Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
374 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 374 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×#709 | C2 | semidirect |
| 2. C5×#4076 | C2 | semidirect |
| 3. C2×C5×D40 | C2 | semidirect |
| 4. C2×C5×#677 | C2 | semidirect |
| 5. C52×C22⋊C8 | C2 | semidirect |
| 6. C5×#3953 | C2 | semidirect |
| 7. C5×#3948 | C2 | semidirect |
| 24. #65023 | C5 | direct (N × H) |
| 39. C5×D20 | D4 | semidirect |
| 42. C5×Dic10 | D4 | semidirect |
| 46. C2×#709 | C2×C5 | semidirect |
| 50. #4076 | C2×C5 | semidirect |
| 51. C2×D40 | C2×C5 | semidirect |
| 52. C2×#677 | C2×C5 | semidirect |
| 56. C5×C22⋊C8 | D5 | semidirect |
| 57. C5×C22⋊C8 | C2×C5 | semidirect |
| 58. #3953 | C2×C5 | semidirect |
| 59. #3948 | C2×C5 | semidirect |
| 152. D20 | C5×D4 | semidirect |
| 155. Dic10 | C5×D4 | semidirect |
| 168. C22⋊C8 | C5×D5 | semidirect |
| 169. C52 | #449 | semidirect |
| 259. C5 | #65023 | direct (N × H) |
| 260. 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×#709 | 2 |
| C5×#4076 | 2 |
| C2×C5×D40 | 2 |
| C2×C5×#677 | 2 |
| C52×C22⋊C8 | 2 |
| C5×#3953 | 2 |
| C5×#3948 | 2 |
| C5×#449 | 5 |
| #65023 | 5 |