Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
205 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 205 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. C4×#6032 | C2 | semidirect |
| 3. C5×#4002 | C2 | semidirect |
| 4. #11716760 | C2 | semidirect |
| 5. #11716759 | C2 | semidirect |
| 39. #4002 | D5 | semidirect |
| 123. C52 | #433 | semidirect |
| 186. C5 | #64998 | semidirect |
| 187. C5 | #65697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11716995 | 2 |
| C4×#6032 | 2 |
| C5×#4002 | 2 |
| #11716760 | 2 |
| #11716759 | 2 |
| #11716753 | 2 |
| #65697 | 5 |
| #64998 | 5 |