Finite Group Databasebeta

← C3×D5×D465 #42124908

Subgroups — C3×D5×D465 #42124908

Order 27900.

212 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 56 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×C31C211yesmaximal, characteristic, complemented
2C3×C5×D465C211yesmaximal, characteristic, complemented
3C3×C3⋊(C5⋊D155)C211yesmaximal, characteristic, complemented
4D5×D465C311yesmaximal, characteristic, direct product factor
5C3×D5×D155—31nomaximal
6C32×C52×C31C2211yescharacteristic, complemented, Hall
7C2×C3×D465—51nomaximal
8C3×D5×D93—51nomaximal
9C3⋊(C5⋊D155)C2×C311yescharacteristic, complemented
10C5×D465C2×C311yescharacteristic, complemented
11C3×C5⋊D155—31no—
12C3×C5×D155—31no—
13C3×C5×D5×C31—21no—
14C3×C5×D5×C31D311yescharacteristic, complemented
15C3×C5×D5×C31C2×C311yescharacteristic, complemented
16D5×D155—31noHall
17C3×D465—51no—
18C3×D465—51no—
19C3×D465—102no—
20C3×D465D511yescharacteristic, direct product factor
21C3×C5×D93—51no—
22C32×D5×C31D511yescharacteristic, complemented
23C2×C32×C5×C31—51no—
24C3×C52×C31—21no—
25C3×C52×C31C2×D311yescharacteristic, complemented
26C3×C52×C31C22×C311yescharacteristic, complemented
27C2×D465—51no—
28C2×C3×D155—151no—
29D5×D93—51no—
30C3×D5×D31—151no—
31C5⋊D155—31no—
32C5×D155—31no—
33C5×D5×C31C3×D311yescharacteristic, complemented
34C32×C5×C31—22no—
35C32×C5×C31C2×D511yescharacteristic, complemented
36C32×C5×C31C2×D511yescharacteristic, complemented
37C2×C3×D93—251noHall
38C2×C3×C5×C31—51no—
39C2×C3×C5×C31—51no—
40C2×C3×C5×C31—101no—
41D465—51no—
42D465—51no—
43D465—102no—
44D465C3×D511yescharacteristic, direct product factor
45C5×D93—51no—
46C3×D155—31no—
47C3×D155—151no—
48C3×D155—151no—
49C3×D155—302no—
50C3×D5×C31—21no—
51C3×D5×C31C3×D511yescharacteristic, complemented
52C3×D5×C31D1511yescharacteristic, complemented
53C3×C5×D31—151no—
54C3×D5×D15—311nomaximal, Hall
55C52×C31C2×C3×D311yescharacteristic, complemented, Hall
56C2×D155—151no—
57D5×D31—151no—
58C2×C32×C31—51no—
59C3×D93—51no—
60C3×D93—251no—
61C3×C5×C31—21no—
62C3×C5×C31—21no—
63C3×C5×C31—22no—
64C3×C5×C31—22no—
65C3×C5×C31—42no—
66C3×C5×C31D3×D511yescharacteristic, complemented
67C3×C5×C31C2×C3×D511yescharacteristic, complemented
68C3×C5×C31C2×C3×D511yescharacteristic, complemented
69C3×C5×C31C2×D1511yescharacteristic, complemented
70C3×C3⋊(C5⋊D5)—311no—
71C3×C5×D15—311no—
72C32×C5×D5D3111yescharacteristic, complemented
73C2×D93—251no—
74C2×C3×D31—751no—
75C2×C5×C31—51no—
76D155—31no—
77D155—151no—
78D155—151no—
79D155—302no—
80C5×D31—151no—
81D5×C31C3×D1511yescharacteristic, complemented
82D5×D15—311no—
83C3×D52—931no—
84C32×C31D5211yescharacteristic, complemented, Hall
85C32×C52C2×D3111yescharacteristic, complemented, Hall
86C2×C3×C31—51no—
87C2×C3×C31—51no—
88C2×C3×C31—101no—
89D93—51no—
90D93—251no—
91C3×D31—151no—
92C3×D31—751no—
93C2×C3×D15—1551no—
94C3×D3×D5—1551no—
95C5×C31—22no—
96C5×C31C3×D3×D511yescharacteristic, complemented
97C5×C31C2×C3×D1511yescharacteristic, complemented
98C3⋊(C5⋊D5)—311no—
99C5×D15—311no—
100C3×C5⋊D5—931no—
101C3×C5×D5—21no—
102C3×C5×D5—931no—
103C3×C5×D5C3×D3111yescharacteristic, complemented
104C3×C5×D5D9311yescharacteristic, complemented
105C2×D31—751noHall
106D52—931noHall
107C3×C31—21no—
108C3×C31C3×D5211yescharacteristic, complemented
109C3×C31D5×D1511yescharacteristic, complemented
110C2×C32×C5—51no—
111C3×D15—311no—
112C3×D15—3102no—
113C3×D15—1551no—
114C3×D15—1551no—
115C3×C5×D3—1551no—
116C32×D5D15511yescharacteristic, complemented
117C3×C52—21no—
118C3×C52C2×C3×D3111yescharacteristic, complemented
119C3×C52C2×D9311yescharacteristic, complemented
120C2×C31—51no—
121D31—151no—
122D31—751no—
123C2×D15—1551no—
124C2×C3×D5—4651no—
125C2×C3×D5—4651no—
126D3×D5—1551no—
127C5⋊D5—931no—
128C5×D5—931no—
129C5×D5C3×D9311yescharacteristic, complemented
130C32×C5—22no—
131C32×C5D5×D3111yescharacteristic, complemented
132C32×C5C2×D15511yescharacteristic, complemented
133C2×C3×D3—7751noHall
134C31C3×D5×D1511yescharacteristic, complemented, Sylow
135C2×C3×C5—51no—
136C2×C3×C5—51no—
137C2×C3×C5—101no—
138C2×C3×C5—4651no—
139D15—311no—
140D15—3102no—
141D15—1551no—
142D15—1551no—
143C3×D5—21no—
144C3×D5—931no—
145C3×D5—9302no—
146C3×D5—4651no—
147C3×D5—4651no—
148C3×D5C3×D15511yescharacteristic, complemented
149C3×D5D46511yescharacteristic, direct product factor
150C5×D3—1551no—
151C52C2×C3×D9311yescharacteristic, complemented, Sylow
152C2×D5—4651no—
153C2×D5—4651no—
154C2×C32—51no—
155C3×D3—7751no—
156C3×D3—1551no—
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5C3×D5×D3111yescharacteristic, complemented
163C3×C5D5×D9311yescharacteristic, complemented
164C3×C5C2×C3×D15511yescharacteristic, complemented
165C3×C5C2×D46511yescharacteristic, complemented
166C22×C3—23251no—
167C2×D3—7751no—
168C2×C5—51no—
169C2×C5—4651no—
170D5—931no—
171D5—9302no—
172D5—4651no—
173D5—4651no—
174D5C3×D46511yescharacteristic, direct product factor
175C32D5×D15511yescharacteristic, complemented, Sylow
176C2×C3—51no—
177C2×C3—51no—
178C2×C3—101no—
179C2×C3—23251no—
180C2×C3—4651no—
181D3—7751no—
182D3—1551no—
183C5—22no—
184C5C3×D5×D9311yescharacteristic, complemented
185C5C2×C3×D46511yescharacteristic, complemented
186C22—23251noSylow
187C3—21no—
188C3C3×D5×D15511yescharacteristic, complemented
189C3D5×D46511yescharacteristic, direct product factor
190C2—51no—
191C2—23251no—
192C2—4651no—
subgroupG/H
center, hypercenterC3D5×D465
commutator, cosocle, hypocenterC3×C52×C31C22×C3
FrattiniC1G
Fitting, socleC32×C52×C31C22
LCSG ▷ C3×C52×C31
UCSC1 ◁ C3

Complements

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

NH ≅ G/Ntype
1. C32×C5×D5×C31C2semidirect
2. C3×C5×D465C2semidirect
3. C3×C3⋊(C5⋊D155)C2semidirect
4. D5×D465C3direct (N × H)
6. C32×C52×C31C22semidirect
9. C3⋊(C5⋊D155)C2×C3semidirect
10. C5×D465C2×C3semidirect
14. C3×C5×D5×C31D3semidirect
15. C3×C5×D5×C31C2×C3semidirect
20. C3×D465D5direct (N × H)
22. C32×D5×C31D5semidirect
25. C3×C52×C31C2×D3semidirect
26. C3×C52×C31C22×C3semidirect
33. C5×D5×C31C3×D3semidirect
35. C32×C5×C31C2×D5semidirect
36. C32×C5×C31C2×D5semidirect
44. D465C3×D5direct (N × H)
51. C3×D5×C31C3×D5semidirect
52. C3×D5×C31D15semidirect
55. C52×C31C2×C3×D3semidirect
66. C3×C5×C31D3×D5semidirect
67. C3×C5×C31C2×C3×D5semidirect
68. C3×C5×C31C2×C3×D5semidirect
69. C3×C5×C31C2×D15semidirect
72. C32×C5×D5D31semidirect
81. D5×C31C3×D15semidirect
84. C32×C31D52semidirect
85. C32×C52C2×D31semidirect
96. C5×C31C3×D3×D5semidirect
97. C5×C31C2×C3×D15semidirect
103. C3×C5×D5C3×D31semidirect
104. C3×C5×D5D93semidirect
108. C3×C31C3×D52semidirect
109. C3×C31D5×D15semidirect
116. C32×D5D155semidirect
118. C3×C52C2×C3×D31semidirect
119. C3×C52C2×D93semidirect
129. C5×D5C3×D93semidirect
131. C32×C5D5×D31semidirect
132. C32×C5C2×D155semidirect
134. C31C3×D5×D15semidirect
148. C3×D5C3×D155semidirect
149. C3×D5D465direct (N × H)
151. C52C2×C3×D93semidirect
162. C3×C5C3×D5×D31semidirect
163. C3×C5D5×D93semidirect
164. C3×C5C2×C3×D155semidirect
165. C3×C5C2×D465semidirect
174. D5C3×D465direct (N × H)
175. C32D5×D155semidirect
184. C5C3×D5×D93semidirect
185. C5C2×C3×D465semidirect
188. C3C3×D5×D155semidirect
189. C3D5×D465direct (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×C312
C3×C5×D4652
C3×C3⋊(C5⋊D155)2
D5×D4653
C3×D5×D1553
C2×C3×D4655
C3×D5×D935
C3×D5×D1531