Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
582 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 149 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 | C5×#383 | C2 |
| prime radical | C22×D20 | C22 |
| hypercenter | #383 | D5 |
| hypocenter | C5 | #2852 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#4022 | C2 | semidirect |
| 2. C2×C42×D5 | C2 | semidirect |
| 3. C5×#383 | C2 | semidirect |
| 4. #64959 | C2 | semidirect |
| 5. #64957 | C2 | semidirect |
| 7. #64942 | C2 | semidirect |
| 35. C42×C5 | D4 | semidirect |
| 48. #383 | D5 | semidirect |
| 94. C2×D5 | #126 | semidirect |
| 117. C42 | D20 | semidirect |
| 145. C5 | #2852 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#4022 | 2 |
| C2×C42×D5 | 2 |
| C5×#383 | 2 |
| #64959 | 2 |
| #64957 | 2 |
| #64954 | 2 |
| #64942 | 2 |
| #2852 | 5 |