Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
327 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 327 conjugacy classes of subgroups — too many to draw. Only its 64 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. #11717347 | C2 | semidirect |
| 3. #11716856 | C2 | semidirect |
| 4. C5×#4013 | C2 | semidirect |
| 5. #11716758 | C2 | semidirect |
| 45. #4013 | D5 | semidirect |
| 142. C52 | #413 | semidirect |
| 220. C5 | #65034 | semidirect |
| 221. C5 | #65761 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87879 | 2 |
| #11717347 | 2 |
| #11716856 | 2 |
| C5×#4013 | 2 |
| #11716758 | 2 |
| #65761 | 5 |
| #65034 | 5 |