Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
952 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 952 conjugacy classes of subgroups — too many to draw. Only its 185 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D5 |
| commutator, socle, cosocle | C23×C5 | C24 |
| Fitting | C22×C5×#41 | C2 |
| hypercenter | C22×#41 | D5 |
| hypocenter | C5 | #2431 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C5×#41 | C2 | semidirect |
| 2. C2×#4093 | C2 | semidirect |
| 3. C2×#4086 | C2 | semidirect |
| 4. C2×#4076 | C2 | semidirect |
| 5. #65519 | C2 | semidirect |
| 6. #65512 | C2 | semidirect |
| 7. #65510 | C2 | semidirect |
| 8. #65502 | C2 | semidirect |
| 9. C4×C22⋊Dic5 | C2 | semidirect |
| 40. C2×C5×Q8 | D4 | semidirect |
| 46. C2×C5×D4 | D4 | semidirect |
| 52. C22×C4×C5 | D4 | semidirect |
| 74. C22×#41 | D5 | semidirect |
| 122. C2×Dic5 | #41 | semidirect |
| 179. C2×Q8 | C22⋊D5 | semidirect |
| 193. C2×D4 | C22⋊D5 | semidirect |
| 202. C22×C4 | C22⋊D5 | semidirect |
| 262. C5 | #2431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×#41 | 2 |
| C2×#4093 | 2 |
| C2×#4086 | 2 |
| C2×#4076 | 2 |
| #65519 | 2 |
| #65512 | 2 |
| #65510 | 2 |
| #65502 | 2 |
| C4×C22⋊Dic5 | 2 |
| #2431 | 5 |