Finite Group Databasebeta

← C29×D15⋊D15 #39908173

Subgroups — C29×D15⋊D15 #39908173

Order 26100.

212 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 50 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×C5×C29×D15C211yesmaximal, characteristic, complemented
2C3×C29×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
3C5×C29×C3⋊D15C211yesmaximal, characteristic, complemented
4C29×D15⋊D5—31nomaximal
5D5×C29×D15—31nomaximal
6C32×C52×C29C2211yescharacteristic, complemented, Hall
7C29×(C3⋊D3)⋊D5—51nomaximal
8D3×C29×D15—51nomaximal
9C29×C3⋊(C5⋊D5)D311yescharacteristic, complemented
10C5×C29×D15—31no—
11C5×C29×D15—31no—
12C5×C29×D15—61no—
13C5×C29×D15D311yescharacteristic, complemented
14C3×C29×C5⋊D5—31no—
15C3×C5×D5×C29—31no—
16D52×C29—91noHall
17C29×C3⋊D15D511yescharacteristic, complemented
18C5×C3⋊D3×C29—51no—
19C3×C29×D15—51no—
20C3×C29×D15—51no—
21C3×C29×D15—102no—
22C3×C29×D15D511yescharacteristic, complemented
23C3×C5×D3×C29—51no—
24C3×C52×C29—21no—
25C3×C52×C29C2×D311yescharacteristic, complemented
26C3×C52×C29C2×D311yescharacteristic, complemented
27C2×C29×D15—151no—
28D3×D5×C29—151no—
29D3×D5×C29—151no—
30D3×D5×C29—151no—
31C29×C5⋊D5—31no—
32C5×D5×C29—31no—
33C5×D5×C29—91no—
34C32×C5×C29—22no—
35C32×C5×C29C2×D511yescharacteristic, complemented
36C32×C5×C29C2×D511yescharacteristic, complemented
37D32×C29—251noHall
38D15⋊D15C2911yesmaximal, characteristic, direct product factor, Hall
39C2×C3×C5×C29—151no—
40C29×D15—31no—
41C29×D15—31no—
42C29×D15—51no—
43C29×D15—51no—
44C29×D15—61no—
45C29×D15—102no—
46C29×D15D1511yescharacteristic, complemented
47C5×D3×C29—51no—
48C5×D3×C29—151no—
49C5×D3×C29—151no—
50C5×D3×C29—301no—
51C3×D5×C29—31no—
52C3×D5×C29—151no—
53C3×D5×C29—151no—
54C3×D5×C29—302no—
55C52×C29D3211yescharacteristic, complemented, Hall
56C2×D5×C29—451no—
57C2×D5×C29—451no—
58C3⋊D3×C29—51no—
59C3×D3×C29—51no—
60C3×D3×C29—251no—
61C5×C3⋊D15C2×C2911yescharacteristic, complemented
62C3×C3⋊(C5⋊D5)C2×C2911yescharacteristic, complemented
63C3×C5×D15C2×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×C29D3×D511yescharacteristic, complemented
71C3×C5×C29D3×D511yescharacteristic, complemented
72C3×C5×C29C2×D1511yescharacteristic, complemented
73C2×D3×C29—751no—
74C2×D3×C29—751no—
75D15⋊D5—31no—
76D5×D15—31no—
77C2×C5×C29—151no—
78C2×C5×C29—451no—
79D5×C29—31no—
80D5×C29—91no—
81D5×C29—151no—
82D5×C29—151no—
83D5×C29—302no—
84C32×C29D5211yescharacteristic, complemented, Hall
85C32×C52C22×C2911yescharacteristic, complemented, Hall
86(C3⋊D3)⋊D5—51no—
87D3×D15—51no—
88C2×C3×C29—151no—
89C2×C3×C29—751no—
90D3×C29—51no—
91D3×C29—151no—
92D3×C29—151no—
93D3×C29—251no—
94D3×C29—301no—
95C3⋊(C5⋊D5)D3×C2911yescharacteristic, complemented
96C5×D15—31no—
97C5×D15—31no—
98C5×D15—61no—
99C5×D15D3×C2911yescharacteristic, complemented
100C3×C5⋊D5—31no—
101C3×C5×D5—31no—
102C5×C29—22no—
103C5×C29D3×D1511yescharacteristic, complemented
104C5×C29(C3⋊D3)⋊D511yescharacteristic, complemented
105C22×C29—2251noHall
106D52—91noHall
107C3⋊D15D5×C2911yescharacteristic, complemented
108C5×C3⋊D3—51no—
109C3×D15—51no—
110C3×D15—51no—
111C3×D15—102no—
112C3×D15D5×C2911yescharacteristic, complemented
113C3×C5×D3—51no—
114C3×C29—21no—
115C3×C29D5×D1511yescharacteristic, complemented
116C3×C29D15⋊D511yescharacteristic, complemented
117C3×C52—21no—
118C3×C52C2×D3×C2911yescharacteristic, complemented
119C3×C52C2×D3×C2911yescharacteristic, complemented
120C2×D15—151no—
121D3×D5—151no—
122D3×D5—151no—
123D3×D5—151no—
124C2×C29—151no—
125C2×C29—451no—
126C2×C29—751no—
127C5⋊D5—31no—
128C5×D5—31no—
129C5×D5—91no—
130C32×C5—22no—
131C32×C5C2×D5×C2911yescharacteristic, complemented
132C32×C5C2×D5×C2911yescharacteristic, complemented
133D32—251noHall
134C2×C3×C5—151no—
135D15—31no—
136D15—31no—
137D15—51no—
138D15—51no—
139D15—61no—
140D15—102no—
141D15C29×D1511yescharacteristic, complemented
142C3×D5—31no—
143C3×D5—151no—
144C3×D5—151no—
145C3×D5—302no—
146C5×D3—51no—
147C5×D3—151no—
148C5×D3—151no—
149C5×D3—301no—
150C29D15⋊D1511yescharacteristic, direct product factor, Sylow
151C52D32×C2911yescharacteristic, complemented, Sylow
152C2×D5—451no—
153C2×D5—451no—
154C3⋊D3—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×C5D3×D5×C2911yescharacteristic, complemented
164C3×C5D3×D5×C2911yescharacteristic, complemented
165C3×C5C2×C29×D1511yescharacteristic, complemented
166C2×D3—751no—
167C2×D3—751no—
168C2×C5—151no—
169C2×C5—451no—
170D5—31no—
171D5—91no—
172D5—151no—
173D5—151no—
174D5—302no—
175C32D52×C2911yescharacteristic, complemented, Sylow
176C2×C3—151no—
177C2×C3—751no—
178D3—51no—
179D3—151no—
180D3—151no—
181D3—251no—
182D3—301no—
183C5—22no—
184C5D3×C29×D1511yescharacteristic, complemented
185C5C29×(C3⋊D3)⋊D511yescharacteristic, complemented
186C22—2251noSylow
187C3—21no—
188C3D5×C29×D1511yescharacteristic, complemented
189C3C29×D15⋊D511yescharacteristic, complemented
190C2—151no—
191C2—451no—
192C2—751no—
subgroupG/H
center, hypercenterC29D15⋊D15
commutator, cosocle, hypocenterC32×C52C22×C29
FrattiniC1G
Fitting, socleC32×C52×C29C22
LCSG ▷ C32×C52
UCSC1 ◁ C29

Complements

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

NH ≅ G/Ntype
1. C3×C5×C29×D15C2semidirect
2. C3×C29×C3⋊(C5⋊D5)C2semidirect
3. C5×C29×C3⋊D15C2semidirect
6. C32×C52×C29C22semidirect
9. C29×C3⋊(C5⋊D5)D3semidirect
13. C5×C29×D15D3semidirect
17. C29×C3⋊D15D5semidirect
22. C3×C29×D15D5semidirect
25. C3×C52×C29C2×D3semidirect
26. C3×C52×C29C2×D3semidirect
35. C32×C5×C29C2×D5semidirect
36. C32×C5×C29C2×D5semidirect
38. D15⋊D15C29direct (N × H)
46. C29×D15D15semidirect
55. C52×C29D32semidirect
61. C5×C3⋊D15C2×C29semidirect
62. C3×C3⋊(C5⋊D5)C2×C29semidirect
63. C3×C5×D15C2×C29semidirect
69. C3×C5×C29D3×D5semidirect
70. C3×C5×C29D3×D5semidirect
71. C3×C5×C29D3×D5semidirect
72. C3×C5×C29C2×D15semidirect
84. C32×C29D52semidirect
85. C32×C52C22×C29semidirect
95. C3⋊(C5⋊D5)D3×C29semidirect
99. C5×D15D3×C29semidirect
103. C5×C29D3×D15semidirect
104. C5×C29(C3⋊D3)⋊D5semidirect
107. C3⋊D15D5×C29semidirect
112. C3×D15D5×C29semidirect
115. C3×C29D5×D15semidirect
116. C3×C29D15⋊D5semidirect
118. C3×C52C2×D3×C29semidirect
119. C3×C52C2×D3×C29semidirect
131. C32×C5C2×D5×C29semidirect
132. C32×C5C2×D5×C29semidirect
141. D15C29×D15semidirect
150. C29D15⋊D15direct (N × H)
151. C52D32×C29semidirect
162. C3×C5D3×D5×C29semidirect
163. C3×C5D3×D5×C29semidirect
164. C3×C5D3×D5×C29semidirect
165. C3×C5C2×C29×D15semidirect
175. C32D52×C29semidirect
184. C5D3×C29×D15semidirect
185. C5C29×(C3⋊D3)⋊D5semidirect
188. C3D5×C29×D15semidirect
189. C3C29×D15⋊D5semidirect

Maximal subgroups

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

subgroupindex
C3×C5×C29×D152
C3×C29×C3⋊(C5⋊D5)2
C5×C29×C3⋊D152
C29×D15⋊D53
D5×C29×D153
C29×(C3⋊D3)⋊D55
D3×C29×D155
D15⋊D1529