Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
306 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 122 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×C8×D5 | C2 | semidirect |
| 3. C52×C4⋊C8 | C2 | semidirect |
| 4. C5×#3952 | C2 | semidirect |
| 5. C4×C5×#168 | C2 | semidirect |
| 16. #65123 | C5 | direct (N × H) |
| 22. C5×D20 | C8 | semidirect |
| 27. C5×#168 | D4 | semidirect |
| 30. C2×C8×D5 | C2×C5 | semidirect |
| 33. C5×C4⋊C8 | D5 | semidirect |
| 34. C5×C4⋊C8 | C2×C5 | semidirect |
| 37. #3952 | C2×C5 | semidirect |
| 38. C4×#168 | C2×C5 | semidirect |
| 42. C2×C5×D5 | C2×C8 | semidirect |
| 44. C4×C52 | C2×C8 | semidirect |
| 89. D20 | C5×C8 | semidirect |
| 98. #168 | C5×D4 | semidirect |
| 101. C4⋊C8 | C5×D5 | semidirect |
| 104. C52 | C8×D4 | semidirect |
| 113. C2×D5 | C2×C5×C8 | semidirect |
| 121. C4×C5 | C8×D5 | semidirect |
| 122. C4×C5 | C2×C5×C8 | semidirect |
| 160. C5 | #65123 | direct (N × H) |
| 161. C5 | C5×C8×D4 | semidirect |
| 168. C4 | C5×C8×D5 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×C8×D5 | 2 |
| C4×C5×D20 | 2 |
| C52×C4⋊C8 | 2 |
| C5×#3952 | 2 |
| C4×C5×#168 | 2 |
| C5×C8×D4 | 5 |
| #65123 | 5 |