Finite Group Databasebeta

← C3×D205⋊D15 #49147124

Subgroups — C3×D205⋊D15 #49147124

Order 36900.

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
1C32×C5×D205C211yesmaximal, characteristic, complemented
2C3×C5×D615C211yesmaximal, characteristic, complemented
3C3×C41×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
4D205⋊D15C311yesmaximal, characteristic, direct product factor
5C3×(C5⋊D5)⋊D41—31nomaximal
6C32×C52×C41C2211yescharacteristic, complemented, Hall
7C3×D15⋊D41—51nomaximal
8C3×D15×D41—51nomaximal
9C41×C3⋊(C5⋊D5)C2×C311yescharacteristic, complemented
10C5×D615C2×C311yescharacteristic, complemented
11C3×C41×C5⋊D5—31no—
12C3×C5×D205—21no—
13C3×C5×D205—31no—
14C3×C5×D205D311yescharacteristic, complemented
15C3×C5×D205C2×C311yescharacteristic, complemented
16(C5⋊D5)⋊D41—31noHall
17C3×D615D511yescharacteristic, complemented
18C3×D15×C41—51no—
19C3×D15×C41—51no—
20C3×D15×C41—102no—
21C3×C5×D123—51no—
22C32×D205D511yescharacteristic, complemented
23C32×C5×D41—51no—
24C3×C52×C41—21no—
25C3×C52×C41C2×D311yescharacteristic, complemented
26C3×C52×C41C22×C311yescharacteristic, complemented
27D15⋊D41—51no—
28D15×D41—51no—
29C3×D5×D41—151no—
30C3×D5×D41—151no—
31C41×C5⋊D5—31no—
32C5×D205—31no—
33C5×D205C3×D311yescharacteristic, complemented
34C32×C5×C41—22no—
35C32×C5×C41C2×D511yescharacteristic, complemented
36C32×C5×C41C2×D511yescharacteristic, complemented
37C3×D3×D41—251noHall
38D615C3×D511yescharacteristic, complemented
39D15×C41—51no—
40D15×C41—51no—
41D15×C41—102no—
42C5×D123—51no—
43C3×D205—21no—
44C3×D205—31no—
45C3×D205C3×D511yescharacteristic, complemented
46C3×D205D1511yescharacteristic, complemented
47C3×D5×C41—151no—
48C3×D5×C41—151no—
49C3×D5×C41—302no—
50C3×C5×D41—51no—
51C3×C5×D41—51no—
52C3×C5×D41—101no—
53C3×C5×D41—151no—
54C52×C41C2×C3×D311yescharacteristic, complemented, Hall
55C3×D5×D15—411nomaximal, Hall
56D5×D41—151no—
57D5×D41—151no—
58C3×D123—51no—
59C3×D3×C41—251no—
60C32×D41—51no—
61C3×C5×C41—22no—
62C3×C5×C41—22no—
63C3×C5×C41—21no—
64C3×C5×C41—21no—
65C3×C5×C41—42no—
66C3×C5×C41D3×D511yescharacteristic, complemented
67C3×C5×C41C2×C3×D511yescharacteristic, complemented
68C3×C5×C41C2×C3×D511yescharacteristic, complemented
69C3×C5×C41C2×D1511yescharacteristic, complemented
70C2×C3×D41—751no—
71D3×D41—251no—
72C3×C3⋊(C5⋊D5)D4111yescharacteristic, complemented
73C3×C5×D15—411no—
74C32×C5×D5—411no—
75D205—31no—
76D205C3×D1511yescharacteristic, complemented
77C5×D41—51no—
78C5×D41—151no—
79D5×C41—151no—
80D5×C41—151no—
81D5×C41—302no—
82C32×C41D5211yescharacteristic, complemented, Hall
83D5×D15—411no—
84C3×D52—1231no—
85C2×C3×C41—751no—
86D123—51no—
87C3×D41—51no—
88C3×D41—51no—
89C3×D41—101no—
90C3×D41—151no—
91D3×C41—251no—
92C32×C52C2×D4111yescharacteristic, complemented, Hall
93C5×C41—22no—
94C5×C41C3×D3×D511yescharacteristic, complemented
95C5×C41C2×C3×D1511yescharacteristic, complemented
96C2×C3×D15—2051no—
97C3×D3×D5—2051no—
98C2×D41—751noHall
99C3⋊(C5⋊D5)C3×D4111yescharacteristic, complemented
100C5×D15—411no—
101C3×C5⋊D5—31no—
102C3×C5×D5—411no—
103C3×C5×D5—411no—
104C3×C5×D5—821no—
105C3×C5×D5—1231no—
106C3×C41—21no—
107C3×C41C3×D5211yescharacteristic, complemented
108C3×C41D5×D1511yescharacteristic, complemented
109D52—1231noHall
110C2×C32×C5—2051no—
111C3×D15—51no—
112C3×D15—51no—
113C3×D15—102no—
114C3×D15—411no—
115C3×C5×D3—2051no—
116C32×D5—411no—
117C2×C41—751no—
118D41—51no—
119D41—151no—
120C3×C52—21no—
121C3×C52D3×D4111yescharacteristic, complemented
122C3×C52C2×C3×D4111yescharacteristic, complemented
123C2×D15—2051no—
124C2×C3×D5—6151no—
125C2×C3×D5—6151no—
126D3×D5—2051no—
127C5⋊D5—31no—
128C5×D5—411no—
129C5×D5—1231no—
130C32×C5—22no—
131C32×C5D5×D4111yescharacteristic, complemented
132C32×C5D5×D4111yescharacteristic, complemented
133C41C3×D5×D1511yescharacteristic, complemented, Sylow
134C2×C3×D3—10251noHall
135C2×C3×C5—6151no—
136C2×C3×C5—4101no—
137C2×C3×C5—2051no—
138C2×C3×C5—2051no—
139D15—51no—
140D15—51no—
141D15—102no—
142D15—411no—
143C3×D5—151no—
144C3×D5—151no—
145C3×D5—302no—
146C3×D5—411no—
147C3×D5—411no—
148C3×D5—821no—
149C3×D5—1231no—
150C5×D3—2051no—
151C52C3×D3×D4111yescharacteristic, complemented, Sylow
152C2×D5—6151no—
153C2×D5—6151no—
154C2×C32—2051no—
155C3×D3—251no—
156C3×D3—2051no—
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5C3×D5×D4111yescharacteristic, complemented
163C3×C5C3×D5×D4111yescharacteristic, complemented
164C3×C5D15×D4111yescharacteristic, complemented
165C3×C5D15⋊D4111yescharacteristic, complemented
166C22×C3—30751no—
167C2×D3—10251no—
168C2×C5—6151no—
169C2×C5—2051no—
170D5—151no—
171D5—151no—
172D5—302no—
173D5—411no—
174D5—1231no—
175C32(C5⋊D5)⋊D4111yescharacteristic, complemented, Sylow
176C2×C3—751no—
177C2×C3—6151no—
178C2×C3—4101no—
179C2×C3—2051no—
180C2×C3—2051no—
181D3—251no—
182D3—2051no—
183C5—22no—
184C5C3×D15×D4111yescharacteristic, complemented
185C5C3×D15⋊D4111yescharacteristic, complemented
186C22—30751noSylow
187C3—21no—
188C3C3×(C5⋊D5)⋊D4111yescharacteristic, complemented
189C3D205⋊D1511yescharacteristic, direct product factor
190C2—751no—
191C2—6151no—
192C2—2051no—
subgroupG/H
center, hypercenterC3D205⋊D15
commutator, cosocle, hypocenterC3×C52×C41C22×C3
FrattiniC1G
Fitting, socleC32×C52×C41C22
LCSG ▷ C3×C52×C41
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C5×D205C2semidirect
2. C3×C5×D615C2semidirect
3. C3×C41×C3⋊(C5⋊D5)C2semidirect
4. D205⋊D15C3direct (N × H)
6. C32×C52×C41C22semidirect
9. C41×C3⋊(C5⋊D5)C2×C3semidirect
10. C5×D615C2×C3semidirect
14. C3×C5×D205D3semidirect
15. C3×C5×D205C2×C3semidirect
17. C3×D615D5semidirect
22. C32×D205D5semidirect
25. C3×C52×C41C2×D3semidirect
26. C3×C52×C41C22×C3semidirect
33. C5×D205C3×D3semidirect
35. C32×C5×C41C2×D5semidirect
36. C32×C5×C41C2×D5semidirect
38. D615C3×D5semidirect
45. C3×D205C3×D5semidirect
46. C3×D205D15semidirect
54. C52×C41C2×C3×D3semidirect
66. C3×C5×C41D3×D5semidirect
67. C3×C5×C41C2×C3×D5semidirect
68. C3×C5×C41C2×C3×D5semidirect
69. C3×C5×C41C2×D15semidirect
72. C3×C3⋊(C5⋊D5)D41semidirect
76. D205C3×D15semidirect
82. C32×C41D52semidirect
92. C32×C52C2×D41semidirect
94. C5×C41C3×D3×D5semidirect
95. C5×C41C2×C3×D15semidirect
99. C3⋊(C5⋊D5)C3×D41semidirect
107. C3×C41C3×D52semidirect
108. C3×C41D5×D15semidirect
121. C3×C52D3×D41semidirect
122. C3×C52C2×C3×D41semidirect
131. C32×C5D5×D41semidirect
132. C32×C5D5×D41semidirect
133. C41C3×D5×D15semidirect
151. C52C3×D3×D41semidirect
162. C3×C5C3×D5×D41semidirect
163. C3×C5C3×D5×D41semidirect
164. C3×C5D15×D41semidirect
165. C3×C5D15⋊D41semidirect
175. C32(C5⋊D5)⋊D41semidirect
184. C5C3×D15×D41semidirect
185. C5C3×D15⋊D41semidirect
188. C3C3×(C5⋊D5)⋊D41semidirect
189. C3D205⋊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×D2052
C3×C5×D6152
C3×C41×C3⋊(C5⋊D5)2
D205⋊D153
C3×(C5⋊D5)⋊D413
C3×D15⋊D415
C3×D15×D415
C3×D5×D1541