Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
296 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 4. #11716674 | C2 | semidirect |
| 5. C5×#3939 | C2 | semidirect |
| 6. #11716617 | C2 | semidirect |
| 7. #11716616 | C2 | semidirect |
| 19. D5×#168 | C4 | semidirect |
| 33. #6029 | C2×C4 | semidirect |
| 34. C5×#168 | C2×C4 | semidirect |
| 49. #3939 | D5 | direct (N × H) |
| 92. C5×D5 | #107 | semidirect |
| 122. #168 | C4×D5 | semidirect |
| 130. C52 | C2×#107 | semidirect |
| 180. D5 | #3939 | direct (N × H) |
| 195. C5 | D5×#107 | semidirect |
| 196. C5 | C2×#3939 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×D5×C4⋊C4 | 2 |
| D5×C4⋊Dic5 | 2 |
| C2×D5×#168 | 2 |
| #11716674 | 2 |
| C5×#3939 | 2 |
| #11716617 | 2 |
| #11716616 | 2 |
| C2×#3939 | 5 |
| D5×#107 | 5 |