Finite Group Databasebeta

← C4⋊(C3⋊((C24⋊C5)⋊C2)) #14514569

Subgroups — C4⋊(C3⋊((C24⋊C5)⋊C2)) #14514569

Order 1920.

716 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 21 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
1C2×C3⋊((C24⋊C5)⋊C2)C212yesmaximal, complemented
2C3×C4×C24⋊C5C211yesmaximal, characteristic, complemented
3C4⋊((C24⋊C5)⋊C2)—31nomaximal, Hall
4C2×C3×C24⋊C5C2211yescharacteristic
5C3⋊((C24⋊C5)⋊C2)—22no—
6#84032—51nomaximal, Hall
7C2×(C24⋊C5)⋊C2—32no—
8C4×C24⋊C5D311yescharacteristic, complemented
9C3×C24⋊C5D411yescharacteristic, complemented
10C24×C3×C4D511yescharacteristic, complemented
11C2×#953—52no—
12C2×#930—53no—
13#5213—56no—
14#5212—53no—
15C2×C24⋊C5C2×D311yescharacteristic
16(C24⋊C5)⋊C2—62no—
17#2847—151noSylow
18D60—161nomaximal
19C25×C3C2×D511yescharacteristic
20C23×C3×C4—53no—
21C23×C3×C4—53no—
22C22×#67—56no—
23C22×D12—51no—
24#953—106no—
25#953—102no—
26C2×#217—56no—
27#930—106no—
28#930—106no—
29C2×(C2×D3)⋊C4—56no—
30C2×C4⋊Dic3—53no—
31C3⋊#95—56no—
32C24⋊C5D1211yescharacteristic, complemented
33C24×C4D1511yescharacteristic, complemented
34C2×#121—153no—
35C2×#120—152no—
36#386—156no—
37#380—153no—
38C2×D15—162no—
39C3×C4×C5—161no—
40C24×C3—53no—
41C24×C3—53no—
42C24×C3D2011yescharacteristic, complemented
43C23×D3—52no—
44C22×C3×C4—51no—
45C22×C3×C4—56no—
46C22×C3×C4—56no—
47C22×C3×C4—53no—
48C22×C3×C4—106no—
49C2×#67—1012no—
50C2×#67—106no—
51C2×#67—106no—
52C2×#67—1012no—
53C22×Dic3—56no—
54C2×D12—103no—
55C2×D12—103no—
56#217—106no—
57#217—106no—
58(C2×D3)⋊C4—1012no—
59C4⋊Dic3—103no—
60C4⋊Dic3—103no—
61D20—481no—
62C25C2×D1511yescharacteristic
63C22×D4—151no—
64C22×D4—156no—
65C23×C4—53no—
66C23×C4—53no—
67#121—306no—
68#121—306no—
69#120—306no—
70#120—302no—
71C2×C4⋊C4—153no—
72C2×C22⋊C4—156no—
73C2×C22⋊C4—156no—
74#95—156no—
75C2×C3×C5—161no—
76D15—322no—
77C23×C3—53no—
78C23×C3—51no—
79C23×C3—56no—
80C23×C3—56no—
81C23×C3—53no—
82C23×C3—106no—
83C22×D3—106no—
84C22×D3—102no—
85C22×D3—106no—
86C2×C3×C4—53no—
87C2×C3×C4—53no—
88C2×C3×C4—56no—
89C2×C3×C4—106no—
90#67—2012no—
91#67—2012no—
92C2×Dic3—106no—
93C2×Dic3—106no—
94C2×Dic3—106no—
95D12—203no—
96D12—201no—
97C2×D5—482no—
98C4×C5—161no—
99C24—53no—
100C24—53no—
101C24—152no—
102C24D6011yescharacteristic, complemented
103C2×D4—303no—
104C2×D4—303no—
105C2×D4—306no—
106C2×D4—306no—
107C2×D4—3012no—
108C2×D4—3012no—
109C22×C4—51no—
110C22×C4—56no—
111C22×C4—56no—
112C22×C4—53no—
113C22×C4—106no—
114C22×C4—156no—
115C4⋊C4—303no—
116C4⋊C4—303no—
117C22⋊C4—3012no—
118C22⋊C4—306no—
119C22⋊C4—306no—
120C3×C5—161noHall
121C22×C3—56no—
122C22×C3—56no—
123C22×C3—51no—
124C22×C3—53no—
125C22×C3—53no—
126C22×C3—106no—
127C2×D3—206no—
128C2×D3—206no—
129C2×D3—202no—
130C3×C4—53no—
131C3×C4(C24⋊C5)⋊C211yescharacteristic, complemented
132Dic3—206no—
133C2×C5—161no—
134D5—962no—
135C23—53no—
136C23—51no—
137C23—56no—
138C23—56no—
139C23—53no—
140C23—106no—
141C23—306no—
142C23—302no—
143C23—306no—
144D4—603no—
145D4—6012no—
146D4—6012no—
147D4—601no—
148C2×C4—53no—
149C2×C4—53no—
150C2×C4—56no—
151C2×C4—106no—
152C2×C4—306no—
153C2×C4—306no—
154C2×C4—306no—
155C2×C3—53no—
156C2×C3—53no—
157C2×C3C2×(C24⋊C5)⋊C211yescharacteristic
158D3—402no—
159C5—161noSylow
160C22—56no—
161C22—56no—
162C22—51no—
163C22—53no—
164C22—53no—
165C22—106no—
166C22—606no—
167C22—606no—
168C22—602no—
169C4—53no—
170C4—606no—
171C4C3⋊((C24⋊C5)⋊C2)11yescharacteristic, complemented
172C3C4⋊((C24⋊C5)⋊C2)11yescharacteristic, complemented, Sylow
173C2—53no—
174C2—53no—
175C2—1202no—
176C2C2×C3⋊((C24⋊C5)⋊C2)11yescharacteristic
subgroupG/H
center, FrattiniC2C2×C3⋊((C24⋊C5)⋊C2)
commutator, cosocleC2×C3×C24⋊C5C22
FittingC24×C3×C4D5
socleC25×C3C2×D5
hypercenterC4C3⋊((C24⋊C5)⋊C2)
hypocenterC3×C24⋊C5D4
LCSG ▷ C2×C3×C24⋊C5 ▷ C3×C24⋊C5
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊((C24⋊C5)⋊C2)C2semidirect
2. C3×C4×C24⋊C5C2semidirect
8. C4×C24⋊C5D3semidirect
9. C3×C24⋊C5D4semidirect
10. C24×C3×C4D5semidirect
32. C24⋊C5D12semidirect
33. C24×C4D15semidirect
42. C24×C3D20semidirect
102. C24D60semidirect
131. C3×C4(C24⋊C5)⋊C2semidirect
171. C4C3⋊((C24⋊C5)⋊C2)semidirect
172. C3C4⋊((C24⋊C5)⋊C2)semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊((C24⋊C5)⋊C2)2
C3×C4×C24⋊C52
C4⋊((C24⋊C5)⋊C2)3
#840325
D6016