Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
694 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 162 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 | C22×D52 |
| commutator, socle, cosocle | C22×C52 | C24 |
| Fitting | C2×C52×Q8 | C22 |
| hypercenter | C2×Q8 | D52 |
| hypocenter | C52 | #550 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C5×#713 | C2 | semidirect |
| 2. Q8×#1039 | C2 | semidirect |
| 3. #11717032 | C2 | semidirect |
| 4. #11717026 | C2 | semidirect |
| 5. C4×#6037 | C2 | semidirect |
| 18. C52×Q8 | D4 | semidirect |
| 28. C2×#713 | D5 | semidirect |
| 41. #1039 | #41 | semidirect |
| 68. C5×Q8 | C22⋊D5 | semidirect |
| 88. C52 | #550 | semidirect |
| 124. Q8 | #6037 | semidirect |
| 134. C5 | #66168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×#713 | 2 |
| Q8×#1039 | 2 |
| #11717032 | 2 |
| #11717026 | 2 |
| C4×#6037 | 2 |
| #66168 | 5 |