Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
366 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 110 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×#676 | C2 | semidirect |
| 3. C5×D5×C4⋊C4 | C2 | semidirect |
| 4. C52×#103 | C2 | semidirect |
| 5. C5×#3967 | C2 | semidirect |
| 6. C5×#3953 | C2 | semidirect |
| 7. C5×#3941 | C2 | semidirect |
| 10. C5×#713 | C4 | semidirect |
| 23. #65092 | C5 | direct (N × H) |
| 27. C52×Q8 | C2×C4 | semidirect |
| 35. C5×D20 | C2×C4 | semidirect |
| 46. C2×#676 | C2×C5 | semidirect |
| 47. D5×C4⋊C4 | C2×C5 | semidirect |
| 50. C5×#103 | D5 | semidirect |
| 51. C5×#103 | C2×C5 | semidirect |
| 54. #3967 | C2×C5 | semidirect |
| 55. #3953 | C2×C5 | semidirect |
| 56. #3941 | C2×C5 | semidirect |
| 81. #713 | C4×C5 | semidirect |
| 115. C5×Q8 | C4×D5 | semidirect |
| 116. C5×Q8 | C2×C4×C5 | semidirect |
| 139. D20 | C2×C4×C5 | semidirect |
| 153. #103 | C5×D5 | semidirect |
| 156. C52 | #417 | semidirect |
| 218. Q8 | C4×C5×D5 | semidirect |
| 234. C5 | #65092 | direct (N × H) |
| 235. C5 | C5×#417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#713 | 2 |
| C2×C5×#676 | 2 |
| C5×D5×C4⋊C4 | 2 |
| C52×#103 | 2 |
| C5×#3967 | 2 |
| C5×#3953 | 2 |
| C5×#3941 | 2 |
| C5×#417 | 5 |
| #65092 | 5 |