Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
316 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 316 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×C5×Dic20 | C2 | semidirect |
| 3. #11716983 | C2 | semidirect |
| 5. C2×#87776 | C2 | semidirect |
| 7. C5×#3947 | C2 | semidirect |
| 45. C2×Dic20 | D5 | semidirect |
| 53. #3947 | D5 | semidirect |
| 144. C52 | #497 | semidirect |
| 208. C5 | #65004 | semidirect |
| 209. C5 | #65479 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87800 | 2 |
| C2×C5×Dic20 | 2 |
| #11716983 | 2 |
| #11716982 | 2 |
| C2×#87776 | 2 |
| C2×#87774 | 2 |
| C5×#3947 | 2 |
| #65479 | 5 |
| #65004 | 5 |