Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
286 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 102 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×C5×#676 | C2 | semidirect |
| 2. C2×C5×C8×D5 | C2 | semidirect |
| 4. C52×C4⋊C8 | C2 | semidirect |
| 5. C5×#3952 | C2 | semidirect |
| 6. C5×#3952 | C2 | semidirect |
| 7. C5×#3935 | C2 | semidirect |
| 22. #65125 | C5 | direct (N × H) |
| 38. C5×#168 | D4 | semidirect |
| 42. C2×#676 | C2×C5 | semidirect |
| 43. C2×C8×D5 | C2×C5 | semidirect |
| 46. C5×C4⋊C8 | D5 | semidirect |
| 47. C5×C4⋊C8 | C2×C5 | semidirect |
| 51. #3952 | C2×C5 | semidirect |
| 52. #3952 | C2×C5 | semidirect |
| 53. #3935 | C2×C5 | semidirect |
| 60. C2×C5×D5 | M16 | semidirect |
| 138. #168 | C5×D4 | semidirect |
| 142. C4⋊C8 | C5×D5 | semidirect |
| 146. C52 | #435 | semidirect |
| 161. C2×D5 | C5×M16 | semidirect |
| 221. C5 | #65125 | direct (N × H) |
| 222. C5 | C5×#435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#676 | 2 |
| C2×C5×C8×D5 | 2 |
| C4×C5×D20 | 2 |
| C52×C4⋊C8 | 2 |
| C5×#3952 | 2 |
| C5×#3935 | 2 |
| C5×#435 | 5 |
| #65125 | 5 |