Finite Group Databasebeta

← C41×D15⋊D15 #49147154

Subgroups — C41×D15⋊D15 #49147154

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
1C3×C5×D15×C41C211yesmaximal, characteristic, complemented
2C3×C41×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
3C5×C41×C3⋊D15C211yesmaximal, characteristic, complemented
4C41×D15⋊D5—31nomaximal
5D5×D15×C41—31nomaximal
6C32×C52×C41C2211yescharacteristic, complemented, Hall
7C41×(C3⋊D3)⋊D5—51nomaximal
8D3×D15×C41—51nomaximal
9C41×C3⋊(C5⋊D5)D311yescharacteristic, complemented
10C5×D15×C41—31no—
11C5×D15×C41—31no—
12C5×D15×C41—61no—
13C5×D15×C41D311yescharacteristic, complemented
14C3×C41×C5⋊D5—31no—
15C3×C5×D5×C41—31no—
16D52×C41—91noHall
17C41×C3⋊D15D511yescharacteristic, complemented
18C5×C3⋊D3×C41—51no—
19C3×D15×C41—51no—
20C3×D15×C41—51no—
21C3×D15×C41—102no—
22C3×D15×C41D511yescharacteristic, complemented
23C3×C5×D3×C41—51no—
24C3×C52×C41—21no—
25C3×C52×C41C2×D311yescharacteristic, complemented
26C3×C52×C41C2×D311yescharacteristic, complemented
27C2×D15×C41—151no—
28D3×D5×C41—151no—
29D3×D5×C41—151no—
30D3×D5×C41—151no—
31C41×C5⋊D5—31no—
32C5×D5×C41—31no—
33C5×D5×C41—91no—
34C32×C5×C41—22no—
35C32×C5×C41C2×D511yescharacteristic, complemented
36C32×C5×C41C2×D511yescharacteristic, complemented
37D32×C41—251noHall
38C2×C3×C5×C41—151no—
39D15×C41—31no—
40D15×C41—31no—
41D15×C41—51no—
42D15×C41—51no—
43D15×C41—61no—
44D15×C41—102no—
45D15×C41D1511yescharacteristic, complemented
46C5×D3×C41—51no—
47C5×D3×C41—151no—
48C5×D3×C41—151no—
49C5×D3×C41—301no—
50C3×D5×C41—31no—
51C3×D5×C41—151no—
52C3×D5×C41—151no—
53C3×D5×C41—302no—
54C52×C41D3211yescharacteristic, complemented, Hall
55D15⋊D15C4111yesmaximal, characteristic, direct product factor, Hall
56C2×D5×C41—451no—
57C2×D5×C41—451no—
58C3⋊D3×C41—51no—
59C3×D3×C41—51no—
60C3×D3×C41—251no—
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×C41D3×D511yescharacteristic, complemented
68C3×C5×C41D3×D511yescharacteristic, complemented
69C3×C5×C41C2×D1511yescharacteristic, complemented
70C2×D3×C41—751no—
71C2×D3×C41—751no—
72C5×C3⋊D15C2×C4111yescharacteristic, complemented
73C3×C3⋊(C5⋊D5)C2×C4111yescharacteristic, complemented
74C3×C5×D15C2×C4111yescharacteristic, complemented
75C2×C5×C41—151no—
76C2×C5×C41—451no—
77D5×C41—31no—
78D5×C41—91no—
79D5×C41—151no—
80D5×C41—151no—
81D5×C41—302no—
82C32×C41D5211yescharacteristic, complemented, Hall
83D15⋊D5—31no—
84D5×D15—31no—
85C2×C3×C41—151no—
86C2×C3×C41—751no—
87D3×C41—51no—
88D3×C41—151no—
89D3×C41—151no—
90D3×C41—251no—
91D3×C41—301no—
92C32×C52C22×C4111yescharacteristic, complemented, Hall
93C5×C41—22no—
94C5×C41D3×D1511yescharacteristic, complemented
95C5×C41(C3⋊D3)⋊D511yescharacteristic, complemented
96(C3⋊D3)⋊D5—51no—
97D3×D15—51no—
98C22×C41—2251noHall
99C3⋊(C5⋊D5)D3×C4111yescharacteristic, complemented
100C5×D15—31no—
101C5×D15—31no—
102C5×D15—61no—
103C5×D15D3×C4111yescharacteristic, complemented
104C3×C5⋊D5—31no—
105C3×C5×D5—31no—
106C3×C41—21no—
107C3×C41D5×D1511yescharacteristic, complemented
108C3×C41D15⋊D511yescharacteristic, complemented
109D52—91noHall
110C3⋊D15D5×C4111yescharacteristic, complemented
111C5×C3⋊D3—51no—
112C3×D15—51no—
113C3×D15—51no—
114C3×D15—102no—
115C3×D15D5×C4111yescharacteristic, complemented
116C3×C5×D3—51no—
117C2×C41—151no—
118C2×C41—451no—
119C2×C41—751no—
120C3×C52—21no—
121C3×C52C2×D3×C4111yescharacteristic, complemented
122C3×C52C2×D3×C4111yescharacteristic, complemented
123C2×D15—151no—
124D3×D5—151no—
125D3×D5—151no—
126D3×D5—151no—
127C5⋊D5—31no—
128C5×D5—31no—
129C5×D5—91no—
130C32×C5—22no—
131C32×C5C2×D5×C4111yescharacteristic, complemented
132C32×C5C2×D5×C4111yescharacteristic, complemented
133C41D15⋊D1511yescharacteristic, direct product factor, Sylow
134D32—251noHall
135C2×C3×C5—151no—
136D15—31no—
137D15—31no—
138D15—51no—
139D15—51no—
140D15—61no—
141D15—102no—
142D15D15×C4111yescharacteristic, complemented
143C3×D5—31no—
144C3×D5—151no—
145C3×D5—151no—
146C3×D5—302no—
147C5×D3—51no—
148C5×D3—151no—
149C5×D3—151no—
150C5×D3—301no—
151C52D32×C4111yescharacteristic, 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×C4111yescharacteristic, complemented
163C3×C5D3×D5×C4111yescharacteristic, complemented
164C3×C5D3×D5×C4111yescharacteristic, complemented
165C3×C5C2×D15×C4111yescharacteristic, complemented
166C2×D3—751no—
167C2×D3—751no—
168C2×C5—151no—
169C2×C5—451no—
170D5—31no—
171D5—91no—
172D5—151no—
173D5—151no—
174D5—302no—
175C32D52×C4111yescharacteristic, complemented, Sylow
176C2×C3—151no—
177C2×C3—751no—
178D3—51no—
179D3—151no—
180D3—151no—
181D3—251no—
182D3—301no—
183C5—22no—
184C5D3×D15×C4111yescharacteristic, complemented
185C5C41×(C3⋊D3)⋊D511yescharacteristic, complemented
186C22—2251noSylow
187C3—21no—
188C3D5×D15×C4111yescharacteristic, complemented
189C3C41×D15⋊D511yescharacteristic, complemented
190C2—151no—
191C2—451no—
192C2—751no—
subgroupG/H
center, hypercenterC41D15⋊D15
commutator, cosocle, hypocenterC32×C52C22×C41
FrattiniC1G
Fitting, socleC32×C52×C41C22
LCSG ▷ C32×C52
UCSC1 ◁ C41

Complements

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

NH ≅ G/Ntype
1. C3×C5×D15×C41C2semidirect
2. C3×C41×C3⋊(C5⋊D5)C2semidirect
3. C5×C41×C3⋊D15C2semidirect
6. C32×C52×C41C22semidirect
9. C41×C3⋊(C5⋊D5)D3semidirect
13. C5×D15×C41D3semidirect
17. C41×C3⋊D15D5semidirect
22. C3×D15×C41D5semidirect
25. C3×C52×C41C2×D3semidirect
26. C3×C52×C41C2×D3semidirect
35. C32×C5×C41C2×D5semidirect
36. C32×C5×C41C2×D5semidirect
45. D15×C41D15semidirect
54. C52×C41D32semidirect
55. D15⋊D15C41direct (N × H)
66. C3×C5×C41D3×D5semidirect
67. C3×C5×C41D3×D5semidirect
68. C3×C5×C41D3×D5semidirect
69. C3×C5×C41C2×D15semidirect
72. C5×C3⋊D15C2×C41semidirect
73. C3×C3⋊(C5⋊D5)C2×C41semidirect
74. C3×C5×D15C2×C41semidirect
82. C32×C41D52semidirect
92. C32×C52C22×C41semidirect
94. C5×C41D3×D15semidirect
95. C5×C41(C3⋊D3)⋊D5semidirect
99. C3⋊(C5⋊D5)D3×C41semidirect
103. C5×D15D3×C41semidirect
107. C3×C41D5×D15semidirect
108. C3×C41D15⋊D5semidirect
110. C3⋊D15D5×C41semidirect
115. C3×D15D5×C41semidirect
121. C3×C52C2×D3×C41semidirect
122. C3×C52C2×D3×C41semidirect
131. C32×C5C2×D5×C41semidirect
132. C32×C5C2×D5×C41semidirect
133. C41D15⋊D15direct (N × H)
142. D15D15×C41semidirect
151. C52D32×C41semidirect
162. C3×C5D3×D5×C41semidirect
163. C3×C5D3×D5×C41semidirect
164. C3×C5D3×D5×C41semidirect
165. C3×C5C2×D15×C41semidirect
175. C32D52×C41semidirect
184. C5D3×D15×C41semidirect
185. C5C41×(C3⋊D3)⋊D5semidirect
188. C3D5×D15×C41semidirect
189. C3C41×D15⋊D5semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D15×C412
C3×C41×C3⋊(C5⋊D5)2
C5×C41×C3⋊D152
C41×D15⋊D53
D5×D15×C413
C41×(C3⋊D3)⋊D55
D3×D15×C415
D15⋊D1541