Finite Group Databasebeta

← C3×D15⋊D155 #42124913

Subgroups — C3×D15⋊D155 #42124913

Order 27900.

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

normal subgroups only

This group has 224 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⋊D155C211yesmaximal, characteristic, complemented
2C3×C5×D15×C31C211yesmaximal, characteristic, complemented
3C3×C5×D465C211yesmaximal, characteristic, complemented
4D15⋊D155C311yesmaximal, characteristic, direct product factor
5C3×D5×D155—31nomaximal
6C32×C52×C31C2211yescharacteristic, complemented, Hall
7C3×D15⋊D31—51nomaximal
8C3×D3×D155—51nomaximal
9C5×D465C2×C311yescharacteristic, complemented
10C5×D15×C31C2×C311yescharacteristic, complemented
11C3×C5⋊D155—21no—
12C3×C5⋊D155D311yescharacteristic, complemented
13C3×C5⋊D155C2×C311yescharacteristic, complemented
14C3×C5×D155—31no—
15C3×C5×D5×C31—31no—
16D5×D155—31noHall
17C3×D465D511yescharacteristic, complemented
18C3×D15×C31D511yescharacteristic, complemented
19C3×C5×D93—51no—
20C3×C5×D3×C31—51no—
21C32×D155—51no—
22C32×D155—51no—
23C32×D155—102no—
24C3×C52×C31—21no—
25C3×C52×C31C2×D311yescharacteristic, complemented
26C3×C52×C31C22×C311yescharacteristic, complemented
27C2×C3×D155—151no—
28D15⋊D31—51no—
29D3×D155—51no—
30C3×D5×D31—151no—
31C5⋊D155C3×D311yescharacteristic, complemented
32C5×D155—31no—
33C5×D5×C31—31no—
34C32×C5×C31—22no—
35C32×C5×C31C2×D511yescharacteristic, complemented
36C32×C5×C31C2×D511yescharacteristic, complemented
37C3×D3×D31—251noHall
38C2×C3×C5×C31—151no—
39D465C3×D511yescharacteristic, complemented
40D15×C31C3×D511yescharacteristic, complemented
41C5×D93—51no—
42C5×D3×C31—51no—
43C3×D155—31no—
44C3×D155—51no—
45C3×D155—51no—
46C3×D155—51no—
47C3×D155—51no—
48C3×D155—102no—
49C3×D155—102no—
50C3×D155—101no—
51C3×D155—101no—
52C3×D155—104no—
53C3×D5×C31—31no—
54C3×C5×D31—151no—
55C3×D15⋊D5—311nomaximal, Hall
56C52×C31C2×C3×D311yescharacteristic, complemented, Hall
57C2×D155—151no—
58D5×D31—151no—
59C3×D93—51no—
60C3×D3×C31—51no—
61C32×D31—251no—
62C3×C5×C31—24no—
63C3×C5×C31—21no—
64C3×C5×C31—21no—
65C3×C5×C31—22no—
66C3×C5×C31—22no—
67C3×C5×C31D3×D511yescharacteristic, complemented
68C3×C5×C31D3×D511yescharacteristic, complemented
69C3×C5×C31C2×C3×D511yescharacteristic, complemented
70C3×C5×C31C2×C3×D511yescharacteristic, complemented
71C3×C5×D15—311no—
72C3×C5×D15D3111yescharacteristic, complemented
73C32×C5⋊D5—311no—
74C2×C3×D31—751no—
75D3×D31—251no—
76C2×C5×C31—151no—
77D155—31no—
78D155—51no—
79D155—51no—
80D155—102no—
81C5×D31—151no—
82D5×C31—31no—
83D15⋊D5—311no—
84C3×D52—931no—
85C32×C31D5211yescharacteristic, complemented, Hall
86C32×C52C2×D3111yescharacteristic, complemented, Hall
87C2×C3×C31—151no—
88D93—51no—
89C3×D31—151no—
90C3×D31—251no—
91C3×D31—251no—
92C3×D31—501no—
93D3×C31—51no—
94C3×D3×D5—1551no—
95C3×D3×D5—1551no—
96C5×C31—22no—
97C5×C31C3×D3×D511yescharacteristic, complemented
98C5×C31C3×D3×D511yescharacteristic, complemented
99C5×D15—311no—
100C5×D15C3×D3111yescharacteristic, complemented
101C3×C5⋊D5—311no—
102C3×C5⋊D5—311no—
103C3×C5⋊D5—621no—
104C3×C5×D5—31no—
105C3×C5×D5—931no—
106C2×D31—751noHall
107D52—931noHall
108C3×C31—21no—
109C3×C31C3×D5211yescharacteristic, complemented
110C3×C31D15⋊D511yescharacteristic, complemented
111C3×D15—311no—
112C3×D15D15511yescharacteristic, complemented
113C3×C5×D3—51no—
114C3×C5×D3—1551no—
115C32×D5—3102no—
116C32×D5—1551no—
117C32×D5—1551no—
118C3×C52—21no—
119C3×C52D3×D3111yescharacteristic, complemented
120C3×C52C2×C3×D3111yescharacteristic, complemented
121C2×C31—151no—
122D31—151no—
123D31—251no—
124C2×C3×D5—4651no—
125C2×C3×D5—4651no—
126D3×D5—1551no—
127D3×D5—1551no—
128C5⋊D5—311no—
129C5×D5—31no—
130C5×D5—931no—
131C32×C5—22no—
132C32×C5D5×D3111yescharacteristic, complemented
133C32×C5C2×D15511yescharacteristic, complemented
134C2×C3×D3—7751noHall
135C31C3×D15⋊D511yescharacteristic, complemented, Sylow
136C2×C3×C5—151no—
137C2×C3×C5—4651no—
138D15—311no—
139D15C3×D15511yescharacteristic, complemented
140C3×D5—31no—
141C3×D5—3102no—
142C3×D5—3102no—
143C3×D5—3104no—
144C3×D5—3101no—
145C3×D5—3101no—
146C3×D5—931no—
147C3×D5—1551no—
148C3×D5—1551no—
149C3×D5—1551no—
150C3×D5—1551no—
151C5×D3—51no—
152C5×D3—1551no—
153C52C3×D3×D3111yescharacteristic, complemented, Sylow
154C2×D5—4651no—
155C2×D5—4651no—
156C2×C32—7751no—
157C3×D3—51no—
158C3×D3—1551no—
159C3×C5—24no—
160C3×C5—21no—
161C3×C5—21no—
162C3×C5—22no—
163C3×C5—22no—
164C3×C5C3×D5×D3111yescharacteristic, complemented
165C3×C5D3×D15511yescharacteristic, complemented
166C3×C5D15⋊D3111yescharacteristic, complemented
167C3×C5C2×C3×D15511yescharacteristic, complemented
168C22×C3—23251no—
169C2×D3—7751no—
170C2×C5—151no—
171C2×C5—4651no—
172D5—31no—
173D5—3102no—
174D5—931no—
175D5—1551no—
176D5—1551no—
177C32D5×D15511yescharacteristic, complemented, Sylow
178C2×C3—7751no—
179C2×C3—7751no—
180C2×C3—15501no—
181C2×C3—151no—
182C2×C3—4651no—
183D3—51no—
184D3—1551no—
185C5—22no—
186C5C3×D3×D15511yescharacteristic, complemented
187C5C3×D15⋊D3111yescharacteristic, complemented
188C22—23251noSylow
189C3—21no—
190C3C3×D5×D15511yescharacteristic, complemented
191C3D15⋊D15511yescharacteristic, direct product factor
192C2—7751no—
193C2—151no—
194C2—4651no—
subgroupG/H
center, hypercenterC3D15⋊D155
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⋊D155C2semidirect
2. C3×C5×D15×C31C2semidirect
3. C3×C5×D465C2semidirect
4. D15⋊D155C3direct (N × H)
6. C32×C52×C31C22semidirect
9. C5×D465C2×C3semidirect
10. C5×D15×C31C2×C3semidirect
12. C3×C5⋊D155D3semidirect
13. C3×C5⋊D155C2×C3semidirect
17. C3×D465D5semidirect
18. C3×D15×C31D5semidirect
25. C3×C52×C31C2×D3semidirect
26. C3×C52×C31C22×C3semidirect
31. C5⋊D155C3×D3semidirect
35. C32×C5×C31C2×D5semidirect
36. C32×C5×C31C2×D5semidirect
39. D465C3×D5semidirect
40. D15×C31C3×D5semidirect
56. C52×C31C2×C3×D3semidirect
67. C3×C5×C31D3×D5semidirect
68. C3×C5×C31D3×D5semidirect
69. C3×C5×C31C2×C3×D5semidirect
70. C3×C5×C31C2×C3×D5semidirect
72. C3×C5×D15D31semidirect
85. C32×C31D52semidirect
86. C32×C52C2×D31semidirect
97. C5×C31C3×D3×D5semidirect
98. C5×C31C3×D3×D5semidirect
100. C5×D15C3×D31semidirect
109. C3×C31C3×D52semidirect
110. C3×C31D15⋊D5semidirect
112. C3×D15D155semidirect
119. C3×C52D3×D31semidirect
120. C3×C52C2×C3×D31semidirect
132. C32×C5D5×D31semidirect
133. C32×C5C2×D155semidirect
135. C31C3×D15⋊D5semidirect
139. D15C3×D155semidirect
153. C52C3×D3×D31semidirect
164. C3×C5C3×D5×D31semidirect
165. C3×C5D3×D155semidirect
166. C3×C5D15⋊D31semidirect
167. C3×C5C2×C3×D155semidirect
177. C32D5×D155semidirect
186. C5C3×D3×D155semidirect
187. C5C3×D15⋊D31semidirect
190. C3C3×D5×D155semidirect
191. C3D15⋊D155direct (N × H)

Maximal subgroups

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

subgroupindex
C32×C5⋊D1552
C3×C5×D15×C312
C3×C5×D4652
D15⋊D1553
C3×D5×D1553
C3×D15⋊D315
C3×D3×D1555
C3×D15⋊D531