Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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. C2×C42×C5 | C2 | semidirect |
| 3. C2×#681 | C2 | semidirect |
| 4. #3937 | C2 | direct (N × H) |
| 10. #709 | C4 | semidirect |
| 12. C2×D20 | C4 | semidirect |
| 14. C2×Dic10 | C4 | semidirect |
| 16. C42×C5 | C22 | semidirect |
| 18. #681 | C22 | semidirect |
| 35. D20 | C2×C4 | semidirect |
| 39. Dic10 | C2×C4 | semidirect |
| 43. C2×C42 | D5 | semidirect |
| 71. C42 | C2×D5 | semidirect |
| 74. C2×C5 | #104 | semidirect |
| 97. C5 | C2×#104 | semidirect |
| 113. C2 | #3937 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#709 | 2 |
| C2×C42×C5 | 2 |
| C2×#681 | 2 |
| #3937 | 2 |
| C2×#104 | 5 |