Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
282 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 282 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. #11716983 | C2 | semidirect |
| 5. #11716677 | C2 | semidirect |
| 6. C5×#3942 | C2 | semidirect |
| 7. #11716612 | C2 | semidirect |
| 52. #3942 | D5 | semidirect |
| 64. C5×Dic5 | SD16 | semidirect |
| 144. C52 | #461 | semidirect |
| 171. Dic5 | #687 | semidirect |
| 213. C5 | #65107 | semidirect |
| 214. C5 | #65308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4039 | 2 |
| #11716983 | 2 |
| C2×#87773 | 2 |
| C2×#87772 | 2 |
| #11716677 | 2 |
| C5×#3942 | 2 |
| #11716612 | 2 |
| #65308 | 5 |
| #65107 | 5 |