Finite Group Databasebeta

← C2×C42×C5×A4 #14511307

Subgroups — C2×C42×C5×A4 #14511307

Order 1920.

1360 conjugacy classes of subgroups; only the 324 normal subgroups are shown.

normal subgroups only

This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 324 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×C4×C5×A4C213yesmaximal
2C42×C5×A4C214yesmaximal, direct product factor
3C23×C42×C5C311yesmaximal, characteristic, complemented, Hall
4C23×C5×A4C2211yescharacteristic
5C2×C4×C5×A4C4112yesdirect product factor
6C2×C4×C5×A4C2216yes—
7C2×C3×C42×C5—41nomaximal
8C2×C42×A4C511yesmaximal, characteristic, direct product factor, Hall
9C24×C4×C5C2×C313yes—
10C22×C42×C5—31no—
11C22×C42×C5—33no—
12C22×C42×C5—34no—
13C22×C42×C5C2×C314yescomplemented
14C22×C5×A4C2×C416yes—
15C22×C5×A4C2311yescharacteristic
16C22×C3×C4×C5—43no—
17C4×C5×A4C2×C4112yesdirect product factor
18C3×C42×C5—44no—
19C22×C4×A4C2×C513yes—
20C42×A4C2×C514yesdirect product factor
21C25×C5C22×C311yescharacteristic
22C23×C4×C5—33no—
23C23×C4×C5—33no—
24C23×C4×C5—36no—
25C23×C4×C5—312no—
26C23×C4×C5C3×C4112yescomplemented
27C23×C4×C5C22×C316yes—
28C2×C42×C5—32no—
29C2×C42×C5—312no—
30C2×C42×C5—33no—
31C2×C42×C5—34no—
32C2×C42×C5—34no—
33C2×C42×C5—312no—
34C2×C42×C5A411yescharacteristic, direct product factor
35C23×C42C3×C511yescharacteristic, complemented, Sylow
36C23×C3×C5—41no—
37C2×C5×A4C4214yesdirect product factor
38C2×C5×A4C22×C413yes—
39C2×C3×C4×C5—412no—
40C2×C3×C4×C5—46no—
41C23×A4C22×C511yescharacteristic
42C2×C4×A4C4×C5112yesdirect product factor
43C2×C4×A4C22×C516yes—
44C2×C3×C42—41no—
45C24×C5—31no—
46C24×C5—36no—
47C24×C5—31no—
48C24×C5C2×C3×C416yes—
49C24×C5C23×C311yescharacteristic
50C22×C4×C5—36no—
51C22×C4×C5—312no—
52C22×C4×C5—324no—
53C22×C4×C5—33no—
54C22×C4×C5—312no—
55C22×C4×C5—312no—
56C22×C4×C5—36no—
57C22×C4×C5—36no—
58C22×C4×C5—36no—
59C22×C4×C5—312no—
60C22×C4×C5—324no—
61C22×C4×C5—312no—
62C22×C4×C5C2×C3×C4112yescomplemented
63C22×C4×C5C2×A413yes—
64C42×C5—38no—
65C42×C5—312no—
66C42×C5C2×A414yesdirect product factor
67C24×C4C2×C3×C513yes—
68C22×C42—31no—
69C22×C42—33no—
70C22×C42—34no—
71C22×C42C2×C3×C514yescomplemented
72C22×C3×C5—46no—
73C22×C3×C5—41no—
74C5×A4C2×C4211yescharacteristic, direct product factor
75C3×C4×C5—412no—
76C22×A4C2×C4×C516yes—
77C22×A4C23×C511yescharacteristic
78C22×C3×C4—43no—
79C4×A4C2×C4×C5112yesdirect product factor
80C3×C42—44no—
81C23×C5—36no—
82C23×C5—33no—
83C23×C5—312no—
84C23×C5—36no—
85C23×C5—38no—
86C23×C5—36no—
87C23×C5—36no—
88C23×C5—31no—
89C23×C5—31no—
90C23×C5C3×C4214yescomplemented
91C23×C5C22×C3×C413yes—
92C23×C5C22×A411yescharacteristic
93C2×C4×C5—324no—
94C2×C4×C5—312no—
95C2×C4×C5—312no—
96C2×C4×C5—36no—
97C2×C4×C5—312no—
98C2×C4×C5—324no—
99C2×C4×C5—312no—
100C2×C4×C5—312no—
101C2×C4×C5C4×A4112yesdirect product factor
102C2×C4×C5C22×A416yes—
103C25C22×C3×C511yescharacteristic
104C23×C4—33no—
105C23×C4—312no—
106C23×C4—33no—
107C23×C4—36no—
108C23×C4C3×C4×C5112yescomplemented
109C23×C4C22×C3×C516yes—
110C2×C42—32no—
111C2×C42—312no—
112C2×C42—33no—
113C2×C42—34no—
114C2×C42—34no—
115C2×C42—312no—
116C2×C42C5×A411yescharacteristic, direct product factor
117C2×C3×C5—43no—
118C2×C3×C5—44no—
119C23×C3—41no—
120C2×A4C42×C514yesdirect product factor
121C2×A4C22×C4×C513yes—
122C2×C3×C4—412no—
123C2×C3×C4—46no—
124C22×C5—34no—
125C22×C5—33no—
126C22×C5—312no—
127C22×C5—32no—
128C22×C5—36no—
129C22×C5—33no—
130C22×C5—33no—
131C22×C5—312no—
132C22×C5—34no—
133C22×C5C2×C3×C4211yescharacteristic, complemented
134C22×C5C2×C4×A416yes—
135C22×C5C23×A411yescharacteristic
136C4×C5—312no—
137C4×C5C2×C4×A4112yesdirect product factor
138C24—31no—
139C24—36no—
140C24—31no—
141C24C2×C3×C4×C516yes—
142C24C23×C3×C511yescharacteristic
143C22×C4—36no—
144C22×C4—312no—
145C22×C4—324no—
146C22×C4—33no—
147C22×C4—312no—
148C22×C4—312no—
149C22×C4—36no—
150C22×C4—36no—
151C22×C4—36no—
152C22×C4—312no—
153C22×C4—324no—
154C22×C4—312no—
155C22×C4C2×C3×C4×C5112yescomplemented
156C22×C4C2×C5×A413yes—
157C42—38no—
158C42—312no—
159C42C2×C5×A414yesdirect product factor
160C3×C5—41noHall
161C22×C3—46no—
162C22×C3—41no—
163A4C2×C42×C511yescharacteristic, direct product factor
164C3×C4—412no—
165C2×C5—34no—
166C2×C5—33no—
167C2×C5—31no—
168C2×C5C42×A414yesdirect product factor
169C2×C5C22×C4×A413yes—
170C23—36no—
171C23—33no—
172C23—312no—
173C23—36no—
174C23—38no—
175C23—36no—
176C23—36no—
177C23—31no—
178C23—31no—
179C23C3×C42×C514yescomplemented
180C23C22×C3×C4×C513yes—
181C23C22×C5×A411yescharacteristic
182C2×C4—324no—
183C2×C4—312no—
184C2×C4—312no—
185C2×C4—36no—
186C2×C4—312no—
187C2×C4—324no—
188C2×C4—312no—
189C2×C4—312no—
190C2×C4C4×C5×A4112yesdirect product factor
191C2×C4C22×C5×A416yes—
192C2×C3—43no—
193C2×C3—44no—
194C5C2×C42×A411yescharacteristic, direct product factor, Sylow
195C22—34no—
196C22—33no—
197C22—312no—
198C22—32no—
199C22—33no—
200C22—36no—
201C22—33no—
202C22—34no—
203C22—312no—
204C22C2×C3×C42×C511yescharacteristic, complemented
205C22C2×C4×C5×A416yes—
206C22C23×C5×A411yescharacteristic
207C4—312no—
208C4C2×C4×C5×A4112yesdirect product factor
209C3—41noSylow
210C2—31no—
211C2—34no—
212C2—33no—
213C2C42×C5×A414yesdirect product factor
214C2C22×C4×C5×A413yes—
subgroupG/H
center, hypercenterC2×C42×C5A4
commutator, hypocenterC22C2×C3×C42×C5
FrattiniC22C23×C5×A4
FittingC23×C42×C5C3
socleC25×C5C22×C3
prime radicalC23×C5×A4C22
cosocleC24C23×C3×C5
LCSG ▷ C22
UCSC1 ◁ C2×C42×C5

Complements

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

NH ≅ G/Ntype
2. C42×C5×A4C2direct (N × H)
3. C23×C42×C5C3semidirect
5. C2×C4×C5×A4C4direct (N × H)
8. C2×C42×A4C5direct (N × H)
13. C22×C42×C5C2×C3semidirect
17. C4×C5×A4C2×C4direct (N × H)
20. C42×A4C2×C5direct (N × H)
26. C23×C4×C5C3×C4semidirect
34. C2×C42×C5A4direct (N × H)
35. C23×C42C3×C5semidirect
37. C2×C5×A4C42direct (N × H)
42. C2×C4×A4C4×C5direct (N × H)
62. C22×C4×C5C2×C3×C4semidirect
66. C42×C5C2×A4direct (N × H)
71. C22×C42C2×C3×C5semidirect
74. C5×A4C2×C42direct (N × H)
79. C4×A4C2×C4×C5direct (N × H)
90. C23×C5C3×C42semidirect
101. C2×C4×C5C4×A4direct (N × H)
108. C23×C4C3×C4×C5semidirect
116. C2×C42C5×A4direct (N × H)
120. C2×A4C42×C5direct (N × H)
133. C22×C5C2×C3×C42semidirect
137. C4×C5C2×C4×A4direct (N × H)
155. C22×C4C2×C3×C4×C5semidirect
159. C42C2×C5×A4direct (N × H)
163. A4C2×C42×C5direct (N × H)
168. C2×C5C42×A4direct (N × H)
179. C23C3×C42×C5semidirect
190. C2×C4C4×C5×A4direct (N × H)
194. C5C2×C42×A4direct (N × H)
204. C22C2×C3×C42×C5semidirect
208. C4C2×C4×C5×A4direct (N × H)
213. C2C42×C5×A4direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C5×A42
C42×C5×A42
C23×C42×C53
C2×C3×C42×C54
C2×C42×A45