Finite Group Databasebeta

← C22×D5×C42⋊C3 #14513973

Subgroups — C22×D5×C42⋊C3 #14513973

Order 1920.

1160 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 1160 conjugacy classes of subgroups — too many to draw. Only its 84 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, complemented
2C2×D5×C42⋊C3C216yesmaximal, direct product factor
3C22×C42×D5C311yesmaximal, characteristic, complemented, Hall
4C22×D5×A4—41nomaximal
5C2×C5×C42⋊C3C2213yescomplemented
6D5×C42⋊C3C2214yesdirect product factor
7C23×C42⋊C3—51nomaximal, Hall
8C23×C4×D5—31no—
9C22×C42×C5C2×C311yescharacteristic, complemented
10C22×C4×Dic5—31no—
11C2×C42×D5—36no—
12C2×C42×D5C2×C316yescomplemented
13C22×C5×A4—41no—
14C2×D5×A4—46no—
15C5×C42⋊C3C2311yescharacteristic, complemented
16C22×C42⋊C3—56no—
17C22×C42⋊C3D511yescharacteristic, direct product factor
18C24×D5A411yescharacteristic
19C23×C4×C5—31no—
20C23×Dic5—31no—
21C22×C4×D5—32no—
22C22×C4×D5—312no—
23C22×C4×D5—32no—
24C22×C4×D5—36no—
25C22×C4×D5—36no—
26C2×C42×C5—33no—
27C2×C42×C5C22×C313yescomplemented
28C2×C4×Dic5—36no—
29C2×C4×Dic5—36no—
30C42×D5—312no—
31C42×D5—38no—
32C42×D5C22×C314yescomplemented
33C23×C42—51noSylow
34C22×C3×D5—161no—
35C2×C5×A4—43no—
36D5×A4—44no—
37C23×A4—201no—
38C2×C42⋊C3—54no—
39C2×C42⋊C3C2×D513yesdirect product factor
40C24×C5C2×A411yescharacteristic
41C23×D5—31no—
42C23×D5—31no—
43C23×D5—36no—
44C23×D5C2×A416yes—
45C22×C4×C5—36no—
46C22×C4×C5—32no—
47C22×C4×C5—33no—
48C22×C4×C5—33no—
49C22×Dic5—36no—
50C22×Dic5—32no—
51C22×Dic5—36no—
52C2×C4×D5—312no—
53C2×C4×D5—312no—
54C2×C4×D5—324no—
55C2×C4×D5—312no—
56C2×C4×D5—324no—
57C2×C4×D5—312no—
58C2×C4×D5—312no—
59C2×C4×D5—34no—
60C42×C5—33no—
61C42×C5—32no—
62C42×C5C23×C311yescharacteristic, complemented
63C4×Dic5—312no—
64C4×Dic5—34no—
65C24×C4—151no—
66C22×C42—56no—
67C22×C42—156no—
68C22×C42—151no—
69C22×C42C3×D511yescharacteristic, complemented
70C22×C3×C5—161no—
71C2×C3×D5—166no—
72C5×A4—41no—
73C22×A4—41no—
74C22×A4—206no—
75C42⋊C3C22×D511yescharacteristic, direct product factor
76C23×C5—33no—
77C23×C5—31no—
78C23×C5C22×A413yes—
79C22×D5—36no—
80C22×D5—38no—
81C22×D5—31no—
82C22×D5—36no—
83C22×D5—36no—
84C22×D5—36no—
85C22×D5—312no—
86C22×D5C42⋊C311yescharacteristic, direct product factor
87C22×D5C22×A414yes—
88C2×C4×C5—36no—
89C2×C4×C5—36no—
90C2×C4×C5—36no—
91C2×C4×C5—36no—
92C2×C4×C5—31no—
93C2×C4×C5—33no—
94C2×Dic5—312no—
95C2×Dic5—312no—
96C2×Dic5—34no—
97C4×D5—324no—
98C4×D5—38no—
99C4×D5—324no—
100C4×D5—38no—
101C25—51no—
102C23×C4—31no—
103C23×C4—156no—
104C23×C4—156no—
105C23×C4—152no—
106C23×C4—1512no—
107C23×C4—152no—
108C23×C4—151no—
109C2×C42—33no—
110C2×C42—54no—
111C2×C42—1512no—
112C2×C42—158no—
113C2×C42—156no—
114C2×C42—156no—
115C2×C42C2×C3×D513yescomplemented
116C2×C3×C5—163no—
117C3×D5—164no—
118C23×C3—801no—
119C2×A4—43no—
120C2×A4—204no—
121C22×C5—33no—
122C22×C5—32no—
123C22×C5—33no—
124C22×C5—33no—
125C22×C5C2×C42⋊C311yescharacteristic, complemented
126C22×C5C23×A411yescharacteristic
127C2×D5—312no—
128C2×D5—36no—
129C2×D5—34no—
130C2×D5—312no—
131C2×D5—34no—
132C2×D5C2×C42⋊C316yesdirect product factor
133C4×C5—32no—
134C4×C5—36no—
135Dic5—38no—
136C24—56no—
137C24—151no—
138C24—156no—
139C24—151no—
140C24D5×A411yescharacteristic
141C22×C4—36no—
142C22×C4—32no—
143C22×C4—33no—
144C22×C4—33no—
145C22×C4—154no—
146C22×C4—1512no—
147C22×C4—1512no—
148C22×C4—1512no—
149C22×C4—1524no—
150C22×C4—1512no—
151C22×C4—1524no—
152C22×C4—1512no—
153C22×C4—156no—
154C22×C4—152no—
155C22×C4—156no—
156C42—33no—
157C42—32no—
158C42—154no—
159C42—1512no—
160C42C22×C3×D511yescharacteristic, complemented
161C3×C5—161noHall
162C22×C3—161no—
163C22×C3—806no—
164A4—41no—
165C2×C5—31no—
166C2×C5—33no—
167C2×C5C22×C42⋊C313yescomplemented
168D5—34no—
169D5C22×C42⋊C314yesdirect product factor
170C23—33no—
171C23—31no—
172C23—51no—
173C23—54no—
174C23—156no—
175C23—156no—
176C23—1512no—
177C23—156no—
178C23—158no—
179C23—156no—
180C23—151no—
181C23C2×D5×A413yes—
182C2×C4—36no—
183C2×C4—36no—
184C2×C4—36no—
185C2×C4—36no—
186C2×C4—31no—
187C2×C4—33no—
188C2×C4—158no—
189C2×C4—1524no—
190C2×C4—158no—
191C2×C4—1524no—
192C2×C4—1512no—
193C2×C4—1512no—
194C2×C4—154no—
195C2×C3—163no—
196C2×C3—804no—
197C5C23×C42⋊C311yescharacteristic, complemented, Sylow
198C22—33no—
199C22—32no—
200C22—33no—
201C22—33no—
202C22—56no—
203C22—154no—
204C22—1512no—
205C22—154no—
206C22—1512no—
207C22—156no—
208C22D5×C42⋊C311yescharacteristic, direct product factor
209C22C22×D5×A411yescharacteristic
210C4—32no—
211C4—36no—
212C4—158no—
213C3—161noSylow
214C2—31no—
215C2—33no—
216C2—54no—
217C2—154no—
218C2C2×D5×C42⋊C313yesdirect product factor
subgroupG/H
center, hypercenterC22D5×C42⋊C3
commutator, cosocle, hypocenterC42×C5C23×C3
FrattiniC22C22×D5×A4
FittingC22×C42×C5C2×C3
socleC24×C5C2×A4
LCSG ▷ C42×C5
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
1. C22×C5×C42⋊C3C2semidirect
2. C2×D5×C42⋊C3C2direct (N × H)
3. C22×C42×D5C3semidirect
5. C2×C5×C42⋊C3C22semidirect
6. D5×C42⋊C3C22direct (N × H)
9. C22×C42×C5C2×C3semidirect
12. C2×C42×D5C2×C3semidirect
15. C5×C42⋊C3C23semidirect
17. C22×C42⋊C3D5direct (N × H)
27. C2×C42×C5C22×C3semidirect
32. C42×D5C22×C3semidirect
39. C2×C42⋊C3C2×D5direct (N × H)
62. C42×C5C23×C3semidirect
69. C22×C42C3×D5semidirect
75. C42⋊C3C22×D5direct (N × H)
86. C22×D5C42⋊C3direct (N × H)
115. C2×C42C2×C3×D5semidirect
125. C22×C5C2×C42⋊C3semidirect
132. C2×D5C2×C42⋊C3direct (N × H)
160. C42C22×C3×D5semidirect
167. C2×C5C22×C42⋊C3semidirect
169. D5C22×C42⋊C3direct (N × H)
197. C5C23×C42⋊C3semidirect
208. C22D5×C42⋊C3direct (N × H)
218. C2C2×D5×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
C2×D5×C42⋊C32
C22×C42×D53
C22×D5×A44
C23×C42⋊C35