Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
262 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 68 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. C4×C5×Dic10 | C2 | semidirect |
| 3. C2×#87775 | C2 | semidirect |
| 5. C4⋊#6029 | C2 | semidirect |
| 6. #11716606 | C2 | semidirect |
| 45. C4×Dic10 | D5 | semidirect |
| 140. C52 | #464 | semidirect |
| 208. C5 | #65317 | semidirect |
| 209. C5 | #65343 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4021 | 2 |
| C4×C5×Dic10 | 2 |
| C2×#87775 | 2 |
| C2×#87772 | 2 |
| C4⋊#6029 | 2 |
| #11716606 | 2 |
| #11716603 | 2 |
| #65343 | 5 |
| #65317 | 5 |