Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
318 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 64 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. C2×C5×D40 | C2 | semidirect |
| 2. #11717032 | C2 | semidirect |
| 3. #11717017 | C2 | semidirect |
| 4. C2×#87770 | C2 | semidirect |
| 5. #11716681 | C2 | semidirect |
| 6. C5×#3953 | C2 | semidirect |
| 7. #11716603 | C2 | semidirect |
| 35. C5×D20 | D4 | semidirect |
| 47. C2×D40 | D5 | semidirect |
| 51. #3953 | D5 | semidirect |
| 69. #1039 | D8 | semidirect |
| 140. D20 | C22⋊D5 | semidirect |
| 155. C52 | #459 | semidirect |
| 238. C5 | #65075 | semidirect |
| 239. C5 | #65439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D40 | 2 |
| #11717032 | 2 |
| #11717017 | 2 |
| C2×#87770 | 2 |
| #11716681 | 2 |
| C5×#3953 | 2 |
| #11716603 | 2 |
| #65439 | 5 |
| #65075 | 5 |