Finite Group Databasebeta

← C5×D15⋊D111 #45686450

Subgroups — C5×D15⋊D111 #45686450

Order 33300.

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
1C3×C5×D15×C37C211yesmaximal, characteristic, complemented
2C3×C5×D555C211yesmaximal, characteristic, complemented
3C52×C3⋊D111C211yesmaximal, characteristic, complemented
4C5×D15⋊D37—31nomaximal
5C5×D5×D111—31nomaximal
6C32×C52×C37C2211yescharacteristic, complemented, Hall
7D15⋊D111C511yesmaximal, characteristic, direct product factor
8C5×D3×D111—51nomaximal
9C5×D555D311yescharacteristic, complemented
10C5×D15×C37D311yescharacteristic, complemented
11C52×D111—31no—
12C52×D111—31no—
13C52×D111—61no—
14C3×C5×D185—31no—
15C3×C5×D5×C37—31no—
16C5×D5×D37—91noHall
17C5×C3⋊D111—22no—
18C5×C3⋊D111D511yescharacteristic, complemented
19C5×C3⋊D111C2×C511yescharacteristic, complemented
20C3×D555C2×C511yescharacteristic, complemented
21C3×D15×C37C2×C511yescharacteristic, complemented
22C3×C5×D111—51no—
23C3×C5×D3×C37—51no—
24C3×C52×C37—21no—
25C3×C52×C37C2×D311yescharacteristic, complemented
26C3×C52×C37C2×D311yescharacteristic, complemented
27C2×C5×D111—151no—
28D15⋊D37—31no—
29D5×D111—31no—
30C5×D3×D37—151no—
31C5×D185—31no—
32C5×D5×C37—31no—
33C52×D37—91no—
34C32×C5×C37—22no—
35C32×C5×C37C2×D511yescharacteristic, complemented
36C32×C5×C37C22×C511yescharacteristic, complemented
37D3×D111—51noHall
38C2×C3×C5×C37—151no—
39D555C5×D311yescharacteristic, complemented
40D15×C37C5×D311yescharacteristic, complemented
41C5×D111—31no—
42C5×D111—31no—
43C5×D111—31no—
44C5×D111—31no—
45C5×D111—51no—
46C5×D111—62no—
47C5×D111—62no—
48C5×D111—61no—
49C5×D111—61no—
50C5×D111—64no—
51C5×D3×C37—51no—
52C3×D185—31no—
53C3×D5×C37—31no—
54C3×C5×D37—151no—
55C52×C37D3211yescharacteristic, complemented, Hall
56C5×(C3⋊D3)⋊D5—371nomaximal, Hall
57C2×C5×D37—451no—
58D5×D37—91no—
59C3⋊D111C5×D511yescharacteristic, complemented
60C3×D111—51no—
61C3×D3×C37—51no—
62C3×C5×C37—24no—
63C3×C5×C37—22no—
64C3×C5×C37—22no—
65C3×C5×C37—21no—
66C3×C5×C37—21no—
67C3×C5×C37D3×D511yescharacteristic, complemented
68C3×C5×C37D3×D511yescharacteristic, complemented
69C3×C5×C37C2×C5×D311yescharacteristic, complemented
70C3×C5×C37C2×C5×D311yescharacteristic, complemented
71C52×C3⋊D3—371no—
72C3×C5×D15—371no—
73C3×C5×D15D3711yescharacteristic, complemented
74C2×D111—151no—
75D3×D37—151no—
76C2×C5×C37—151no—
77D185—31no—
78C5×D37—91no—
79C5×D37—91no—
80C5×D37—151no—
81C5×D37—182no—
82D5×C37—31no—
83C32×C37C2×C5×D511yescharacteristic, complemented, Hall
84C5×D3×D5—1111no—
85C5×D3×D5—1111no—
86C32×C52C2×D3711yescharacteristic, complemented, Hall
87C2×C3×C37—151no—
88D111—31no—
89D111—31no—
90D111—51no—
91D111—61no—
92C3×D37—151no—
93D3×C37—51no—
94C5×C37—22no—
95C5×C37C5×D3211yescharacteristic, complemented
96C5×C37(C3⋊D3)⋊D511yescharacteristic, complemented
97(C3⋊D3)⋊D5—371no—
98C5×D32—1851no—
99C5×D15—371no—
100C5×D15D11111yescharacteristic, complemented
101C52×D3—1111no—
102C52×D3—1111no—
103C52×D3—2221no—
104C3×C5×D5—31no—
105C3×C5×D5—1111no—
106C2×D37—451noHall
107C3×C37—21no—
108C3×C37C5×D3×D511yescharacteristic, complemented
109C3×C37C5×D3×D511yescharacteristic, complemented
110C2×C5×D5—3331noHall
111C5×C3⋊D3—371no—
112C5×C3⋊D3—371no—
113C5×C3⋊D3—742no—
114C3×D15—371no—
115C3×D15C5×D3711yescharacteristic, complemented
116C3×C5×D3—51no—
117C3×C5×D3—1851no—
118C3×C52—21no—
119C3×C52D3×D3711yescharacteristic, complemented
120C3×C52C2×D11111yescharacteristic, complemented
121C2×C37—151no—
122D37—91no—
123D37—151no—
124C2×C5×D3—5551no—
125C2×C5×D3—5551no—
126D3×D5—1111no—
127D3×D5—1111no—
128C2×C52—3331no—
129C5×D5—31no—
130C5×D5—1111no—
131C32×C5—22no—
132C32×C5D5×D3711yescharacteristic, complemented
133C32×C5C2×C5×D3711yescharacteristic, complemented
134C37C5×(C3⋊D3)⋊D511yescharacteristic, complemented, Sylow
135D32—1851noHall
136C2×C3×C5—151no—
137C2×C3×C5—5551no—
138D15—371no—
139D15C5×D11111yescharacteristic, complemented
140C3×D5—31no—
141C3×D5—1111no—
142C5×D3—51no—
143C5×D3—1111no—
144C5×D3—1111no—
145C5×D3—1111no—
146C5×D3—1111no—
147C5×D3—1851no—
148C5×D3—2222no—
149C5×D3—2222no—
150C5×D3—2221no—
151C5×D3—2221no—
152C5×D3—2224no—
153C52D3×D11111yescharacteristic, complemented, Sylow
154C22×C5—16651no—
155C2×D5—3331no—
156C3⋊D3—371no—
157C3×D3—51no—
158C3×D3—1851no—
159C3×C5—24no—
160C3×C5—21no—
161C3×C5—21no—
162C3×C5—22no—
163C3×C5—22no—
164C3×C5C5×D3×D3711yescharacteristic, complemented
165C3×C5D5×D11111yescharacteristic, complemented
166C3×C5D15⋊D3711yescharacteristic, complemented
167C3×C5C2×C5×D11111yescharacteristic, complemented
168C2×D3—5551no—
169C2×D3—5551no—
170C2×C5—151no—
171C2×C5—5551no—
172C2×C5—3331no—
173C2×C5—3331no—
174C2×C5—6662no—
175D5—31no—
176D5—1111no—
177C32C5×D5×D3711yescharacteristic, complemented, Sylow
178C2×C3—151no—
179C2×C3—5551no—
180D3—51no—
181D3—1111no—
182D3—1111no—
183D3—1851no—
184D3—2221no—
185C5—22no—
186C5C5×D3×D11111yescharacteristic, complemented
187C5D15⋊D11111yescharacteristic, direct product factor
188C22—16651noSylow
189C3—21no—
190C3C5×D5×D11111yescharacteristic, complemented
191C3C5×D15⋊D3711yescharacteristic, complemented
192C2—151no—
193C2—5551no—
194C2—3331no—
subgroupG/H
center, hypercenterC5D15⋊D111
commutator, cosocle, hypocenterC32×C5×C37C22×C5
FrattiniC1G
Fitting, socleC32×C52×C37C22
LCSG ▷ C32×C5×C37
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C3×C5×D15×C37C2semidirect
2. C3×C5×D555C2semidirect
3. C52×C3⋊D111C2semidirect
6. C32×C52×C37C22semidirect
7. D15⋊D111C5direct (N × H)
9. C5×D555D3semidirect
10. C5×D15×C37D3semidirect
18. C5×C3⋊D111D5semidirect
19. C5×C3⋊D111C2×C5semidirect
20. C3×D555C2×C5semidirect
21. C3×D15×C37C2×C5semidirect
25. C3×C52×C37C2×D3semidirect
26. C3×C52×C37C2×D3semidirect
35. C32×C5×C37C2×D5semidirect
36. C32×C5×C37C22×C5semidirect
39. D555C5×D3semidirect
40. D15×C37C5×D3semidirect
55. C52×C37D32semidirect
59. C3⋊D111C5×D5semidirect
67. C3×C5×C37D3×D5semidirect
68. C3×C5×C37D3×D5semidirect
69. C3×C5×C37C2×C5×D3semidirect
70. C3×C5×C37C2×C5×D3semidirect
73. C3×C5×D15D37semidirect
83. C32×C37C2×C5×D5semidirect
86. C32×C52C2×D37semidirect
95. C5×C37C5×D32semidirect
96. C5×C37(C3⋊D3)⋊D5semidirect
100. C5×D15D111semidirect
108. C3×C37C5×D3×D5semidirect
109. C3×C37C5×D3×D5semidirect
115. C3×D15C5×D37semidirect
119. C3×C52D3×D37semidirect
120. C3×C52C2×D111semidirect
132. C32×C5D5×D37semidirect
133. C32×C5C2×C5×D37semidirect
134. C37C5×(C3⋊D3)⋊D5semidirect
139. D15C5×D111semidirect
153. C52D3×D111semidirect
164. C3×C5C5×D3×D37semidirect
165. C3×C5D5×D111semidirect
166. C3×C5D15⋊D37semidirect
167. C3×C5C2×C5×D111semidirect
177. C32C5×D5×D37semidirect
186. C5C5×D3×D111semidirect
187. C5D15⋊D111direct (N × H)
190. C3C5×D5×D111semidirect
191. C3C5×D15⋊D37semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D15×C372
C3×C5×D5552
C52×C3⋊D1112
C5×D15⋊D373
C5×D5×D1113
D15⋊D1115
C5×D3×D1115
C5×(C3⋊D3)⋊D537