Finite Group Databasebeta

← C7×D5×D9×C29 #49141289

Subgroups — C7×D5×D9×C29 #49141289

Order 36540.

120 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 52 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
1C7×C29×D45C211yesmaximal, characteristic, complemented
2C5×C7×D9×C29C211yesmaximal, characteristic, complemented
3C7×C9×D5×C29C211yesmaximal, characteristic, complemented
4D3×C7×D5×C29—31nomaximal
5C5×C7×C9×C29C2211yescharacteristic, complemented, Hall
6C2×C7×D9×C29—51nomaximal, Hall
7C7×C29×D15—31no—
8C5×D3×C7×C29—31no—
9C3×C7×D5×C29D311yescharacteristic
10D5×D9×C29C711yesmaximal, characteristic, direct product factor, Hall
11C2×C7×D5×C29—91noHall
12C7×D9×C29—51no—
13C7×D9×C29D511yescharacteristic, direct product factor
14C2×C7×C9×C29—51no—
15C3×C5×C7×C29C2×D311yescharacteristic
16C29×D45C2×C711yescharacteristic, complemented
17C5×D9×C29C2×C711yescharacteristic, complemented
18C9×D5×C29C2×C711yescharacteristic, complemented
19C2×D3×C7×C29—151no—
20C7×D5×C29—91no—
21C7×D5×C29D911yescharacteristic, direct product factor
22C2×C5×C7×C29—91no—
23C7×C9×C29C2×D511yescharacteristic, complemented, Hall
24D3×D5×C29—31no—
25C5×C9×C29C22×C711yescharacteristic, complemented, Hall
26C7×D5×D9C2911yesmaximal, characteristic, direct product factor, Hall
27C2×C3×C7×C29—51no—
28D3×C7×C29—31no—
29D3×C7×C29—151no—
30C2×D9×C29—51noHall
31C5×C7×C29C2×D911yescharacteristic, complemented, Hall
32C29×D15—31no—
33C5×D3×C29—31no—
34C3×D5×C29D3×C711yescharacteristic
35C22×C7×C29—451noHall
36C7×D45C2×C2911yescharacteristic, complemented
37C5×C7×D9C2×C2911yescharacteristic, complemented
38C7×C9×D5C2×C2911yescharacteristic, complemented
39C3×C7×C29D3×D511yescharacteristic
40C2×D5×C29—91noHall
41C2×C9×C29—51no—
42D9×C29—51no—
43D9×C29C7×D511yescharacteristic, direct product factor
44C3×C5×C29C2×D3×C711yescharacteristic
45D3×C7×D5—31no—
46C2×C7×C29—51no—
47C2×C7×C29—91no—
48C2×C7×C29—451no—
49C2×D3×C29—151no—
50C5×C7×C9C22×C2911yescharacteristic, complemented, Hall
51C2×C5×C29—91no—
52D5×C29—91no—
53D5×C29C7×D911yescharacteristic, direct product factor
54C9×C29C2×C7×D511yescharacteristic, complemented, Hall
55C2×C7×D9—51noHall
56C7×D15—31no—
57C5×D3×C7—31no—
58C3×C7×D5D3×C2911yescharacteristic
59C7×C29D5×D911yescharacteristic, direct product factor, Hall
60D5×D9C7×C2911yescharacteristic, direct product factor, Hall
61C2×C3×C29—51no—
62D3×C29—31no—
63D3×C29—151no—
64C5×C29C2×C7×D911yescharacteristic, complemented, Hall
65C2×C7×D5—91noHall
66C2×C7×C9—51no—
67C7×D9—51no—
68C7×D9D5×C2911yescharacteristic, direct product factor
69C22×C29—451noHall
70C3×C5×C7C2×D3×C2911yescharacteristic
71D45C2×C7×C2911yescharacteristic, complemented
72C9×D5C2×C7×C2911yescharacteristic, complemented
73C5×D9C2×C7×C2911yescharacteristic, complemented
74C3×C29D3×C7×D511yescharacteristic
75C2×D3×C7—151no—
76C2×C5×C7—91no—
77C7×D5—91no—
78C7×D5D9×C2911yescharacteristic, direct product factor
79C7×C9C2×D5×C2911yescharacteristic, complemented, Hall
80D3×D5—31no—
81C2×C29—51no—
82C2×C29—91no—
83C2×C29—451no—
84C5×C9C22×C7×C2911yescharacteristic, complemented, Hall
85C2×C3×C7—51no—
86D3×C7—31no—
87D3×C7—151no—
88C2×D9—51noHall
89C5×C7C2×D9×C2911yescharacteristic, complemented, Hall
90D15—31no—
91C3×D5D3×C7×C2911yescharacteristic
92C5×D3—31no—
93C29C7×D5×D911yescharacteristic, direct product factor, Sylow
94C22×C7—451noHall
95C3×C7D3×D5×C2911yescharacteristic
96C2×D5—91noHall
97C2×C9—51no—
98D9—51no—
99D9C7×D5×C2911yescharacteristic, direct product factor
100C3×C5C2×D3×C7×C2911yescharacteristic
101C2×C7—51no—
102C2×C7—91no—
103C2×C7—451no—
104C2×D3—151no—
105C2×C5—91no—
106D5—91no—
107D5C7×D9×C2911yescharacteristic, direct product factor
108C9C2×C7×D5×C2911yescharacteristic, complemented, Sylow
109C7D5×D9×C2911yescharacteristic, direct product factor, Sylow
110C2×C3—51no—
111D3—31no—
112D3—151no—
113C5C2×C7×D9×C2911yescharacteristic, complemented, Sylow
114C22—451noSylow
115C3D3×C7×D5×C2911yescharacteristic
116C2—51no—
117C2—91no—
118C2—451no—
subgroupG/H
center, hypercenterC7×C29D5×D9
commutator, cosocle, hypocenterC5×C9C22×C7×C29
FrattiniC3D3×C7×D5×C29
FittingC5×C7×C9×C29C22
socleC3×C5×C7×C29C2×D3
LCSG ▷ C5×C9
UCSC1 ◁ C7×C29

Complements

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

NH ≅ G/Ntype
1. C7×C29×D45C2semidirect
2. C5×C7×D9×C29C2semidirect
3. C7×C9×D5×C29C2semidirect
5. C5×C7×C9×C29C22semidirect
10. D5×D9×C29C7direct (N × H)
13. C7×D9×C29D5direct (N × H)
16. C29×D45C2×C7semidirect
17. C5×D9×C29C2×C7semidirect
18. C9×D5×C29C2×C7semidirect
21. C7×D5×C29D9direct (N × H)
23. C7×C9×C29C2×D5semidirect
25. C5×C9×C29C22×C7semidirect
26. C7×D5×D9C29direct (N × H)
31. C5×C7×C29C2×D9semidirect
36. C7×D45C2×C29semidirect
37. C5×C7×D9C2×C29semidirect
38. C7×C9×D5C2×C29semidirect
43. D9×C29C7×D5direct (N × H)
50. C5×C7×C9C22×C29semidirect
53. D5×C29C7×D9direct (N × H)
54. C9×C29C2×C7×D5semidirect
59. C7×C29D5×D9direct (N × H)
60. D5×D9C7×C29direct (N × H)
64. C5×C29C2×C7×D9semidirect
68. C7×D9D5×C29direct (N × H)
71. D45C2×C7×C29semidirect
72. C9×D5C2×C7×C29semidirect
73. C5×D9C2×C7×C29semidirect
78. C7×D5D9×C29direct (N × H)
79. C7×C9C2×D5×C29semidirect
84. C5×C9C22×C7×C29semidirect
89. C5×C7C2×D9×C29semidirect
93. C29C7×D5×D9direct (N × H)
99. D9C7×D5×C29direct (N × H)
107. D5C7×D9×C29direct (N × H)
108. C9C2×C7×D5×C29semidirect
109. C7D5×D9×C29direct (N × H)
113. C5C2×C7×D9×C29semidirect

Maximal subgroups

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

subgroupindex
C7×C29×D452
C5×C7×D9×C292
C7×C9×D5×C292
D3×C7×D5×C293
C2×C7×D9×C295
D5×D9×C297
C7×D5×D929