Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
344 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 344 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. C22×C52×C8 | C2 | semidirect |
| 2. C5×#4076 | C2 | semidirect |
| 3. C2×C5×D40 | C2 | semidirect |
| 4. C5×#3953 | C2 | semidirect |
| 5. C5×#3950 | C2 | semidirect |
| 16. #65404 | C5 | direct (N × H) |
| 28. C52×C8 | D4 | semidirect |
| 31. C22×C5×C8 | D5 | semidirect |
| 32. C22×C5×C8 | C2×C5 | semidirect |
| 34. #4076 | C2×C5 | semidirect |
| 35. C2×D40 | C2×C5 | semidirect |
| 38. #3953 | C2×C5 | semidirect |
| 39. #3950 | C2×C5 | semidirect |
| 42. C22×C52 | D8 | semidirect |
| 108. C5×C8 | C22⋊D5 | semidirect |
| 109. C5×C8 | C5×D4 | semidirect |
| 111. C22×C8 | C5×D5 | semidirect |
| 115. C52 | #466 | semidirect |
| 127. C22×C5 | D40 | semidirect |
| 128. C22×C5 | C5×D8 | semidirect |
| 179. C8 | C5×C22⋊D5 | semidirect |
| 181. C5 | #65404 | direct (N × H) |
| 182. C5 | C5×#466 | semidirect |
| 188. C22 | C5×D40 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×C8 | 2 |
| C5×#4076 | 2 |
| C2×C5×D40 | 2 |
| C5×#3953 | 2 |
| C5×#3950 | 2 |
| C5×#466 | 5 |
| #65404 | 5 |