Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
318 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 78 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. C5×#4039 | C2 | semidirect |
| 2. #11717013 | C2 | semidirect |
| 4. #11716676 | C2 | semidirect |
| 5. C5×#3939 | C2 | semidirect |
| 6. #11716603 | C2 | semidirect |
| 7. Dic5×#168 | C2 | semidirect |
| 19. #87771 | C4 | semidirect |
| 27. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 32. C5×D20 | C2×C4 | semidirect |
| 36. C5×#168 | C2×C4 | semidirect |
| 41. #4039 | D5 | semidirect |
| 50. #3939 | D5 | semidirect |
| 64. C5×Dic5 | D8 | semidirect |
| 125. D20 | C4×D5 | semidirect |
| 133. #168 | C4×D5 | semidirect |
| 141. C52 | C4×D8 | semidirect |
| 174. Dic5 | #686 | semidirect |
| 217. C5 | #65161 | semidirect |
| 218. C5 | C4×#686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4039 | 2 |
| #11717013 | 2 |
| C2×#87771 | 2 |
| #11716676 | 2 |
| C5×#3939 | 2 |
| #11716603 | 2 |
| Dic5×#168 | 2 |
| C4×#686 | 5 |
| #65161 | 5 |