C22⋊#168 | D5 | semidirect |
| 167. C52 | #452 | semidirect |
| 252. C5 | #65022 | semidirect |
| 253. C5 | #65528 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#709 | 2 |
| #11717244 | 2 |
| C2×#87776 | 2 |
| C2×#87773 | 2 |
| C5×C22⋊#168 | 2 |
| #11716607 | 2 |
| #11716604 | 2 |
| #65528 | 5 |
| #65022 | 5 |