Finite Group Databasebeta

← #42124938

Subgroups — #42124938

Order 27900.

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

normal subgroups only

This group has 212 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×D465C211yesmaximal, characteristic, complemented
2C3×C3⋊(C5⋊D155)C211yesmaximal, characteristic, complemented
3C5×C31×C3⋊D15C211yesmaximal, characteristic, complemented
4D15⋊D155—31nomaximal
5D15×D155—31nomaximal
6C32×C52×C31C2211yescharacteristic, complemented, Hall
7(C3⋊D3)⋊D155—51nomaximal
8D93⋊D15—51nomaximal
9C3⋊(C5⋊D155)D311yescharacteristic, complemented
10C5×D465D311yescharacteristic, complemented
11C5×D15×C31—31no—
12C5×D15×C31—31no—
13C5×D15×C31—61no—
14C3×C5⋊D155—31no—
15C3×C5×D155—31no—
16D5×D155—91noHall
17C31×C3⋊D15D511yescharacteristic, complemented
18C5×C3⋊D3×C31—51no—
19C3×D465—51no—
20C3×D465—51no—
21C3×D465—102no—
22C3×D465D511yescharacteristic, complemented
23C3×C5×D93—51no—
24C3×C52×C31—21no—
25C3×C52×C31C2×D311yescharacteristic, complemented
26C3×C52×C31C2×D311yescharacteristic, complemented
27D15⋊D31—151no—
28D3×D155—151no—
29D3×D155—151no—
30D15×D31—151no—
31C5⋊D155—31no—
32C5×D155—31no—
33C5×D5×C31—91no—
34C32×C5×C31—22no—
35C32×C5×C31C2×D511yescharacteristic, complemented
36C32×C5×C31C2×D511yescharacteristic, complemented
37(C3⋊D3)⋊D31—251noHall
38D465—51no—
39D465—51no—
40D465—102no—
41D465D1511yescharacteristic, complemented
42D15×C31—31no—
43D15×C31—31no—
44D15×C31—61no—
45C5×D93—51no—
46C5×D3×C31—151no—
47C5×D3×C31—151no—
48C5×D3×C31—301no—
49C3×D155—31no—
50C3×D155—151no—
51C3×D155—151no—
52C3×D155—302no—
53C3×C5×D31—151no—
54D15⋊D15—311nomaximal, Hall
55C52×C31D3211yescharacteristic, complemented, Hall
56C2×D155—451no—
57D5×D31—451no—
58C3⋊D3×C31—51no—
59C3×D93—51no—
60C3×D93—251no—
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×C31D3×D511yescharacteristic, complemented
68C3×C5×C31D3×D511yescharacteristic, complemented
69C3×C5×C31C2×D1511yescharacteristic, complemented
70C5×C3⋊D15D3111yescharacteristic, complemented
71C3×C3⋊(C5⋊D5)—311no—
72C3×C5×D15—311no—
73D3×D31—751no—
74D3×D31—751no—
75C2×C5×C31—451no—
76D155—31no—
77D155—151no—
78D155—151no—
79D155—302no—
80C5×D31—151no—
81D5×C31—91no—
82D15⋊D5—931no—
83D5×D15—931no—
84C32×C31D5211yescharacteristic, complemented, Hall
85C32×C52C2×D3111yescharacteristic, complemented, Hall
86D93—51no—
87D93—251no—
88C3×D31—151no—
89C3×D31—751no—
90D3×C31—151no—
91D3×C31—151no—
92D3×C31—301no—
93(C3⋊D3)⋊D5—1551no—
94D3×D15—1551no—
95C5×C31—22no—
96C5×C31D3×D1511yescharacteristic, complemented
97C5×C31(C3⋊D3)⋊D511yescharacteristic, complemented
98C3⋊(C5⋊D5)—311no—
99C5×D15—31no—
100C5×D15—31no—
101C5×D15—61no—
102C5×D15—311no—
103C3×C5⋊D5—931no—
104C3×C5×D5—931no—
105C2×D31—2251noHall
106D52—2791noHall
107C3×C31—21no—
108C3×C31D5×D1511yescharacteristic, complemented
109C3×C31D15⋊D511yescharacteristic, complemented
110C3⋊D15D15511yescharacteristic, complemented
111C5×C3⋊D3—51no—
112C3×D15—311no—
113C3×D15—3102no—
114C3×D15—1551no—
115C3×D15—1551no—
116C3×C5×D3—1551no—
117C3×C52—21no—
118C3×C52D3×D3111yescharacteristic, complemented
119C3×C52D3×D3111yescharacteristic, complemented
120C2×C31—451no—
121D31—151no—
122D31—751no—
123C2×D15—4651no—
124D3×D5—4651no—
125D3×D5—4651no—
126D3×D5—4651no—
127C5⋊D5—931no—
128C5×D5—91no—
129C5×D5—931no—
130C32×C5—22no—
131C32×C5D5×D3111yescharacteristic, complemented
132C32×C5C2×D15511yescharacteristic, complemented
133D32—7751noHall
134C31D15⋊D1511yescharacteristic, complemented, Sylow
135C2×C3×C5—4651no—
136D15—31no—
137D15—31no—
138D15—61no—
139D15—311no—
140D15—3102no—
141D15—1551no—
142D15—1551no—
143C3×D5—931no—
144C3×D5—9302no—
145C3×D5—4651no—
146C3×D5—4651no—
147C5×D3—151no—
148C5×D3—151no—
149C5×D3—301no—
150C5×D3—1551no—
151C52(C3⋊D3)⋊D3111yescharacteristic, complemented, Sylow
152C2×D5—13951no—
153C2×D5—13951no—
154C3⋊D3—51no—
155C3×D3—7751no—
156C3×D3—1551no—
157C3×C5—21no—
158C3×C5—21no—
159C3×C5—22no—
160C3×C5—22no—
161C3×C5—42no—
162C3×C5D15×D3111yescharacteristic, complemented
163C3×C5D3×D15511yescharacteristic, complemented
164C3×C5D3×D15511yescharacteristic, complemented
165C3×C5D15⋊D3111yescharacteristic, complemented
166C2×D3—23251no—
167C2×D3—23251no—
168C2×C5—451no—
169C2×C5—4651no—
170D5—91no—
171D5—931no—
172D5—9302no—
173D5—4651no—
174D5—4651no—
175C32D5×D15511yescharacteristic, complemented, Sylow
176C2×C3—23251no—
177C2×C3—4651no—
178D3—7751no—
179D3—151no—
180D3—151no—
181D3—301no—
182D3—1551no—
183C5—22no—
184C5D93⋊D1511yescharacteristic, complemented
185C5(C3⋊D3)⋊D15511yescharacteristic, complemented
186C22—69751noSylow
187C3—21no—
188C3D15×D15511yescharacteristic, complemented
189C3D15⋊D15511yescharacteristic, complemented
190C2—23251no—
191C2—451no—
192C2—4651no—
subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C52×C31C22
LCSG ▷ C32×C52×C31
UCSC1

Complements

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

NH ≅ G/Ntype
1. C3×C5×D465C2semidirect
2. C3×C3⋊(C5⋊D155)C2semidirect
3. C5×C31×C3⋊D15C2semidirect
6. C32×C52×C31C22semidirect
9. C3⋊(C5⋊D155)D3semidirect
10. C5×D465D3semidirect
17. C31×C3⋊D15D5semidirect
22. C3×D465D5semidirect
25. C3×C52×C31C2×D3semidirect
26. C3×C52×C31C2×D3semidirect
35. C32×C5×C31C2×D5semidirect
36. C32×C5×C31C2×D5semidirect
41. D465D15semidirect
55. C52×C31D32semidirect
66. C3×C5×C31D3×D5semidirect
67. C3×C5×C31D3×D5semidirect
68. C3×C5×C31D3×D5semidirect
69. C3×C5×C31C2×D15semidirect
70. C5×C3⋊D15D31semidirect
84. C32×C31D52semidirect
85. C32×C52C2×D31semidirect
96. C5×C31D3×D15semidirect
97. C5×C31(C3⋊D3)⋊D5semidirect
108. C3×C31D5×D15semidirect
109. C3×C31D15⋊D5semidirect
110. C3⋊D15D155semidirect
118. C3×C52D3×D31semidirect
119. C3×C52D3×D31semidirect
131. C32×C5D5×D31semidirect
132. C32×C5C2×D155semidirect
134. C31D15⋊D15semidirect
151. C52(C3⋊D3)⋊D31semidirect
162. C3×C5D15×D31semidirect
163. C3×C5D3×D155semidirect
164. C3×C5D3×D155semidirect
165. C3×C5D15⋊D31semidirect
175. C32D5×D155semidirect
184. C5D93⋊D15semidirect
185. C5(C3⋊D3)⋊D155semidirect
188. C3D15×D155semidirect
189. C3D15⋊D155semidirect

Maximal subgroups

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

subgroupindex
C3×C5×D4652
C3×C3⋊(C5⋊D155)2
C5×C31×C3⋊D152
D15⋊D1553
D15×D1553
(C3⋊D3)⋊D1555
D93⋊D155
D15⋊D1531