Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
356 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 356 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×C52×SD16 | C2 | semidirect |
| 2. C5×#4093 | C2 | semidirect |
| 3. C2×C5×#688 | C2 | semidirect |
| 4. C5×#4086 | C2 | semidirect |
| 5. C2×C5×#686 | C2 | semidirect |
| 6. C2×C5×D40 | C2 | semidirect |
| 7. C5×#3947 | C2 | semidirect |
| 22. #65465 | C5 | direct (N × H) |
| 38. C52×C8 | D4 | semidirect |
| 39. C5×#168 | D4 | semidirect |
| 42. C2×C5×SD16 | D5 | semidirect |
| 43. C2×C5×SD16 | C2×C5 | semidirect |
| 48. #4093 | C2×C5 | semidirect |
| 49. C2×#688 | C2×C5 | semidirect |
| 50. #4086 | C2×C5 | semidirect |
| 51. C2×#686 | C2×C5 | semidirect |
| 52. C2×D40 | C2×C5 | semidirect |
| 54. #3947 | C2×C5 | semidirect |
| 141. C5×C8 | C22⋊D5 | semidirect |
| 142. C5×C8 | C5×D4 | semidirect |
| 143. #168 | C5×D4 | semidirect |
| 145. C2×SD16 | C5×D5 | semidirect |
| 151. C52 | #496 | semidirect |
| 222. C8 | C5×C22⋊D5 | semidirect |
| 224. C5 | #65465 | direct (N × H) |
| 225. C5 | C5×#496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C52×SD16 | 2 |
| C5×#4093 | 2 |
| C2×C5×#688 | 2 |
| C5×#4086 | 2 |
| C2×C5×#686 | 2 |
| C2×C5×D40 | 2 |
| C5×#3947 | 2 |
| C5×#496 | 5 |
| #65465 | 5 |