Finite Group Databasebeta

← C3×D5×C29×D15 #39908140

Subgroups — C3×D5×C29×D15 #39908140

Order 26100.

212 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 64 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×C5×D5×C29C211yesmaximal, characteristic, complemented
2C3×C5×C29×D15C211yesmaximal, characteristic, complemented
3C3×C29×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
4D5×C29×D15C311yesmaximal, characteristic, direct product factor
5C3×D52×C29—31nomaximal
6C32×C52×C29C2211yescharacteristic, complemented, Hall
7C2×C3×C29×D15—51nomaximal
8C3×D3×D5×C29—51nomaximal
9C29×C3⋊(C5⋊D5)C2×C311yescharacteristic, complemented
10C5×C29×D15C2×C311yescharacteristic, complemented
11C3×C29×C5⋊D5—31no—
12C3×C5×D5×C29—21no—
13C3×C5×D5×C29—31no—
14C3×C5×D5×C29D311yescharacteristic, complemented
15C3×C5×D5×C29C2×C311yescharacteristic, complemented
16D52×C29—31noHall
17C3×C29×D15—51no—
18C3×C29×D15—51no—
19C3×C29×D15—102no—
20C3×C29×D15D511yescharacteristic, direct product factor
21C3×C5×D3×C29—51no—
22C32×D5×C29D511yescharacteristic, complemented
23C2×C32×C5×C29—51no—
24C3×C52×C29—21no—
25C3×C52×C29C2×D311yescharacteristic, complemented
26C3×C52×C29C22×C311yescharacteristic, complemented
27C2×C29×D15—51no—
28C2×C3×D5×C29—151no—
29C2×C3×D5×C29—151no—
30D3×D5×C29—51no—
31C29×C5⋊D5—31no—
32C5×D5×C29—31no—
33C5×D5×C29C3×D311yescharacteristic, complemented
34C32×C5×C29—22no—
35C32×C5×C29C2×D511yescharacteristic, complemented
36C32×C5×C29C2×D511yescharacteristic, complemented
37C2×C3×D3×C29—251noHall
38C3×D5×D15C2911yesmaximal, characteristic, direct product factor, Hall
39C2×C3×C5×C29—51no—
40C2×C3×C5×C29—51no—
41C2×C3×C5×C29—101no—
42C2×C3×C5×C29—151no—
43C29×D15—51no—
44C29×D15—51no—
45C29×D15—102no—
46C29×D15C3×D511yescharacteristic, direct product factor
47C5×D3×C29—51no—
48C3×D5×C29—21no—
49C3×D5×C29—31no—
50C3×D5×C29—151no—
51C3×D5×C29—151no—
52C3×D5×C29—302no—
53C3×D5×C29C3×D511yescharacteristic, complemented
54C3×D5×C29D1511yescharacteristic, direct product factor
55C52×C29C2×C3×D311yescharacteristic, complemented, Hall
56C2×D5×C29—151no—
57C2×D5×C29—151no—
58C2×C32×C29—51no—
59C3×D3×C29—51no—
60C3×D3×C29—251no—
61C3×C3⋊(C5⋊D5)C2×C2911yescharacteristic, complemented
62C3×C5×D15C2×C2911yescharacteristic, complemented
63C32×C5×D5C2×C2911yescharacteristic, complemented
64C3×C5×C29—22no—
65C3×C5×C29—22no—
66C3×C5×C29—21no—
67C3×C5×C29—21no—
68C3×C5×C29—42no—
69C3×C5×C29D3×D511yescharacteristic, complemented
70C3×C5×C29C2×C3×D511yescharacteristic, complemented
71C3×C5×C29C2×C3×D511yescharacteristic, complemented
72C3×C5×C29C2×D1511yescharacteristic, complemented
73C22×C3×C29—751no—
74C2×D3×C29—251no—
75D5×D15C3×C2911yescharacteristic, direct product factor
76C3×D52—31no—
77C2×C5×C29—51no—
78C2×C5×C29—151no—
79D5×C29—31no—
80D5×C29—151no—
81D5×C29—151no—
82D5×C29—302no—
83D5×C29C3×D1511yescharacteristic, direct product factor
84C32×C29D5211yescharacteristic, complemented, Hall
85C32×C52C22×C2911yescharacteristic, complemented, Hall
86C2×C3×D15—51no—
87C3×D3×D5—51no—
88C2×C3×C29—51no—
89C2×C3×C29—51no—
90C2×C3×C29—101no—
91C2×C3×C29—151no—
92C2×C3×C29—751no—
93D3×C29—51no—
94D3×C29—251no—
95C3⋊(C5⋊D5)C2×C3×C2911yescharacteristic, complemented
96C5×D15C2×C3×C2911yescharacteristic, complemented
97C3×C5⋊D5—31no—
98C3×C5×D5—21no—
99C3×C5×D5—31no—
100C3×C5×D5D3×C2911yescharacteristic, complemented
101C3×C5×D5C2×C3×C2911yescharacteristic, complemented
102C5×C29—22no—
103C5×C29C3×D3×D511yescharacteristic, complemented
104C5×C29C2×C3×D1511yescharacteristic, complemented
105C22×C29—751noHall
106D52—31noHall
107C2×C32×C5—51no—
108C3×D15—51no—
109C3×D15—51no—
110C3×D15—102no—
111C3×D15D5×C2911yescharacteristic, direct product factor
112C3×C5×D3—51no—
113C32×D5D5×C2911yescharacteristic, complemented
114C3×C29—21no—
115C3×C29C3×D5211yescharacteristic, complemented
116C3×C29D5×D1511yescharacteristic, direct product factor
117C3×C52—21no—
118C3×C52C2×D3×C2911yescharacteristic, complemented
119C3×C52C22×C3×C2911yescharacteristic, complemented
120C2×D15—51no—
121C2×C3×D5—151no—
122C2×C3×D5—151no—
123D3×D5—51no—
124C2×C29—51no—
125C2×C29—151no—
126C2×C29—751no—
127C5⋊D5—31no—
128C5×D5—31no—
129C5×D5C3×D3×C2911yescharacteristic, complemented
130C32×C5—22no—
131C32×C5C2×D5×C2911yescharacteristic, complemented
132C32×C5C2×D5×C2911yescharacteristic, complemented
133C2×C3×D3—251noHall
134C2×C3×C5—51no—
135C2×C3×C5—51no—
136C2×C3×C5—101no—
137C2×C3×C5—151no—
138D15—51no—
139D15—51no—
140D15—102no—
141D15C3×D5×C2911yescharacteristic, direct product factor
142C3×D5—21no—
143C3×D5—31no—
144C3×D5—151no—
145C3×D5—151no—
146C3×D5—302no—
147C3×D5C3×D5×C2911yescharacteristic, complemented
148C3×D5C29×D1511yescharacteristic, direct product factor
149C5×D3—51no—
150C29C3×D5×D1511yescharacteristic, direct product factor, Sylow
151C52C2×C3×D3×C2911yescharacteristic, complemented, Sylow
152C2×D5—151no—
153C2×D5—151no—
154C2×C32—51no—
155C3×D3—51no—
156C3×D3—251no—
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5D3×D5×C2911yescharacteristic, complemented
163C3×C5C2×C3×D5×C2911yescharacteristic, complemented
164C3×C5C2×C3×D5×C2911yescharacteristic, complemented
165C3×C5C2×C29×D1511yescharacteristic, complemented
166C22×C3—751no—
167C2×D3—251no—
168C2×C5—51no—
169C2×C5—151no—
170D5—31no—
171D5—151no—
172D5—151no—
173D5—302no—
174D5C3×C29×D1511yescharacteristic, direct product factor
175C32D52×C2911yescharacteristic, complemented, Sylow
176C2×C3—51no—
177C2×C3—51no—
178C2×C3—101no—
179C2×C3—151no—
180C2×C3—751no—
181D3—51no—
182D3—251no—
183C5—22no—
184C5C3×D3×D5×C2911yescharacteristic, complemented
185C5C2×C3×C29×D1511yescharacteristic, complemented
186C22—751noSylow
187C3—21no—
188C3C3×D52×C2911yescharacteristic, complemented
189C3D5×C29×D1511yescharacteristic, direct product factor
190C2—51no—
191C2—151no—
192C2—751no—
subgroupG/H
center, hypercenterC3×C29D5×D15
commutator, cosocle, hypocenterC3×C52C22×C3×C29
FrattiniC1G
Fitting, socleC32×C52×C29C22
LCSG ▷ C3×C52
UCSC1 ◁ C3×C29

Complements

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

NH ≅ G/Ntype
1. C32×C5×D5×C29C2semidirect
2. C3×C5×C29×D15C2semidirect
3. C3×C29×C3⋊(C5⋊D5)C2semidirect
4. D5×C29×D15C3direct (N × H)
6. C32×C52×C29C22semidirect
9. C29×C3⋊(C5⋊D5)C2×C3semidirect
10. C5×C29×D15C2×C3semidirect
14. C3×C5×D5×C29D3semidirect
15. C3×C5×D5×C29C2×C3semidirect
20. C3×C29×D15D5direct (N × H)
22. C32×D5×C29D5semidirect
25. C3×C52×C29C2×D3semidirect
26. C3×C52×C29C22×C3semidirect
33. C5×D5×C29C3×D3semidirect
35. C32×C5×C29C2×D5semidirect
36. C32×C5×C29C2×D5semidirect
38. C3×D5×D15C29direct (N × H)
46. C29×D15C3×D5direct (N × H)
53. C3×D5×C29C3×D5semidirect
54. C3×D5×C29D15direct (N × H)
55. C52×C29C2×C3×D3semidirect
61. C3×C3⋊(C5⋊D5)C2×C29semidirect
62. C3×C5×D15C2×C29semidirect
63. C32×C5×D5C2×C29semidirect
69. C3×C5×C29D3×D5semidirect
70. C3×C5×C29C2×C3×D5semidirect
71. C3×C5×C29C2×C3×D5semidirect
72. C3×C5×C29C2×D15semidirect
75. D5×D15C3×C29direct (N × H)
83. D5×C29C3×D15direct (N × H)
84. C32×C29D52semidirect
85. C32×C52C22×C29semidirect
95. C3⋊(C5⋊D5)C2×C3×C29semidirect
96. C5×D15C2×C3×C29semidirect
100. C3×C5×D5D3×C29semidirect
101. C3×C5×D5C2×C3×C29semidirect
103. C5×C29C3×D3×D5semidirect
104. C5×C29C2×C3×D15semidirect
111. C3×D15D5×C29direct (N × H)
113. C32×D5D5×C29semidirect
115. C3×C29C3×D52semidirect
116. C3×C29D5×D15direct (N × H)
118. C3×C52C2×D3×C29semidirect
119. C3×C52C22×C3×C29semidirect
129. C5×D5C3×D3×C29semidirect
131. C32×C5C2×D5×C29semidirect
132. C32×C5C2×D5×C29semidirect
141. D15C3×D5×C29direct (N × H)
147. C3×D5C3×D5×C29semidirect
148. C3×D5C29×D15direct (N × H)
150. C29C3×D5×D15direct (N × H)
151. C52C2×C3×D3×C29semidirect
162. C3×C5D3×D5×C29semidirect
163. C3×C5C2×C3×D5×C29semidirect
164. C3×C5C2×C3×D5×C29semidirect
165. C3×C5C2×C29×D15semidirect
174. D5C3×C29×D15direct (N × H)
175. C32D52×C29semidirect
184. C5C3×D3×D5×C29semidirect
185. C5C2×C3×C29×D15semidirect
188. C3C3×D52×C29semidirect
189. C3D5×C29×D15direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5×D5×C292
C3×C5×C29×D152
C3×C29×C3⋊(C5⋊D5)2
D5×C29×D153
C3×D52×C293
C2×C3×C29×D155
C3×D3×D5×C295
C3×D5×D1529