Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1088 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D52 |
| commutator, cosocle | C22×C52 | C24 |
| Frattini | C22 | C22×D52 |
| Fitting | C22×C4×C52 | C22 |
| socle | C23×C52 | C23 |
| hypercenter | C22×C4 | D52 |
| hypocenter | C52 | C2×#121 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C4×C5⋊D5 | C2 | semidirect |
| 2. C22×#6038 | C2 | semidirect |
| 3. C22×#6037 | C2 | semidirect |
| 4. C2×C5×#685 | C2 | semidirect |
| 5. C2×#87781 | C2 | semidirect |
| 6. #11717030 | C2 | direct (N × H) |
| 12. C2×C4×C5⋊D5 | C22 | semidirect |
| 15. C2×#6038 | C22 | semidirect |
| 17. C2×#6037 | C22 | semidirect |
| 18. C5×#685 | C22 | semidirect |
| 19. #87781 | C22 | semidirect |
| 24. C22×C5⋊D5 | D4 | semidirect |
| 32. C2×#1039 | D4 | semidirect |
| 45. C2×#685 | D5 | semidirect |
| 55. C2×C5⋊D5 | C2×D4 | semidirect |
| 61. #1039 | C2×D4 | semidirect |
| 84. #685 | C2×D5 | semidirect |
| 87. C2×C52 | #121 | semidirect |
| 134. C52 | C2×#121 | semidirect |
| 183. C2×C5 | #4030 | semidirect |
| 209. C5 | C2×#4030 | semidirect |
| 227. C2 | #11717030 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C5⋊D5 | 2 |
| C22×#6038 | 2 |
| C22×#6037 | 2 |
| C2×C5×#685 | 2 |
| C2×#87781 | 2 |
| #11717030 | 2 |
| C2×#4030 | 5 |