Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
432 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 113 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. #11717208 | C2 | semidirect |
| 3. C52×#106 | C2 | semidirect |
| 5. #11716681 | C2 | semidirect |
| 7. #11716675 | C2 | semidirect |
| 28. C4⋊(C5⋊D5) | Q8 | semidirect |
| 35. C5×#106 | D5 | semidirect |
| 83. #106 | C5⋊D5 | semidirect |
| 87. C52 | #476 | semidirect |
| 127. C5 | #65159 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717213 | 2 |
| #11717208 | 2 |
| C52×#106 | 2 |
| #11716688 | 2 |
| #11716681 | 2 |
| #11716676 | 2 |
| #11716675 | 2 |
| #65159 | 5 |