Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
294 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D5 |
| commutator, socle, cosocle | C22×C5 | C24 |
| Fitting | C5×C22⋊Q8 | C2 |
| hypercenter | C22⋊Q8 | D5 |
| hypocenter | C5 | #537 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#713 | C2 | semidirect |
| 2. C2×#709 | C2 | semidirect |
| 3. C5×C22⋊Q8 | C2 | semidirect |
| 4. #4092 | C2 | semidirect |
| 5. #4076 | C2 | semidirect |
| 6. #4042 | C2 | semidirect |
| 7. #4041 | C2 | semidirect |
| 8. #4041 | C2 | semidirect |
| 9. D5×C4⋊C4 | C2 | semidirect |
| 10. #4030 | C2 | semidirect |
| 11. #4030 | C2 | semidirect |
| 61. C4×D5 | D4 | semidirect |
| 67. C22⋊Q8 | D5 | semidirect |
| 151. C5 | #537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#713 | 2 |
| C2×#709 | 2 |
| C5×C22⋊Q8 | 2 |
| #4092 | 2 |
| #4076 | 2 |
| #4042 | 2 |
| #4041 | 2 |
| D5×C4⋊C4 | 2 |
| #4030 | 2 |
| #537 | 5 |