Finite Group Databasebeta

← C3×C5×D15⋊D31 #42124902

Subgroups — C3×C5×D15⋊D31 #42124902

Order 27900.

212 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 60 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×C52×D93C211yesmaximal, characteristic, complemented
3C3×C5×D15×C31C211yesmaximal, characteristic, complemented
4C5×D15⋊D31C311yesmaximal, characteristic, direct product factor
5C3×C5×D5×D31—31nomaximal
6C32×C52×C31C2211yescharacteristic, complemented, Hall
7C3×D15⋊D31C511yesmaximal, characteristic, direct product factor
8C3×C5×D3×D31—51nomaximal
9C5×D15×C31C2×C311yescharacteristic, complemented
10C52×D93C2×C311yescharacteristic, complemented
11C3×C5×D155—21no—
12C3×C5×D155D311yescharacteristic, complemented
13C3×C5×D155C2×C311yescharacteristic, complemented
14C3×C5×D5×C31—31no—
15C3×C52×D31—31no—
16C5×D5×D31—31noHall
17C3×D15×C31C2×C511yescharacteristic, complemented
18C3×C5×D93—22no—
19C3×C5×D93D511yescharacteristic, complemented
20C3×C5×D93C2×C511yescharacteristic, complemented
21C3×C5×D3×C31—51no—
22C32×D155C2×C511yescharacteristic, complemented
23C32×C5×D31—51no—
24C3×C52×C31—21no—
25C3×C52×C31C2×D311yescharacteristic, complemented
26C3×C52×C31C22×C311yescharacteristic, complemented
27C2×C3×C5×D31—151no—
28D15⋊D31C3×C511yescharacteristic, direct product factor
29C5×D3×D31—51no—
30C3×D5×D31—31no—
31C5×D155C3×D311yescharacteristic, complemented
32C5×D5×C31—31no—
33C52×D31—31no—
34C32×C5×C31—22no—
35C32×C5×C31C2×D511yescharacteristic, complemented
36C32×C5×C31C22×C511yescharacteristic, complemented
37C3×D3×D31—51noHall
38C2×C3×C5×C31—151no—
39D15×C31C2×C3×C511yescharacteristic, complemented
40C5×D93—22no—
41C5×D93C3×D511yescharacteristic, complemented
42C5×D93C2×C3×C511yescharacteristic, complemented
43C5×D3×C31—51no—
44C3×D155—21no—
45C3×D155C5×D311yescharacteristic, complemented
46C3×D155C2×C3×C511yescharacteristic, complemented
47C3×D5×C31—31no—
48C3×C5×D31—31no—
49C3×C5×D31—31no—
50C3×C5×D31—51no—
51C3×C5×D31—51no—
52C3×C5×D31—62no—
53C3×C5×D31—101no—
54C3×C5×D3×D5—311nomaximal, Hall
55C52×C31C2×C3×D311yescharacteristic, complemented, Hall
56C2×C5×D31—151no—
57D5×D31—31no—
58C3×D93C5×D511yescharacteristic, complemented
59C3×D3×C31—51no—
60C32×D31—51no—
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×C5×D311yescharacteristic, complemented
69C3×C5×C31C22×C3×C511yescharacteristic, complemented
70C3×C5×D15D3111yescharacteristic, complemented
71C3×C52×D3—311no—
72C32×C5×D5—311no—
73C2×C3×D31—151no—
74D3×D31—51no—
75C2×C5×C31—151no—
76D155C3×C5×D311yescharacteristic, complemented
77C5×D31—31no—
78C5×D31—31no—
79C5×D31—51no—
80C5×D31—62no—
81D5×C31—31no—
82C2×C3×C5×D5—931no—
83C5×D3×D5—311no—
84C32×C31C2×C5×D511yescharacteristic, complemented, Hall
85C32×C52C2×D3111yescharacteristic, complemented, Hall
86C2×C3×C31—151no—
87D93C3×C5×D511yescharacteristic, complemented
88C3×D31—31no—
89C3×D31—51no—
90C3×D31—51no—
91C3×D31—101no—
92D3×C31—51no—
93C2×C3×C5×D3—1551no—
94C3×D3×D5—311no—
95C5×C31—22no—
96C5×C31C3×D3×D511yescharacteristic, complemented
97C5×C31C2×C3×C5×D311yescharacteristic, complemented
98C2×C3×C52—931no—
99C5×D15C3×D3111yescharacteristic, complemented
100C52×D3—311no—
101C3×C5×D5—31no—
102C3×C5×D5—311no—
103C3×C5×D5—311no—
104C3×C5×D5—621no—
105C2×D31—151noHall
106C2×C5×D5—931noHall
107C3×C31—21no—
108C3×C31C5×D3×D511yescharacteristic, complemented
109C3×C31C2×C3×C5×D511yescharacteristic, complemented
110C2×C32×C5—1551no—
111C3×D15C5×D3111yescharacteristic, complemented
112C3×C5×D3—51no—
113C3×C5×D3—311no—
114C3×C5×D3—311no—
115C3×C5×D3—622no—
116C32×D5—311no—
117C3×C52—21no—
118C3×C52D3×D3111yescharacteristic, complemented
119C3×C52C2×C3×D3111yescharacteristic, complemented
120C2×C31—151no—
121D31—31no—
122D31—51no—
123C22×C3×C5—4651no—
124C2×C5×D3—1551no—
125C2×C3×D5—931no—
126D3×D5—311no—
127C2×C52—931no—
128C5×D5—31no—
129C5×D5—311no—
130C32×C5—22no—
131C32×C5D5×D3111yescharacteristic, complemented
132C32×C5C2×C5×D3111yescharacteristic, complemented
133C2×C3×D3—1551noHall
134C31C3×C5×D3×D511yescharacteristic, complemented, Sylow
135C2×C3×C5—151no—
136C2×C3×C5—3101no—
137C2×C3×C5—931no—
138C2×C3×C5—931no—
139C2×C3×C5—1551no—
140C2×C3×C5—1551no—
141C2×C3×C5—1862no—
142D15C3×C5×D3111yescharacteristic, complemented
143C3×D5—31no—
144C3×D5—311no—
145C3×D5—311no—
146C3×D5—621no—
147C5×D3—51no—
148C5×D3—311no—
149C5×D3—311no—
150C5×D3—622no—
151C52C3×D3×D3111yescharacteristic, complemented, Sylow
152C22×C5—4651no—
153C2×D5—931no—
154C2×C32—1551no—
155C3×D3—51no—
156C3×D3—311no—
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5C3×D5×D3111yescharacteristic, complemented
163C3×C5C5×D3×D3111yescharacteristic, complemented
164C3×C5D15⋊D3111yescharacteristic, direct product factor
165C3×C5C2×C3×C5×D3111yescharacteristic, complemented
166C22×C3—4651no—
167C2×D3—1551no—
168C2×C5—151no—
169C2×C5—931no—
170C2×C5—931no—
171C2×C5—1551no—
172C2×C5—1862no—
173D5—31no—
174D5—311no—
175C32C5×D5×D3111yescharacteristic, complemented, Sylow
176C2×C3—151no—
177C2×C3—3101no—
178C2×C3—931no—
179C2×C3—1551no—
180C2×C3—1551no—
181D3—51no—
182D3—311no—
183C5—22no—
184C5C3×C5×D3×D3111yescharacteristic, complemented
185C5C3×D15⋊D3111yescharacteristic, direct product factor
186C22—4651noSylow
187C3—21no—
188C3C3×C5×D5×D3111yescharacteristic, complemented
189C3C5×D15⋊D3111yescharacteristic, direct product factor
190C2—151no—
191C2—931no—
192C2—1551no—
subgroupG/H
center, hypercenterC3×C5D15⋊D31
commutator, cosocle, hypocenterC3×C5×C31C22×C3×C5
FrattiniC1G
Fitting, socleC32×C52×C31C22
LCSG ▷ C3×C5×C31
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×D155C2semidirect
2. C3×C52×D93C2semidirect
3. C3×C5×D15×C31C2semidirect
4. C5×D15⋊D31C3direct (N × H)
6. C32×C52×C31C22semidirect
7. C3×D15⋊D31C5direct (N × H)
9. C5×D15×C31C2×C3semidirect
10. C52×D93C2×C3semidirect
12. C3×C5×D155D3semidirect
13. C3×C5×D155C2×C3semidirect
17. C3×D15×C31C2×C5semidirect
19. C3×C5×D93D5semidirect
20. C3×C5×D93C2×C5semidirect
22. C32×D155C2×C5semidirect
25. C3×C52×C31C2×D3semidirect
26. C3×C52×C31C22×C3semidirect
28. D15⋊D31C3×C5direct (N × H)
31. C5×D155C3×D3semidirect
35. C32×C5×C31C2×D5semidirect
36. C32×C5×C31C22×C5semidirect
39. D15×C31C2×C3×C5semidirect
41. C5×D93C3×D5semidirect
42. C5×D93C2×C3×C5semidirect
45. C3×D155C5×D3semidirect
46. C3×D155C2×C3×C5semidirect
55. C52×C31C2×C3×D3semidirect
58. C3×D93C5×D5semidirect
66. C3×C5×C31D3×D5semidirect
67. C3×C5×C31C2×C3×D5semidirect
68. C3×C5×C31C2×C5×D3semidirect
69. C3×C5×C31C22×C3×C5semidirect
70. C3×C5×D15D31semidirect
76. D155C3×C5×D3semidirect
84. C32×C31C2×C5×D5semidirect
85. C32×C52C2×D31semidirect
87. D93C3×C5×D5semidirect
96. C5×C31C3×D3×D5semidirect
97. C5×C31C2×C3×C5×D3semidirect
99. C5×D15C3×D31semidirect
108. C3×C31C5×D3×D5semidirect
109. C3×C31C2×C3×C5×D5semidirect
111. C3×D15C5×D31semidirect
118. C3×C52D3×D31semidirect
119. C3×C52C2×C3×D31semidirect
131. C32×C5D5×D31semidirect
132. C32×C5C2×C5×D31semidirect
134. C31C3×C5×D3×D5semidirect
142. D15C3×C5×D31semidirect
151. C52C3×D3×D31semidirect
162. C3×C5C3×D5×D31semidirect
163. C3×C5C5×D3×D31semidirect
164. C3×C5D15⋊D31direct (N × H)
165. C3×C5C2×C3×C5×D31semidirect
175. C32C5×D5×D31semidirect
184. C5C3×C5×D3×D31semidirect
185. C5C3×D15⋊D31direct (N × H)
188. C3C3×C5×D5×D31semidirect
189. C3C5×D15⋊D31direct (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×C52×D932
C3×C5×D15×C312
C5×D15⋊D313
C3×C5×D5×D313
C3×D15⋊D315
C3×C5×D3×D315
C3×C5×D3×D531