Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
252 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 90 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×#4094 | C2 | semidirect |
| 3. C5×#4053 | C2 | semidirect |
| 4. C52×#104 | C2 | semidirect |
| 5. C5×#3954 | C2 | semidirect |
| 6. C5×#3937 | C2 | semidirect |
| 7. C5×#3935 | C2 | semidirect |
| 12. C5×#689 | C4 | semidirect |
| 13. C5×#688 | C4 | semidirect |
| 14. C5×#687 | C4 | semidirect |
| 15. C5×#686 | C4 | semidirect |
| 24. #65112 | C5 | direct (N × H) |
| 45. #4094 | C2×C5 | semidirect |
| 46. #4053 | C2×C5 | semidirect |
| 50. C5×#104 | D5 | semidirect |
| 51. C5×#104 | C2×C5 | semidirect |
| 53. #3954 | C2×C5 | semidirect |
| 54. #3937 | C2×C5 | semidirect |
| 55. #3935 | C2×C5 | semidirect |
| 86. #689 | C4×C5 | semidirect |
| 87. #688 | C4×C5 | semidirect |
| 88. #687 | C4×C5 | semidirect |
| 89. #686 | C4×C5 | semidirect |
| 146. #104 | C5×D5 | semidirect |
| 148. C52 | #444 | semidirect |
| 214. C5 | #65112 | direct (N × H) |
| 215. C5 | C5×#444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C5×#4096 | 2 |
| C5×#4094 | 2 |
| C5×#4053 | 2 |
| C52×#104 | 2 |
| C5×#3954 | 2 |
| C5×#3937 | 2 |
| C5×#3935 | 2 |
| C5×#444 | 5 |
| #65112 | 5 |