Finite Group Databasebeta

← C3×C5×D5×D93 #42124900

Subgroups — C3×C5×D5×D93 #42124900

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×D5×C31C211yesmaximal, characteristic, complemented
2C3×C52×D93C211yesmaximal, characteristic, complemented
3C3×C5×D465C211yesmaximal, characteristic, complemented
4C5×D5×D93C311yesmaximal, characteristic, direct product factor
5C3×C5×D5×D31—31nomaximal
6C32×C52×C31C2211yescharacteristic, complemented, Hall
7C2×C3×C5×D93—51nomaximal
8C3×D5×D93C511yesmaximal, characteristic, direct product factor
9C5×D465C2×C311yescharacteristic, complemented
10C52×D93C2×C311yescharacteristic, complemented
11C3×C5×D155—31no—
12C3×C5×D5×C31—21no—
13C3×C5×D5×C31D311yescharacteristic, complemented
14C3×C5×D5×C31C2×C311yescharacteristic, complemented
15C3×C52×D31—31no—
16C5×D5×D31—31noHall
17C3×D465C2×C511yescharacteristic, complemented
18C3×C5×D93—22no—
19C3×C5×D93—51no—
20C3×C5×D93D511yescharacteristic, direct product factor
21C3×C5×D93C2×C511yescharacteristic, complemented
22C32×D5×C31C2×C511yescharacteristic, complemented
23C2×C32×C5×C31—51no—
24C3×C52×C31—21no—
25C3×C52×C31C2×D311yescharacteristic, complemented
26C3×C52×C31C22×C311yescharacteristic, complemented
27C2×C5×D93—51no—
28C2×C3×C5×D31—151no—
29D5×D93C3×C511yescharacteristic, direct product factor
30C3×D5×D31—31no—
31C5×D155—31no—
32C5×D5×C31C3×D311yescharacteristic, complemented
33C52×D31—31no—
34C32×C5×C31—22no—
35C32×C5×C31C2×D511yescharacteristic, complemented
36C32×C5×C31C22×C511yescharacteristic, complemented
37C2×C3×D93—51noHall
38C2×C3×C5×C31—51no—
39C2×C3×C5×C31—51no—
40C2×C3×C5×C31—101no—
41D465C2×C3×C511yescharacteristic, complemented
42C5×D93—22no—
43C5×D93—51no—
44C5×D93C3×D511yescharacteristic, direct product factor
45C5×D93C2×C3×C511yescharacteristic, complemented
46C3×D155—31no—
47C3×D5×C31—21no—
48C3×D5×C31C5×D311yescharacteristic, complemented
49C3×D5×C31C2×C3×C511yescharacteristic, complemented
50C3×C5×D31—31no—
51C3×C5×D31—31no—
52C3×C5×D31—62no—
53C3×C5×D31—151no—
54C3×C5×D3×D5—311nomaximal, Hall
55C52×C31C2×C3×D311yescharacteristic, complemented, Hall
56C2×C5×D31—151no—
57D5×D31—31no—
58C2×C32×C31—51no—
59C3×D93—51no—
60C3×D93C5×D511yescharacteristic, direct product factor
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×D3—311no—
72C32×C5×D5D3111yescharacteristic, complemented
73C2×D93—51no—
74C2×C3×D31—151no—
75C2×C5×C31—51no—
76D155—31no—
77C5×D31—31no—
78C5×D31—31no—
79C5×D31—62no—
80C5×D31—151no—
81D5×C31C3×C5×D311yescharacteristic, complemented
82C2×C3×C5×D5—931no—
83C5×D3×D5—311no—
84C32×C31C2×C5×D511yescharacteristic, complemented, Hall
85C32×C52C2×D3111yescharacteristic, complemented, Hall
86C2×C3×C31—51no—
87C2×C3×C31—51no—
88C2×C3×C31—101no—
89D93—51no—
90D93C3×C5×D511yescharacteristic, direct product factor
91C3×D31—31no—
92C3×D31—151no—
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×D15—311no—
100C52×D3—311no—
101C3×C5×D5—21no—
102C3×C5×D5—931no—
103C3×C5×D5C3×D3111yescharacteristic, complemented
104C3×C5×D5D9311yescharacteristic, direct product factor
105C2×D31—151noHall
106C2×C5×D5—931noHall
107C3×C31—21no—
108C3×C31C5×D3×D511yescharacteristic, complemented
109C3×C31C2×C3×C5×D511yescharacteristic, complemented
110C2×C32×C5—51no—
111C3×D15—311no—
112C3×C5×D3—311no—
113C3×C5×D3—311no—
114C3×C5×D3—622no—
115C3×C5×D3—1551no—
116C32×D5C5×D3111yescharacteristic, complemented
117C3×C52—21no—
118C3×C52C2×C3×D3111yescharacteristic, complemented
119C3×C52C2×D9311yescharacteristic, complemented
120C2×C31—51no—
121D31—31no—
122D31—151no—
123C22×C3×C5—4651no—
124C2×C5×D3—1551no—
125C2×C3×D5—931no—
126D3×D5—311no—
127C2×C52—931no—
128C5×D5—931no—
129C5×D5C3×D9311yescharacteristic, direct product factor
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—51no—
136C2×C3×C5—51no—
137C2×C3×C5—101no—
138C2×C3×C5—931no—
139C2×C3×C5—931no—
140C2×C3×C5—1862no—
141C2×C3×C5—4651no—
142D15—311no—
143C3×D5—21no—
144C3×D5—931no—
145C3×D5C3×C5×D3111yescharacteristic, complemented
146C3×D5C5×D9311yescharacteristic, direct product factor
147C5×D3—311no—
148C5×D3—311no—
149C5×D3—622no—
150C5×D3—1551no—
151C52C2×C3×D9311yescharacteristic, complemented, Sylow
152C22×C5—4651no—
153C2×D5—931no—
154C2×C32—51no—
155C3×D3—311no—
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, direct product factor
164C3×C5C2×C3×C5×D3111yescharacteristic, complemented
165C3×C5C2×C5×D9311yescharacteristic, complemented
166C22×C3—4651no—
167C2×D3—1551no—
168C2×C5—51no—
169C2×C5—931no—
170C2×C5—931no—
171C2×C5—1862no—
172C2×C5—4651no—
173D5—931no—
174D5C3×C5×D9311yescharacteristic, direct product factor
175C32C5×D5×D3111yescharacteristic, complemented, Sylow
176C2×C3—51no—
177C2×C3—51no—
178C2×C3—101no—
179C2×C3—931no—
180C2×C3—4651no—
181D3—311no—
182D3—1551no—
183C5—22no—
184C5C3×D5×D9311yescharacteristic, direct product factor
185C5C2×C3×C5×D9311yescharacteristic, complemented
186C22—4651noSylow
187C3—21no—
188C3C3×C5×D5×D3111yescharacteristic, complemented
189C3C5×D5×D9311yescharacteristic, direct product factor
190C2—51no—
191C2—931no—
192C2—4651no—
subgroupG/H
center, hypercenterC3×C5D5×D93
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×D5×C31C2semidirect
2. C3×C52×D93C2semidirect
3. C3×C5×D465C2semidirect
4. C5×D5×D93C3direct (N × H)
6. C32×C52×C31C22semidirect
8. C3×D5×D93C5direct (N × H)
9. C5×D465C2×C3semidirect
10. C52×D93C2×C3semidirect
13. C3×C5×D5×C31D3semidirect
14. C3×C5×D5×C31C2×C3semidirect
17. C3×D465C2×C5semidirect
20. C3×C5×D93D5direct (N × H)
21. C3×C5×D93C2×C5semidirect
22. C32×D5×C31C2×C5semidirect
25. C3×C52×C31C2×D3semidirect
26. C3×C52×C31C22×C3semidirect
29. D5×D93C3×C5direct (N × H)
32. C5×D5×C31C3×D3semidirect
35. C32×C5×C31C2×D5semidirect
36. C32×C5×C31C22×C5semidirect
41. D465C2×C3×C5semidirect
44. C5×D93C3×D5direct (N × H)
45. C5×D93C2×C3×C5semidirect
48. C3×D5×C31C5×D3semidirect
49. C3×D5×C31C2×C3×C5semidirect
55. C52×C31C2×C3×D3semidirect
60. C3×D93C5×D5direct (N × H)
66. C3×C5×C31D3×D5semidirect
67. C3×C5×C31C2×C3×D5semidirect
68. C3×C5×C31C2×C5×D3semidirect
69. C3×C5×C31C22×C3×C5semidirect
72. C32×C5×D5D31semidirect
81. D5×C31C3×C5×D3semidirect
84. C32×C31C2×C5×D5semidirect
85. C32×C52C2×D31semidirect
90. D93C3×C5×D5direct (N × H)
96. C5×C31C3×D3×D5semidirect
97. C5×C31C2×C3×C5×D3semidirect
103. C3×C5×D5C3×D31semidirect
104. C3×C5×D5D93direct (N × H)
108. C3×C31C5×D3×D5semidirect
109. C3×C31C2×C3×C5×D5semidirect
116. C32×D5C5×D31semidirect
118. C3×C52C2×C3×D31semidirect
119. C3×C52C2×D93semidirect
129. C5×D5C3×D93direct (N × H)
131. C32×C5D5×D31semidirect
132. C32×C5C2×C5×D31semidirect
134. C31C3×C5×D3×D5semidirect
145. C3×D5C3×C5×D31semidirect
146. C3×D5C5×D93direct (N × H)
151. C52C2×C3×D93semidirect
162. C3×C5C3×D5×D31semidirect
163. C3×C5D5×D93direct (N × H)
164. C3×C5C2×C3×C5×D31semidirect
165. C3×C5C2×C5×D93semidirect
174. D5C3×C5×D93direct (N × H)
175. C32C5×D5×D31semidirect
184. C5C3×D5×D93direct (N × H)
185. C5C2×C3×C5×D93semidirect
188. C3C3×C5×D5×D31semidirect
189. C3C5×D5×D93direct (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×C52×D932
C3×C5×D4652
C5×D5×D933
C3×C5×D5×D313
C2×C3×C5×D935
C3×D5×D935
C3×C5×D3×D531