Finite Group Databasebeta

← C22×C3×(C24⋊C5)⋊C2 #14511524

Subgroups — C22×C3×(C24⋊C5)⋊C2 #14511524

Order 1920.

2356 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 2356 conjugacy classes of subgroups — too many to draw. Only its 52 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×C3×C24⋊C5C211yesmaximal, characteristic, complemented
2C2×C3×(C24⋊C5)⋊C2C216yesmaximal, direct product factor
3C22×(C24⋊C5)⋊C2C311yesmaximal, characteristic, direct product factor, Hall
4C2×C3×C24⋊C5C2213yescomplemented
5C3×(C24⋊C5)⋊C2C2214yesdirect product factor
6C22×C3×#120—51nomaximal, Hall
7C22×C24⋊C5C2×C311yescharacteristic, complemented
8C2×(C24⋊C5)⋊C2C2×C316yesdirect product factor
9C3×C24⋊C5C2311yescharacteristic, complemented
10C26×C3D511yescharacteristic, complemented
11C23×C3×D4—53no—
12C2×C3×#120—518no—
13C2×C3×#120—56no—
14C22×C3×C22⋊C4—53no—
15C2×C24⋊C5C22×C313yescomplemented
16(C24⋊C5)⋊C2C22×C314yesdirect product factor
17C22×#120—51noSylow
18C22×C3×D5—161nomaximal
19C25×C3—53no—
20C25×C3—59no—
21C25×C3—51no—
22C25×C3C2×D513yescomplemented
23C22×C3×D4—518no—
24C22×C3×D4—518no—
25C22×C3×D4—1018no—
26C22×C3×D4—106no—
27C23×C3×C4—53no—
28C3×#120—536no—
29C3×#120—524no—
30C3×#120—54no—
31C2×C3×C22⋊C4—518no—
32C2×C3×C22⋊C4—518no—
33C24⋊C5C23×C311yescharacteristic, complemented
34C26C3×D511yescharacteristic, complemented
35C23×D4—53no—
36C2×#120—518no—
37C2×#120—56no—
38C22×C22⋊C4—53no—
39C22×C3×C5—161no—
40C2×C3×D5—166no—
41C24×C3—51no—
42C24×C3—59no—
43C24×C3—518no—
44C24×C3—56no—
45C24×C3—59no—
46C24×C3—59no—
47C24×C3—56no—
48C24×C3—56no—
49C24×C3—1018no—
50C24×C3—1018no—
51C24×C3—109no—
52C24×C3—103no—
53C24×C3C22×D511yescharacteristic, complemented
54C2×C3×D4—512no—
55C2×C3×D4—536no—
56C2×C3×D4—1036no—
57C2×C3×D4—1036no—
58C2×C3×D4—1036no—
59C2×C3×D4—1036no—
60C22×C3×C4—518no—
61C22×C3×C4—109no—
62C22×C3×C4—103no—
63C3×C22⋊C4—512no—
64C3×C22⋊C4—536no—
65C22×D5—161no—
66C25—53no—
67C25—59no—
68C25—51no—
69C25C2×C3×D513yescomplemented
70C22×D4—518no—
71C22×D4—518no—
72C22×D4—1018no—
73C22×D4—106no—
74C23×C4—53no—
75#120—536no—
76#120—524no—
77#120—54no—
78C2×C22⋊C4—518no—
79C2×C22⋊C4—518no—
80C2×C3×C5—163no—
81C3×D5—164no—
82C23×C3—53no—
83C23×C3—53no—
84C23×C3—59no—
85C23×C3—53no—
86C23×C3—518no—
87C23×C3—518no—
88C23×C3—518no—
89C23×C3—59no—
90C23×C3—518no—
91C23×C3—54no—
92C23×C3—1018no—
93C23×C3—1018no—
94C23×C3—1036no—
95C23×C3—1018no—
96C23×C3—1018no—
97C23×C3—1018no—
98C23×C3—206no—
99C23×C3—209no—
100C23×C3—201no—
101C3×D4—1024no—
102C3×D4—1072no—
103C2×C3×C4—512no—
104C2×C3×C4—1018no—
105C2×C3×C4—1018no—
106C22×C5—161no—
107C2×D5—166no—
108C24—51no—
109C24—59no—
110C24—518no—
111C24—56no—
112C24—59no—
113C24—59no—
114C24—56no—
115C24—56no—
116C24—1018no—
117C24—1018no—
118C24—109no—
119C24—103no—
120C24C22×C3×D511yescharacteristic, complemented
121C2×D4—512no—
122C2×D4—536no—
123C2×D4—1036no—
124C2×D4—1036no—
125C2×D4—1036no—
126C2×D4—1036no—
127C22×C4—518no—
128C22×C4—109no—
129C22×C4—103no—
130C22⋊C4—512no—
131C22⋊C4—536no—
132C3×C5—161noHall
133C22×C3—56no—
134C22×C3—518no—
135C22×C3—51no—
136C22×C3—59no—
137C22×C3—56no—
138C22×C3—59no—
139C22×C3—59no—
140C22×C3—1018no—
141C22×C3—1018no—
142C22×C3—1012no—
143C22×C3—2018no—
144C22×C3—206no—
145C22×C3(C24⋊C5)⋊C211yescharacteristic, direct product factor
146C3×C4—1012no—
147C2×C5—163no—
148D5—164no—
149C23—53no—
150C23—53no—
151C23—59no—
152C23—53no—
153C23—518no—
154C23—518no—
155C23—518no—
156C23—59no—
157C23—518no—
158C23—54no—
159C23—1018no—
160C23—1018no—
161C23—1036no—
162C23—1018no—
163C23—1018no—
164C23—1018no—
165C23—206no—
166C23—209no—
167C23—201no—
168D4—1024no—
169D4—1072no—
170C2×C4—512no—
171C2×C4—1018no—
172C2×C4—1018no—
173C2×C3—53no—
174C2×C3—59no—
175C2×C3—204no—
176C2×C3C2×(C24⋊C5)⋊C213yesdirect product factor
177C5—161noSylow
178C22—56no—
179C22—518no—
180C22—51no—
181C22—59no—
182C22—56no—
183C22—59no—
184C22—59no—
185C22—1018no—
186C22—1018no—
187C22—1012no—
188C22—2018no—
189C22—206no—
190C22C3×(C24⋊C5)⋊C211yescharacteristic, direct product factor
191C4—1012no—
192C3C22×(C24⋊C5)⋊C211yescharacteristic, direct product factor, Sylow
193C2—53no—
194C2—59no—
195C2—204no—
196C2C2×C3×(C24⋊C5)⋊C213yesdirect product factor
subgroupG/H
center, hypercenterC22×C3(C24⋊C5)⋊C2
commutator, cosocle, hypocenterC24⋊C5C23×C3
FrattiniC1G
Fitting, socleC26×C3D5
LCSG ▷ C24⋊C5
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×C24⋊C5C2semidirect
2. C2×C3×(C24⋊C5)⋊C2C2direct (N × H)
3. C22×(C24⋊C5)⋊C2C3direct (N × H)
4. C2×C3×C24⋊C5C22semidirect
5. C3×(C24⋊C5)⋊C2C22direct (N × H)
7. C22×C24⋊C5C2×C3semidirect
8. C2×(C24⋊C5)⋊C2C2×C3direct (N × H)
9. C3×C24⋊C5C23semidirect
10. C26×C3D5semidirect
15. C2×C24⋊C5C22×C3semidirect
16. (C24⋊C5)⋊C2C22×C3direct (N × H)
22. C25×C3C2×D5semidirect
33. C24⋊C5C23×C3semidirect
34. C26C3×D5semidirect
53. C24×C3C22×D5semidirect
69. C25C2×C3×D5semidirect
120. C24C22×C3×D5semidirect
145. C22×C3(C24⋊C5)⋊C2direct (N × H)
176. C2×C3C2×(C24⋊C5)⋊C2direct (N × H)
190. C22C3×(C24⋊C5)⋊C2direct (N × H)
192. C3C22×(C24⋊C5)⋊C2direct (N × H)
196. C2C2×C3×(C24⋊C5)⋊C2direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C24⋊C52
C2×C3×(C24⋊C5)⋊C22
C22×(C24⋊C5)⋊C23
C22×C3×#1205
C22×C3×D516