Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
264 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 78 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. C5×D5×C4⋊C4 | C2 | semidirect |
| 3. C52×#106 | C2 | semidirect |
| 4. C5×#3953 | C2 | semidirect |
| 5. C5×#3952 | C2 | semidirect |
| 6. C5×#3941 | C2 | semidirect |
| 7. C5×#3940 | C2 | semidirect |
| 20. #65152 | C5 | direct (N × H) |
| 39. D5×C4⋊C4 | C2×C5 | semidirect |
| 42. C5×#106 | D5 | semidirect |
| 43. C5×#106 | C2×C5 | semidirect |
| 47. #3953 | C2×C5 | semidirect |
| 48. #3952 | C2×C5 | semidirect |
| 49. #3941 | C2×C5 | semidirect |
| 50. #3940 | C2×C5 | semidirect |
| 132. #106 | C5×D5 | semidirect |
| 136. C52 | #481 | semidirect |
| 208. C5 | #65152 | direct (N × H) |
| 209. C5 | C5×#481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4041 | 2 |
| C5×D5×C4⋊C4 | 2 |
| C52×#106 | 2 |
| C5×#3953 | 2 |
| C5×#3952 | 2 |
| C5×#3941 | 2 |
| C5×#3940 | 2 |
| C5×#481 | 5 |
| #65152 | 5 |