Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
170 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 71 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×C4×Dic5 | C2 | semidirect |
| 3. C2×#681 | C2 | semidirect |
| 4. #3969 | C2 | direct (N × H) |
| 7. C5×#41 | C4 | semidirect |
| 9. C2×C5×Q8 | C4 | semidirect |
| 11. C2×C5×D4 | C4 | semidirect |
| 16. C4×Dic5 | C22 | semidirect |
| 18. #681 | C22 | semidirect |
| 24. C5×Q8 | C2×C4 | semidirect |
| 28. C5×D4 | C2×C4 | semidirect |
| 59. #41 | Dic5 | semidirect |
| 61. C2×Q8 | Dic5 | semidirect |
| 63. C2×D4 | Dic5 | semidirect |
| 75. C2×C5 | #104 | semidirect |
| 80. Q8 | C2×Dic5 | semidirect |
| 84. D4 | C2×Dic5 | semidirect |
| 97. C5 | C2×#104 | semidirect |
| 113. C2 | #3969 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#41 | 2 |
| C2×C4×Dic5 | 2 |
| C2×#681 | 2 |
| #3969 | 2 |
| C2×#104 | 5 |