Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
960 conjugacy classes of subgroups; only the 280 normal subgroups are shown.
This group has 960 conjugacy classes of subgroups — too many to draw. Only its 280 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. C22×D5×Dic5 | C2 | semidirect |
| 3. C2×C4×#1039 | C2 | semidirect |
| 4. C2×C5×C4⋊Dic5 | C2 | semidirect |
| 5. C2×#87778 | C2 | semidirect |
| 6. #11717017 | C2 | direct (N × H) |
| 12. C2×C5×D20 | C4 | semidirect |
| 15. C2×D5×Dic5 | C22 | semidirect |
| 16. C4×#1039 | C22 | semidirect |
| 17. C5×C4⋊Dic5 | C22 | semidirect |
| 18. #87778 | C22 | semidirect |
| 24. C22×C5×D5 | C2×C4 | semidirect |
| 26. C2×C4×C52 | C2×C4 | semidirect |
| 29. C2×#1039 | D4 | semidirect |
| 34. C5×D20 | C2×C4 | semidirect |
| 44. C2×C4⋊Dic5 | D5 | semidirect |
| 56. C2×C5×D5 | C22×C4 | semidirect |
| 57. C4×C52 | C22×C4 | semidirect |
| 59. #1039 | C2×D4 | semidirect |
| 78. C2×D20 | Dic5 | semidirect |
| 85. C4⋊Dic5 | C2×D5 | semidirect |
| 90. C2×C52 | C4×D4 | semidirect |
| 104. C22×D5 | C2×Dic5 | semidirect |
| 111. C2×C4×C5 | C4×D5 | semidirect |
| 112. C2×C4×C5 | C2×Dic5 | semidirect |
| 130. D20 | C2×Dic5 | semidirect |
| 138. C52 | C2×C4×D4 | semidirect |
| 158. C2×D5 | C22×Dic5 | semidirect |
| 161. C4×C5 | C2×C4×D5 | semidirect |
| 162. C4×C5 | C22×Dic5 | semidirect |
| 187. C2×C5 | #4039 | semidirect |
| 188. C2×C5 | D4×Dic5 | semidirect |
| 209. C2×C4 | D5×Dic5 | semidirect |
| 212. C5 | C2×#4039 | semidirect |
| 213. C5 | C2×D4×Dic5 | semidirect |
| 225. C4 | C2×D5×Dic5 | semidirect |
| 227. C2 | #11717017 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D20 | 2 |
| C22×D5×Dic5 | 2 |
| C2×C4×#1039 | 2 |
| C2×C5×C4⋊Dic5 | 2 |
| C2×#87778 | 2 |
| #11717017 | 2 |
| C2×D4×Dic5 | 5 |
| C2×#4039 | 5 |