Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
408 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 111 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. #11717210 | C2 | semidirect |
| 3. C52×#106 | C2 | semidirect |
| 5. #11716681 | C2 | semidirect |
| 7. #11716674 | C2 | semidirect |
| 34. C5×#106 | D5 | semidirect |
| 81. #106 | C5⋊D5 | semidirect |
| 85. C52 | #478 | semidirect |
| 124. C5 | #65160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717213 | 2 |
| #11717210 | 2 |
| C52×#106 | 2 |
| #11716688 | 2 |
| #11716681 | 2 |
| #11716676 | 2 |
| #11716674 | 2 |
| #65160 | 5 |