Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
672 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 672 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 |
|---|---|---|
| 2. C2×#87872 | C2 | semidirect |
| 3. C2×C8×C5⋊D5 | C2 | semidirect |
| 4. C2×C5×#677 | C2 | semidirect |
| 5. C2×#87772 | C2 | semidirect |
| 6. #11716914 | C2 | direct (N × H) |
| 10. C2×C5×Dic10 | C22 | semidirect |
| 17. #87872 | C22 | semidirect |
| 18. C2×C52×C8 | C22 | semidirect |
| 19. C2×#6029 | C22 | semidirect |
| 20. C8×C5⋊D5 | C22 | semidirect |
| 21. C5×#677 | C22 | semidirect |
| 22. #87772 | C22 | semidirect |
| 36. C5×Dic10 | C23 | semidirect |
| 40. C52×C8 | C23 | semidirect |
| 41. #6029 | C23 | semidirect |
| 48. C2×#677 | D5 | semidirect |
| 52. C2×C5⋊D5 | SD16 | semidirect |
| 74. C2×Dic10 | C2×D5 | semidirect |
| 77. C2×C5×C8 | C2×D5 | semidirect |
| 82. #677 | C2×D5 | semidirect |
| 86. C2×C52 | C2×SD16 | semidirect |
| 88. C5⋊D5 | C2×SD16 | semidirect |
| 116. Dic10 | C22×D5 | semidirect |
| 118. C5×C8 | C22×D5 | semidirect |
| 127. C52 | C22×SD16 | semidirect |
| 162. C2×C8 | D52 | semidirect |
| 166. C2×C5 | D5×SD16 | semidirect |
| 188. C8 | C2×D52 | semidirect |
| 190. C5 | C2×D5×SD16 | semidirect |
| 203. C2 | #11716914 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87877 | 2 |
| C2×#87872 | 2 |
| C2×C8×C5⋊D5 | 2 |
| C2×C5×#677 | 2 |
| C2×#87772 | 2 |
| #11716914 | 2 |
| C2×D5×SD16 | 5 |