Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
399 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 399 conjugacy classes of subgroups — too many to draw. Only its 68 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. D5×#704 | C2 | semidirect |
| 3. #11716856 | C2 | semidirect |
| 4. C5×#4013 | C2 | semidirect |
| 5. #11716757 | C2 | semidirect |
| 15. #87853 | C22 | semidirect |
| 16. C5×#704 | C22 | semidirect |
| 48. #4013 | D5 | direct (N × H) |
| 91. #704 | C2×D5 | semidirect |
| 105. C5×D5 | #100 | semidirect |
| 157. C52 | C2×#100 | semidirect |
| 232. D5 | #4013 | direct (N × H) |
| 255. C5 | D5×#100 | semidirect |
| 256. C5 | C2×#4013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5×C22⋊D5 | 2 |
| D5×#704 | 2 |
| #11716856 | 2 |
| C5×#4013 | 2 |
| #11716757 | 2 |
| C2×#4013 | 5 |
| D5×#100 | 5 |