Finite Group Databasebeta

← C29×D35⋊(C3⋊D3) #49141666

Subgroups — C29×D35⋊(C3⋊D3) #49141666

Order 36540.

240 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 70 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×C29×D35C211yesmaximal, characteristic, complemented
2C5×C29×C3⋊D21C211yesmaximal, characteristic, complemented
3C7×C29×C3⋊D15C211yesmaximal, characteristic, complemented
4C29×D15⋊D7—34nomaximal
5C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
6D7×C3⋊D3×C29—51nomaximal, Hall
7C7×C29×D15—34no—
8C5×C29×D21—34no—
9C3×C29×D35D314yescomplemented
10D5×C3⋊D3×C29—71nomaximal, Hall
11D5×D7×C29—91noHall
12C29×C3⋊D21D511yescharacteristic, complemented
13C7×C3⋊D3×C29—51no—
14C32×D7×C29—51no—
15C3×C5×C7×C29C2×D314yescomplemented
16C29×C3⋊D15D711yescharacteristic, complemented
17C5×C3⋊D3×C29—71no—
18C32×D5×C29—71no—
19D3×D7×C29—154no—
20C29×D35C3⋊D311yescharacteristic, complemented
21C7×D5×C29—91no—
22C5×D7×C29—91no—
23C32×C7×C29C2×D511yescharacteristic, complemented, Hall
24D3×D5×C29—214no—
25C32×C5×C29C2×D711yescharacteristic, complemented, Hall
26D35⋊(C3⋊D3)C2911yesmaximal, characteristic, direct product factor, Hall
27C29×D21—34no—
28D3×C7×C29—154no—
29C3×D7×C29—54no—
30C2×C3⋊D3×C29—351noHall
31C5×C7×C29C2×C3⋊D311yescharacteristic, complemented, Hall
32C29×D15—34no—
33C5×D3×C29—214no—
34C3×D5×C29—74no—
35C2×D7×C29—451noHall
36C7×C3⋊D15C2×C2911yescharacteristic, complemented
37C5×C3⋊D21C2×C2911yescharacteristic, complemented
38C32×D35C2×C2911yescharacteristic, complemented
39C3×C7×C29D3×D514yescomplemented
40C2×D5×C29—631noHall
41C2×C32×C29—351no—
42C3⋊D3×C29—51no—
43C3⋊D3×C29—71no—
44C3×C5×C29D3×D714yescomplemented
45D15⋊D7—34no—
46C2×C7×C29—451no—
47D7×C29—51no—
48D7×C29—91no—
49C2×D3×C29—1054no—
50C32×C5×C7C22×C2911yescharacteristic, complemented, Hall
51C2×C5×C29—631no—
52D5×C29—71no—
53D5×C29—91no—
54C32×C29D5×D711yescharacteristic, complemented, Hall
55D7×C3⋊D3—51noHall
56C7×D15—34no—
57C5×D21—34no—
58C3×D35D3×C2914yescomplemented
59C7×C29D5×C3⋊D311yescharacteristic, complemented, Hall
60D5×C3⋊D3—71noHall
61C2×C3×C29—354no—
62D3×C29—154no—
63D3×C29—214no—
64C5×C29D7×C3⋊D311yescharacteristic, complemented, Hall
65D5×D7—91noHall
66C3⋊D21D5×C2911yescharacteristic, complemented
67C7×C3⋊D3—51no—
68C32×D7—51no—
69C22×C29—3151noHall
70C3×C5×C7C2×D3×C2914yescomplemented
71C3⋊D15D7×C2911yescharacteristic, complemented
72C5×C3⋊D3—71no—
73C32×D5—71no—
74C3×C29D15⋊D714yescomplemented
75D3×D7—154no—
76D35C3⋊D3×C2911yescharacteristic, complemented
77C5×D7—91no—
78C7×D5—91no—
79C32×C7C2×D5×C2911yescharacteristic, complemented, Hall
80D3×D5—214no—
81C2×C29—351no—
82C2×C29—451no—
83C2×C29—631no—
84C32×C5C2×D7×C2911yescharacteristic, complemented, Hall
85D21—34no—
86C3×D7—54no—
87D3×C7—154no—
88C2×C3⋊D3—351noHall
89C5×C7C2×C3⋊D3×C2911yescharacteristic, complemented, Hall
90D15—34no—
91C3×D5—74no—
92C5×D3—214no—
93C29D35⋊(C3⋊D3)11yescharacteristic, direct product factor, Sylow
94C2×D7—451noHall
95C3×C7D3×D5×C2914yescomplemented
96C2×D5—631noHall
97C2×C32—351no—
98C3⋊D3—51no—
99C3⋊D3—71no—
100C3×C5D3×D7×C2914yescomplemented
101C2×C7—451no—
102D7—51no—
103D7—91no—
104C2×D3—1054no—
105C2×C5—631no—
106D5—71no—
107D5—91no—
108C32D5×D7×C2911yescharacteristic, complemented, Sylow
109C7D5×C3⋊D3×C2911yescharacteristic, complemented, Sylow
110C2×C3—354no—
111D3—154no—
112D3—214no—
113C5D7×C3⋊D3×C2911yescharacteristic, complemented, Sylow
114C22—3151noSylow
115C3C29×D15⋊D714yescomplemented
116C2—351no—
117C2—451no—
118C2—631no—
subgroupG/H
center, hypercenterC29D35⋊(C3⋊D3)
commutator, cosocle, hypocenterC32×C5×C7C22×C29
FrattiniC1G
Fitting, socleC32×C5×C7×C29C22
LCSG ▷ C32×C5×C7
UCSC1 ◁ C29

Complements

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

NH ≅ G/Ntype
1. C32×C29×D35C2semidirect
2. C5×C29×C3⋊D21C2semidirect
3. C7×C29×C3⋊D15C2semidirect
5. C32×C5×C7×C29C22semidirect
9. C3×C29×D35D3semidirect
12. C29×C3⋊D21D5semidirect
15. C3×C5×C7×C29C2×D3semidirect
16. C29×C3⋊D15D7semidirect
20. C29×D35C3⋊D3semidirect
23. C32×C7×C29C2×D5semidirect
25. C32×C5×C29C2×D7semidirect
26. D35⋊(C3⋊D3)C29direct (N × H)
31. C5×C7×C29C2×C3⋊D3semidirect
36. C7×C3⋊D15C2×C29semidirect
37. C5×C3⋊D21C2×C29semidirect
38. C32×D35C2×C29semidirect
39. C3×C7×C29D3×D5semidirect
44. C3×C5×C29D3×D7semidirect
50. C32×C5×C7C22×C29semidirect
54. C32×C29D5×D7semidirect
58. C3×D35D3×C29semidirect
59. C7×C29D5×C3⋊D3semidirect
64. C5×C29D7×C3⋊D3semidirect
66. C3⋊D21D5×C29semidirect
70. C3×C5×C7C2×D3×C29semidirect
71. C3⋊D15D7×C29semidirect
74. C3×C29D15⋊D7semidirect
76. D35C3⋊D3×C29semidirect
79. C32×C7C2×D5×C29semidirect
84. C32×C5C2×D7×C29semidirect
89. C5×C7C2×C3⋊D3×C29semidirect
93. C29D35⋊(C3⋊D3)direct (N × H)
95. C3×C7D3×D5×C29semidirect
100. C3×C5D3×D7×C29semidirect
108. C32D5×D7×C29semidirect
109. C7D5×C3⋊D3×C29semidirect
113. C5D7×C3⋊D3×C29semidirect
115. C3C29×D15⋊D7semidirect

Maximal subgroups

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

subgroupindex
C32×C29×D352
C5×C29×C3⋊D212
C7×C29×C3⋊D152
C29×D15⋊D73
D7×C3⋊D3×C295
D5×C3⋊D3×C297
D35⋊(C3⋊D3)29