Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
276 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 74 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. C2×C52×SD16 | C2 | semidirect |
| 2. C5×#4088 | C2 | semidirect |
| 4. C5×#4047 | C2 | semidirect |
| 5. C5×#3968 | C2 | semidirect |
| 6. C5×#3965 | C2 | semidirect |
| 7. C5×#3951 | C2 | semidirect |
| 24. #65466 | C5 | direct (N × H) |
| 44. C2×C5×SD16 | D5 | semidirect |
| 45. C2×C5×SD16 | C2×C5 | semidirect |
| 47. #4088 | C2×C5 | semidirect |
| 49. #4047 | C2×C5 | semidirect |
| 53. #3968 | C2×C5 | semidirect |
| 54. #3965 | C2×C5 | semidirect |
| 55. #3951 | C2×C5 | semidirect |
| 147. C2×SD16 | C5×D5 | semidirect |
| 152. C52 | #471 | semidirect |
| 218. C5 | #65466 | direct (N × H) |
| 219. C5 | C5×#471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×SD16 | 2 |
| C5×#4088 | 2 |
| C5×#4078 | 2 |
| C5×#4047 | 2 |
| C5×#3968 | 2 |
| C5×#3965 | 2 |
| C5×#3951 | 2 |
| C5×#471 | 5 |
| #65466 | 5 |