Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
346 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 86 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×#689 | C2 | semidirect |
| 3. C2×C5×#677 | C2 | semidirect |
| 4. C5×#4043 | C2 | semidirect |
| 5. C52×#103 | C2 | semidirect |
| 6. C5×#3952 | C2 | semidirect |
| 7. C5×#3941 | C2 | semidirect |
| 24. #65099 | C5 | direct (N × H) |
| 49. C2×#689 | C2×C5 | semidirect |
| 50. C2×#677 | C2×C5 | semidirect |
| 51. #4043 | C2×C5 | semidirect |
| 53. C5×#103 | D5 | semidirect |
| 54. C5×#103 | C2×C5 | semidirect |
| 57. #3952 | C2×C5 | semidirect |
| 58. #3941 | C2×C5 | semidirect |
| 159. #103 | C5×D5 | semidirect |
| 162. C52 | #452 | semidirect |
| 242. C5 | #65099 | direct (N × H) |
| 243. C5 | C5×#452 | 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×#689 | 2 |
| C2×C5×#677 | 2 |
| C5×#4043 | 2 |
| C52×#103 | 2 |
| C5×#3952 | 2 |
| C5×#3941 | 2 |
| C5×#452 | 5 |
| #65099 | 5 |