Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1104 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 208 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×#127 |
| 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×C5×D20 | C2 | semidirect |
| 2. C22×#6037 | C2 | semidirect |
| 3. C2×C4×#1039 | C2 | semidirect |
| 4. #11717032 | C2 | direct (N × H) |
| 9. C2×C5×D20 | C22 | semidirect |
| 11. C2×#6037 | C22 | semidirect |
| 12. C4×#1039 | C22 | semidirect |
| 18. C2×C4×C52 | D4 | semidirect |
| 20. C2×#1039 | D4 | semidirect |
| 26. C22×D20 | D5 | semidirect |
| 36. C4×C52 | C2×D4 | semidirect |
| 37. #1039 | C2×D4 | semidirect |
| 49. C2×D20 | C2×D5 | semidirect |
| 53. C2×C52 | #127 | semidirect |
| 68. C2×C4×C5 | C22⋊D5 | semidirect |
| 80. C52 | C2×#127 | semidirect |
| 94. C4×C5 | C2×C22⋊D5 | semidirect |
| 109. C2×C5 | #4086 | semidirect |
| 121. C2×C4 | #6037 | semidirect |
| 124. C5 | C2×#4086 | semidirect |
| 132. C4 | C2×#6037 | semidirect |
| 134. C2 | #11717032 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×D20 | 2 |
| C22×#6037 | 2 |
| C2×C4×#1039 | 2 |
| #11717032 | 2 |
| C2×#4086 | 5 |