Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
162 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 60 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 |
|---|---|---|
| 4. #4009 | C2 | direct (N × H) |
| 6. C2×C5×Q8 | C4 | semidirect |
| 9. Q8×D5 | C4 | semidirect |
| 14. C2×Dic10 | C4 | semidirect |
| 25. C5×Q8 | C2×C4 | semidirect |
| 39. Dic10 | C2×C4 | semidirect |
| 63. C2×Q8 | AGL(1,𝔽5) | semidirect |
| 72. C2×C5 | #103 | semidirect |
| 74. D5 | #103 | semidirect |
| 83. Q8 | C2×AGL(1,𝔽5) | semidirect |
| 97. C5 | C2×#103 | semidirect |
| 113. C2 | #4009 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D5 | 2 |
| C2×C4⋊AGL(1,𝔽5) | 2 |
| C2×D5⋊C8 | 2 |
| #4009 | 2 |
| C2×#103 | 5 |