Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
324 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 324 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 |
| 3. C5×#4070 | C2 | semidirect |
| 4. C2×C5×#677 | C2 | semidirect |
| 5. C5×#3953 | C2 | semidirect |
| 6. C5×#3949 | C2 | semidirect |
| 7. C5×#3948 | C2 | semidirect |
| 22. #65403 | C5 | direct (N × H) |
| 38. C52×C8 | D4 | semidirect |
| 41. C22×C5×C8 | D5 | semidirect |
| 42. C22×C5×C8 | C2×C5 | semidirect |
| 46. #4070 | C2×C5 | semidirect |
| 47. C2×#677 | C2×C5 | semidirect |
| 51. #3953 | C2×C5 | semidirect |
| 52. #3949 | C2×C5 | semidirect |
| 53. #3948 | C2×C5 | semidirect |
| 56. C22×C52 | SD16 | semidirect |
| 140. C5×C8 | C22⋊D5 | semidirect |
| 141. C5×C8 | C5×D4 | semidirect |
| 143. C22×C8 | C5×D5 | semidirect |
| 149. C52 | #465 | semidirect |
| 161. C22×C5 | #677 | semidirect |
| 162. C22×C5 | C5×SD16 | semidirect |
| 225. C8 | C5×C22⋊D5 | semidirect |
| 227. C5 | #65403 | direct (N × H) |
| 228. C5 | C5×#465 | semidirect |
| 234. C22 | C5×#677 | 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 |
| C5×#4070 | 2 |
| C2×C5×#677 | 2 |
| C5×#3953 | 2 |
| C5×#3949 | 2 |
| C5×#3948 | 2 |
| C5×#465 | 5 |
| #65403 | 5 |