Finite Group Databasebeta

← C2×C4×C5×C42⋊C3 #14510882

Subgroups — C2×C4×C5×C42⋊C3 #14510882

Order 1920.

504 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 64 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
1C22×C5×C42⋊C3C211yesmaximal, characteristic
2C4×C5×C42⋊C3C212yesmaximal, direct product factor
3C2×C43×C5C311yesmaximal, characteristic, complemented, Hall
4C2×C4×C5×A4—41nomaximal
5C2×C5×C42⋊C3C412yesdirect product factor
6C2×C5×C42⋊C3C2211yescharacteristic
7C2×C4×C42⋊C3C511yesmaximal, characteristic, direct product factor, Hall
8C22×C42×C5—31no—
9C22×C42×C5—31no—
10C22×C42×C5C2×C311yescharacteristic
11C43×C5—32no—
12C43×C5C2×C312yescomplemented
13C22×C5×A4—41no—
14C4×C5×A4—42no—
15C5×C42⋊C3C2×C411yescharacteristic, direct product factor
16C22×C42⋊C3C2×C511yescharacteristic
17C4×C42⋊C3C2×C512yesdirect product factor
18C23×C4×C5—31no—
19C23×C4×C5—31no—
20C23×C4×C5A411yescharacteristic
21C2×C42×C5—31no—
22C2×C42×C5—32no—
23C2×C42×C5—32no—
24C2×C42×C5—32no—
25C2×C42×C5—38no—
26C2×C42×C5—32no—
27C2×C42×C5—34no—
28C2×C42×C5—32no—
29C2×C42×C5—32no—
30C2×C42×C5—32no—
31C2×C42×C5C3×C412yescomplemented
32C2×C42×C5C22×C311yescharacteristic
33C2×C43C3×C511yescharacteristic, complemented, Sylow
34C2×C5×A4—42no—
35C2×C5×A4—41no—
36C2×C3×C4×C5—161no—
37C2×C4×A4—41no—
38C2×C42⋊C3C4×C512yesdirect product factor
39C2×C42⋊C3C22×C511yescharacteristic
40C24×C5C2×A411yescharacteristic
41C22×C4×C5—38no—
42C22×C4×C5—32no—
43C22×C4×C5—34no—
44C22×C4×C5—32no—
45C22×C4×C5—32no—
46C22×C4×C5—32no—
47C22×C4×C5—32no—
48C22×C4×C5—32no—
49C22×C4×C5—31no—
50C22×C4×C5—32no—
51C22×C4×C5—31no—
52C22×C4×C5—31no—
53C22×C4×C5—31no—
54C22×C4×C5—32no—
55C22×C4×C5C2×A412yes—
56C42×C5—32no—
57C42×C5—31no—
58C42×C5—38no—
59C42×C5—38no—
60C42×C5—34no—
61C42×C5—34no—
62C42×C5—34no—
63C42×C5—34no—
64C42×C5—32no—
65C42×C5C2×C3×C411yescharacteristic, complemented
66C22×C42—31no—
67C22×C42—31no—
68C22×C42C2×C3×C511yescharacteristic
69C43—32no—
70C43C2×C3×C512yescomplemented
71C22×C3×C5—161no—
72C5×A4—41no—
73C3×C4×C5—162no—
74C22×A4—41no—
75C4×A4—42no—
76C42⋊C3C2×C4×C511yescharacteristic, direct product factor
77C23×C5—32no—
78C23×C5—31no—
79C23×C5—31no—
80C23×C5C4×A412yes—
81C23×C5C22×A411yescharacteristic
82C2×C4×C5—32no—
83C2×C4×C5—38no—
84C2×C4×C5—32no—
85C2×C4×C5—32no—
86C2×C4×C5—34no—
87C2×C4×C5—32no—
88C2×C4×C5—34no—
89C2×C4×C5—34no—
90C2×C4×C5—38no—
91C2×C4×C5—38no—
92C2×C4×C5—34no—
93C2×C4×C5—34no—
94C2×C4×C5—32no—
95C2×C4×C5—31no—
96C2×C4×C5—31no—
97C2×C4×C5—32no—
98C2×C4×C5—31no—
99C2×C4×C5—32no—
100C2×C4×C5—32no—
101C2×C4×C5—32no—
102C2×C4×C5C42⋊C311yescharacteristic, direct product factor
103C23×C4—31no—
104C23×C4—31no—
105C23×C4C5×A411yescharacteristic
106C2×C42—31no—
107C2×C42—32no—
108C2×C42—32no—
109C2×C42—32no—
110C2×C42—38no—
111C2×C42—32no—
112C2×C42—34no—
113C2×C42—32no—
114C2×C42—32no—
115C2×C42—32no—
116C2×C42C3×C4×C512yescomplemented
117C2×C42C22×C3×C511yescharacteristic
118C2×C3×C5—162no—
119C2×C3×C5—161no—
120C2×A4—42no—
121C2×A4—41no—
122C2×C3×C4—161no—
123C22×C5—31no—
124C22×C5—32no—
125C22×C5—32no—
126C22×C5—32no—
127C22×C5—32no—
128C22×C5—31no—
129C22×C5—31no—
130C22×C5C2×C42⋊C311yescharacteristic
131C22×C5C2×C4×A411yescharacteristic
132C4×C5—38no—
133C4×C5—32no—
134C4×C5—32no—
135C4×C5—34no—
136C4×C5—32no—
137C4×C5C2×C42⋊C312yesdirect product factor
138C24C2×C5×A411yescharacteristic
139C22×C4—38no—
140C22×C4—32no—
141C22×C4—34no—
142C22×C4—32no—
143C22×C4—32no—
144C22×C4—32no—
145C22×C4—32no—
146C22×C4—32no—
147C22×C4—31no—
148C22×C4—32no—
149C22×C4—31no—
150C22×C4—31no—
151C22×C4—31no—
152C22×C4—32no—
153C22×C4C2×C5×A412yes—
154C42—32no—
155C42—31no—
156C42—38no—
157C42—38no—
158C42—34no—
159C42—34no—
160C42—34no—
161C42—34no—
162C42—32no—
163C42C2×C3×C4×C511yescharacteristic, complemented
164C3×C5—161noHall
165C22×C3—161no—
166A4—41no—
167C3×C4—162no—
168C2×C5—31no—
169C2×C5—31no—
170C2×C5—32no—
171C2×C5C4×C42⋊C312yesdirect product factor
172C2×C5C22×C42⋊C311yescharacteristic
173C23—32no—
174C23—31no—
175C23—31no—
176C23C4×C5×A412yes—
177C23C22×C5×A411yescharacteristic
178C2×C4—32no—
179C2×C4—32no—
180C2×C4—38no—
181C2×C4—32no—
182C2×C4—32no—
183C2×C4—34no—
184C2×C4—34no—
185C2×C4—34no—
186C2×C4—38no—
187C2×C4—34no—
188C2×C4—34no—
189C2×C4—38no—
190C2×C4—32no—
191C2×C4—31no—
192C2×C4—32no—
193C2×C4—31no—
194C2×C4—31no—
195C2×C4—32no—
196C2×C4—32no—
197C2×C4—32no—
198C2×C4C5×C42⋊C311yescharacteristic, direct product factor
199C2×C3—162no—
200C2×C3—161no—
201C5C2×C4×C42⋊C311yescharacteristic, direct product factor, Sylow
202C22—31no—
203C22—32no—
204C22—32no—
205C22—32no—
206C22—32no—
207C22—31no—
208C22—31no—
209C22C2×C5×C42⋊C311yescharacteristic
210C22C2×C4×C5×A411yescharacteristic
211C4—32no—
212C4—32no—
213C4—34no—
214C4—38no—
215C4—32no—
216C4C2×C5×C42⋊C312yesdirect product factor
217C3—161noSylow
218C2—31no—
219C2—31no—
220C2—32no—
221C2C4×C5×C42⋊C312yesdirect product factor
222C2C22×C5×C42⋊C311yescharacteristic
subgroupG/H
center, hypercenterC2×C4×C5C42⋊C3
commutator, hypocenterC42C2×C3×C4×C5
FrattiniC23C22×C5×A4
FittingC2×C43×C5C3
socleC24×C5C2×A4
prime radicalC22×C5×C42⋊C3C2
cosocleC2×C42C22×C3×C5
LCSG ▷ C42
UCSC1 ◁ C2×C4×C5

Complements

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

NH ≅ G/Ntype
2. C4×C5×C42⋊C3C2direct (N × H)
3. C2×C43×C5C3semidirect
5. C2×C5×C42⋊C3C4direct (N × H)
7. C2×C4×C42⋊C3C5direct (N × H)
12. C43×C5C2×C3semidirect
15. C5×C42⋊C3C2×C4direct (N × H)
17. C4×C42⋊C3C2×C5direct (N × H)
31. C2×C42×C5C3×C4semidirect
33. C2×C43C3×C5semidirect
38. C2×C42⋊C3C4×C5direct (N × H)
65. C42×C5C2×C3×C4semidirect
70. C43C2×C3×C5semidirect
76. C42⋊C3C2×C4×C5direct (N × H)
102. C2×C4×C5C42⋊C3direct (N × H)
116. C2×C42C3×C4×C5semidirect
137. C4×C5C2×C42⋊C3direct (N × H)
163. C42C2×C3×C4×C5semidirect
171. C2×C5C4×C42⋊C3direct (N × H)
198. C2×C4C5×C42⋊C3direct (N × H)
201. C5C2×C4×C42⋊C3direct (N × H)
216. C4C2×C5×C42⋊C3direct (N × H)
221. C2C4×C5×C42⋊C3direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×C42⋊C32
C4×C5×C42⋊C32
C2×C43×C53
C2×C4×C5×A44
C2×C4×C42⋊C35