Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
352 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 352 conjugacy classes of subgroups — too many to draw. Only its 94 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×#4090 | C2 | semidirect |
| 3. C2×C5×#688 | C2 | semidirect |
| 5. C2×C5×#687 | C2 | semidirect |
| 6. C2×C5×#677 | C2 | semidirect |
| 7. C5×C8×Dic5 | C2 | semidirect |
| 22. #65464 | C5 | direct (N × H) |
| 38. C52×C8 | D4 | semidirect |
| 39. C5×#168 | D4 | semidirect |
| 44. C2×C5×SD16 | D5 | semidirect |
| 45. C2×C5×SD16 | C2×C5 | semidirect |
| 48. #4090 | C2×C5 | semidirect |
| 49. C2×#688 | C2×C5 | semidirect |
| 51. C2×#687 | C2×C5 | semidirect |
| 52. C2×#677 | C2×C5 | semidirect |
| 54. C8×Dic5 | C2×C5 | semidirect |
| 64. C5×Dic5 | SD16 | semidirect |
| 139. C5×C8 | C22⋊D5 | semidirect |
| 140. C5×C8 | C5×D4 | semidirect |
| 141. #168 | C5×D4 | semidirect |
| 145. C2×SD16 | C5×D5 | semidirect |
| 149. C52 | #492 | semidirect |
| 175. Dic5 | C5×SD16 | semidirect |
| 216. C8 | C5×C22⋊D5 | semidirect |
| 218. C5 | #65464 | direct (N × H) |
| 219. C5 | C5×#492 | 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×#4090 | 2 |
| C2×C5×#688 | 2 |
| C5×#4086 | 2 |
| C2×C5×#687 | 2 |
| C2×C5×#677 | 2 |
| C5×C8×Dic5 | 2 |
| C5×#492 | 5 |
| #65464 | 5 |