Finite Group DatabasebetaFinite Group DatabasebetaOrder 320.
334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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 | C4×C5×D4 | C2 |
| hypercenter | C4×D4 | D5 |
| hypocenter | C5 | #546 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#709 | C2 | semidirect |
| 2. C22×D20 | C2 | semidirect |
| 3. C4×C5×D4 | C2 | semidirect |
| 4. #4083 | C2 | semidirect |
| 5. #4076 | C2 | semidirect |
| 6. #4070 | C2 | semidirect |
| 7. #4040 | C2 | semidirect |
| 8. #4030 | C2 | semidirect |
| 9. D5×C22⋊C4 | C2 | semidirect |
| 10. #4021 | C2 | semidirect |
| 11. C4×D20 | C2 | semidirect |
| 15. C22×C4×C5 | C22 | semidirect |
| 16. C2×C22⋊D5 | C22 | semidirect |
| 17. C2×C22⋊D5 | C22 | semidirect |
| 23. C2×C4×D5 | C22 | semidirect |
| 24. C2×C4×D5 | C22 | semidirect |
| 25. C2×Dic10 | C22 | semidirect |
| 26. C5×C4⋊C4 | C22 | semidirect |
| 28. C5×C22⋊C4 | C22 | semidirect |
| 29. C42×C5 | C22 | semidirect |
| 31. #685 | C22 | semidirect |
| 32. #685 | C22 | semidirect |
| 33. #685 | C22 | semidirect |
| 34. #685 | C22 | semidirect |
| 35. C4⋊Dic5 | C22 | semidirect |
| 36. #683 | C22 | semidirect |
| 59. D20 | D4 | semidirect |
| 72. C4×D4 | D5 | semidirect |
| 79. C22×C5 | #41 | semidirect |
| 108. C22×C4 | C2×D5 | semidirect |
| 111. C4⋊C4 | C2×D5 | semidirect |
| 118. C22⋊C4 | C2×D5 | semidirect |
| 119. C42 | C2×D5 | semidirect |
| 152. C5 | #546 | semidirect |
| 165. C22 | #709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#709 | 2 |
| C22×D20 | 2 |
| C4×C5×D4 | 2 |
| #4083 | 2 |
| #4076 | 2 |
| #4070 | 2 |
| #4040 | 2 |
| #4030 | 2 |
| D5×C22⋊C4 | 2 |
| #4021 | 2 |
| C4×D20 | 2 |
| #546 | 5 |