Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
364 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
| 3. C5×#4092 | C2 | semidirect |
| 4. C2×C5×#688 | C2 | semidirect |
| 5. C5×#3967 | C2 | semidirect |
| 6. C5×#3953 | C2 | semidirect |
| 7. C5×#3952 | C2 | semidirect |
| 24. #65476 | C5 | direct (N × H) |
| 47. C2×C5×Q16 | D5 | semidirect |
| 48. C2×C5×Q16 | C2×C5 | semidirect |
| 51. #4092 | C2×C5 | semidirect |
| 52. C2×#688 | C2×C5 | semidirect |
| 56. #3967 | C2×C5 | semidirect |
| 57. #3953 | C2×C5 | semidirect |
| 58. #3952 | C2×C5 | semidirect |
| 159. C2×Q16 | C5×D5 | semidirect |
| 165. C52 | #452 | semidirect |
| 245. C5 | #65476 | direct (N × H) |
| 246. C5 | C5×#452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#713 | 2 |
| C2×C52×Q16 | 2 |
| C5×#4092 | 2 |
| C2×C5×#688 | 2 |
| C5×#3967 | 2 |
| C5×#3953 | 2 |
| C5×#3952 | 2 |
| C5×#452 | 5 |
| #65476 | 5 |