Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
310 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 62 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. #11717037 | C2 | semidirect |
| 3. C5×#3939 | C2 | semidirect |
| 4. #11716613 | C2 | semidirect |
| 22. C4⋊(C5⋊D5) | Q8 | semidirect |
| 34. #3939 | D5 | semidirect |
| 92. C52 | #474 | semidirect |
| 142. C5 | #65179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11717213 | 2 |
| #11717037 | 2 |
| C5×#3939 | 2 |
| #11716613 | 2 |
| #11716605 | 2 |
| #65179 | 5 |