Finite Group Databasebeta

← ((C31⋊C3)⋊C5)⋊#595 #44539281

Subgroups — ((C31⋊C3)⋊C5)⋊#595 #44539281

Order 31620.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D17×(C31⋊C3)⋊C5C211yesmaximal, characteristic
2ΓL(1,𝔽32)⋊#595C311yesmaximal, characteristic, complemented, Hall
3C17×(C31⋊C3)⋊C5C411yescharacteristic, complemented, Hall
4(C31⋊C3)⋊#595C511yesmaximal, characteristic, complemented, Hall
5D17×ΓL(1,𝔽32)C2×C311yescharacteristic
6D17×C31⋊C3C2×C511yescharacteristic
7C17×ΓL(1,𝔽32)C3×C411yescharacteristic, complemented, Hall
8C31⋊#595C3×C511yescharacteristic, complemented, Hall
9((C31⋊C3)⋊C4)⋊C5—171nomaximal, Hall
10C17×C31⋊C3C4×C511yescharacteristic, complemented, Hall
11C31×D17C2×C3×C511yescharacteristic
12C3×C5×#595—311nomaximal, Hall
13C2×(C31⋊C3)⋊C5—171no—
14Dic31⋊C5—171noHall
15C17×C31C3×C4×C511yescharacteristic, complemented, Hall
16C3×C5×D17—311no—
17(C31⋊C3)⋊C5#59511yescharacteristic, complemented, Hall
18(C31⋊C3)⋊C4—171noHall
19C5×#595—311noHall
20C2×ΓL(1,𝔽32)—171no—
21C3×C5×C17—311noHall
22C3×#595—311noHall
23C2×C31⋊C3—171no—
24C5×D17—311no—
25ΓL(1,𝔽32)C3×#59511yescharacteristic, complemented, Hall
26Dic31—171noHall
27C3×D17—311no—
28C31⋊C3C5×#59511yescharacteristic, complemented, Hall
29C5×C17—311noHall
30#595—311noHall
31C2×C31—171no—
32C3×C4×C5—5271noHall
33C3×C17—311noHall
34D17AGL(1,𝔽31)11yescharacteristic
35C31C3×C5×#59511yescharacteristic, complemented, Sylow
36C2×C3×C5—5271no—
37C4×C5—5271noHall
38C17((C31⋊C3)⋊C4)⋊C511yescharacteristic, complemented, Sylow
39C3×C5—311noHall
40C3×C4—5271noHall
41C2×C5—5271no—
42C2×C3—5271no—
43C5—311noSylow
44C4—5271noSylow
45C3—311noSylow
46C2—171no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC17×C31C3×C4×C5
prime radicalD17×(C31⋊C3)⋊C5C2
cosocleC31×D17C2×C3×C5
LCSG ▷ C17×C31
UCSC1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. ΓL(1,𝔽32)⋊#595C3semidirect
3. C17×(C31⋊C3)⋊C5C4semidirect
4. (C31⋊C3)⋊#595C5semidirect
7. C17×ΓL(1,𝔽32)C3×C4semidirect
8. C31⋊#595C3×C5semidirect
10. C17×C31⋊C3C4×C5semidirect
15. C17×C31C3×C4×C5semidirect
17. (C31⋊C3)⋊C5#595semidirect
25. ΓL(1,𝔽32)C3×#595semidirect
28. C31⋊C3C5×#595semidirect
35. C31C3×C5×#595semidirect
38. C17((C31⋊C3)⋊C4)⋊C5semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
D17×(C31⋊C3)⋊C52
ΓL(1,𝔽32)⋊#5953
(C31⋊C3)⋊#5955
((C31⋊C3)⋊C4)⋊C517
C3×C5×#59531