Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
342 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 119 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. C22×C4×D5 | C2 | semidirect |
| 3. C2×C5×C4⋊C4 | C2 | semidirect |
| 4. C2×#685 | C2 | semidirect |
| 5. C2×#685 | C2 | semidirect |
| 6. C2×#685 | C2 | semidirect |
| 7. C2×#683 | C2 | semidirect |
| 8. #4040 | C2 | direct (N × H) |
| 19. C2×C4×D5 | C22 | semidirect |
| 20. C5×C4⋊C4 | C22 | semidirect |
| 21. #685 | C22 | semidirect |
| 22. #685 | C22 | semidirect |
| 23. #685 | C22 | semidirect |
| 24. #683 | C22 | semidirect |
| 51. C2×C4⋊C4 | D5 | semidirect |
| 84. C4⋊C4 | C2×D5 | semidirect |
| 88. C2×C5 | #123 | semidirect |
| 115. C5 | C2×#123 | semidirect |
| 135. C2 | #4040 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D20 | 2 |
| C22×C4×D5 | 2 |
| C2×C5×C4⋊C4 | 2 |
| C2×#685 | 2 |
| C2×#683 | 2 |
| #4040 | 2 |
| C2×#123 | 5 |