Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
278 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 64 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. D5×C4⋊Dic5 | C2 | semidirect |
| 3. #11716688 | C2 | semidirect |
| 4. C5×#3952 | C2 | semidirect |
| 5. C5×#3950 | C2 | semidirect |
| 6. #11716616 | C2 | semidirect |
| 7. #11716605 | C2 | semidirect |
| 46. #3952 | D5 | semidirect |
| 48. #3950 | D5 | semidirect |
| 138. C52 | #480 | semidirect |
| 213. C5 | #65025 | semidirect |
| 214. C5 | #65171 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717027 | 2 |
| D5×C4⋊Dic5 | 2 |
| #11716688 | 2 |
| C5×#3952 | 2 |
| C5×#3950 | 2 |
| #11716616 | 2 |
| #11716605 | 2 |
| #65171 | 5 |
| #65025 | 5 |