Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
122 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 44 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. Q8×AGL(1,𝔽5) | C2 | semidirect |
| 4. #4009 | C2 | semidirect |
| 6. #3993 | C2 | semidirect |
| 7. C8×AGL(1,𝔽5) | C2 | semidirect |
| 18. C5×SD16 | C4 | semidirect |
| 19. #688 | C4 | semidirect |
| 20. #687 | C4 | semidirect |
| 21. #677 | C4 | semidirect |
| 30. C5×Q8 | C2×C4 | semidirect |
| 37. Dic10 | C2×C4 | semidirect |
| 39. C5×C8 | C2×C4 | semidirect |
| 40. #168 | C2×C4 | semidirect |
| 56. AGL(1,𝔽5) | SD16 | direct (N × H) |
| 67. SD16 | AGL(1,𝔽5) | direct (N × H) |
| 84. Q8 | C2×AGL(1,𝔽5) | semidirect |
| 97. C8 | C2×AGL(1,𝔽5) | semidirect |
| 98. C5 | C4×SD16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×AGL(1,𝔽5) | 2 |
| D4×AGL(1,𝔽5) | 2 |
| D5×SD16 | 2 |
| #4009 | 2 |
| #4007 | 2 |
| #3993 | 2 |
| C8×AGL(1,𝔽5) | 2 |
| C4×SD16 | 5 |