Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
290 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 105 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×#124 | C2 |
| hypercenter | #124 | D5 |
| hypocenter | C5 | #548 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Q8×D5 | C2 | semidirect |
| 2. C2×#711 | C2 | semidirect |
| 3. C5×#124 | C2 | semidirect |
| 4. #4092 | C2 | semidirect |
| 5. #4084 | C2 | semidirect |
| 6. #4031 | C2 | semidirect |
| 7. #4030 | C2 | semidirect |
| 8. #4027 | C2 | semidirect |
| 9. #4024 | C2 | semidirect |
| 10. C4×D20 | C2 | semidirect |
| 11. C4×Dic10 | C2 | semidirect |
| 59. Dic10 | D4 | semidirect |
| 63. #124 | D5 | semidirect |
| 80. C2×D5 | #41 | semidirect |
| 142. C5 | #548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D5 | 2 |
| C2×#711 | 2 |
| C5×#124 | 2 |
| #4092 | 2 |
| #4084 | 2 |
| #4031 | 2 |
| #4030 | 2 |
| #4027 | 2 |
| #4024 | 2 |
| C4×D20 | 2 |
| C4×Dic10 | 2 |
| #548 | 5 |