Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
311 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 311 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 |
|---|---|---|
| 3. #11716848 | C2 | semidirect |
| 4. C5×#4005 | C2 | semidirect |
| 5. #11716758 | C2 | semidirect |
| 46. #4005 | D5 | direct (N × H) |
| 91. C5×D5 | #101 | semidirect |
| 139. C52 | C2×#101 | semidirect |
| 186. D5 | #4005 | direct (N × H) |
| 207. C5 | D5×#101 | semidirect |
| 208. C5 | C2×#4005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×Dic10 | 2 |
| D5×#704 | 2 |
| #11716848 | 2 |
| C5×#4005 | 2 |
| #11716758 | 2 |
| C2×#4005 | 5 |
| D5×#101 | 5 |