Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
294 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 111 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 | C2×C5×#41 | C2 |
| hypercenter | C2×#41 | D5 |
| hypocenter | C5 | #537 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#41 | C2 | semidirect |
| 2. C2×#709 | C2 | semidirect |
| 3. #4092 | C2 | semidirect |
| 4. #4085 | C2 | semidirect |
| 5. #4084 | C2 | semidirect |
| 6. #4076 | C2 | semidirect |
| 7. C2×C4⋊Dic5 | C2 | semidirect |
| 8. #4070 | C2 | semidirect |
| 35. C2×C4×C5 | D4 | semidirect |
| 48. C2×#41 | D5 | semidirect |
| 109. C2×C4 | C22⋊D5 | semidirect |
| 113. C5 | #537 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#41 | 2 |
| C2×#709 | 2 |
| #4092 | 2 |
| #4085 | 2 |
| #4084 | 2 |
| #4076 | 2 |
| C2×C4⋊Dic5 | 2 |
| #4070 | 2 |
| #537 | 5 |