Finite Group Databasebeta

← C2×C3×C7×C29×D15 #49141684

Subgroups — C2×C3×C7×C29×D15 #49141684

Order 36540.

176 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C3×C7×C29×D15C212yesmaximal, direct product factor
2C2×C32×C5×C7×C29C211yesmaximal, characteristic, complemented
3C2×C3×C7×D5×C29—31nomaximal
4C2×C7×C29×D15C311yesmaximal, characteristic, direct product factor
5C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
6C2×C3×D3×C7×C29—51nomaximal, Hall
7C7×C29×D15C2×C312yesdirect product factor
8C3×C7×D5×C29—32no—
9C2×C3×C5×C7×C29—21no—
10C2×C3×C5×C7×C29D311yescharacteristic, complemented
11C2×C3×C5×C7×C29C2×C311yescharacteristic, complemented
12C2×C3×C29×D15C711yesmaximal, characteristic, direct product factor, Hall
13C2×C7×D5×C29—31noHall
14C3×D3×C7×C29—52no—
15C2×C32×C7×C29D511yescharacteristic, complemented
16C3×C5×C7×C29—21no—
17C3×C5×C7×C29C2×D311yescharacteristic, complemented
18C3×C5×C7×C29C22×C311yescharacteristic, complemented
19C3×C29×D15C2×C712yesdirect product factor
20C2×C32×C5×C29C2×C711yescharacteristic, complemented
21C2×D3×C7×C29—51no—
22C22×C3×C7×C29—151no—
23C7×D5×C29—32no—
24C2×C5×C7×C29C3×D311yescharacteristic, complemented
25C32×C7×C29C2×D511yescharacteristic, complemented, Hall
26C2×C29×D15C3×C711yescharacteristic, direct product factor
27C2×C3×D5×C29—31no—
28C32×C5×C29C22×C711yescharacteristic, complemented, Hall
29C2×C3×C7×D15C2911yesmaximal, characteristic, direct product factor, Hall
30C2×C3×C7×C29—21no—
31C2×C3×C7×C29—152no—
32C2×C3×C7×C29C3×D511yescharacteristic, complemented
33C2×C3×C7×C29D1511yescharacteristic, direct product factor
34D3×C7×C29—52no—
35C2×C3×D3×C29—51noHall
36C5×C7×C29C2×C3×D311yescharacteristic, complemented, Hall
37C2×C3×C5×C29—21no—
38C2×C3×C5×C29D3×C711yescharacteristic, complemented
39C2×C3×C5×C29C2×C3×C711yescharacteristic, complemented
40C29×D15C2×C3×C712yesdirect product factor
41C3×D5×C29—32no—
42C22×C7×C29—151noHall
43C2×C32×C5×C7C2×C2911yescharacteristic, complemented
44C3×C7×D15C2×C2912yesdirect product factor
45C3×C7×C29—21no—
46C3×C7×C29C2×C3×D511yescharacteristic, complemented
47C3×C7×C29C2×D1511yescharacteristic, direct product factor
48C2×D5×C29—31noHall
49C2×C32×C29C7×D511yescharacteristic, complemented
50C3×D3×C29—52no—
51C3×C5×C29—21no—
52C3×C5×C29C2×D3×C711yescharacteristic, complemented
53C3×C5×C29C22×C3×C711yescharacteristic, complemented
54C2×C7×D15C3×C2911yescharacteristic, direct product factor
55C2×C3×C7×D5—31no—
56C2×C7×C29—152no—
57C2×C7×C29C3×D1511yescharacteristic, direct product factor
58C22×C3×C29—151no—
59C2×D3×C29—51no—
60C32×C5×C7C22×C2911yescharacteristic, complemented, Hall
61C2×C5×C29C3×D3×C711yescharacteristic, complemented
62D5×C29—32no—
63C32×C29C2×C7×D511yescharacteristic, complemented, Hall
64C2×C3×D3×C7—51noHall
65C2×C3×C5×C7—21no—
66C2×C3×C5×C7D3×C2911yescharacteristic, complemented
67C2×C3×C5×C7C2×C3×C2911yescharacteristic, complemented
68C7×D15C2×C3×C2912yesdirect product factor
69C3×C7×D5—32no—
70C7×C29C2×C3×D1511yescharacteristic, direct product factor, Hall
71C2×C3×D15C7×C2911yescharacteristic, direct product factor, Hall
72C2×C3×C29—21no—
73C2×C3×C29—152no—
74C2×C3×C29C3×C7×D511yescharacteristic, complemented
75C2×C3×C29C7×D1511yescharacteristic, direct product factor
76D3×C29—52no—
77C5×C29C2×C3×D3×C711yescharacteristic, complemented, Hall
78C2×C7×D5—31noHall
79C2×C32×C7D5×C2911yescharacteristic, complemented
80C3×D3×C7—52no—
81C22×C29—151noHall
82C3×C5×C7—21no—
83C3×C5×C7C2×D3×C2911yescharacteristic, complemented
84C3×C5×C7C22×C3×C2911yescharacteristic, complemented
85C2×C32×C5C2×C7×C2911yescharacteristic, complemented
86C3×D15C2×C7×C2912yesdirect product factor
87C3×C29—21no—
88C3×C29C2×C3×C7×D511yescharacteristic, complemented
89C3×C29C2×C7×D1511yescharacteristic, direct product factor
90C22×C3×C7—151no—
91C2×D3×C7—51no—
92C2×C5×C7C3×D3×C2911yescharacteristic, complemented
93C7×D5—32no—
94C32×C7C2×D5×C2911yescharacteristic, complemented, Hall
95C2×D15C3×C7×C2911yescharacteristic, direct product factor
96C2×C3×D5—31no—
97C2×C29—152no—
98C2×C29C3×C7×D1511yescharacteristic, direct product factor
99C32×C5C22×C7×C2911yescharacteristic, complemented, Hall
100C2×C3×C7—21no—
101C2×C3×C7—152no—
102C2×C3×C7C3×D5×C2911yescharacteristic, complemented
103C2×C3×C7C29×D1511yescharacteristic, direct product factor
104D3×C7—52no—
105C2×C3×D3—51noHall
106C5×C7C2×C3×D3×C2911yescharacteristic, complemented, Hall
107C2×C3×C5—21no—
108C2×C3×C5D3×C7×C2911yescharacteristic, complemented
109C2×C3×C5C2×C3×C7×C2911yescharacteristic, complemented
110D15C2×C3×C7×C2912yesdirect product factor
111C3×D5—32no—
112C29C2×C3×C7×D1511yescharacteristic, direct product factor, Sylow
113C22×C7—151noHall
114C3×C7—21no—
115C3×C7C2×C3×D5×C2911yescharacteristic, complemented
116C3×C7C2×C29×D1511yescharacteristic, direct product factor
117C2×D5—31noHall
118C2×C32C7×D5×C2911yescharacteristic, complemented
119C3×D3—52no—
120C3×C5—21no—
121C3×C5C22×C3×C7×C2911yescharacteristic, complemented
122C3×C5C2×D3×C7×C2911yescharacteristic, complemented
123C2×C7—152no—
124C2×C7C3×C29×D1511yescharacteristic, direct product factor
125C22×C3—151no—
126C2×D3—51no—
127C2×C5C3×D3×C7×C2911yescharacteristic, complemented
128D5—32no—
129C32C2×C7×D5×C2911yescharacteristic, complemented, Sylow
130C7C2×C3×C29×D1511yescharacteristic, direct product factor, Sylow
131C2×C3—21no—
132C2×C3—152no—
133C2×C3C3×C7×D5×C2911yescharacteristic, complemented
134C2×C3C7×C29×D1511yescharacteristic, direct product factor
135D3—52no—
136C5C2×C3×D3×C7×C2911yescharacteristic, complemented, Sylow
137C22—151noSylow
138C3—21no—
139C3C2×C7×C29×D1511yescharacteristic, direct product factor
140C3C2×C3×C7×D5×C2911yescharacteristic, complemented
141C2—152no—
142C2C3×C7×C29×D1511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C7×C29D15
commutator, cosocle, hypocenterC3×C5C22×C3×C7×C29
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C29C2
LCSG ▷ C3×C5
UCSC1 ◁ C2×C3×C7×C29

Complements

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

NH ≅ G/Ntype
1. C3×C7×C29×D15C2direct (N × H)
2. C2×C32×C5×C7×C29C2semidirect
4. C2×C7×C29×D15C3direct (N × H)
5. C32×C5×C7×C29C22semidirect
7. C7×C29×D15C2×C3direct (N × H)
10. C2×C3×C5×C7×C29D3semidirect
11. C2×C3×C5×C7×C29C2×C3semidirect
12. C2×C3×C29×D15C7direct (N × H)
15. C2×C32×C7×C29D5semidirect
17. C3×C5×C7×C29C2×D3semidirect
18. C3×C5×C7×C29C22×C3semidirect
19. C3×C29×D15C2×C7direct (N × H)
20. C2×C32×C5×C29C2×C7semidirect
24. C2×C5×C7×C29C3×D3semidirect
25. C32×C7×C29C2×D5semidirect
26. C2×C29×D15C3×C7direct (N × H)
28. C32×C5×C29C22×C7semidirect
29. C2×C3×C7×D15C29direct (N × H)
32. C2×C3×C7×C29C3×D5semidirect
33. C2×C3×C7×C29D15direct (N × H)
36. C5×C7×C29C2×C3×D3semidirect
38. C2×C3×C5×C29D3×C7semidirect
39. C2×C3×C5×C29C2×C3×C7semidirect
40. C29×D15C2×C3×C7direct (N × H)
43. C2×C32×C5×C7C2×C29semidirect
44. C3×C7×D15C2×C29direct (N × H)
46. C3×C7×C29C2×C3×D5semidirect
47. C3×C7×C29C2×D15direct (N × H)
49. C2×C32×C29C7×D5semidirect
52. C3×C5×C29C2×D3×C7semidirect
53. C3×C5×C29C22×C3×C7semidirect
54. C2×C7×D15C3×C29direct (N × H)
57. C2×C7×C29C3×D15direct (N × H)
60. C32×C5×C7C22×C29semidirect
61. C2×C5×C29C3×D3×C7semidirect
63. C32×C29C2×C7×D5semidirect
66. C2×C3×C5×C7D3×C29semidirect
67. C2×C3×C5×C7C2×C3×C29semidirect
68. C7×D15C2×C3×C29direct (N × H)
70. C7×C29C2×C3×D15direct (N × H)
71. C2×C3×D15C7×C29direct (N × H)
74. C2×C3×C29C3×C7×D5semidirect
75. C2×C3×C29C7×D15direct (N × H)
77. C5×C29C2×C3×D3×C7semidirect
79. C2×C32×C7D5×C29semidirect
83. C3×C5×C7C2×D3×C29semidirect
84. C3×C5×C7C22×C3×C29semidirect
85. C2×C32×C5C2×C7×C29semidirect
86. C3×D15C2×C7×C29direct (N × H)
88. C3×C29C2×C3×C7×D5semidirect
89. C3×C29C2×C7×D15direct (N × H)
92. C2×C5×C7C3×D3×C29semidirect
94. C32×C7C2×D5×C29semidirect
95. C2×D15C3×C7×C29direct (N × H)
98. C2×C29C3×C7×D15direct (N × H)
99. C32×C5C22×C7×C29semidirect
102. C2×C3×C7C3×D5×C29semidirect
103. C2×C3×C7C29×D15direct (N × H)
106. C5×C7C2×C3×D3×C29semidirect
108. C2×C3×C5D3×C7×C29semidirect
109. C2×C3×C5C2×C3×C7×C29semidirect
110. D15C2×C3×C7×C29direct (N × H)
112. C29C2×C3×C7×D15direct (N × H)
115. C3×C7C2×C3×D5×C29semidirect
116. C3×C7C2×C29×D15direct (N × H)
118. C2×C32C7×D5×C29semidirect
121. C3×C5C22×C3×C7×C29semidirect
122. C3×C5C2×D3×C7×C29semidirect
124. C2×C7C3×C29×D15direct (N × H)
127. C2×C5C3×D3×C7×C29semidirect
129. C32C2×C7×D5×C29semidirect
130. C7C2×C3×C29×D15direct (N × H)
133. C2×C3C3×C7×D5×C29semidirect
134. C2×C3C7×C29×D15direct (N × H)
136. C5C2×C3×D3×C7×C29semidirect
139. C3C2×C7×C29×D15direct (N × H)
140. C3C2×C3×C7×D5×C29semidirect
142. C2C3×C7×C29×D15direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C7×C29×D152
C2×C32×C5×C7×C292
C2×C3×C7×D5×C293
C2×C7×C29×D153
C2×C3×D3×C7×C295
C2×C3×C29×D157
C2×C3×C7×D1529