Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
330 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 330 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 | C5×#124 | C2 |
| prime radical | C2×D4×D5 | C2 |
| hypercenter | #124 | D5 |
| hypocenter | C5 | C2×#124 |
| 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 |
| 3. C5×#124 | C2 | semidirect |
| 4. #4093 | C2 | semidirect |
| 5. #4082 | C2 | semidirect |
| 6. #4031 | C2 | semidirect |
| 7. D5×C22⋊C4 | C2 | semidirect |
| 8. #4021 | C2 | semidirect |
| 9. C42×D5 | C2 | semidirect |
| 11. C2×C5×Q8 | C22 | semidirect |
| 20. C2×Dic10 | C22 | semidirect |
| 21. C2×Dic10 | C22 | semidirect |
| 22. C5×C22⋊C4 | C22 | semidirect |
| 23. C42×C5 | C22 | semidirect |
| 24. C22⋊Dic5 | C22 | semidirect |
| 25. #685 | C22 | semidirect |
| 26. #685 | C22 | semidirect |
| 27. C4×Dic5 | C22 | semidirect |
| 28. C4×Dic5 | C22 | semidirect |
| 56. #124 | D5 | direct (N × H) |
| 77. C2×Q8 | C2×D5 | semidirect |
| 88. C22⋊C4 | C2×D5 | semidirect |
| 91. C42 | C2×D5 | semidirect |
| 96. D5 | #124 | direct (N × H) |
| 117. C5 | C2×#124 | 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×D4×D5 | 2 |
| C5×#124 | 2 |
| #4093 | 2 |
| #4082 | 2 |
| #4031 | 2 |
| D5×C22⋊C4 | 2 |
| #4021 | 2 |
| C42×D5 | 2 |
| C2×#124 | 5 |