Finite Group DatabasebetaFinite Group DatabasebetaOrder 1600.
1168 conjugacy classes of subgroups; only the 307 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 307 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 | C4×C52×D4 | C2 |
| hypercenter | C4×D4 | C5⋊D5 |
| hypocenter | C52 | #547 |
| LCS | G ▷ C22×C52 ▷ C52 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#87902 | C2 | semidirect |
| 2. C4×C52×D4 | C2 | semidirect |
| 3. #11717250 | C2 | semidirect |
| 4. C2×C4⋊#1039 | C2 | semidirect |
| 5. #11717217 | C2 | semidirect |
| 6. #11717206 | C2 | semidirect |
| 7. C4×C4⋊(C5⋊D5) | C2 | semidirect |
| 8. #11717189 | C2 | semidirect |
| 29. C52×D4 | D4 | semidirect |
| 43. C4×C5×D4 | D5 | semidirect |
| 60. C4×C52 | #41 | semidirect |
| 88. C5×D4 | D20 | semidirect |
| 107. C4×D4 | C5⋊D5 | semidirect |
| 109. C52 | #547 | semidirect |
| 120. C4×C5 | #711 | semidirect |
| 150. D4 | C4⋊(C5⋊D5) | semidirect |
| 160. C5 | #65889 | semidirect |
| 173. C4 | #87902 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#87902 | 2 |
| C4×C52×D4 | 2 |
| #11717250 | 2 |
| C2×C4⋊#1039 | 2 |
| #11717217 | 2 |
| #11717206 | 2 |
| C4×C4⋊(C5⋊D5) | 2 |
| #11717189 | 2 |
| #65889 | 5 |