Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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. #4088 | C2 | semidirect |
| 2. C2×#688 | C2 | semidirect |
| 4. #4053 | C2 | semidirect |
| 5. C5×#101 | C2 | semidirect |
| 6. #3955 | C2 | semidirect |
| 7. #3954 | C2 | semidirect |
| 45. #101 | D5 | semidirect |
| 90. C5 | #471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4088 | 2 |
| C2×#688 | 2 |
| #4054 | 2 |
| #4053 | 2 |
| C5×#101 | 2 |
| #3955 | 2 |
| #3954 | 2 |
| #471 | 5 |