Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
399 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 399 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 2. C5×D5⋊M16 | C2 | semidirect |
| 3. C5×#4013 | C2 | semidirect |
| 11. C5×#704 | C22 | semidirect |
| 14. D5⋊#100 | C5 | direct (N × H) |
| 32. D5⋊M16 | C2×C5 | semidirect |
| 34. #4013 | C2×C5 | semidirect |
| 63. #704 | C22×C5 | semidirect |
| 75. C5×D5 | #100 | semidirect |
| 110. C52 | C2×#100 | semidirect |
| 163. D5 | C5×#100 | semidirect |
| 179. C5 | C2×C5×#100 | semidirect |
| 180. C5 | D5⋊#100 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×D5 | 2 |
| C5×D5⋊M16 | 2 |
| C5×#4013 | 2 |
| D5⋊#100 | 5 |
| C2×C5×#100 | 5 |