Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
330 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D5 |
| commutator, socle, cosocle | C22×C5 | C24 |
| Frattini | C22 | C23×D5 |
| Fitting | C5×#117 | C2 |
| hypercenter | #117 | D5 |
| hypocenter | C5 | #525 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C2×C4 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#709 | C2 | semidirect |
| 2. C22×C4×D5 | C2 | semidirect |
| 3. C5×#117 | C2 | semidirect |
| 4. #4043 | C2 | semidirect |
| 5. #4041 | C2 | semidirect |
| 6. #4032 | C2 | semidirect |
| 7. #4028 | C2 | semidirect |
| 8. C4×D20 | C2 | semidirect |
| 15. C2×D20 | C22 | semidirect |
| 19. C2×C4×D5 | C22 | semidirect |
| 20. C2×Dic10 | C22 | semidirect |
| 21. C5×C4⋊C4 | C22 | semidirect |
| 23. C42×C5 | C22 | semidirect |
| 25. #685 | C22 | semidirect |
| 26. C4⋊Dic5 | C22 | semidirect |
| 33. C2×C4×C5 | D4 | semidirect |
| 54. #117 | D5 | semidirect |
| 63. C2×D5 | #41 | semidirect |
| 82. C4⋊C4 | C2×D5 | semidirect |
| 86. C42 | C2×D5 | semidirect |
| 107. C2×C4 | D20 | semidirect |
| 111. C5 | #525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#709 | 2 |
| C22×C4×D5 | 2 |
| C5×#117 | 2 |
| #4043 | 2 |
| #4041 | 2 |
| #4032 | 2 |
| #4028 | 2 |
| C4×D20 | 2 |
| #525 | 5 |