Finite Group Databasebeta

← C3×D5×C17×D15 #29505977

Subgroups — C3×D5×C17×D15 #29505977

Order 15300.

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
1C3×C17×C3⋊(C5⋊D5)C211yesmaximal, characteristic, complemented
2C3×C5×C17×D15C211yesmaximal, characteristic, complemented
3C32×C5×D5×C17C211yesmaximal, characteristic, complemented
4D5×C17×D15C311yesmaximal, characteristic, direct product factor
5C3×D52×C17—31nomaximal
6C32×C52×C17C2211yescharacteristic, complemented, Hall
7C2×C3×C17×D15—51nomaximal
8C3×D3×D5×C17—51nomaximal
9C17×C3⋊(C5⋊D5)C2×C311yescharacteristic, complemented
10C5×C17×D15C2×C311yescharacteristic, complemented
11C3×C17×C5⋊D5—31no—
12C3×C5×D5×C17—21no—
13C3×C5×D5×C17—31no—
14C3×C5×D5×C17D311yescharacteristic, complemented
15C3×C5×D5×C17C2×C311yescharacteristic, complemented
16D52×C17—31noHall
17C2×C32×C5×C17—51no—
18C3×C17×D15—51no—
19C3×C17×D15—51no—
20C3×C17×D15—102no—
21C3×C17×D15D511yescharacteristic, direct product factor
22C3×C5×D3×C17—51no—
23C32×D5×C17D511yescharacteristic, complemented
24C3×C52×C17—21no—
25C3×C52×C17C2×D311yescharacteristic, complemented
26C3×C52×C17C22×C311yescharacteristic, complemented
27C2×C17×D15—51no—
28C2×C3×D5×C17—151no—
29C2×C3×D5×C17—151no—
30D3×D5×C17—51no—
31C3×D5×D15C1711yesmaximal, characteristic, direct product factor, Hall
32C17×C5⋊D5—31no—
33C5×D5×C17—31no—
34C5×D5×C17C3×D311yescharacteristic, complemented
35C32×C5×C17—22no—
36C32×C5×C17C2×D511yescharacteristic, complemented
37C32×C5×C17C2×D511yescharacteristic, complemented
38C2×C3×D3×C17—251noHall
39C2×C3×C5×C17—51no—
40C2×C3×C5×C17—51no—
41C2×C3×C5×C17—101no—
42C2×C3×C5×C17—151no—
43C17×D15—51no—
44C17×D15—51no—
45C17×D15—102no—
46C17×D15C3×D511yescharacteristic, direct product factor
47C5×D3×C17—51no—
48C3×D5×C17—21no—
49C3×D5×C17—31no—
50C3×D5×C17—151no—
51C3×D5×C17—151no—
52C3×D5×C17—302no—
53C3×D5×C17C3×D511yescharacteristic, complemented
54C3×D5×C17D1511yescharacteristic, direct product factor
55C3×C3⋊(C5⋊D5)C2×C1711yescharacteristic, complemented
56C3×C5×D15C2×C1711yescharacteristic, complemented
57C32×C5×D5C2×C1711yescharacteristic, complemented
58C52×C17C2×C3×D311yescharacteristic, complemented, Hall
59C2×D5×C17—151no—
60C2×D5×C17—151no—
61C2×C32×C17—51no—
62C3×D3×C17—51no—
63C3×D3×C17—251no—
64D5×D15C3×C1711yescharacteristic, direct product factor
65C3×D52—31no—
66C3×C5×C17—21no—
67C3×C5×C17—21no—
68C3×C5×C17—22no—
69C3×C5×C17—22no—
70C3×C5×C17—42no—
71C3×C5×C17D3×D511yescharacteristic, complemented
72C3×C5×C17C2×C3×D511yescharacteristic, complemented
73C3×C5×C17C2×C3×D511yescharacteristic, complemented
74C3×C5×C17C2×D1511yescharacteristic, complemented
75C32×C52C22×C1711yescharacteristic, complemented, Hall
76C22×C3×C17—751no—
77C2×D3×C17—251no—
78C2×C3×D15—51no—
79C3×D3×D5—51no—
80C2×C5×C17—51no—
81C2×C5×C17—151no—
82D5×C17—31no—
83D5×C17—151no—
84D5×C17—151no—
85D5×C17—302no—
86D5×C17C3×D1511yescharacteristic, direct product factor
87C32×C17D5211yescharacteristic, complemented, Hall
88C3⋊(C5⋊D5)C2×C3×C1711yescharacteristic, complemented
89C5×D15C2×C3×C1711yescharacteristic, complemented
90C3×C5⋊D5—31no—
91C3×C5×D5—21no—
92C3×C5×D5—31no—
93C3×C5×D5D3×C1711yescharacteristic, complemented
94C3×C5×D5C2×C3×C1711yescharacteristic, complemented
95C2×C3×C17—51no—
96C2×C3×C17—51no—
97C2×C3×C17—101no—
98C2×C3×C17—151no—
99C2×C3×C17—751no—
100D3×C17—51no—
101D3×C17—251no—
102D52—31noHall
103C2×C32×C5—51no—
104C3×D15—51no—
105C3×D15—51no—
106C3×D15—102no—
107C3×D15D5×C1711yescharacteristic, direct product factor
108C3×C5×D3—51no—
109C32×D5D5×C1711yescharacteristic, complemented
110C5×C17—22no—
111C5×C17C3×D3×D511yescharacteristic, complemented
112C5×C17C2×C3×D1511yescharacteristic, complemented
113C3×C52—21no—
114C3×C52C2×D3×C1711yescharacteristic, complemented
115C3×C52C22×C3×C1711yescharacteristic, complemented
116C22×C17—751noHall
117C2×D15—51no—
118C2×C3×D5—151no—
119C2×C3×D5—151no—
120D3×D5—51no—
121C3×C17—21no—
122C3×C17C3×D5211yescharacteristic, complemented
123C3×C17D5×D1511yescharacteristic, direct product factor
124C5⋊D5—31no—
125C5×D5—31no—
126C5×D5C3×D3×C1711yescharacteristic, complemented
127C32×C5—22no—
128C32×C5C2×D5×C1711yescharacteristic, complemented
129C32×C5C2×D5×C1711yescharacteristic, complemented
130C2×C3×D3—251noHall
131C2×C17—51no—
132C2×C17—151no—
133C2×C17—751no—
134C2×C3×C5—51no—
135C2×C3×C5—51no—
136C2×C3×C5—101no—
137C2×C3×C5—151no—
138D15—51no—
139D15—51no—
140D15—102no—
141D15C3×D5×C1711yescharacteristic, direct product factor
142C3×D5—21no—
143C3×D5—31no—
144C3×D5—151no—
145C3×D5—151no—
146C3×D5—302no—
147C3×D5C3×D5×C1711yescharacteristic, complemented
148C3×D5C17×D1511yescharacteristic, direct product factor
149C5×D3—51no—
150C52C2×C3×D3×C1711yescharacteristic, complemented, Sylow
151C2×D5—151no—
152C2×D5—151no—
153C2×C32—51no—
154C3×D3—51no—
155C3×D3—251no—
156C17C3×D5×D1511yescharacteristic, direct product factor, Sylow
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5D3×D5×C1711yescharacteristic, complemented
163C3×C5C2×C3×D5×C1711yescharacteristic, complemented
164C3×C5C2×C3×D5×C1711yescharacteristic, complemented
165C3×C5C2×C17×D1511yescharacteristic, complemented
166C22×C3—751no—
167C2×D3—251no—
168C2×C5—51no—
169C2×C5—151no—
170D5—31no—
171D5—151no—
172D5—151no—
173D5—302no—
174D5C3×C17×D1511yescharacteristic, direct product factor
175C32D52×C1711yescharacteristic, 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×C1711yescharacteristic, complemented
185C5C2×C3×C17×D1511yescharacteristic, complemented
186C22—751noSylow
187C3—21no—
188C3C3×D52×C1711yescharacteristic, complemented
189C3D5×C17×D1511yescharacteristic, direct product factor
190C2—51no—
191C2—151no—
192C2—751no—
subgroupG/H
center, hypercenterC3×C17D5×D15
commutator, cosocle, hypocenterC3×C52C22×C3×C17
FrattiniC1G
Fitting, socleC32×C52×C17C22
LCSG ▷ C3×C52
UCSC1 ◁ C3×C17

Complements

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

NH ≅ G/Ntype
1. C3×C17×C3⋊(C5⋊D5)C2semidirect
2. C3×C5×C17×D15C2semidirect
3. C32×C5×D5×C17C2semidirect
4. D5×C17×D15C3direct (N × H)
6. C32×C52×C17C22semidirect
9. C17×C3⋊(C5⋊D5)C2×C3semidirect
10. C5×C17×D15C2×C3semidirect
14. C3×C5×D5×C17D3semidirect
15. C3×C5×D5×C17C2×C3semidirect
21. C3×C17×D15D5direct (N × H)
23. C32×D5×C17D5semidirect
25. C3×C52×C17C2×D3semidirect
26. C3×C52×C17C22×C3semidirect
31. C3×D5×D15C17direct (N × H)
34. C5×D5×C17C3×D3semidirect
36. C32×C5×C17C2×D5semidirect
37. C32×C5×C17C2×D5semidirect
46. C17×D15C3×D5direct (N × H)
53. C3×D5×C17C3×D5semidirect
54. C3×D5×C17D15direct (N × H)
55. C3×C3⋊(C5⋊D5)C2×C17semidirect
56. C3×C5×D15C2×C17semidirect
57. C32×C5×D5C2×C17semidirect
58. C52×C17C2×C3×D3semidirect
64. D5×D15C3×C17direct (N × H)
71. C3×C5×C17D3×D5semidirect
72. C3×C5×C17C2×C3×D5semidirect
73. C3×C5×C17C2×C3×D5semidirect
74. C3×C5×C17C2×D15semidirect
75. C32×C52C22×C17semidirect
86. D5×C17C3×D15direct (N × H)
87. C32×C17D52semidirect
88. C3⋊(C5⋊D5)C2×C3×C17semidirect
89. C5×D15C2×C3×C17semidirect
93. C3×C5×D5D3×C17semidirect
94. C3×C5×D5C2×C3×C17semidirect
107. C3×D15D5×C17direct (N × H)
109. C32×D5D5×C17semidirect
111. C5×C17C3×D3×D5semidirect
112. C5×C17C2×C3×D15semidirect
114. C3×C52C2×D3×C17semidirect
115. C3×C52C22×C3×C17semidirect
122. C3×C17C3×D52semidirect
123. C3×C17D5×D15direct (N × H)
126. C5×D5C3×D3×C17semidirect
128. C32×C5C2×D5×C17semidirect
129. C32×C5C2×D5×C17semidirect
141. D15C3×D5×C17direct (N × H)
147. C3×D5C3×D5×C17semidirect
148. C3×D5C17×D15direct (N × H)
150. C52C2×C3×D3×C17semidirect
156. C17C3×D5×D15direct (N × H)
162. C3×C5D3×D5×C17semidirect
163. C3×C5C2×C3×D5×C17semidirect
164. C3×C5C2×C3×D5×C17semidirect
165. C3×C5C2×C17×D15semidirect
174. D5C3×C17×D15direct (N × H)
175. C32D52×C17semidirect
184. C5C3×D3×D5×C17semidirect
185. C5C2×C3×C17×D15semidirect
188. C3C3×D52×C17semidirect
189. C3D5×C17×D15direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C17×C3⋊(C5⋊D5)2
C3×C5×C17×D152
C32×C5×D5×C172
D5×C17×D153
C3×D52×C173
C2×C3×C17×D155
C3×D3×D5×C175
C3×D5×D1517