Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
343 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 343 conjugacy classes of subgroups — too many to draw. Only its 72 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. C2×#87829 | C2 | semidirect |
| 3. C2×#87827 | C2 | semidirect |
| 4. C22⋊#6032 | C2 | semidirect |
| 5. C5×C22⋊#170 | C2 | semidirect |
| 6. #11716753 | C2 | semidirect |
| 7. #11716753 | C2 | semidirect |
| 55. C22⋊#170 | D5 | semidirect |
| 166. C52 | #408 | semidirect |
| 259. C5 | #65016 | semidirect |
| 260. C5 | #65776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87879 | 2 |
| C2×#87829 | 2 |
| C2×#87827 | 2 |
| C22⋊#6032 | 2 |
| C5×C22⋊#170 | 2 |
| #11716753 | 2 |
| #65776 | 5 |
| #65016 | 5 |