Finite Group Databasebeta

← C5×#85547 #14511285

Subgroups — C5×#85547 #14511285

Order 1920.

320 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 20 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
2C5×#1896—31nomaximal, Hall
3C5×#1020—41nomaximal
4C5×#857—42nomaximal
5#85547C511yesmaximal, characteristic, direct product factor, Hall
6C5×#525—31no—
7C22×C42×C5D311yescharacteristic, complemented
8C2×C5×#104—32no—
9C5×#407—31no—
10C5×#339—32no—
11C5×C22⋊A4—41no—
12C5×C42⋊C3—42no—
13C5×C42⋊C3—81no—
14C22⋊(C42⋊C3)C2×C511yescharacteristic, complemented
15C2×C5×#41—31no—
16C23×C4×C5—31no—
17C2×C5×M16—32no—
18C5×#123—61no—
19C5×C22⋊Q8—32no—
20C5×#121—32no—
21C5×#120—61no—
22C4×C5×D4—62no—
23C5×#117—31no—
24C2×C42×C5—32no—
25C2×C42×C5—61no—
26C5×#104—62no—
27C5×#104—62no—
28C5×C22⋊C8—62no—
29#1896—31noSylow
30C5×S4—161no—
31C5×S4—162no—
32#1020—41no—
33#857—42no—
34C24×C5S411yescharacteristic
35C5×#41—62no—
36C5×#41—62no—
37C2×C5×Q8—31no—
38C2×C5×D4—31no—
39C2×C5×D4—62no—
40C2×C5×D4—61no—
41C22×C4×C5—31no—
42C22×C4×C5—31no—
43C22×C4×C5—32no—
44C22×C4×C5—32no—
45C22×C4×C5—62no—
46C22×C4×C5—62no—
47C22×C4×C5—61no—
48C5×M16—62no—
49C5×M16—62no—
50C2×C5×C8—62no—
51C5×C4⋊C4—32no—
52C5×C4⋊C4—62no—
53C5×C22⋊C4—62no—
54C5×C22⋊C4—61no—
55C5×C22⋊C4—62no—
56C42×C5—21no—
57C42×C5—32no—
58C42×C5—61no—
59C42×C5—61no—
60C42×C5S412yescomplemented
61#525—31no—
62C22×C42C5×D311yescharacteristic, complemented
63C2×#104—32no—
64#407—31no—
65#339—32no—
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—
75C23×C5—61no—
76C5×Q8—62no—
77C5×D4—62no—
78C5×D4—122no—
79C5×D4—121no—
80C5×D4—122no—
81C5×D4—121no—
82C2×C4×C5—31no—
83C2×C4×C5—31no—
84C2×C4×C5—32no—
85C2×C4×C5—32no—
86C2×C4×C5—32no—
87C2×C4×C5—64no—
88C2×C4×C5—64no—
89C2×C4×C5—61no—
90C2×C4×C5—61no—
91C2×C4×C5—62no—
92C2×C4×C5—61no—
93C2×C4×C5—122no—
94C5×C8—122no—
95C2×#41—31no—
96C23×C4—31no—
97C2×M16—32no—
98#123—61no—
99C22⋊Q8—32no—
100#121—32no—
101#120—61no—
102C4×D4—62no—
103#117—31no—
104C2×C42—32no—
105C2×C42—61no—
106#104—62no—
107#104—62no—
108C22⋊C8—62no—
109C5×D3—641no—
110S4—161no—
111S4—162no—
112C22×C5—21no—
113C22×C5—31no—
114C22×C5—31no—
115C22×C5—32no—
116C22×C5—62no—
117C22×C5—61no—
118C22×C5—121no—
119C22×C5—122no—
120C22×C5#85712yescomplemented
121C22×C5#102011yescharacteristic
122C4×C5—32no—
123C4×C5—32no—
124C4×C5—62no—
125C4×C5—121no—
126C4×C5—122no—
127C24C5×S411yescharacteristic
128#41—62no—
129#41—62no—
130C2×Q8—31no—
131C2×D4—31no—
132C2×D4—62no—
133C2×D4—61no—
134C22×C4—31no—
135C22×C4—32no—
136C22×C4—31no—
137C22×C4—32no—
138C22×C4—62no—
139C22×C4—62no—
140C22×C4—61no—
141M16—62no—
142M16—62no—
143C2×C8—62no—
144C4⋊C4—32no—
145C4⋊C4—62no—
146C22⋊C4—62no—
147C22⋊C4—61no—
148C22⋊C4—62no—
149C42—21no—
150C42—32no—
151C42—61no—
152C42—61no—
153C42C5×S412yescomplemented
154C3×C5—641noHall
155A4—162no—
156A4—161no—
157A4—321no—
158C2×C5—31no—
159C2×C5—32no—
160C2×C5—61no—
161C2×C5—241no—
162C23—32no—
163C23—31no—
164C23—61no—
165C23—61no—
166Q8—62no—
167D4—62no—
168D4—121no—
169D4—122no—
170D4—122no—
171D4—121no—
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—62no—
182C2×C4—61no—
183C2×C4—122no—
184C8—122no—
185D3—641no—
186C5#8554711yescharacteristic, direct product factor, Sylow
187C22—21no—
188C22—31no—
189C22—31no—
190C22—32no—
191C22—62no—
192C22—61no—
193C22—121no—
194C22—122no—
195C22C5×#85712yescomplemented
196C22C5×#102011yescharacteristic
197C4—32no—
198C4—32no—
199C4—62no—
200C4—121no—
201C4—122no—
202C3—641noSylow
203C2—31no—
204C2—32no—
205C2—61no—
206C2—241no—
subgroupG/H
center, hypercenterC5#85547
commutator, cosocle, hypocenterC22⋊(C42⋊C3)C2×C5
FrattiniC22C5×#1020
FittingC22×C42×C5D3
socleC24×C5S4
LCSG ▷ C22⋊(C42⋊C3)
UCSC1 ◁ C5

Complements

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

NH ≅ G/Ntype
1. C5×C22⋊(C42⋊C3)C2semidirect
5. #85547C5direct (N × H)
7. C22×C42×C5D3semidirect
14. C22⋊(C42⋊C3)C2×C5semidirect
60. C42×C5S4semidirect
62. C22×C42C5×D3semidirect
120. C22×C5#857semidirect
153. C42C5×S4semidirect
186. C5#85547direct (N × H)
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
C5×#18963
C5×#10204
C5×#8574
#855475