Finite Group Databasebeta

← C5⋊#85547 #14513949

Subgroups — C5⋊#85547 #14513949

Order 1920.

320 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 19 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
1C5×C22⋊(C42⋊C3)C211yesmaximal, characteristic, complemented
2#10602325—31nomaximal, Hall
3C5⋊#1020—41nomaximal
4C5⋊#857—42nomaximal
5#85547—51nomaximal, Hall
6C22×C42×C5D311yescharacteristic, complemented
7#66125—31no—
8#65496—31no—
9C2×#3937—32no—
10#64743—32no—
11C5×C22⋊A4—41no—
12C5×C42⋊C3—42no—
13C5×C42⋊C3—81no—
14C22⋊(C42⋊C3)D511yescharacteristic, complemented
15C23×C4×C5—31no—
16C2×#709—31no—
17C2×C42×C5—32no—
18C2×C42×C5—61no—
19#4099—61no—
20#4076—32no—
21#4075—61no—
22C4×C22⋊D5—62no—
23#4072—31no—
24#4070—32no—
25C2×#681—32no—
26C22⋊#168—62no—
27#3937—62no—
28#3937—62no—
29#1896—151noSylow
30C5⋊S4—161no—
31C5⋊S4—162no—
32#1020—201no—
33#857—202no—
34C24×C5S411yescharacteristic
35C22×C4×C5—31no—
36C22×C4×C5—31no—
37C22×C4×C5—32no—
38C22×C4×C5—32no—
39C22×C4×C5—62no—
40C22×C4×C5—62no—
41C2×C22⋊D5—61no—
42C2×C22⋊D5—62no—
43#709—62no—
44#709—62no—
45C2×D20—31no—
46C2×C4×D5—61no—
47C2×Dic10—31no—
48C42×C5—21no—
49C42×C5—32no—
50C42×C5—61no—
51C42×C5S412yescomplemented
52C22⋊Dic5—62no—
53C22⋊Dic5—61no—
54#685—62no—
55C4⋊Dic5—32no—
56#683—62no—
57C4×Dic5—61no—
58#681—62no—
59#681—62no—
60C2×#168—62no—
61#525—151no—
62C22×C42D1511yescharacteristic, complemented
63C2×#104—152no—
64#407—151no—
65#339—152no—
66C5×A4—162no—
67C5×A4—161no—
68C5×A4—321no—
69C22⋊A4—41no—
70C42⋊C3—42no—
71C42⋊C3—81no—
72C23×C5—32no—
73C23×C5—31no—
74C23×C5—61no—
75C22×D5—61no—
76C2×C4×C5—31no—
77C2×C4×C5—32no—
78C2×C4×C5—31no—
79C2×C4×C5—32no—
80C2×C4×C5—32no—
81C2×C4×C5—64no—
82C2×C4×C5—64no—
83C2×C4×C5—61no—
84C2×C4×C5—61no—
85C22⋊D5—121no—
86C22⋊D5—122no—
87C22⋊D5—122no—
88C22⋊D5—121no—
89C2×Dic5—62no—
90C2×Dic5—61no—
91D20—62no—
92C4×D5—122no—
93Dic10—62no—
94#168—122no—
95C2×#41—151no—
96C23×C4—31no—
97C2×M16—152no—
98#123—301no—
99C22⋊Q8—152no—
100#121—152no—
101#120—301no—
102C4×D4—302no—
103#117—151no—
104C2×C42—32no—
105C2×C42—61no—
106#104—302no—
107#104—302no—
108C22⋊C8—302no—
109D15—641no—
110S4—801no—
111S4—802no—
112C22×C5—21no—
113C22×C5—31no—
114C22×C5—31no—
115C22×C5—32no—
116C22×C5—62no—
117C22×C5—61no—
118C22×C5#85712yescomplemented
119C22×C5#102011yescharacteristic
120C2×D5—121no—
121C2×D5—122no—
122C4×C5—32no—
123C4×C5—32no—
124C4×C5—62no—
125Dic5—121no—
126Dic5—122no—
127C24C5⋊S411yescharacteristic
128#41—302no—
129#41—302no—
130C2×Q8—151no—
131C2×D4—151no—
132C2×D4—302no—
133C2×D4—301no—
134C22×C4—31no—
135C22×C4—32no—
136C22×C4—31no—
137C22×C4—32no—
138C22×C4—62no—
139C22×C4—62no—
140C22×C4—301no—
141M16—302no—
142M16—302no—
143C2×C8—302no—
144C4⋊C4—152no—
145C4⋊C4—302no—
146C22⋊C4—302no—
147C22⋊C4—301no—
148C22⋊C4—302no—
149C42—21no—
150C42—32no—
151C42—61no—
152C42—301no—
153C42C5⋊S412yescomplemented
154C3×C5—641noHall
155A4—162no—
156A4—161no—
157A4—321no—
158C2×C5—31no—
159C2×C5—32no—
160C2×C5—61no—
161D5—241no—
162C23—32no—
163C23—31no—
164C23—61no—
165C23—301no—
166Q8—302no—
167D4—302no—
168D4—601no—
169D4—602no—
170D4—602no—
171D4—601no—
172C2×C4—31no—
173C2×C4—31no—
174C2×C4—32no—
175C2×C4—32no—
176C2×C4—32no—
177C2×C4—64no—
178C2×C4—64no—
179C2×C4—61no—
180C2×C4—61no—
181C2×C4—302no—
182C2×C4—301no—
183C2×C4—602no—
184C8—602no—
185D3—3201no—
186C5#8554711yescharacteristic, complemented, Sylow
187C22—21no—
188C22—31no—
189C22—31no—
190C22—32no—
191C22—62no—
192C22—61no—
193C22—601no—
194C22—602no—
195C22C5⋊#85712yescomplemented
196C22C5⋊#102011yescharacteristic
197C4—32no—
198C4—32no—
199C4—62no—
200C4—601no—
201C4—602no—
202C3—641noSylow
203C2—31no—
204C2—32no—
205C2—61no—
206C2—1201no—
subgroupG/H
center, hypercenterC1G
commutator, cosocle, hypocenterC5×C22⋊(C42⋊C3)C2
FrattiniC22C5⋊#1020
FittingC22×C42×C5D3
socleC24×C5S4
LCSG ▷ C5×C22⋊(C42⋊C3)
UCSC1

Complements

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

NH ≅ G/Ntype
1. C5×C22⋊(C42⋊C3)C2semidirect
6. C22×C42×C5D3semidirect
14. C22⋊(C42⋊C3)D5semidirect
51. C42×C5S4semidirect
62. C22×C42D15semidirect
118. C22×C5#857semidirect
153. C42C5⋊S4semidirect
186. C5#85547semidirect
195. C22C5⋊#857semidirect

Maximal subgroups

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

subgroupindex
C5×C22⋊(C42⋊C3)2
#106023253
C5⋊#10204
C5⋊#8574
#855475