Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
392 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 126 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. C22×C52×C8 | C2 | semidirect |
| 3. C5×#4072 | C2 | semidirect |
| 4. C5×#3953 | C2 | semidirect |
| 5. C5×#3948 | C2 | semidirect |
| 9. C5×#709 | C4 | semidirect |
| 19. #65402 | C5 | direct (N × H) |
| 38. C22×C5×C8 | D5 | semidirect |
| 39. C22×C5×C8 | C2×C5 | semidirect |
| 41. #4072 | C2×C5 | semidirect |
| 44. #3953 | C2×C5 | semidirect |
| 45. #3948 | C2×C5 | semidirect |
| 67. #709 | C4×C5 | semidirect |
| 125. C22×C8 | C5×D5 | semidirect |
| 129. C52 | #416 | semidirect |
| 195. C5 | #65402 | direct (N × H) |
| 196. C5 | C5×#416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#709 | 2 |
| C22×C52×C8 | 2 |
| C5×#4072 | 2 |
| C5×#3953 | 2 |
| C5×#3948 | 2 |
| C5×#416 | 5 |
| #65402 | 5 |