Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
712 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 130 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×C22⋊Dic5 | C2 | semidirect |
| 3. C2×C5×C22⋊Dic5 | C2 | semidirect |
| 4. C2×C5×#683 | C2 | semidirect |
| 5. C5×#3963 | C2 | semidirect |
| 17. #65511 | C5 | direct (N × H) |
| 36. C2×C5×Dic5 | D4 | semidirect |
| 43. C2×C22⋊Dic5 | C2×C5 | semidirect |
| 44. C2×C22⋊Dic5 | C2×C5 | semidirect |
| 45. C2×#683 | C2×C5 | semidirect |
| 47. #3963 | C2×C5 | semidirect |
| 143. C2×Dic5 | C5×D4 | semidirect |
| 149. C52 | #394 | semidirect |
| 243. C5 | #65511 | direct (N × H) |
| 244. C5 | C5×#394 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C52×D4 | 2 |
| C2×C5×C22⋊Dic5 | 2 |
| C2×C5×#683 | 2 |
| C5×#3963 | 2 |
| C5×#394 | 5 |
| #65511 | 5 |