Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
1492 conjugacy classes of subgroups; only the 553 normal subgroups are shown.
This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 553 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 | C24×D5 |
| commutator, socle, cosocle | C22×C5 | C25 |
| Fitting | C2×C5×2−1+4 | C2 |
| hypercenter | C2×2−1+4 | D5 |
| hypocenter | C5 | #3486 |
| LCS | G ▷ C22×C5 ▷ C5 | |
| UCS | C1 ◁ C22 ◁ C2×2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×2−1+4 | C2 | semidirect |
| 2. C22×Q8×D5 | C2 | semidirect |
| 3. #66165 | C2 | semidirect |
| 4. #66162 | C2 | semidirect |
| 5. #66159 | C2 | semidirect |
| 6. Q8×C22⋊D5 | C2 | semidirect |
| 7. #66146 | C2 | semidirect |
| 10. C2×C5×#41 | C22 | semidirect |
| 12. C22×C5×Q8 | C22 | semidirect |
| 18. Q8×Dic5 | C22 | semidirect |
| 19. #4090 | C22 | semidirect |
| 22. #4082 | C22 | semidirect |
| 26. #4070 | C22 | semidirect |
| 32. C2×C5×Q8 | D4 | semidirect |
| 52. C2×2−1+4 | D5 | semidirect |
| 80. C2×#41 | C2×D5 | semidirect |
| 85. C22×Q8 | C2×D5 | semidirect |
| 105. C2×D5 | 2−1+4 | semidirect |
| 117. C2×Q8 | C22⋊D5 | semidirect |
| 158. C5 | #3486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×2−1+4 | 2 |
| C22×Q8×D5 | 2 |
| #66165 | 2 |
| #66162 | 2 |
| #66159 | 2 |
| Q8×C22⋊D5 | 2 |
| #66146 | 2 |
| #3486 | 5 |