Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
339 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 339 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | #1042 |
| commutator, hypocenter | C52 | C2×C4×C8 |
| Frattini | C22 | C22×#1042 |
| Fitting | C42×C52 | C4 |
| socle | C22×C52 | C22×C4 |
| prime radical | C22×C5×D5 | C2×C4 |
| cosocle | C2×C5×Dic5 | C23 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C4×#6032 | C2 | semidirect |
| 7. D5⋊#168 | C4 | direct (N × H) |
| 18. C4×C5×D5 | C8 | semidirect |
| 20. #6032 | C2×C4 | semidirect |
| 31. C4×C52 | C2×C8 | semidirect |
| 32. C5×Dic5 | C2×C8 | semidirect |
| 52. C5×D5 | C4×C8 | semidirect |
| 67. C4×D5 | #168 | semidirect |
| 74. C52 | C2×C4×C8 | semidirect |
| 86. C4×C5 | C2×#168 | semidirect |
| 88. C4×C5 | D5⋊C8 | semidirect |
| 90. Dic5 | C2×#168 | semidirect |
| 106. D5 | C4×#168 | semidirect |
| 116. C5 | C2×C4×#168 | semidirect |
| 117. C5 | C4×D5⋊C8 | semidirect |
| 123. C4 | D5⋊#168 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D5⋊#168 | 2 |
| C42×C5×D5 | 2 |
| C4×#6032 | 2 |
| C4×D5⋊C8 | 5 |
| C2×C4×#168 | 5 |