Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
384 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 1. C2×C5×Q8×D5 | C2 | semidirect |
| 2. C2×C52×SD16 | C2 | semidirect |
| 4. C2×C5×#687 | C2 | semidirect |
| 5. C5×#3967 | C2 | semidirect |
| 6. C5×#3952 | C2 | semidirect |
| 7. C5×#3948 | C2 | semidirect |
| 24. #65459 | C5 | direct (N × H) |
| 28. C52×Q8 | D4 | semidirect |
| 42. C5×Dic10 | D4 | semidirect |
| 46. C2×Q8×D5 | C2×C5 | semidirect |
| 49. C2×C5×SD16 | D5 | semidirect |
| 50. C2×C5×SD16 | C2×C5 | semidirect |
| 53. C2×#687 | C2×C5 | semidirect |
| 57. #3967 | C2×C5 | semidirect |
| 58. #3952 | C2×C5 | semidirect |
| 59. #3948 | C2×C5 | semidirect |
| 66. C2×C5×D5 | SD16 | semidirect |
| 125. C5×Q8 | C22⋊D5 | semidirect |
| 126. C5×Q8 | C5×D4 | semidirect |
| 155. Dic10 | C5×D4 | semidirect |
| 163. C2×SD16 | C5×D5 | semidirect |
| 168. C52 | #448 | semidirect |
| 186. C2×D5 | C5×SD16 | semidirect |
| 237. Q8 | C5×C22⋊D5 | semidirect |
| 252. C5 | #65459 | direct (N × H) |
| 253. C5 | C5×#448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×D5 | 2 |
| C2×C52×SD16 | 2 |
| C5×#4084 | 2 |
| C2×C5×#687 | 2 |
| C5×#3967 | 2 |
| C5×#3952 | 2 |
| C5×#3948 | 2 |
| C5×#448 | 5 |
| #65459 | 5 |