Finite Group Databasebeta

← C3⋊D3×C29×D35 #49141662

Subgroups — C3⋊D3×C29×D35 #49141662

Order 36540.

240 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 72 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×C7×C3⋊D3×C29C211yesmaximal, characteristic, complemented
3C29×C3⋊D105C211yesmaximal, characteristic, complemented
4D3×C29×D35—34nomaximal
5C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
6D7×C3⋊D3×C29—51nomaximal, Hall
7C29×D105—34no—
8C5×D3×C7×C29—34no—
9C3×C29×D35D314yescomplemented
10D5×C3⋊D3×C29—71nomaximal, Hall
11C2×C29×D35—91noHall
12C29×C3⋊D21—51no—
13C7×C3⋊D3×C29D511yescharacteristic, complemented
14C32×D7×C29—51no—
15C3×C5×C7×C29C2×D314yescomplemented
16C29×C3⋊D15—71no—
17C5×C3⋊D3×C29D711yescharacteristic, complemented
18C32×D5×C29—71no—
19D3×D7×C29—154no—
20C29×D35—91no—
21C29×D35C3⋊D311yescharacteristic, direct product factor
22C2×C5×C7×C29—91no—
23C32×C7×C29C2×D511yescharacteristic, complemented, Hall
24D3×D5×C29—214no—
25C32×C5×C29C2×D711yescharacteristic, complemented, Hall
26C3⋊D3×D35C2911yesmaximal, characteristic, direct product factor, Hall
27C29×D21—154no—
28D3×C7×C29—34no—
29C3×D7×C29—54no—
30C2×C3⋊D3×C29—351noHall
31C5×C7×C29C2×C3⋊D311yescharacteristic, complemented, Hall
32C29×D15—214no—
33C5×D3×C29—34no—
34C3×D5×C29—74no—
35C2×D7×C29—451noHall
36C3⋊D105C2×C2911yescharacteristic, complemented
37C5×C7×C3⋊D3C2×C2911yescharacteristic, complemented
38C32×D35C2×C2911yescharacteristic, complemented
39C3×C7×C29D3×D514yescomplemented
40C2×D5×C29—631noHall
41C2×C32×C29—351no—
42C3⋊D3×C29—351no—
43C3⋊D3×C29D3511yescharacteristic, direct product factor
44C3×C5×C29D3×D714yescomplemented
45D3×D35—34no—
46C2×C7×C29—91no—
47D7×C29—51no—
48D7×C29—451no—
49C2×D3×C29—1054no—
50C32×C5×C7C22×C2911yescharacteristic, complemented, Hall
51C2×C5×C29—91no—
52D5×C29—71no—
53D5×C29—631no—
54C32×C29C2×D3511yescharacteristic, complemented, Hall
55D7×C3⋊D3—51noHall
56D105—34no—
57C5×D3×C7—34no—
58C3×D35D3×C2914yescomplemented
59C7×C29D5×C3⋊D311yescharacteristic, complemented, Hall
60D5×C3⋊D3—71noHall
61C2×C3×C29—354no—
62D3×C29—34no—
63D3×C29—1054no—
64C5×C29D7×C3⋊D311yescharacteristic, complemented, Hall
65C2×D35—91noHall
66C3⋊D21—51no—
67C7×C3⋊D3D5×C2911yescharacteristic, complemented
68C32×D7—51no—
69C22×C29—3151noHall
70C3×C5×C7C2×D3×C2914yescomplemented
71C3⋊D15—71no—
72C5×C3⋊D3D7×C2911yescharacteristic, complemented
73C32×D5—71no—
74C3×C29D3×D3514yescomplemented
75D3×D7—154no—
76C2×C5×C7—91no—
77D35—91no—
78D35C3⋊D3×C2911yescharacteristic, direct product factor
79C32×C7C2×D5×C2911yescharacteristic, complemented, Hall
80D3×D5—214no—
81C2×C29—91no—
82C2×C29—351no—
83C2×C29—3151no—
84C32×C5C2×D7×C2911yescharacteristic, complemented, Hall
85D21—154no—
86C3×D7—54no—
87D3×C7—34no—
88C2×C3⋊D3—351noHall
89C5×C7C2×C3⋊D3×C2911yescharacteristic, complemented, Hall
90D15—214no—
91C3×D5—74no—
92C5×D3—34no—
93C29C3⋊D3×D3511yescharacteristic, direct product factor, Sylow
94C2×D7—451noHall
95C3×C7D3×D5×C2914yescomplemented
96C2×D5—631noHall
97C2×C32—351no—
98C3⋊D3—351no—
99C3⋊D3C29×D3511yescharacteristic, direct product factor
100C3×C5D3×D7×C2914yescomplemented
101C2×C7—91no—
102D7—51no—
103D7—451no—
104C2×D3—1054no—
105C2×C5—91no—
106D5—71no—
107D5—631no—
108C32C2×C29×D3511yescharacteristic, complemented, Sylow
109C7D5×C3⋊D3×C2911yescharacteristic, complemented, Sylow
110C2×C3—354no—
111D3—34no—
112D3—1054no—
113C5D7×C3⋊D3×C2911yescharacteristic, complemented, Sylow
114C22—3151noSylow
115C3D3×C29×D3514yescomplemented
116C2—91no—
117C2—351no—
118C2—3151no—
subgroupG/H
center, hypercenterC29C3⋊D3×D35
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×C7×C3⋊D3×C29C2semidirect
3. C29×C3⋊D105C2semidirect
5. C32×C5×C7×C29C22semidirect
9. C3×C29×D35D3semidirect
13. C7×C3⋊D3×C29D5semidirect
15. C3×C5×C7×C29C2×D3semidirect
17. C5×C3⋊D3×C29D7semidirect
21. C29×D35C3⋊D3direct (N × H)
23. C32×C7×C29C2×D5semidirect
25. C32×C5×C29C2×D7semidirect
26. C3⋊D3×D35C29direct (N × H)
31. C5×C7×C29C2×C3⋊D3semidirect
36. C3⋊D105C2×C29semidirect
37. C5×C7×C3⋊D3C2×C29semidirect
38. C32×D35C2×C29semidirect
39. C3×C7×C29D3×D5semidirect
43. C3⋊D3×C29D35direct (N × H)
44. C3×C5×C29D3×D7semidirect
50. C32×C5×C7C22×C29semidirect
54. C32×C29C2×D35semidirect
58. C3×D35D3×C29semidirect
59. C7×C29D5×C3⋊D3semidirect
64. C5×C29D7×C3⋊D3semidirect
67. C7×C3⋊D3D5×C29semidirect
70. C3×C5×C7C2×D3×C29semidirect
72. C5×C3⋊D3D7×C29semidirect
74. C3×C29D3×D35semidirect
78. D35C3⋊D3×C29direct (N × H)
79. C32×C7C2×D5×C29semidirect
84. C32×C5C2×D7×C29semidirect
89. C5×C7C2×C3⋊D3×C29semidirect
93. C29C3⋊D3×D35direct (N × H)
95. C3×C7D3×D5×C29semidirect
99. C3⋊D3C29×D35direct (N × H)
100. C3×C5D3×D7×C29semidirect
108. C32C2×C29×D35semidirect
109. C7D5×C3⋊D3×C29semidirect
113. C5D7×C3⋊D3×C29semidirect
115. C3D3×C29×D35semidirect

Maximal subgroups

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

subgroupindex
C32×C29×D352
C5×C7×C3⋊D3×C292
C29×C3⋊D1052
D3×C29×D353
D7×C3⋊D3×C295
D5×C3⋊D3×C297
C3⋊D3×D3529