Finite Group Databasebeta

← C32×C7×C5⋊D55 #46831659

Subgroups — C32×C7×C5⋊D55 #46831659

Order 34650.

384 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C52×C7×C11C211yesmaximal, characteristic, complemented, Hall
2C3×C7×C5⋊D55C314yesmaximal, direct product factor
3C32×C7×D55—56nomaximal
4C3×C52×C7×C11C2×C314yescomplemented
5C32×C5⋊D55C711yesmaximal, characteristic, direct product factor, Hall
6C7×C5⋊D55C3211yescharacteristic, direct product factor, Hall
7C32×C5×C7×C11D516yescomplemented
8C32×C7×C5⋊D5—111nomaximal, Hall
9C32×C52×C11C2×C711yescharacteristic, complemented, Hall
10C3×C7×D55—524no—
11C52×C7×C11C2×C3211yescharacteristic, complemented, Hall
12C3×C5⋊D55C3×C714yesdirect product factor
13C32×C52×C7D1111yescharacteristic, complemented, Hall
14C32×C7×D11—251noHall
15C3×C5×C7×C11C3×D5124yescomplemented
16C3×C7×C5⋊D5—114no—
17C32×D55—56no—
18C3×C52×C11C2×C3×C714yescomplemented
19C7×D55—56no—
20C32×C7×C11C5⋊D511yescharacteristic, complemented, Hall
21C32×C7×D5—556no—
22C5⋊D55C32×C711yescharacteristic, direct product factor, Hall
23C3×C52×C7C3×D1114yescomplemented
24C32×C5×C11C7×D516yescomplemented
25C3×C7×D11—254no—
26C32×C5⋊D5—111noHall
27C5×C7×C11C32×D516yescomplemented
28C7×C5⋊D5—111noHall
29C3×D55—524no—
30C32×C5×C7D5516yescomplemented
31C52×C11C2×C32×C711yescharacteristic, complemented, Hall
32C3×C7×C11C3×C5⋊D514yescomplemented
33C32×C52C7×D1111yescharacteristic, complemented, Hall
34C3×C7×D5—5524no—
35C32×D11—251noHall
36C52×C7C32×D1111yescharacteristic, complemented, Hall
37C3×C5×C11C3×C7×D5124yescomplemented
38C7×D11—251noHall
39C3×C5⋊D5—114no—
40C2×C32×C7—2751noHall
41D55—56no—
42C3×C5×C7C3×D55124yescomplemented
43C32×C11C7×C5⋊D511yescharacteristic, complemented, Hall
44C32×D5—556no—
45C7×C11C32×C5⋊D511yescharacteristic, complemented, Hall
46C3×C52C3×C7×D1114yescomplemented
47C7×D5—556no—
48C3×D11—254no—
49C32×C7C5⋊D5511yescharacteristic, direct product factor, Hall
50C5×C11C32×C7×D516yescomplemented
51C5⋊D5—111noHall
52C32×C5C7×D5516yescomplemented
53C2×C3×C7—2754no—
54C5×C7C32×D5516yescomplemented
55C3×C11C3×C7×C5⋊D514yescomplemented
56C3×D5—5524no—
57C52C32×C7×D1111yescharacteristic, complemented, Sylow
58D11—251noHall
59C3×C7C3×C5⋊D5514yesdirect product factor
60C2×C32—2751noHall
61C3×C5C3×C7×D55124yescomplemented
62C2×C7—2751noHall
63C11C32×C7×C5⋊D511yescharacteristic, complemented, Sylow
64D5—556no—
65C32C7×C5⋊D5511yescharacteristic, direct product factor, Sylow
66C7C32×C5⋊D5511yescharacteristic, direct product factor, Sylow
67C2×C3—2754no—
68C5C32×C7×D5516yescomplemented
69C3C3×C7×C5⋊D5514yesdirect product factor
70C2—2751noSylow
subgroupG/H
center, hypercenterC32×C7C5⋊D55
commutator, cosocle, hypocenterC52×C11C2×C32×C7
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C52×C11
UCSC1 ◁ C32×C7

Complements

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

NH ≅ G/Ntype
1. C32×C52×C7×C11C2semidirect
2. C3×C7×C5⋊D55C3direct (N × H)
4. C3×C52×C7×C11C2×C3semidirect
5. C32×C5⋊D55C7direct (N × H)
6. C7×C5⋊D55C32direct (N × H)
7. C32×C5×C7×C11D5semidirect
9. C32×C52×C11C2×C7semidirect
11. C52×C7×C11C2×C32semidirect
12. C3×C5⋊D55C3×C7direct (N × H)
13. C32×C52×C7D11semidirect
15. C3×C5×C7×C11C3×D5semidirect
18. C3×C52×C11C2×C3×C7semidirect
20. C32×C7×C11C5⋊D5semidirect
22. C5⋊D55C32×C7direct (N × H)
23. C3×C52×C7C3×D11semidirect
24. C32×C5×C11C7×D5semidirect
27. C5×C7×C11C32×D5semidirect
30. C32×C5×C7D55semidirect
31. C52×C11C2×C32×C7semidirect
32. C3×C7×C11C3×C5⋊D5semidirect
33. C32×C52C7×D11semidirect
36. C52×C7C32×D11semidirect
37. C3×C5×C11C3×C7×D5semidirect
42. C3×C5×C7C3×D55semidirect
43. C32×C11C7×C5⋊D5semidirect
45. C7×C11C32×C5⋊D5semidirect
46. C3×C52C3×C7×D11semidirect
49. C32×C7C5⋊D55direct (N × H)
50. C5×C11C32×C7×D5semidirect
52. C32×C5C7×D55semidirect
54. C5×C7C32×D55semidirect
55. C3×C11C3×C7×C5⋊D5semidirect
57. C52C32×C7×D11semidirect
59. C3×C7C3×C5⋊D55direct (N × H)
61. C3×C5C3×C7×D55semidirect
63. C11C32×C7×C5⋊D5semidirect
65. C32C7×C5⋊D55direct (N × H)
66. C7C32×C5⋊D55direct (N × H)
68. C5C32×C7×D55semidirect
69. C3C3×C7×C5⋊D55direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C52×C7×C112
C3×C7×C5⋊D553
C32×C7×D555
C32×C5⋊D557
C32×C7×C5⋊D511