Finite Group Databasebeta

← C5×C7×C3⋊D165 #46831679

Subgroups — C5×C7×C3⋊D165 #46831679

Order 34650.

240 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×C52×C7×C11C211yesmaximal, characteristic, complemented, Hall
2C5×C7×D165—34nomaximal
3C7×C3⋊D165C511yesmaximal, characteristic, direct product factor
4C5×C7×C3⋊D33—51nomaximal
5C3×C52×C7×C11D314yescomplemented
6C5×C3⋊D165C711yesmaximal, characteristic, direct product factor, Hall
7C5×C7×D55—91noHall
8C32×C5×C7×C11—22no—
9C32×C5×C7×C11D511yescharacteristic, complemented
10C32×C5×C7×C11C2×C511yescharacteristic, complemented
11C5×C7×C3⋊D15—111nomaximal, Hall
12C32×C52×C11C2×C711yescharacteristic, complemented, Hall
13C7×D165—34no—
14C5×C7×D33—154no—
15C52×C7×C11C3⋊D311yescharacteristic, complemented, Hall
16C5×D165—34no—
17C32×C52×C7D1111yescharacteristic, complemented, Hall
18C7×C3⋊D33—51noHall
19C3×C5×C7×C11—28no—
20C3×C5×C7×C11C5×D314yescomplemented
21C3×C5×C7×C11D1514yescomplemented
22C5×C7×D15—334no—
23C3⋊D165C5×C711yescharacteristic, direct product factor
24C5×C3⋊D33—51no—
25C3×C52×C11D3×C714yescomplemented
26C7×D55—91no—
27C5×C7×D11—451no—
28C32×C7×C11C5×D511yescharacteristic, complemented, Hall
29C7×C3⋊D15—111no—
30C5×C7×C3⋊D3—551no—
31C5×D55—91noHall
32C3×C52×C7D3314yescomplemented
33C32×C5×C11—22no—
34C32×C5×C11C7×D511yescharacteristic, complemented
35C32×C5×C11C2×C5×C711yescharacteristic, complemented
36C7×D33—154no—
37C5×C3⋊D15—111noHall
38C5×C7×C11—22no—
39C5×C7×C11C5×C3⋊D311yescharacteristic, complemented
40C5×C7×C11C3⋊D1511yescharacteristic, complemented
41C5×C7×D5—991noHall
42D165—34no—
43C5×D33—154no—
44C32×C5×C7—22no—
45C32×C5×C7C5×D1111yescharacteristic, complemented
46C32×C5×C7D5511yescharacteristic, complemented
47C52×C11C7×C3⋊D311yescharacteristic, complemented, Hall
48C3×C7×C11C5×D1514yescomplemented
49C32×C52C7×D1111yescharacteristic, complemented, Hall
50C7×D15—334no—
51C5×D3×C7—1654no—
52C3⋊D33—51noHall
53C52×C7C3⋊D3311yescharacteristic, complemented, Hall
54C3×C5×C11—28no—
55C3×C5×C11C5×D3×C714yescomplemented
56C3×C5×C11C7×D1514yescomplemented
57C7×D11—451noHall
58C5×D15—334no—
59C7×C3⋊D3—551noHall
60D55—91no—
61C5×D11—451no—
62C3×C5×C7—28no—
63C3×C5×C7C5×D3314yescomplemented
64C3×C5×C7D16514yescomplemented
65C32×C11C5×C7×D511yescharacteristic, complemented, Hall
66C3⋊D15—111no—
67C5×C3⋊D3—551no—
68C7×C11C5×C3⋊D1511yescharacteristic, complemented, Hall
69C3×C52C7×D3314yescomplemented
70C2×C5×C7—4951no—
71C7×D5—991no—
72D33—154no—
73C32×C7C5×D5511yescharacteristic, complemented, Hall
74C5×C11—22no—
75C5×C11C5×C7×C3⋊D311yescharacteristic, complemented
76C5×C11C7×C3⋊D1511yescharacteristic, complemented
77C5×D5—991noHall
78C32×C5—22no—
79C32×C5C5×C7×D1111yescharacteristic, complemented
80C32×C5C7×D5511yescharacteristic, complemented
81D3×C7—1654no—
82C5×C7—22no—
83C5×C7C5×C3⋊D3311yescharacteristic, complemented
84C5×C7C3⋊D16511yescharacteristic, direct product factor
85C3×C11C5×C7×D1514yescomplemented
86D15—334no—
87C5×D3—1654no—
88C52C7×C3⋊D3311yescharacteristic, complemented, Sylow
89D11—451noHall
90C3×C7C5×D16514yescomplemented
91C3⋊D3—551noHall
92C3×C5—28no—
93C3×C5C5×C7×D3314yescomplemented
94C3×C5C7×D16514yescomplemented
95C2×C7—4951noHall
96C11C5×C7×C3⋊D1511yescharacteristic, complemented, Sylow
97C2×C5—4951no—
98D5—991no—
99C32C5×C7×D5511yescharacteristic, complemented, Sylow
100C7C5×C3⋊D16511yescharacteristic, direct product factor, Sylow
101D3—1654no—
102C5—22no—
103C5C5×C7×C3⋊D3311yescharacteristic, complemented
104C5C7×C3⋊D16511yescharacteristic, direct product factor
105C3C5×C7×D16514yescomplemented
106C2—4951noSylow
subgroupG/H
center, hypercenterC5×C7C3⋊D165
commutator, cosocle, hypocenterC32×C5×C11C2×C5×C7
FrattiniC1G
Fitting, socleC32×C52×C7×C11C2
LCSG ▷ C32×C5×C11
UCSC1 ◁ C5×C7

Complements

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

NH ≅ G/Ntype
1. C32×C52×C7×C11C2semidirect
3. C7×C3⋊D165C5direct (N × H)
5. C3×C52×C7×C11D3semidirect
6. C5×C3⋊D165C7direct (N × H)
9. C32×C5×C7×C11D5semidirect
10. C32×C5×C7×C11C2×C5semidirect
12. C32×C52×C11C2×C7semidirect
15. C52×C7×C11C3⋊D3semidirect
17. C32×C52×C7D11semidirect
20. C3×C5×C7×C11C5×D3semidirect
21. C3×C5×C7×C11D15semidirect
23. C3⋊D165C5×C7direct (N × H)
25. C3×C52×C11D3×C7semidirect
28. C32×C7×C11C5×D5semidirect
32. C3×C52×C7D33semidirect
34. C32×C5×C11C7×D5semidirect
35. C32×C5×C11C2×C5×C7semidirect
39. C5×C7×C11C5×C3⋊D3semidirect
40. C5×C7×C11C3⋊D15semidirect
45. C32×C5×C7C5×D11semidirect
46. C32×C5×C7D55semidirect
47. C52×C11C7×C3⋊D3semidirect
48. C3×C7×C11C5×D15semidirect
49. C32×C52C7×D11semidirect
53. C52×C7C3⋊D33semidirect
55. C3×C5×C11C5×D3×C7semidirect
56. C3×C5×C11C7×D15semidirect
63. C3×C5×C7C5×D33semidirect
64. C3×C5×C7D165semidirect
65. C32×C11C5×C7×D5semidirect
68. C7×C11C5×C3⋊D15semidirect
69. C3×C52C7×D33semidirect
73. C32×C7C5×D55semidirect
75. C5×C11C5×C7×C3⋊D3semidirect
76. C5×C11C7×C3⋊D15semidirect
79. C32×C5C5×C7×D11semidirect
80. C32×C5C7×D55semidirect
83. C5×C7C5×C3⋊D33semidirect
84. C5×C7C3⋊D165direct (N × H)
85. C3×C11C5×C7×D15semidirect
88. C52C7×C3⋊D33semidirect
90. C3×C7C5×D165semidirect
93. C3×C5C5×C7×D33semidirect
94. C3×C5C7×D165semidirect
96. C11C5×C7×C3⋊D15semidirect
99. C32C5×C7×D55semidirect
100. C7C5×C3⋊D165direct (N × H)
103. C5C5×C7×C3⋊D33semidirect
104. C5C7×C3⋊D165direct (N × H)
105. C3C5×C7×D165semidirect

Maximal subgroups

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

subgroupindex
C32×C52×C7×C112
C5×C7×D1653
C7×C3⋊D1655
C5×C7×C3⋊D335
C5×C3⋊D1657
C5×C7×C3⋊D1511