Finite Group Databasebeta

← C3×C5×D3×D155 #42124901

Subgroups — C3×C5×D3×D155 #42124901

Order 27900.

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
1C32×C5×D155C211yesmaximal, characteristic, complemented
2C3×C52×D3×C31C211yesmaximal, characteristic, complemented
3C3×C5×D465C211yesmaximal, characteristic, complemented
4C2×C3×C5×D155—31nomaximal
5C5×D3×D155C311yesmaximal, characteristic, direct product factor
6C32×C52×C31C2211yescharacteristic, complemented, Hall
7C3×D3×D155C511yesmaximal, characteristic, direct product factor
8C3×C5×D3×D31—51nomaximal
9C5×D465C2×C311yescharacteristic, complemented
10C52×D3×C31C2×C311yescharacteristic, complemented
11C3×C5×D155—21no—
12C3×C5×D155—31no—
13C3×C5×D155D311yescharacteristic, direct product factor
14C3×C5×D155C2×C311yescharacteristic, complemented
15C2×C3×C52×C31—31no—
16C2×C5×D155—31noHall
17C3×D465C2×C511yescharacteristic, complemented
18C3×C5×D93—51no—
19C3×C5×D3×C31—22no—
20C3×C5×D3×C31D511yescharacteristic, complemented
21C3×C5×D3×C31C2×C511yescharacteristic, complemented
22C32×D155C2×C511yescharacteristic, complemented
23C32×C5×D31—51no—
24C3×C52×C31—21no—
25C3×C52×C31C2×D311yescharacteristic, complemented
26C3×C52×C31C22×C311yescharacteristic, complemented
27C2×C3×D155—31no—
28C2×C3×C5×D31—151no—
29D3×D155C3×C511yescharacteristic, direct product factor
30C5×D3×D31—51no—
31C2×C52×C31—31no—
32C5×D155—31no—
33C5×D155C3×D311yescharacteristic, direct product factor
34C32×C5×C31—22no—
35C32×C5×C31C2×D511yescharacteristic, complemented
36C32×C5×C31C22×C511yescharacteristic, complemented
37C3×D3×D31—51noHall
38C2×C3×C5×C31—31no—
39C2×C3×C5×C31—31no—
40C2×C3×C5×C31—62no—
41D465C2×C3×C511yescharacteristic, complemented
42C5×D93—51no—
43C5×D3×C31—22no—
44C5×D3×C31C3×D511yescharacteristic, complemented
45C5×D3×C31C2×C3×C511yescharacteristic, complemented
46C3×D155—21no—
47C3×D155—31no—
48C3×D155C5×D311yescharacteristic, direct product factor
49C3×D155C2×C3×C511yescharacteristic, complemented
50C3×C5×D31—51no—
51C3×C5×D31—51no—
52C3×C5×D31—101no—
53C3×C5×D31—151no—
54C3×C5×D3×D5—311nomaximal, Hall
55C52×C31C2×C3×D311yescharacteristic, complemented, Hall
56C2×D155—31no—
57C2×C5×D31—151no—
58C3×D93—51no—
59C3×D3×C31C5×D511yescharacteristic, complemented
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×D15—311no—
71C3×C52×D3D3111yescharacteristic, complemented
72C32×C5×D5—311no—
73C2×C3×D31—151no—
74D3×D31—51no—
75C2×C5×C31—31no—
76C2×C5×C31—31no—
77C2×C5×C31—62no—
78D155—31no—
79D155C3×C5×D311yescharacteristic, direct product factor
80C5×D31—51no—
81C5×D31—151no—
82C2×C3×C5×D5—931no—
83C5×D3×D5—311no—
84C32×C31C2×C5×D511yescharacteristic, complemented, Hall
85C32×C52C2×D3111yescharacteristic, complemented, Hall
86C2×C3×C31—31no—
87D93—51no—
88C3×D31—51no—
89C3×D31—51no—
90C3×D31—101no—
91C3×D31—151no—
92D3×C31C3×C5×D511yescharacteristic, complemented
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—31no—
99C5×D15—311no—
100C52×D3C3×D3111yescharacteristic, complemented
101C3×C5×D5—311no—
102C3×C5×D5—311no—
103C3×C5×D5—621no—
104C3×C5×D5—931no—
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×D15—311no—
112C3×C5×D3—22no—
113C3×C5×D3—1551no—
114C3×C5×D3C5×D3111yescharacteristic, complemented
115C3×C5×D3D15511yescharacteristic, direct product factor
116C32×D5—311no—
117C3×C52—21no—
118C3×C52D3×D3111yescharacteristic, complemented
119C3×C52C2×C3×D3111yescharacteristic, complemented
120C2×C31—31no—
121D31—51no—
122D31—151no—
123C22×C3×C5—4651no—
124C2×C5×D3—1551no—
125C2×C3×D5—931no—
126D3×D5—311no—
127C2×C52—31no—
128C5×D5—311no—
129C5×D5—931no—
130C32×C5—22no—
131C32×C5C2×C5×D3111yescharacteristic, complemented
132C32×C5C2×D15511yescharacteristic, complemented
133C2×C3×D3—1551noHall
134C31C3×C5×D3×D511yescharacteristic, complemented, Sylow
135C2×C3×C5—31no—
136C2×C3×C5—31no—
137C2×C3×C5—62no—
138C2×C3×C5—3101no—
139C2×C3×C5—1551no—
140C2×C3×C5—1551no—
141C2×C3×C5—4651no—
142D15—311no—
143C3×D5—311no—
144C3×D5—311no—
145C3×D5—621no—
146C3×D5—931no—
147C5×D3—22no—
148C5×D3—1551no—
149C5×D3C3×C5×D3111yescharacteristic, complemented
150C5×D3C3×D15511yescharacteristic, direct product factor
151C52C3×D3×D3111yescharacteristic, complemented, Sylow
152C22×C5—4651no—
153C2×D5—931no—
154C2×C32—1551no—
155C3×D3—1551no—
156C3×D3C5×D15511yescharacteristic, direct product factor
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5C5×D3×D3111yescharacteristic, complemented
163C3×C5D3×D15511yescharacteristic, direct product factor
164C3×C5C2×C3×C5×D3111yescharacteristic, complemented
165C3×C5C2×C3×D15511yescharacteristic, complemented
166C22×C3—4651no—
167C2×D3—1551no—
168C2×C5—31no—
169C2×C5—31no—
170C2×C5—62no—
171C2×C5—1551no—
172C2×C5—4651no—
173D5—311no—
174D5—931no—
175C32C2×C5×D15511yescharacteristic, complemented, Sylow
176C2×C3—31no—
177C2×C3—3101no—
178C2×C3—1551no—
179C2×C3—1551no—
180C2×C3—4651no—
181D3—1551no—
182D3C3×C5×D15511yescharacteristic, direct product factor
183C5—22no—
184C5C3×C5×D3×D3111yescharacteristic, complemented
185C5C3×D3×D15511yescharacteristic, direct product factor
186C22—4651noSylow
187C3—21no—
188C3C5×D3×D15511yescharacteristic, direct product factor
189C3C2×C3×C5×D15511yescharacteristic, complemented
190C2—31no—
191C2—1551no—
192C2—4651no—
subgroupG/H
center, hypercenterC3×C5D3×D155
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×D3×C31C2semidirect
3. C3×C5×D465C2semidirect
5. C5×D3×D155C3direct (N × H)
6. C32×C52×C31C22semidirect
7. C3×D3×D155C5direct (N × H)
9. C5×D465C2×C3semidirect
10. C52×D3×C31C2×C3semidirect
13. C3×C5×D155D3direct (N × H)
14. C3×C5×D155C2×C3semidirect
17. C3×D465C2×C5semidirect
20. C3×C5×D3×C31D5semidirect
21. C3×C5×D3×C31C2×C5semidirect
22. C32×D155C2×C5semidirect
25. C3×C52×C31C2×D3semidirect
26. C3×C52×C31C22×C3semidirect
29. D3×D155C3×C5direct (N × H)
33. C5×D155C3×D3direct (N × H)
35. C32×C5×C31C2×D5semidirect
36. C32×C5×C31C22×C5semidirect
41. D465C2×C3×C5semidirect
44. C5×D3×C31C3×D5semidirect
45. C5×D3×C31C2×C3×C5semidirect
48. C3×D155C5×D3direct (N × H)
49. C3×D155C2×C3×C5semidirect
55. C52×C31C2×C3×D3semidirect
59. C3×D3×C31C5×D5semidirect
66. C3×C5×C31D3×D5semidirect
67. C3×C5×C31C2×C3×D5semidirect
68. C3×C5×C31C2×C5×D3semidirect
69. C3×C5×C31C22×C3×C5semidirect
71. C3×C52×D3D31semidirect
79. D155C3×C5×D3direct (N × H)
84. C32×C31C2×C5×D5semidirect
85. C32×C52C2×D31semidirect
92. D3×C31C3×C5×D5semidirect
96. C5×C31C3×D3×D5semidirect
97. C5×C31C2×C3×C5×D3semidirect
100. C52×D3C3×D31semidirect
108. C3×C31C5×D3×D5semidirect
109. C3×C31C2×C3×C5×D5semidirect
114. C3×C5×D3C5×D31semidirect
115. C3×C5×D3D155direct (N × H)
118. C3×C52D3×D31semidirect
119. C3×C52C2×C3×D31semidirect
131. C32×C5C2×C5×D31semidirect
132. C32×C5C2×D155semidirect
134. C31C3×C5×D3×D5semidirect
149. C5×D3C3×C5×D31semidirect
150. C5×D3C3×D155direct (N × H)
151. C52C3×D3×D31semidirect
156. C3×D3C5×D155direct (N × H)
162. C3×C5C5×D3×D31semidirect
163. C3×C5D3×D155direct (N × H)
164. C3×C5C2×C3×C5×D31semidirect
165. C3×C5C2×C3×D155semidirect
175. C32C2×C5×D155semidirect
182. D3C3×C5×D155direct (N × H)
184. C5C3×C5×D3×D31semidirect
185. C5C3×D3×D155direct (N × H)
188. C3C5×D3×D155direct (N × H)
189. C3C2×C3×C5×D155semidirect

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×D3×C312
C3×C5×D4652
C2×C3×C5×D1553
C5×D3×D1553
C3×D3×D1555
C3×C5×D3×D315
C3×C5×D3×D531