Finite Group Databasebeta

← C5×(#92150⋊C3)⋊C5 #49137339

Subgroups — C5×(#92150⋊C3)⋊C5 #49137339

Order 36300.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×((C11⋊D11)⋊C3)⋊C5C211yesmaximal, characteristic
2C5×#92150⋊C5C311yesmaximal, characteristic, complemented, Hall
3C5×(C112⋊C3)⋊C5C411yescharacteristic, complemented, Hall
4C5×#92150⋊C3C511yesmaximal, characteristic, complemented
5(#92150⋊C3)⋊C5C515yesmaximal, direct product factor
6C5×#11925892C2×C311yescharacteristic
7C5×(C11⋊D11)⋊C3C2×C511yescharacteristic
8((C11⋊D11)⋊C3)⋊C5C2×C515yes—
9C5×#10597243C3×C411yescharacteristic, complemented, Hall
10C5×#92150C3×C511yescharacteristic, complemented
11#92150⋊C5C3×C515yescomplemented
12C5×C112⋊C3C4×C511yescharacteristic, complemented
13(C112⋊C3)⋊C5C4×C515yescomplemented
14#92150⋊C3C5211yescharacteristic, complemented, Hall
15C5×C11⋊D11C2×C3×C511yescharacteristic
16#11925892C2×C3×C515yes—
17(C11⋊D11)⋊C3C2×C5211yescharacteristic
18C5×C112C3×C4×C511yescharacteristic, complemented
19#10597243C3×C4×C515yescomplemented
20C5×AGL(1,𝔽11)—662no—
21#92150C3×C5211yescharacteristic, complemented, Hall
22C112⋊C3C4×C5211yescharacteristic, complemented, Hall
23C3×C4×C52—1211nomaximal, Hall
24C5×C11⋊C5—662no—
25C11⋊D11C2×C3×C5211yescharacteristic
26C2×C3×C52—1211no—
27C112C3×C4×C5211yescharacteristic, complemented, Sylow
28C5×D11—3302no—
29AGL(1,𝔽11)—6610no—
30C4×C52—1211noHall
31C3×C52—1211noHall
32C3×C4×C5—1211no—
33C3×C4×C5—1215no—
34C5×C11—62no—
35C11⋊C5—6610no—
36C2×C52—1211no—
37C2×C3×C5—6051no—
38C2×C3×C5—1215no—
39C52—1211noSylow
40D11—3302no—
41C4×C5—1211no—
42C4×C5—1215no—
43C3×C5—6051no—
44C3×C5—1215no—
45C3×C4—1211noHall
46C11—62no—
47C2×C5—6051no—
48C2×C5—1215no—
49C2×C3—6051no—
50C5—1215no—
51C5(#92150⋊C3)⋊C511yescharacteristic, direct product factor
52C4—1211noSylow
53C3—6051noSylow
54C2—6051no—
subgroupG/H
center, hypercenterC5(#92150⋊C3)⋊C5
commutator, hypocenterC112C3×C4×C52
FrattiniC1G
Fitting, socleC5×C112C3×C4×C5
prime radicalC5×((C11⋊D11)⋊C3)⋊C5C2
cosocleC11⋊D11C2×C3×C52
LCSG ▷ C112
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
2. C5×#92150⋊C5C3semidirect
3. C5×(C112⋊C3)⋊C5C4semidirect
4. C5×#92150⋊C3C5semidirect
5. (#92150⋊C3)⋊C5C5direct (N × H)
9. C5×#10597243C3×C4semidirect
10. C5×#92150C3×C5semidirect
11. #92150⋊C5C3×C5semidirect
12. C5×C112⋊C3C4×C5semidirect
13. (C112⋊C3)⋊C5C4×C5semidirect
14. #92150⋊C3C52semidirect
18. C5×C112C3×C4×C5semidirect
19. #10597243C3×C4×C5semidirect
21. #92150C3×C52semidirect
22. C112⋊C3C4×C52semidirect
27. C112C3×C4×C52semidirect
51. C5(#92150⋊C3)⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C5×((C11⋊D11)⋊C3)⋊C52
C5×#92150⋊C53
C5×#92150⋊C35
(#92150⋊C3)⋊C55
C3×C4×C52121