Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
752 conjugacy classes of subgroups; only the 240 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 240 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. #11717246 | C2 | semidirect |
| 3. C5×#4072 | C2 | semidirect |
| 4. D5×C22⋊Dic5 | C2 | semidirect |
| 5. #11717017 | C2 | semidirect |
| 6. Dic5×D20 | C2 | semidirect |
| 9. C2×C5×D20 | C4 | semidirect |
| 12. C2×D5×Dic5 | C22 | semidirect |
| 14. C4⋊#1039 | C22 | semidirect |
| 15. C4×#1039 | C22 | semidirect |
| 17. C5×C4⋊Dic5 | C22 | semidirect |
| 18. C4×C5×Dic5 | C22 | semidirect |
| 19. #87778 | C22 | semidirect |
| 24. C22×C5×D5 | C2×C4 | semidirect |
| 26. C2×C4×C52 | C2×C4 | semidirect |
| 31. C5×D20 | C2×C4 | semidirect |
| 32. C5×D20 | C2×C4 | semidirect |
| 43. #4072 | D5 | semidirect |
| 66. C2×D20 | Dic5 | semidirect |
| 82. C4⋊Dic5 | C2×D5 | semidirect |
| 86. C4×Dic5 | C2×D5 | semidirect |
| 99. C22×D5 | C2×Dic5 | semidirect |
| 107. C2×C4×C5 | C4×D5 | semidirect |
| 108. C2×C4×C5 | C2×Dic5 | semidirect |
| 118. D20 | C2×Dic5 | semidirect |
| 119. D20 | C2×Dic5 | semidirect |
| 127. C52 | #518 | semidirect |
| 187. C2×C4 | D5×Dic5 | semidirect |
| 191. C5 | #65855 | semidirect |
| 192. C5 | #66132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D20 | 2 |
| #11717246 | 2 |
| C5×#4072 | 2 |
| D5×C22⋊Dic5 | 2 |
| #11717017 | 2 |
| Dic5×D20 | 2 |
| #66132 | 5 |
| #65855 | 5 |