Finite Group DatabasebetaFinite Group DatabasebetaOrder 640.
1224 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 201 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×#380 | C2 |
| hypercenter | #380 | D5 |
| hypocenter | C5 | #2847 |
| LCS | G ▷ C23×C5 ▷ C5 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C4×D5 | C2 | semidirect |
| 2. C2×#4076 | C2 | semidirect |
| 3. C2×#4041 | C2 | semidirect |
| 4. C2×#4028 | C2 | semidirect |
| 5. C5×#380 | C2 | semidirect |
| 6. #65276 | C2 | semidirect |
| 7. #65247 | C2 | semidirect |
| 8. #64954 | C2 | semidirect |
| 14. C22×D20 | C22 | semidirect |
| 19. C2×C5×C4⋊C4 | C22 | semidirect |
| 23. C2×#685 | C22 | semidirect |
| 24. C2×#685 | C22 | semidirect |
| 25. C2×C4⋊Dic5 | C22 | semidirect |
| 28. C5×#95 | C22 | semidirect |
| 29. #3963 | C22 | semidirect |
| 36. C23×D5 | D4 | semidirect |
| 40. C22×C4×C5 | D4 | semidirect |
| 62. C2×C4×D5 | D4 | semidirect |
| 76. #380 | D5 | semidirect |
| 134. C2×C4⋊C4 | C2×D5 | semidirect |
| 140. #95 | C2×D5 | semidirect |
| 145. C22×C5 | #121 | semidirect |
| 163. C2×D5 | #121 | semidirect |
| 166. C4×C5 | #120 | semidirect |
| 197. C22×C4 | D20 | semidirect |
| 258. C5 | #2847 | semidirect |
| 276. C22 | #4041 | semidirect |
| 286. C4 | #4028 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D5 | 2 |
| C2×#4076 | 2 |
| C2×#4041 | 2 |
| C2×#4028 | 2 |
| C5×#380 | 2 |
| #65276 | 2 |
| #65247 | 2 |
| #64954 | 2 |
| #2847 | 5 |