Finite Group Databasebeta

← D3×C11⋊C5×D55 #49137501

Subgroups — D3×C11⋊C5×D55 #49137501

Order 36300.

200 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 48 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
1C11⋊C5×D165C211yesmaximal, characteristic, complemented
2C5×D3×C11×C11⋊C5C211yesmaximal, characteristic, complemented
3C3×C11⋊C5×D55C211yesmaximal, characteristic, complemented
4C2×C11⋊C5×D55—31nomaximal, Hall
5C3×C5×C11×C11⋊C5C2211yescharacteristic, complemented, Hall
6D3×C11×D55C511yesmaximal, characteristic, complemented
7D3×D11×C11⋊C5—51nomaximal
8C2×C5×C11×C11⋊C5—31no—
9C11⋊C5×D55—31no—
10C11⋊C5×D55D311yescharacteristic, direct product factor
11C11×D165C2×C511yescharacteristic, complemented
12C5×D3×C112C2×C511yescharacteristic, complemented
13C3×C11×D55C2×C511yescharacteristic, complemented
14C11⋊C5×D33—51no—
15D3×C11×C11⋊C5—22no—
16D3×C11×C11⋊C5D511yescharacteristic, complemented
17C3×D11×C11⋊C5—51no—
18C5×D3×D55—111nomaximal
19D3×D5×C11⋊C5—111nomaximal
20C5×C11×C11⋊C5C2×D311yescharacteristic, complemented, Hall
21C2×C11×D55—31no—
22C2×D11×C11⋊C5—151no—
23C3×C5×C112C22×C511yescharacteristic, complemented
24C3×C11×C11⋊C5—22no—
25C3×C11×C11⋊C5C2×D511yescharacteristic, complemented
26C5×D165—111no—
27C52×D3×C11—111no—
28C3×C5×D55—111no—
29D15×C11⋊C5—111no—
30C5×D3×C11⋊C5D1111yescharacteristic, complemented
31C3×D5×C11⋊C5—111no—
32D3×C11×D11—51noHall
33C2×C5×C112—31no—
34C11×D55—31no—
35C11×D55C5×D311yescharacteristic, complemented
36C2×C11×C11⋊C5—31no—
37C2×C11×C11⋊C5—62no—
38D11×C11⋊C5—51no—
39D11×C11⋊C5—151no—
40C2×C5×D55—331no—
41C2×D5×C11⋊C5—331no—
42C3×C52×C11—111no—
43C3×C5×C11⋊C5C2×D1111yescharacteristic, complemented
44C11×D33—51no—
45D3×C112C5×D511yescharacteristic, complemented
46C3×C11×D11—51no—
47D3×D55C11⋊C511yescharacteristic, direct product factor
48D3×D5×C11—111no—
49C5×D3×D11—551no—
50C2×D3×C11⋊C5—551no—
51C5×C112C2×C5×D311yescharacteristic, complemented
52C11×C11⋊C5—22no—
53C11×C11⋊C5D3×D511yescharacteristic, complemented
54C2×C52×C11—331no—
55C5×D55—111no—
56C5×D55—331no—
57C2×C5×C11⋊C5—31no—
58D5×C11⋊C5—111no—
59D5×C11⋊C5—331no—
60C2×C11×D11—151noHall
61C3×C112C2×C5×D511yescharacteristic, complemented, Hall
62D165C2×C11⋊C511yescharacteristic, complemented
63C11×D15—111no—
64C5×D33—551no—
65C5×D3×C11—101no—
66C5×D3×C11—111no—
67C5×D3×C11—222no—
68C5×D3×C11C2×C11⋊C511yescharacteristic, complemented
69C5×D3×C11C5×D1111yescharacteristic, complemented
70C3×D55C2×C11⋊C511yescharacteristic, complemented
71C3×D5×C11—111no—
72C3×C5×D11—551no—
73C2×C3×C11⋊C5—551no—
74D3×C11⋊C5—22no—
75D3×C11⋊C5—551no—
76D3×C11⋊C5D5511yescharacteristic, direct product factor
77C5×D3×D5—1211noHall
78C52×C11—111no—
79C5×C11⋊C5D3×D1111yescharacteristic, complemented
80C2×C112—31no—
81C11×D11—51no—
82C11×D11—151no—
83C2×D55—31no—
84C2×D5×C11—331no—
85C2×C5×D11—1651no—
86C22×C11⋊C5—1651no—
87C3×C5×C11—101no—
88C3×C5×C11—111no—
89C3×C5×C11—222no—
90C3×C5×C11C22×C11⋊C511yescharacteristic, complemented
91C3×C5×C11C2×C5×D1111yescharacteristic, complemented
92C3×C11⋊C5—22no—
93C3×C11⋊C5C2×D5511yescharacteristic, complemented
94C5×D15—1211no—
95C52×D3—111no—
96C3×C5×D5—1211no—
97C2×D3×C11—551no—
98D3×D11—51no—
99C112C5×D3×D511yescharacteristic, complemented, Sylow
100C2×C5×C11—31no—
101C2×C5×C11—31no—
102C2×C5×C11—301no—
103C2×C5×C11—331no—
104C2×C5×C11—662no—
105D55—31no—
106D55D3×C11⋊C511yescharacteristic, direct product factor
107C5×D11—551no—
108C5×D11—1651no—
109D5×C11—111no—
110D5×C11—331no—
111C2×C11⋊C5—31no—
112C2×C11⋊C5—62no—
113C2×C11⋊C5—551no—
114C2×C11⋊C5—1651no—
115C2×C5×D5—3631noHall
116C3×C52—111noHall
117C2×C3×C11—551no—
118D33—51no—
119C3×D11—51no—
120D3×C11—101no—
121D3×C11—551no—
122D3×C11D5×C11⋊C511yescharacteristic, complemented
123D3×C11C5×D5511yescharacteristic, complemented
124C2×C5×D3—6051no—
125D3×D5—111no—
126C5×C11—101no—
127C5×C11—111no—
128C5×C11—222no—
129C5×C11C2×D3×C11⋊C511yescharacteristic, complemented
130C5×C11C5×D3×D1111yescharacteristic, complemented
131C11⋊C5—22no—
132C11⋊C5D3×D5511yescharacteristic, direct product factor
133C2×C52—331no—
134C5×D5—3631no—
135C5×D5—1211no—
136C22×C11—1651no—
137C2×D11—151no—
138C3×C11—101no—
139C3×C11C2×D5×C11⋊C511yescharacteristic, complemented
140C3×C11C2×C5×D5511yescharacteristic, complemented
141C2×C3×C5—6051no—
142D15—111no—
143C3×D5—111no—
144C5×D3—111no—
145C5×D3—222no—
146C5×D3—6051no—
147C5×D3D11×C11⋊C511yescharacteristic, complemented
148C52—111noSylow
149C2×C11—31no—
150C2×C11—31no—
151C2×C11—301no—
152C2×C11—551no—
153C2×C11—1651no—
154D11—51no—
155D11—151no—
156C22×C5—18151no—
157C2×D5—331no—
158C3×C5—111no—
159C3×C5—222no—
160C3×C5C2×D11×C11⋊C511yescharacteristic, complemented
161C2×D3—551noHall
162C11—101no—
163C11D3×D5×C11⋊C511yescharacteristic, complemented
164C11C5×D3×D5511yescharacteristic, complemented
165C2×C5—31no—
166C2×C5—18151no—
167C2×C5—331no—
168C2×C5—662no—
169C2×C5—6051no—
170D5—111no—
171D5—331no—
172C2×C3—551no—
173D3—551no—
174D3C11⋊C5×D5511yescharacteristic, direct product factor
175C5—111no—
176C5—222no—
177C5D3×D11×C11⋊C511yescharacteristic, complemented
178C22—1651noSylow
179C3C2×C11⋊C5×D5511yescharacteristic, complemented, Sylow
180C2—31no—
181C2—551no—
182C2—1651no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C112C22×C5
LCSG ▷ C3×C5×C112
UCSC1

Complements

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

NH ≅ G/Ntype
1. C11⋊C5×D165C2semidirect
2. C5×D3×C11×C11⋊C5C2semidirect
3. C3×C11⋊C5×D55C2semidirect
5. C3×C5×C11×C11⋊C5C22semidirect
6. D3×C11×D55C5semidirect
10. C11⋊C5×D55D3direct (N × H)
11. C11×D165C2×C5semidirect
12. C5×D3×C112C2×C5semidirect
13. C3×C11×D55C2×C5semidirect
16. D3×C11×C11⋊C5D5semidirect
20. C5×C11×C11⋊C5C2×D3semidirect
23. C3×C5×C112C22×C5semidirect
25. C3×C11×C11⋊C5C2×D5semidirect
30. C5×D3×C11⋊C5D11semidirect
35. C11×D55C5×D3semidirect
43. C3×C5×C11⋊C5C2×D11semidirect
45. D3×C112C5×D5semidirect
47. D3×D55C11⋊C5direct (N × H)
51. C5×C112C2×C5×D3semidirect
53. C11×C11⋊C5D3×D5semidirect
61. C3×C112C2×C5×D5semidirect
62. D165C2×C11⋊C5semidirect
68. C5×D3×C11C2×C11⋊C5semidirect
69. C5×D3×C11C5×D11semidirect
70. C3×D55C2×C11⋊C5semidirect
76. D3×C11⋊C5D55direct (N × H)
79. C5×C11⋊C5D3×D11semidirect
90. C3×C5×C11C22×C11⋊C5semidirect
91. C3×C5×C11C2×C5×D11semidirect
93. C3×C11⋊C5C2×D55semidirect
99. C112C5×D3×D5semidirect
106. D55D3×C11⋊C5direct (N × H)
122. D3×C11D5×C11⋊C5semidirect
123. D3×C11C5×D55semidirect
129. C5×C11C2×D3×C11⋊C5semidirect
130. C5×C11C5×D3×D11semidirect
132. C11⋊C5D3×D55direct (N × H)
139. C3×C11C2×D5×C11⋊C5semidirect
140. C3×C11C2×C5×D55semidirect
147. C5×D3D11×C11⋊C5semidirect
160. C3×C5C2×D11×C11⋊C5semidirect
163. C11D3×D5×C11⋊C5semidirect
164. C11C5×D3×D55semidirect
174. D3C11⋊C5×D55direct (N × H)
177. C5D3×D11×C11⋊C5semidirect
179. C3C2×C11⋊C5×D55semidirect

Maximal subgroups

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

subgroupindex
C11⋊C5×D1652
C5×D3×C11×C11⋊C52
C3×C11⋊C5×D552
C2×C11⋊C5×D553
D3×C11×D555
D3×D11×C11⋊C55
C5×D3×D5511
D3×D5×C11⋊C511