Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
366 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 366 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×C5×#688 | C2 | semidirect |
| 3. C2×C5×D40 | C2 | semidirect |
| 4. C5×#4041 | C2 | semidirect |
| 5. C52×#103 | C2 | semidirect |
| 6. C5×#3952 | C2 | semidirect |
| 7. C5×#3941 | C2 | semidirect |
| 24. #65100 | C5 | direct (N × H) |
| 29. C52×Q8 | D4 | semidirect |
| 39. C5×D20 | D4 | semidirect |
| 46. C2×#713 | C2×C5 | semidirect |
| 50. C2×#688 | C2×C5 | semidirect |
| 51. C2×D40 | C2×C5 | semidirect |
| 52. #4041 | C2×C5 | semidirect |
| 54. C5×#103 | D5 | semidirect |
| 55. C5×#103 | C2×C5 | semidirect |
| 58. #3952 | C2×C5 | semidirect |
| 59. #3941 | C2×C5 | semidirect |
| 125. C5×Q8 | D20 | semidirect |
| 126. C5×Q8 | C5×D4 | semidirect |
| 152. D20 | C5×D4 | semidirect |
| 165. #103 | C5×D5 | semidirect |
| 168. C52 | #449 | semidirect |
| 238. Q8 | C5×D20 | semidirect |
| 255. C5 | #65100 | direct (N × H) |
| 256. 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×C5×#688 | 2 |
| C2×C5×D40 | 2 |
| C5×#4041 | 2 |
| C52×#103 | 2 |
| C5×#3952 | 2 |
| C5×#3941 | 2 |
| C5×#449 | 5 |
| #65100 | 5 |