Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
392 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 1. C2×C5×#713 | C2 | semidirect |
| 2. C2×C52×SD16 | C2 | semidirect |
| 3. C5×#4084 | C2 | semidirect |
| 4. C2×C5×#686 | C2 | semidirect |
| 5. C5×#3967 | C2 | semidirect |
| 6. C5×#3953 | C2 | semidirect |
| 7. C5×#3952 | C2 | semidirect |
| 24. #65461 | C5 | direct (N × H) |
| 29. C52×Q8 | D4 | semidirect |
| 39. C5×D20 | D4 | semidirect |
| 46. C2×#713 | C2×C5 | semidirect |
| 48. C2×C5×SD16 | D5 | semidirect |
| 49. C2×C5×SD16 | C2×C5 | semidirect |
| 52. #4084 | C2×C5 | semidirect |
| 53. C2×#686 | C2×C5 | semidirect |
| 57. #3967 | C2×C5 | semidirect |
| 58. #3953 | C2×C5 | semidirect |
| 59. #3952 | C2×C5 | semidirect |
| 127. C5×Q8 | C22⋊D5 | semidirect |
| 128. C5×Q8 | C5×D4 | semidirect |
| 155. D20 | C5×D4 | semidirect |
| 165. C2×SD16 | C5×D5 | semidirect |
| 171. C52 | #449 | semidirect |
| 244. Q8 | C5×C22⋊D5 | semidirect |
| 261. C5 | #65461 | direct (N × H) |
| 262. C5 | C5×#449 | 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×C52×SD16 | 2 |
| C5×#4084 | 2 |
| C2×C5×#686 | 2 |
| C5×#3967 | 2 |
| C5×#3953 | 2 |
| C5×#3952 | 2 |
| C5×#449 | 5 |
| #65461 | 5 |