Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1040 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 1040 conjugacy classes of subgroups — too many to draw. Only its 211 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×C5⋊D5 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C52×#120 | C2 |
| hypercenter | #120 | C5⋊D5 |
| hypocenter | C52 | H(3,𝔽4) |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ #120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C52×#120 | C2 | semidirect |
| 2. #11717273 | C2 | semidirect |
| 3. #11717257 | C2 | semidirect |
| 4. #11717256 | C2 | semidirect |
| 5. #11717205 | C2 | semidirect |
| 6. C24×C52 | C22 | semidirect |
| 7. C23×C5⋊D5 | C22 | semidirect |
| 10. C2×#6045 | C22 | semidirect |
| 11. C52×C22⋊C4 | C22 | semidirect |
| 12. C22⋊#1039 | C22 | semidirect |
| 13. C22⋊#1039 | C22 | semidirect |
| 14. #87808 | C22 | semidirect |
| 15. C4×#1039 | C22 | semidirect |
| 27. C5×#120 | D5 | semidirect |
| 41. C24×C5 | C2×D5 | semidirect |
| 46. C5×C22⋊C4 | C2×D5 | semidirect |
| 70. #120 | C5⋊D5 | semidirect |
| 71. C52 | H(3,𝔽4) | semidirect |
| 82. C24 | C2×C5⋊D5 | semidirect |
| 89. C22⋊C4 | C2×C5⋊D5 | semidirect |
| 105. C5 | #65928 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C52×#120 | 2 |
| #11717273 | 2 |
| #11717257 | 2 |
| #11717256 | 2 |
| #11717205 | 2 |
| #65928 | 5 |