Finite Group Databasebeta

← #37528699

Subgroups — #37528699

Order 23100.

192 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 43 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⋊D385C211yesmaximal, characteristic, complemented
2C5×C7×D165C211yesmaximal, characteristic, complemented
3C5×C11×D105C211yesmaximal, characteristic, complemented
4D35×D55—31nomaximal, Hall
5C3×C52×C7×C11C2211yescharacteristic, complemented, Hall
6D21⋊D55—51nomaximal
7D33⋊D35—51nomaximal
8C5⋊D385D311yescharacteristic, complemented
9C5×C11×D35—31no—
10C5×C7×D55—31no—
11D15⋊D55—71nomaximal, Hall
12C11×D105D511yescharacteristic, complemented
13C7×D165D511yescharacteristic, complemented
14C5×C11×D21—51no—
15C5×C7×D33—51no—
16C3×D385—51no—
17C3×D385—51no—
18C3×D385—102no—
19D15⋊D35—111nomaximal, Hall
20C52×C7×C11C2×D311yescharacteristic, complemented, Hall
21C5×D165D711yescharacteristic, complemented
22C5×C11×D15—71no—
23C3×C5⋊D55—71no—
24D7×D55—151no—
25D11×D35—151no—
26C3×C5×C7×C11—22no—
27C3×C5×C7×C11C2×D511yescharacteristic, complemented
28C3×C5×C7×C11C2×D511yescharacteristic, complemented
29D5×D55—211noHall
30C5×D105D1111yescharacteristic, complemented
31C5×C7×D15—111no—
32C3×C5⋊D35—111no—
33D21⋊D11—251noHall
34C3×C52×C11C2×D711yescharacteristic, complemented, Hall
35D385—51no—
36D385—51no—
37D385—102no—
38C11×D35—31no—
39C7×D55—31no—
40C5×C11×D7—151no—
41C5×C7×D11—151no—
42D5×D35—331noHall
43D15⋊D11—351no—
44D3×D55—351no—
45C5⋊D55—71no—
46C5×D55—31no—
47C5×D5×C11—211no—
48C3×C52×C7C2×D1111yescharacteristic, complemented, Hall
49C11×D21—51no—
50C7×D33—51no—
51C3×D77—251no—
52D15⋊D7—551no—
53D3×D35—551no—
54C5×C7×C11—22no—
55C5×C7×C11D3×D511yescharacteristic, complemented
56C5×C7×C11D3×D511yescharacteristic, complemented
57C5⋊D35—111no—
58C5×D35—31no—
59C5×C7×D5—331no—
60D165D3511yescharacteristic, complemented
61C11×D15—71no—
62C5×D33—51no—
63C5×D3×C11—351no—
64C3×D55—351no—
65C3×D55—351no—
66C3×D55—702no—
67D7×D11—751noHall
68D15⋊D5—771noHall
69C52×C11D3×D711yescharacteristic, complemented, Hall
70C3×C7×C11D5211yescharacteristic, complemented, Hall
71C2×D55—1051no—
72D5×D11—1051no—
73D105D5511yescharacteristic, complemented
74C7×D15—111no—
75C5×D21—51no—
76C5×D3×C7—551no—
77C3×D35—551no—
78C3×D35—551no—
79C3×D35—1102no—
80C52×C7D3×D1111yescharacteristic, complemented, Hall
81C3×C5×C11—22no—
82C3×C5×C11D5×D711yescharacteristic, complemented
83C3×C5×C11C2×D3511yescharacteristic, complemented
84D77—251no—
85C7×D11—151no—
86C11×D7—151no—
87C5×D15—71no—
88C5×D15—111no—
89C3×C5⋊D5—771no—
90C2×D35—1651no—
91D5×D7—1651no—
92D3×D11—1751noHall
93C2×C5×C11—1051no—
94D55—31no—
95D55—351no—
96D55—351no—
97D55—702no—
98C5×D11—151no—
99D5×C11—211no—
100C3×C5×C7—22no—
101C3×C5×C7D5×D1111yescharacteristic, complemented
102C3×C5×C7C2×D5511yescharacteristic, complemented
103D52—2311noHall
104D3×D7—2751noHall
105C7×C11D15⋊D511yescharacteristic, complemented, Hall
106C3×C52D7×D1111yescharacteristic, complemented, Hall
107C2×C5×C7—1651no—
108D35—31no—
109D35—551no—
110D35—551no—
111D35—1102no—
112C5×D7—151no—
113C7×D5—331no—
114D33—51no—
115C3×D11—1751no—
116D3×C11—351no—
117D3×D5—3851no—
118D3×D5—3851no—
119C5×C11—22no—
120C5×C11D3×D3511yescharacteristic, complemented
121C5×C11D15⋊D711yescharacteristic, complemented
122C5⋊D5—771no—
123C5×D5—211no—
124C5×D5—331no—
125C2×D11—5251noHall
126D21—51no—
127C3×D7—2751no—
128D3×C7—551no—
129C5×C7—22no—
130C5×C7D3×D5511yescharacteristic, complemented
131C5×C7D15⋊D1111yescharacteristic, complemented
132C3×C11D5×D3511yescharacteristic, complemented, Hall
133D15—71no—
134D15—111no—
135C3×D5—7702no—
136C3×D5—3851no—
137C3×D5—3851no—
138C5×D3—351no—
139C5×D3—551no—
140C2×D7—8251noHall
141C52D21⋊D1111yescharacteristic, complemented, Sylow
142C2×C11—1051no—
143D11—151no—
144D11—1751no—
145C3×C7D5×D5511yescharacteristic, complemented, Hall
146C2×D5—11551no—
147C2×D5—11551no—
148C3×C5—22no—
149C3×C5D11×D3511yescharacteristic, complemented
150C3×C5D7×D5511yescharacteristic, complemented
151C2×C7—1651no—
152D7—151no—
153D7—2751no—
154C2×D3—19251noHall
155C11D15⋊D3511yescharacteristic, complemented, Sylow
156C2×C5—1051no—
157C2×C5—1651no—
158D5—7702no—
159D5—211no—
160D5—331no—
161D5—3851no—
162D5—3851no—
163C7D15⋊D5511yescharacteristic, complemented, Sylow
164C2×C3—19251no—
165D3—351no—
166D3—551no—
167C5—22no—
168C5D33⋊D3511yescharacteristic, complemented
169C5D21⋊D5511yescharacteristic, complemented
170C22—57751noSylow
171C3D35×D5511yescharacteristic, complemented, Sylow
172C2—1051no—
173C2—19251no—
174C2—1651no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C52×C7×C11C22
LCSG ▷ C3×C52×C7×C11
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5⋊D385C2semidirect
2. C5×C7×D165C2semidirect
3. C5×C11×D105C2semidirect
5. C3×C52×C7×C11C22semidirect
8. C5⋊D385D3semidirect
12. C11×D105D5semidirect
13. C7×D165D5semidirect
20. C52×C7×C11C2×D3semidirect
21. C5×D165D7semidirect
27. C3×C5×C7×C11C2×D5semidirect
28. C3×C5×C7×C11C2×D5semidirect
30. C5×D105D11semidirect
34. C3×C52×C11C2×D7semidirect
48. C3×C52×C7C2×D11semidirect
55. C5×C7×C11D3×D5semidirect
56. C5×C7×C11D3×D5semidirect
60. D165D35semidirect
69. C52×C11D3×D7semidirect
70. C3×C7×C11D52semidirect
73. D105D55semidirect
80. C52×C7D3×D11semidirect
82. C3×C5×C11D5×D7semidirect
83. C3×C5×C11C2×D35semidirect
101. C3×C5×C7D5×D11semidirect
102. C3×C5×C7C2×D55semidirect
105. C7×C11D15⋊D5semidirect
106. C3×C52D7×D11semidirect
120. C5×C11D3×D35semidirect
121. C5×C11D15⋊D7semidirect
130. C5×C7D3×D55semidirect
131. C5×C7D15⋊D11semidirect
132. C3×C11D5×D35semidirect
141. C52D21⋊D11semidirect
145. C3×C7D5×D55semidirect
149. C3×C5D11×D35semidirect
150. C3×C5D7×D55semidirect
155. C11D15⋊D35semidirect
163. C7D15⋊D55semidirect
168. C5D33⋊D35semidirect
169. C5D21⋊D55semidirect
171. C3D35×D55semidirect

Maximal subgroups

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

subgroupindex
C3×C5⋊D3852
C5×C7×D1652
C5×C11×D1052
D35×D553
D21⋊D555
D33⋊D355
D15⋊D557
D15⋊D3511