Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
366 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 366 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×C5×Dic10 | C2 | semidirect |
| 3. C2×C5×#677 | C2 | semidirect |
| 4. C52×C22⋊C8 | C2 | semidirect |
| 5. C5×#3948 | C2 | semidirect |
| 18. #65027 | C5 | direct (N × H) |
| 31. C5×Dic10 | D4 | semidirect |
| 34. C22×Dic10 | C2×C5 | semidirect |
| 38. C2×#677 | C2×C5 | semidirect |
| 41. C5×C22⋊C8 | D5 | semidirect |
| 42. C5×C22⋊C8 | C2×C5 | semidirect |
| 43. #3948 | C2×C5 | semidirect |
| 46. C22×C52 | SD16 | semidirect |
| 114. Dic10 | C5×D4 | semidirect |
| 122. C22⋊C8 | C5×D5 | semidirect |
| 123. C52 | #448 | semidirect |
| 135. C22×C5 | #677 | semidirect |
| 136. C22×C5 | C5×SD16 | semidirect |
| 192. C5 | #65027 | direct (N × H) |
| 193. C5 | C5×#448 | semidirect |
| 199. C22 | C5×#677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×Dic10 | 2 |
| C5×#4076 | 2 |
| C2×C5×#677 | 2 |
| C52×C22⋊C8 | 2 |
| C5×#3948 | 2 |
| C5×#448 | 5 |
| #65027 | 5 |