Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
444 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 90 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×C52×SD16 | C2 | semidirect |
| 3. C5×#4092 | C2 | semidirect |
| 4. C2×C5×#688 | C2 | semidirect |
| 5. C5×#3964 | C2 | semidirect |
| 6. C5×#3953 | C2 | semidirect |
| 7. C5×#3952 | C2 | semidirect |
| 9. C2×C52×Q8 | C22 | semidirect |
| 17. C2×C52×C8 | C22 | semidirect |
| 20. C5×C4⋊Dic5 | C22 | semidirect |
| 22. C2×C5×#168 | C22 | semidirect |
| 24. #65458 | C5 | direct (N × H) |
| 50. C2×C5×SD16 | D5 | semidirect |
| 51. C2×C5×SD16 | C2×C5 | semidirect |
| 53. #4092 | C2×C5 | semidirect |
| 54. C2×#688 | C2×C5 | semidirect |
| 58. #3964 | C2×C5 | semidirect |
| 59. #3953 | C2×C5 | semidirect |
| 60. #3952 | C2×C5 | semidirect |
| 71. C2×C5×D5 | SD16 | semidirect |
| 80. C2×C5×Q8 | C2×D5 | semidirect |
| 81. C2×C5×Q8 | C22×C5 | semidirect |
| 101. C2×C5×C8 | C2×D5 | semidirect |
| 102. C2×C5×C8 | C22×C5 | semidirect |
| 108. C4⋊Dic5 | C22×C5 | semidirect |
| 110. C2×#168 | C22×C5 | semidirect |
| 170. C2×SD16 | C5×D5 | semidirect |
| 175. C52 | #450 | semidirect |
| 201. C2×D5 | C5×SD16 | semidirect |
| 216. C2×Q8 | C2×C5×D5 | semidirect |
| 226. C2×C8 | C2×C5×D5 | semidirect |
| 268. C5 | #65458 | direct (N × H) |
| 269. C5 | C5×#450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×D4×D5 | 2 |
| C2×C52×SD16 | 2 |
| C5×#4092 | 2 |
| C2×C5×#688 | 2 |
| C5×#3964 | 2 |
| C5×#3953 | 2 |
| C5×#3952 | 2 |
| C5×#450 | 5 |
| #65458 | 5 |