Finite Group Databasebeta

← C22×C3×(C112⋊C3)⋊C5 #36345177

Subgroups — C22×C3×(C112⋊C3)⋊C5 #36345177

Order 21780.

200 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×(C112⋊C3)⋊C5C213yesmaximal, direct product factor
2C22×C3×#10597243C311yesmaximal, characteristic, complemented
3C22×(C112⋊C3)⋊C5C313yesmaximal, direct product factor
4C3×(C112⋊C3)⋊C5C2211yescharacteristic, direct product factor, Hall
5C22×C3×C112⋊C3C511yesmaximal, characteristic, complemented, Hall
6C2×C3×#10597243C2×C313yescomplemented
7C2×(C112⋊C3)⋊C5C2×C319yesdirect product factor
8C22×#10597243C3211yescharacteristic, complemented, Hall
9C2×C3×C112⋊C3C2×C513yescomplemented
10C3×#10597243C22×C311yescharacteristic, complemented
11(C112⋊C3)⋊C5C22×C313yesdirect product factor
12C22×C3×C112C3×C511yescharacteristic, complemented
13C22×C112⋊C3C3×C513yescomplemented
14C2×#10597243C2×C3213yescomplemented
15C3×C112⋊C3C22×C511yescharacteristic, complemented, Hall
16C2×C3×C112C2×C3×C513yescomplemented
17C2×C112⋊C3C2×C3×C519yescomplemented
18C22×C3×C11⋊C5—334no—
19#10597243C22×C3211yescharacteristic, complemented, Hall
20C22×C112C32×C511yescharacteristic, complemented, Hall
21C3×C112C22×C3×C511yescharacteristic, complemented
22C112⋊C3C22×C3×C513yescomplemented
23C2×C3×C11⋊C5—3312no—
24C2×C112C2×C32×C513yescomplemented
25C22×C11⋊C5—334no—
26C22×C32×C5—1211nomaximal, Hall
27C3×C11⋊C5—334no—
28C22×C3×C11—34no—
29C112C22×C32×C511yescharacteristic, complemented, Sylow
30C2×C11⋊C5—3312no—
31C2×C32×C5—1213no—
32C2×C3×C11—312no—
33C22×C3×C5—1213no—
34C22×C3×C5—1211no—
35C11⋊C5—334no—
36C32×C5—1211noHall
37C22×C11—34no—
38C22×C32—1211noHall
39C3×C11—34no—
40C2×C3×C5—1219no—
41C2×C3×C5—1213no—
42C2×C11—312no—
43C22×C5—1211noHall
44C2×C32—1213no—
45C3×C5—1213no—
46C3×C5—1211no—
47C22×C3—1213no—
48C22×C3(C112⋊C3)⋊C511yescharacteristic, direct product factor
49C11—34no—
50C2×C5—1213no—
51C32—1211noSylow
52C2×C3—1219no—
53C2×C3C2×(C112⋊C3)⋊C513yesdirect product factor
54C5—1211noSylow
55C22C3×(C112⋊C3)⋊C511yescharacteristic, direct product factor, Sylow
56C3—1213no—
57C3C22×(C112⋊C3)⋊C511yescharacteristic, direct product factor
58C2C2×C3×(C112⋊C3)⋊C513yesdirect product factor
subgroupG/H
center, hypercenterC22×C3(C112⋊C3)⋊C5
commutator, cosocle, hypocenterC112C22×C32×C5
FrattiniC1G
Fitting, socleC22×C3×C112C3×C5
LCSG ▷ C112
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×(C112⋊C3)⋊C5C2direct (N × H)
2. C22×C3×#10597243C3semidirect
3. C22×(C112⋊C3)⋊C5C3direct (N × H)
4. C3×(C112⋊C3)⋊C5C22direct (N × H)
5. C22×C3×C112⋊C3C5semidirect
6. C2×C3×#10597243C2×C3semidirect
7. C2×(C112⋊C3)⋊C5C2×C3direct (N × H)
8. C22×#10597243C32semidirect
9. C2×C3×C112⋊C3C2×C5semidirect
10. C3×#10597243C22×C3semidirect
11. (C112⋊C3)⋊C5C22×C3direct (N × H)
12. C22×C3×C112C3×C5semidirect
13. C22×C112⋊C3C3×C5semidirect
14. C2×#10597243C2×C32semidirect
15. C3×C112⋊C3C22×C5semidirect
16. C2×C3×C112C2×C3×C5semidirect
17. C2×C112⋊C3C2×C3×C5semidirect
19. #10597243C22×C32semidirect
20. C22×C112C32×C5semidirect
21. C3×C112C22×C3×C5semidirect
22. C112⋊C3C22×C3×C5semidirect
24. C2×C112C2×C32×C5semidirect
29. C112C22×C32×C5semidirect
48. C22×C3(C112⋊C3)⋊C5direct (N × H)
53. C2×C3C2×(C112⋊C3)⋊C5direct (N × H)
55. C22C3×(C112⋊C3)⋊C5direct (N × H)
57. C3C22×(C112⋊C3)⋊C5direct (N × H)
58. C2C2×C3×(C112⋊C3)⋊C5direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×(C112⋊C3)⋊C52
C22×C3×#105972433
C22×(C112⋊C3)⋊C53
C22×C3×C112⋊C35
C22×C32×C5121