Finite Group Databasebeta

← C2×C3×C29×D105 #49141686

Subgroups — C2×C3×C29×D105 #49141686

Order 36540.

176 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 76 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×C29×D105C212yesmaximal, direct product factor
2C2×C32×C5×C7×C29C211yesmaximal, characteristic, complemented
3C2×C3×C29×D35—31nomaximal
4C2×C29×D105C311yesmaximal, characteristic, direct product factor
5C32×C5×C7×C29C2211yescharacteristic, complemented, Hall
6C2×C3×C29×D21—51nomaximal, Hall
7C29×D105C2×C312yesdirect product factor
8C3×C29×D35—32no—
9C2×C3×C5×C7×C29—21no—
10C2×C3×C5×C7×C29D311yescharacteristic, complemented
11C2×C3×C5×C7×C29C2×C311yescharacteristic, complemented
12C2×C3×C29×D15—71nomaximal, Hall
13C2×C29×D35—31noHall
14C3×C29×D21—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×D15—72no—
20C2×C32×C5×C29D711yescharacteristic, complemented
21C2×C29×D21—51no—
22C2×C3×D7×C29—151no—
23C29×D35—32no—
24C2×C5×C7×C29C3×D311yescharacteristic, complemented
25C32×C7×C29C2×D511yescharacteristic, complemented, Hall
26C2×C29×D15—71no—
27C2×C3×D5×C29—211no—
28C32×C5×C29C2×D711yescharacteristic, complemented, Hall
29C2×C3×D105C2911yesmaximal, characteristic, direct product factor, Hall
30C2×C3×C7×C29—21no—
31C2×C3×C7×C29C3×D511yescharacteristic, complemented
32C2×C3×C7×C29D1511yescharacteristic, complemented
33C29×D21—52no—
34C3×D7×C29—152no—
35C2×C3×D3×C29—351noHall
36C5×C7×C29C2×C3×D311yescharacteristic, complemented, Hall
37C2×C3×C5×C29—21no—
38C2×C3×C5×C29C3×D711yescharacteristic, complemented
39C2×C3×C5×C29D2111yescharacteristic, complemented
40C29×D15—72no—
41C3×D5×C29—212no—
42C2×D7×C29—151noHall
43C2×C32×C5×C7C2×C2911yescharacteristic, complemented
44C3×D105C2×C2912yesdirect product factor
45C3×C7×C29—21no—
46C3×C7×C29C2×C3×D511yescharacteristic, complemented
47C3×C7×C29C2×D1511yescharacteristic, complemented
48C2×D5×C29—211noHall
49C2×C32×C29D3511yescharacteristic, complemented
50C3×D3×C29—352no—
51C3×C5×C29—21no—
52C3×C5×C29C2×C3×D711yescharacteristic, complemented
53C3×C5×C29C2×D2111yescharacteristic, complemented
54C2×D105C3×C2911yescharacteristic, direct product factor
55C2×C3×D35—31no—
56C2×C7×C29C3×D1511yescharacteristic, complemented
57D7×C29—152no—
58C22×C3×C29—1051no—
59C2×D3×C29—351no—
60C32×C5×C7C22×C2911yescharacteristic, complemented, Hall
61C2×C5×C29C3×D2111yescharacteristic, complemented
62D5×C29—212no—
63C32×C29C2×D3511yescharacteristic, complemented, Hall
64C2×C3×D21—51noHall
65C2×C3×C5×C7—21no—
66C2×C3×C5×C7D3×C2911yescharacteristic, complemented
67C2×C3×C5×C7C2×C3×C2911yescharacteristic, complemented
68D105C2×C3×C2912yesdirect product factor
69C3×D35—32no—
70C7×C29C2×C3×D1511yescharacteristic, complemented, Hall
71C2×C3×D15—71noHall
72C2×C3×C29—21no—
73C2×C3×C29—1052no—
74C2×C3×C29C3×D3511yescharacteristic, complemented
75C2×C3×C29D10511yescharacteristic, direct product factor
76D3×C29—352no—
77C5×C29C2×C3×D2111yescharacteristic, complemented, Hall
78C2×D35—31noHall
79C2×C32×C7D5×C2911yescharacteristic, complemented
80C3×D21—52no—
81C22×C29—1051noHall
82C3×C5×C7—21no—
83C3×C5×C7C2×D3×C2911yescharacteristic, complemented
84C3×C5×C7C22×C3×C2911yescharacteristic, complemented
85C2×C32×C5D7×C2911yescharacteristic, complemented
86C3×D15—72no—
87C3×C29—21no—
88C3×C29C2×C3×D3511yescharacteristic, complemented
89C3×C29C2×D10511yescharacteristic, direct product factor
90C2×D21—51no—
91C2×C3×D7—151no—
92C2×C5×C7C3×D3×C2911yescharacteristic, complemented
93D35—32no—
94C32×C7C2×D5×C2911yescharacteristic, complemented, Hall
95C2×D15—71no—
96C2×C3×D5—211no—
97C2×C29—1052no—
98C2×C29C3×D10511yescharacteristic, direct product factor
99C32×C5C2×D7×C2911yescharacteristic, complemented, Hall
100C2×C3×C7—21no—
101C2×C3×C7C3×D5×C2911yescharacteristic, complemented
102C2×C3×C7C29×D1511yescharacteristic, complemented
103D21—52no—
104C3×D7—152no—
105C2×C3×D3—351noHall
106C5×C7C2×C3×D3×C2911yescharacteristic, complemented, Hall
107C2×C3×C5—21no—
108C2×C3×C5C3×D7×C2911yescharacteristic, complemented
109C2×C3×C5C29×D2111yescharacteristic, complemented
110D15—72no—
111C3×D5—212no—
112C29C2×C3×D10511yescharacteristic, direct product factor, Sylow
113C2×D7—151noHall
114C3×C7—21no—
115C3×C7C2×C3×D5×C2911yescharacteristic, complemented
116C3×C7C2×C29×D1511yescharacteristic, complemented
117C2×D5—211noHall
118C2×C32C29×D3511yescharacteristic, complemented
119C3×D3—352no—
120C3×C5—21no—
121C3×C5C2×C3×D7×C2911yescharacteristic, complemented
122C3×C5C2×C29×D2111yescharacteristic, complemented
123C2×C7C3×C29×D1511yescharacteristic, complemented
124D7—152no—
125C22×C3—1051no—
126C2×D3—351no—
127C2×C5C3×C29×D2111yescharacteristic, complemented
128D5—212no—
129C32C2×C29×D3511yescharacteristic, complemented, Sylow
130C7C2×C3×C29×D1511yescharacteristic, complemented, Sylow
131C2×C3—21no—
132C2×C3—1052no—
133C2×C3C3×C29×D3511yescharacteristic, complemented
134C2×C3C29×D10511yescharacteristic, direct product factor
135D3—352no—
136C5C2×C3×C29×D2111yescharacteristic, complemented, Sylow
137C22—1051noSylow
138C3—21no—
139C3C2×C29×D10511yescharacteristic, direct product factor
140C3C2×C3×C29×D3511yescharacteristic, complemented
141C2—1052no—
142C2C3×C29×D10511yescharacteristic, direct product factor
subgroupG/H
center, hypercenterC2×C3×C29D105
commutator, cosocle, hypocenterC3×C5×C7C22×C3×C29
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C29C2
LCSG ▷ C3×C5×C7
UCSC1 ◁ C2×C3×C29

Complements

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

NH ≅ G/Ntype
1. C3×C29×D105C2direct (N × H)
2. C2×C32×C5×C7×C29C2semidirect
4. C2×C29×D105C3direct (N × H)
5. C32×C5×C7×C29C22semidirect
7. C29×D105C2×C3direct (N × H)
10. C2×C3×C5×C7×C29D3semidirect
11. C2×C3×C5×C7×C29C2×C3semidirect
15. C2×C32×C7×C29D5semidirect
17. C3×C5×C7×C29C2×D3semidirect
18. C3×C5×C7×C29C22×C3semidirect
20. C2×C32×C5×C29D7semidirect
24. C2×C5×C7×C29C3×D3semidirect
25. C32×C7×C29C2×D5semidirect
28. C32×C5×C29C2×D7semidirect
29. C2×C3×D105C29direct (N × H)
31. C2×C3×C7×C29C3×D5semidirect
32. C2×C3×C7×C29D15semidirect
36. C5×C7×C29C2×C3×D3semidirect
38. C2×C3×C5×C29C3×D7semidirect
39. C2×C3×C5×C29D21semidirect
43. C2×C32×C5×C7C2×C29semidirect
44. C3×D105C2×C29direct (N × H)
46. C3×C7×C29C2×C3×D5semidirect
47. C3×C7×C29C2×D15semidirect
49. C2×C32×C29D35semidirect
52. C3×C5×C29C2×C3×D7semidirect
53. C3×C5×C29C2×D21semidirect
54. C2×D105C3×C29direct (N × H)
56. C2×C7×C29C3×D15semidirect
60. C32×C5×C7C22×C29semidirect
61. C2×C5×C29C3×D21semidirect
63. C32×C29C2×D35semidirect
66. C2×C3×C5×C7D3×C29semidirect
67. C2×C3×C5×C7C2×C3×C29semidirect
68. D105C2×C3×C29direct (N × H)
70. C7×C29C2×C3×D15semidirect
74. C2×C3×C29C3×D35semidirect
75. C2×C3×C29D105direct (N × H)
77. C5×C29C2×C3×D21semidirect
79. C2×C32×C7D5×C29semidirect
83. C3×C5×C7C2×D3×C29semidirect
84. C3×C5×C7C22×C3×C29semidirect
85. C2×C32×C5D7×C29semidirect
88. C3×C29C2×C3×D35semidirect
89. C3×C29C2×D105direct (N × H)
92. C2×C5×C7C3×D3×C29semidirect
94. C32×C7C2×D5×C29semidirect
98. C2×C29C3×D105direct (N × H)
99. C32×C5C2×D7×C29semidirect
101. C2×C3×C7C3×D5×C29semidirect
102. C2×C3×C7C29×D15semidirect
106. C5×C7C2×C3×D3×C29semidirect
108. C2×C3×C5C3×D7×C29semidirect
109. C2×C3×C5C29×D21semidirect
112. C29C2×C3×D105direct (N × H)
115. C3×C7C2×C3×D5×C29semidirect
116. C3×C7C2×C29×D15semidirect
118. C2×C32C29×D35semidirect
121. C3×C5C2×C3×D7×C29semidirect
122. C3×C5C2×C29×D21semidirect
123. C2×C7C3×C29×D15semidirect
127. C2×C5C3×C29×D21semidirect
129. C32C2×C29×D35semidirect
130. C7C2×C3×C29×D15semidirect
133. C2×C3C3×C29×D35semidirect
134. C2×C3C29×D105direct (N × H)
136. C5C2×C3×C29×D21semidirect
139. C3C2×C29×D105direct (N × H)
140. C3C2×C3×C29×D35semidirect
142. C2C3×C29×D105direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C29×D1052
C2×C32×C5×C7×C292
C2×C3×C29×D353
C2×C29×D1053
C2×C3×C29×D215
C2×C3×C29×D157
C2×C3×D10529