Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
752 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 144 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×Q8×C5⋊D5 | C2 | semidirect |
| 3. C2×C5×#688 | C2 | semidirect |
| 4. #11717058 | C2 | direct (N × H) |
| 5. C2×#87773 | C2 | semidirect |
| 6. C2×#87767 | C2 | semidirect |
| 8. C2×C52×Q8 | C22 | semidirect |
| 10. Q8×C5⋊D5 | C22 | semidirect |
| 14. C2×#6045 | C22 | semidirect |
| 19. C5×#688 | C22 | semidirect |
| 20. C2×C5×#168 | C22 | semidirect |
| 21. #87773 | C22 | semidirect |
| 22. #87767 | C22 | semidirect |
| 29. C52×Q8 | C23 | semidirect |
| 39. #6045 | C23 | semidirect |
| 43. C5×#168 | C23 | semidirect |
| 48. C2×#688 | D5 | semidirect |
| 54. C2×C5⋊D5 | SD16 | semidirect |
| 66. C2×C5×Q8 | C2×D5 | semidirect |
| 86. #688 | C2×D5 | semidirect |
| 88. C2×#168 | C2×D5 | semidirect |
| 92. C2×C52 | C2×SD16 | semidirect |
| 94. C5⋊D5 | C2×SD16 | semidirect |
| 105. C5×Q8 | C22×D5 | semidirect |
| 132. #168 | C22×D5 | semidirect |
| 139. C52 | C22×SD16 | semidirect |
| 166. C2×Q8 | D52 | semidirect |
| 180. C2×C5 | D5×SD16 | semidirect |
| 193. Q8 | C2×D52 | semidirect |
| 206. C5 | C2×D5×SD16 | semidirect |
| 220. C2 | #11717058 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C5⋊D5 | 2 |
| C2×#87877 | 2 |
| C2×C5×#688 | 2 |
| #11717058 | 2 |
| C2×#87773 | 2 |
| C2×#87767 | 2 |
| C2×D5×SD16 | 5 |