Finite Group Databasebeta

← C3×C5×D3×D205 #49147111

Subgroups — C3×C5×D3×D205 #49147111

Order 36900.

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×D205C211yesmaximal, characteristic, complemented
2C3×C52×D3×C41C211yesmaximal, characteristic, complemented
3C3×C5×D615C211yesmaximal, characteristic, complemented
4C2×C3×C5×D205—31nomaximal
5C5×D3×D205C311yesmaximal, characteristic, direct product factor
6C32×C52×C41C2211yescharacteristic, complemented, Hall
7C3×D3×D205C511yesmaximal, characteristic, direct product factor
8C3×C5×D3×D41—51nomaximal
9C5×D615C2×C311yescharacteristic, complemented
10C52×D3×C41C2×C311yescharacteristic, complemented
11C3×C5×D205—21no—
12C3×C5×D205—31no—
13C3×C5×D205D311yescharacteristic, direct product factor
14C3×C5×D205C2×C311yescharacteristic, complemented
15C2×C3×C52×C41—31no—
16C2×C5×D205—31noHall
17C3×D615C2×C511yescharacteristic, complemented
18C3×C5×D123—51no—
19C3×C5×D3×C41—22no—
20C3×C5×D3×C41D511yescharacteristic, complemented
21C3×C5×D3×C41C2×C511yescharacteristic, complemented
22C32×D205C2×C511yescharacteristic, complemented
23C32×C5×D41—51no—
24C3×C52×C41—21no—
25C3×C52×C41C2×D311yescharacteristic, complemented
26C3×C52×C41C22×C311yescharacteristic, complemented
27C2×C3×C5×D41—151no—
28C2×C3×D205—31no—
29D3×D205C3×C511yescharacteristic, direct product factor
30C5×D3×D41—51no—
31C5×D205—31no—
32C5×D205C3×D311yescharacteristic, direct product factor
33C2×C52×C41—31no—
34C32×C5×C41—22no—
35C32×C5×C41C2×D511yescharacteristic, complemented
36C32×C5×C41C22×C511yescharacteristic, complemented
37C3×D3×D41—51noHall
38C2×C3×C5×C41—31no—
39C2×C3×C5×C41—31no—
40C2×C3×C5×C41—62no—
41D615C2×C3×C511yescharacteristic, complemented
42C5×D123—51no—
43C5×D3×C41—22no—
44C5×D3×C41C3×D511yescharacteristic, complemented
45C5×D3×C41C2×C3×C511yescharacteristic, complemented
46C3×D205—21no—
47C3×D205—31no—
48C3×D205C5×D311yescharacteristic, direct product factor
49C3×D205C2×C3×C511yescharacteristic, complemented
50C3×C5×D41—51no—
51C3×C5×D41—51no—
52C3×C5×D41—101no—
53C3×C5×D41—151no—
54C52×C41C2×C3×D311yescharacteristic, complemented, Hall
55C3×C5×D3×D5—411nomaximal, Hall
56C2×D205—31no—
57C2×C5×D41—151no—
58C3×D123—51no—
59C3×D3×C41C5×D511yescharacteristic, complemented
60C32×D41—51no—
61C3×C5×C41—22no—
62C3×C5×C41—22no—
63C3×C5×C41—21no—
64C3×C5×C41—21no—
65C3×C5×C41—42no—
66C3×C5×C41D3×D511yescharacteristic, complemented
67C3×C5×C41C2×C3×D511yescharacteristic, complemented
68C3×C5×C41C2×C5×D311yescharacteristic, complemented
69C3×C5×C41C22×C3×C511yescharacteristic, complemented
70C2×C3×D41—151no—
71D3×D41—51no—
72C3×C5×D15—411no—
73C3×C52×D3D4111yescharacteristic, complemented
74C32×C5×D5—411no—
75C2×C5×C41—31no—
76C2×C5×C41—31no—
77C2×C5×C41—62no—
78D205—31no—
79D205C3×C5×D311yescharacteristic, direct product factor
80C5×D41—51no—
81C5×D41—151no—
82C32×C41C2×C5×D511yescharacteristic, complemented, Hall
83C2×C3×C5×D5—1231no—
84C5×D3×D5—411no—
85C2×C3×C41—31no—
86D123—51no—
87C3×D41—51no—
88C3×D41—51no—
89C3×D41—101no—
90C3×D41—151no—
91D3×C41C3×C5×D511yescharacteristic, complemented
92C32×C52C2×D4111yescharacteristic, complemented, Hall
93C5×C41—22no—
94C5×C41C3×D3×D511yescharacteristic, complemented
95C5×C41C2×C3×C5×D311yescharacteristic, complemented
96C2×C3×C5×D3—2051no—
97C3×D3×D5—411no—
98C2×D41—151noHall
99C2×C3×C52—31no—
100C5×D15—411no—
101C52×D3C3×D4111yescharacteristic, complemented
102C3×C5×D5—411no—
103C3×C5×D5—411no—
104C3×C5×D5—821no—
105C3×C5×D5—1231no—
106C3×C41—21no—
107C3×C41C5×D3×D511yescharacteristic, complemented
108C3×C41C2×C3×C5×D511yescharacteristic, complemented
109C2×C5×D5—1231noHall
110C2×C32×C5—2051no—
111C3×D15—411no—
112C3×C5×D3—22no—
113C3×C5×D3—2051no—
114C3×C5×D3C5×D4111yescharacteristic, complemented
115C3×C5×D3D20511yescharacteristic, direct product factor
116C32×D5—411no—
117C2×C41—31no—
118D41—51no—
119D41—151no—
120C3×C52—21no—
121C3×C52D3×D4111yescharacteristic, complemented
122C3×C52C2×C3×D4111yescharacteristic, complemented
123C22×C3×C5—6151no—
124C2×C5×D3—2051no—
125C2×C3×D5—1231no—
126D3×D5—411no—
127C2×C52—31no—
128C5×D5—411no—
129C5×D5—1231no—
130C32×C5—22no—
131C32×C5C2×C5×D4111yescharacteristic, complemented
132C32×C5C2×D20511yescharacteristic, complemented
133C41C3×C5×D3×D511yescharacteristic, complemented, Sylow
134C2×C3×D3—2051noHall
135C2×C3×C5—31no—
136C2×C3×C5—31no—
137C2×C3×C5—62no—
138C2×C3×C5—6151no—
139C2×C3×C5—4101no—
140C2×C3×C5—2051no—
141C2×C3×C5—2051no—
142D15—411no—
143C3×D5—411no—
144C3×D5—411no—
145C3×D5—821no—
146C3×D5—1231no—
147C5×D3—22no—
148C5×D3—2051no—
149C5×D3C3×C5×D4111yescharacteristic, complemented
150C5×D3C3×D20511yescharacteristic, direct product factor
151C52C3×D3×D4111yescharacteristic, complemented, Sylow
152C22×C5—6151no—
153C2×D5—1231no—
154C2×C32—2051no—
155C3×D3—2051no—
156C3×D3C5×D20511yescharacteristic, direct product factor
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5C5×D3×D4111yescharacteristic, complemented
163C3×C5D3×D20511yescharacteristic, direct product factor
164C3×C5C2×C3×D20511yescharacteristic, complemented
165C3×C5C2×C3×C5×D4111yescharacteristic, complemented
166C22×C3—6151no—
167C2×D3—2051no—
168C2×C5—31no—
169C2×C5—31no—
170C2×C5—62no—
171C2×C5—6151no—
172C2×C5—2051no—
173D5—411no—
174D5—1231no—
175C32C2×C5×D20511yescharacteristic, complemented, Sylow
176C2×C3—31no—
177C2×C3—6151no—
178C2×C3—4101no—
179C2×C3—2051no—
180C2×C3—2051no—
181D3—2051no—
182D3C3×C5×D20511yescharacteristic, direct product factor
183C5—22no—
184C5C3×C5×D3×D4111yescharacteristic, complemented
185C5C3×D3×D20511yescharacteristic, direct product factor
186C22—6151noSylow
187C3—21no—
188C3C5×D3×D20511yescharacteristic, direct product factor
189C3C2×C3×C5×D20511yescharacteristic, complemented
190C2—31no—
191C2—6151no—
192C2—2051no—
subgroupG/H
center, hypercenterC3×C5D3×D205
commutator, cosocle, hypocenterC3×C5×C41C22×C3×C5
FrattiniC1G
Fitting, socleC32×C52×C41C22
LCSG ▷ C3×C5×C41
UCSC1 ◁ C3×C5

Complements

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

NH ≅ G/Ntype
1. C32×C5×D205C2semidirect
2. C3×C52×D3×C41C2semidirect
3. C3×C5×D615C2semidirect
5. C5×D3×D205C3direct (N × H)
6. C32×C52×C41C22semidirect
7. C3×D3×D205C5direct (N × H)
9. C5×D615C2×C3semidirect
10. C52×D3×C41C2×C3semidirect
13. C3×C5×D205D3direct (N × H)
14. C3×C5×D205C2×C3semidirect
17. C3×D615C2×C5semidirect
20. C3×C5×D3×C41D5semidirect
21. C3×C5×D3×C41C2×C5semidirect
22. C32×D205C2×C5semidirect
25. C3×C52×C41C2×D3semidirect
26. C3×C52×C41C22×C3semidirect
29. D3×D205C3×C5direct (N × H)
32. C5×D205C3×D3direct (N × H)
35. C32×C5×C41C2×D5semidirect
36. C32×C5×C41C22×C5semidirect
41. D615C2×C3×C5semidirect
44. C5×D3×C41C3×D5semidirect
45. C5×D3×C41C2×C3×C5semidirect
48. C3×D205C5×D3direct (N × H)
49. C3×D205C2×C3×C5semidirect
54. C52×C41C2×C3×D3semidirect
59. C3×D3×C41C5×D5semidirect
66. C3×C5×C41D3×D5semidirect
67. C3×C5×C41C2×C3×D5semidirect
68. C3×C5×C41C2×C5×D3semidirect
69. C3×C5×C41C22×C3×C5semidirect
73. C3×C52×D3D41semidirect
79. D205C3×C5×D3direct (N × H)
82. C32×C41C2×C5×D5semidirect
91. D3×C41C3×C5×D5semidirect
92. C32×C52C2×D41semidirect
94. C5×C41C3×D3×D5semidirect
95. C5×C41C2×C3×C5×D3semidirect
101. C52×D3C3×D41semidirect
107. C3×C41C5×D3×D5semidirect
108. C3×C41C2×C3×C5×D5semidirect
114. C3×C5×D3C5×D41semidirect
115. C3×C5×D3D205direct (N × H)
121. C3×C52D3×D41semidirect
122. C3×C52C2×C3×D41semidirect
131. C32×C5C2×C5×D41semidirect
132. C32×C5C2×D205semidirect
133. C41C3×C5×D3×D5semidirect
149. C5×D3C3×C5×D41semidirect
150. C5×D3C3×D205direct (N × H)
151. C52C3×D3×D41semidirect
156. C3×D3C5×D205direct (N × H)
162. C3×C5C5×D3×D41semidirect
163. C3×C5D3×D205direct (N × H)
164. C3×C5C2×C3×D205semidirect
165. C3×C5C2×C3×C5×D41semidirect
175. C32C2×C5×D205semidirect
182. D3C3×C5×D205direct (N × H)
184. C5C3×C5×D3×D41semidirect
185. C5C3×D3×D205direct (N × H)
188. C3C5×D3×D205direct (N × H)
189. C3C2×C3×C5×D205semidirect

Maximal subgroups

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

subgroupindex
C32×C5×D2052
C3×C52×D3×C412
C3×C5×D6152
C2×C3×C5×D2053
C5×D3×D2053
C3×D3×D2055
C3×C5×D3×D415
C3×C5×D3×D541