Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
356 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 90 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. C2×C52×Q16 | C2 | semidirect |
| 4. C2×C5×#689 | C2 | semidirect |
| 5. C5×#3967 | C2 | semidirect |
| 7. C5×#3948 | C2 | semidirect |
| 24. #65475 | C5 | direct (N × H) |
| 48. C2×C5×Q16 | D5 | semidirect |
| 49. C2×C5×Q16 | C2×C5 | semidirect |
| 52. C2×#689 | C2×C5 | semidirect |
| 56. #3967 | C2×C5 | semidirect |
| 58. #3948 | C2×C5 | semidirect |
| 62. C2×C5×D5 | Q16 | semidirect |
| 157. C2×Q16 | C5×D5 | semidirect |
| 162. C52 | #451 | semidirect |
| 171. C2×D5 | C5×Q16 | semidirect |
| 236. C5 | #65475 | direct (N × H) |
| 237. C5 | C5×#451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×D5 | 2 |
| C2×C52×Q16 | 2 |
| C5×#4092 | 2 |
| C2×C5×#689 | 2 |
| C5×#3967 | 2 |
| C5×#3952 | 2 |
| C5×#3948 | 2 |
| C5×#451 | 5 |
| #65475 | 5 |