Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
760 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 251 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. #11717246 | C2 | semidirect |
| 3. C2×#87804 | C2 | semidirect |
| 4. #11716699 | C2 | semidirect |
| 8. C2×C52×D4 | C4 | semidirect |
| 12. C4⋊#1039 | C22 | semidirect |
| 15. C2×#6029 | C22 | semidirect |
| 47. C2×C5×D4 | Dic5 | semidirect |
| 77. C52 | #418 | semidirect |
| 91. C2×D4 | #1039 | semidirect |
| 116. C5 | #65504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D4 | 2 |
| #11717246 | 2 |
| C2×#87804 | 2 |
| #11716699 | 2 |
| #65504 | 5 |