Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
504 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 74 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. C4×#6036 | C2 | semidirect |
| 3. #11716936 | C2 | semidirect |
| 4. C5×#3969 | C2 | semidirect |
| 5. #11716611 | C2 | semidirect |
| 7. #87904 | C4 | semidirect |
| 8. Q8×C5⋊D5 | C4 | semidirect |
| 10. #87902 | C4 | semidirect |
| 12. D4×C5⋊D5 | C4 | semidirect |
| 18. C4×C5×Dic5 | C22 | semidirect |
| 19. C5×#681 | C22 | semidirect |
| 26. C52×Q8 | C2×C4 | semidirect |
| 28. C52×D4 | C2×C4 | semidirect |
| 37. C4⋊(C5⋊D5) | C2×C4 | semidirect |
| 46. #6045 | C2×C4 | semidirect |
| 55. #3969 | D5 | semidirect |
| 98. C4×Dic5 | C2×D5 | semidirect |
| 99. #681 | C2×D5 | semidirect |
| 108. C5⋊D5 | #104 | semidirect |
| 114. C5×Q8 | C4×D5 | semidirect |
| 118. C5×D4 | C4×D5 | semidirect |
| 165. C52 | C2×#104 | semidirect |
| 227. Q8 | #6036 | semidirect |
| 234. D4 | #6036 | semidirect |
| 250. C5 | D5×#104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×C5⋊D5 | 2 |
| C4×#6036 | 2 |
| #11716936 | 2 |
| C5×#3969 | 2 |
| #11716611 | 2 |
| D5×#104 | 5 |