Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
286 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 286 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. C2×C5×#677 | C2 | semidirect |
| 2. #11717017 | C2 | semidirect |
| 3. #11716981 | C2 | semidirect |
| 5. #11716681 | C2 | semidirect |
| 6. C5×#3953 | C2 | semidirect |
| 7. #11716606 | C2 | semidirect |
| 45. C2×#677 | D5 | semidirect |
| 49. #3953 | D5 | semidirect |
| 146. C52 | #463 | semidirect |
| 221. C5 | #65076 | semidirect |
| 222. C5 | #65454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#677 | 2 |
| #11717017 | 2 |
| #11716981 | 2 |
| C2×#87770 | 2 |
| #11716681 | 2 |
| C5×#3953 | 2 |
| #11716606 | 2 |
| #65454 | 5 |
| #65076 | 5 |