Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
344 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 344 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 |
|---|---|---|
| 1. C2×C52×D8 | C2 | semidirect |
| 2. C5×#4084 | C2 | semidirect |
| 3. C2×C5×C8×D5 | C2 | semidirect |
| 4. C5×#3964 | C2 | semidirect |
| 5. C5×#3950 | C2 | semidirect |
| 16. #65446 | C5 | direct (N × H) |
| 27. C52×C8 | D4 | semidirect |
| 30. C2×C5×D8 | D5 | semidirect |
| 31. C2×C5×D8 | C2×C5 | semidirect |
| 34. #4084 | C2×C5 | semidirect |
| 35. C2×C8×D5 | C2×C5 | semidirect |
| 38. #3964 | C2×C5 | semidirect |
| 39. #3950 | C2×C5 | semidirect |
| 46. C2×C5×D5 | D8 | semidirect |
| 104. C5×C8 | C22⋊D5 | semidirect |
| 105. C5×C8 | C5×D4 | semidirect |
| 107. C2×D8 | C5×D5 | semidirect |
| 112. C52 | #466 | semidirect |
| 130. C2×D5 | C5×D8 | semidirect |
| 175. C8 | C5×C22⋊D5 | semidirect |
| 177. C5 | #65446 | direct (N × H) |
| 178. C5 | C5×#466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×D8 | 2 |
| C5×#4084 | 2 |
| C2×C5×C8×D5 | 2 |
| C5×#3964 | 2 |
| C5×#3950 | 2 |
| C5×#466 | 5 |
| #65446 | 5 |