Finite Group Databasebeta

← #72230592

Subgroups — #72230592

Order 3600.

560 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C2×C3×D15⋊D5C212yesmaximal, complemented
2#14268303C212yesmaximal, complemented
3C5×#67157C212yesmaximal, complemented
4C3⋊Dic3×C5⋊D5C211yesmaximal, characteristic, complemented
5#11925420—32nomaximal
6C2×C3×C5×D15C2214yescomplemented
7C2×C32×C5⋊D5C2211yescharacteristic
8C3×D15⋊D5—24no—
9C3⋊(C3⋊#1039)C2211yescharacteristic, complemented
10C52×C3⋊Dic3C2211yescharacteristic, complemented
11D5×#625—52nomaximal
12C2×D15⋊D5D312yescomplemented
13C2×C3×D52—32no—
14#10597121—34no—
15Dic3×C5⋊D5—32no—
16Dic3×C5⋊D5—61no—
17C5×#1202—34no—
18C2×C32×C52C2311yescharacteristic
19C3×C5×D15—24no—
20C32×C5⋊D5D412yescomplemented
21#87877—91noHall
22C2×C3×D3×D5—54no—
23#67157D512yescomplemented
24#67150—54no—
25C5×#625—52no—
26D5×C3⋊Dic3—52no—
27D5×C3⋊Dic3—102no—
28C2×C5×D15C2×D314yescomplemented
29C2×C3×C5⋊D5—21no—
30C2×C3×C5⋊D5C2×D312yes—
31C2×C3×C5×D5—34no—
32D15⋊D5—24no—
33C3×D52—64no—
34C3⋊#1039—32no—
35C3⋊#1039—61no—
36C52×Dic3—32no—
37C52×Dic3—61no—
38D5×#67—154no—
39C32×C52C2×D411yescharacteristic, complemented, Hall
40C2×D52—32no—
41C4×C5⋊D5—91no—
42C5×D20—92no—
43#6037—92no—
44C2×C3×D15C2×D514yescomplemented
45C2×C3×C5×D3—54no—
46C2×C32×D5—52no—
47C2×C32×D5—102no—
48C3×D3×D5—108no—
49C3⋊Dic15—52no—
50C3⋊Dic15—102no—
51C5×C3⋊Dic3—22no—
52C5×C3⋊Dic3C2×D512yescomplemented
53C2×C3×C52—21no—
54C2×C3×C52C22×D312yes—
55C5×D15—24no—
56C3×C5⋊D5—22no—
57C3×C5⋊D5#6714yescomplemented
58C3×C5×D5—64no—
59C2×#625—251noHall
60C22×C3×D5—154no—
61C2×D3×D5—54no—
62#1220—154no—
63C5×#67—154no—
64#1202—34no—
65#1201—154no—
66D5×Dic3—154no—
67D5×Dic3—304no—
68D5×Dic3—302no—
69D5×Dic3—304no—
70C2×C5⋊D5D3211yescharacteristic
71C2×C5×D5—34no—
72D52—64no—
73C4×C52—91no—
74#1039—91no—
75C2×C32×C5—22no—
76C2×C32×C5C22×D512yes—
77C3×D15—24no—
78C3×C5×D3—104no—
79C32×D5—54no—
80C32×D5—104no—
81D4×D5—452no—
82C3×C52—21no—
83C3×C52C2×#6712yescomplemented
84C22×C3×D3—252no—
85C2×C3⋊Dic3—251no—
86#625—52no—
87#625—252no—
88C22×C3×C5—154no—
89C2×D15D3×D514yescomplemented
90C2×C5×D3—54no—
91C2×C3×D5—34no—
92C2×C3×D5—54no—
93C2×C3×D5—104no—
94C2×C3×D5—102no—
95C2×C3×D5—104no—
96C2×C3×D5—308no—
97D3×D5—108no—
98Dic15—154no—
99Dic15—304no—
100Dic15—302no—
101Dic15—304no—
102C5×Dic3—34no—
103C5×Dic3—64no—
104C5×Dic3—62no—
105C5×Dic3—64no—
106C2×C52C2×D3211yescharacteristic
107C5⋊D5#62512yescomplemented
108C5×D5—64no—
109C2×#67—752no—
110C32×C5—22no—
111C32×C5D4×D512yescomplemented
112C22×D5—154no—
113C5×D4—452no—
114C22⋊D5—454no—
115D20—92no—
116C4×D5—452no—
117C4×D5—902no—
118C22×C32—251no—
119C2×C3×D3—54no—
120C2×C3×D3—504no—
121C3⋊Dic3—251no—
122C3⋊Dic3D5211yescharacteristic, complemented
123C2×C3×C5—24no—
124C2×C3×C5—22no—
125C2×C3×C5—24no—
126C2×C3×C5—304no—
127C2×C3×C5C2×D3×D514yes—
128D15—24no—
129C3×D5—58no—
130C3×D5—64no—
131C3×D5—108no—
132C3×D5—104no—
133C3×D5—108no—
134C5×D3—104no—
135C52C2×#62511yescharacteristic, complemented, Sylow
136C23×C3—752no—
137C22×D3—252no—
138#67—154no—
139#67—754no—
140C2×Dic3—752no—
141C2×Dic3—1501no—
142C22×C5—154no—
143C2×D5—34no—
144C2×D5—52no—
145C2×D5—102no—
146C2×D5—308no—
147C4×C5—92no—
148C4×C5—182no—
149Dic5—452no—
150Dic5—902no—
151C2×C32—252no—
152C2×C32C2×D5211yescharacteristic
153C3×D3—104no—
154C2×D4—2251noSylow
155C3×C5—24no—
156C3×C5—22no—
157C3×C5—24no—
158C3×C5D5×#6714yescomplemented
159C22×C3—154no—
160C22×C3—252no—
161C22×C3—501no—
162C22×C3—1504no—
163C2×D3—54no—
164C2×D3—504no—
165Dic3—32no—
166Dic3—61no—
167Dic3—752no—
168Dic3—1501no—
169C2×C5—22no—
170C2×C5—304no—
171C2×C5D32×D512yes—
172D5—54no—
173D5—64no—
174D5—104no—
175C32#8787711yescharacteristic, complemented, Sylow
176C23—752no—
177D4—452no—
178D4—2252no—
179C2×C4—2251no—
180C2×C3—21no—
181C2×C3—254no—
182C2×C3—304no—
183C2×C3—502no—
184C2×C3D3×D5212yes—
185D3—104no—
186C5—22no—
187C5D5×#62512yescomplemented
188C22—154no—
189C22—251no—
190C22—1504no—
191C4—91no—
192C4—2251no—
193C3—21no—
194C3#1192542012yescomplemented
195C2—252no—
196C2—304no—
197C2#1426848711yescharacteristic
subgroupG/H
center, Frattini, hypercenterC2#14268487
commutator, Fitting, socle, cosocleC2×C32×C52C23
hypocenterC32×C52C2×D4
LCSG ▷ C2×C32×C52 ▷ C32×C52
UCSC1 ◁ C2

Complements

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

NH ≅ G/Ntype
1. C2×C3×D15⋊D5C2semidirect
2. #14268303C2semidirect
3. C5×#67157C2semidirect
4. C3⋊Dic3×C5⋊D5C2semidirect
6. C2×C3×C5×D15C22semidirect
9. C3⋊(C3⋊#1039)C22semidirect
10. C52×C3⋊Dic3C22semidirect
12. C2×D15⋊D5D3semidirect
20. C32×C5⋊D5D4semidirect
23. #67157D5semidirect
28. C2×C5×D15C2×D3semidirect
39. C32×C52C2×D4semidirect
44. C2×C3×D15C2×D5semidirect
52. C5×C3⋊Dic3C2×D5semidirect
57. C3×C5⋊D5#67semidirect
83. C3×C52C2×#67semidirect
89. C2×D15D3×D5semidirect
107. C5⋊D5#625semidirect
111. C32×C5D4×D5semidirect
122. C3⋊Dic3D52semidirect
135. C52C2×#625semidirect
158. C3×C5D5×#67semidirect
175. C32#87877semidirect
187. C5D5×#625semidirect
194. C3#11925420semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D15⋊D52
#142683032
C5×#671572
C3⋊Dic3×C5⋊D52
#119254203
D5×#6255