Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
324 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 1. #11717256 | C2 | semidirect |
| 3. #11717017 | C2 | semidirect |
| 4. C2×#87773 | C2 | semidirect |
| 5. C5×#3964 | C2 | semidirect |
| 6. #11716613 | C2 | semidirect |
| 7. #11716608 | C2 | semidirect |
| 49. #3964 | D5 | semidirect |
| 152. C52 | #463 | semidirect |
| 232. C5 | #65076 | semidirect |
| 233. C5 | #65442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717256 | 2 |
| C2×C5×#686 | 2 |
| #11717017 | 2 |
| C2×#87773 | 2 |
| C5×#3964 | 2 |
| #11716613 | 2 |
| #11716608 | 2 |
| #65442 | 5 |
| #65076 | 5 |