Finite Group DatabasebetaFinite Group DatabasebetaOrder 3200.
534 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 4. #170⋊#170 | C2 | semidirect |
| 32. #87827 | C8 | semidirect |
| 59. #6032 | C2×C8 | semidirect |
| 61. C5×#170 | C2×C8 | semidirect |
| 146. C5⋊D5 | #322 | semidirect |
| 183. #170 | D5⋊C8 | semidirect |
| 201. C52 | C2×#322 | semidirect |
| 278. C5 | #10603806 | semidirect |
| 279. C5 | #10603807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13103890 | 2 |
| C4×#87827 | 2 |
| #170⋊#170 | 2 |
| #10603807 | 5 |
| #10603806 | 5 |