Finite Group Databasebeta

← C4×C3⋊((C24⋊C5)⋊C2) #14514568

Subgroups — C4×C3⋊((C24⋊C5)⋊C2) #14514568

Order 1920.

716 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 23 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)C211yesmaximal, characteristic
2C3×C4×C24⋊C5C211yesmaximal, characteristic, complemented
3C3⋊#66245C211yesmaximal, characteristic, complemented
4C4×(C24⋊C5)⋊C2—31nomaximal, Hall
5C2×C3×C24⋊C5C2211yescharacteristic
6C3⋊((C24⋊C5)⋊C2)C412yesdirect product factor
7C4×#953—51nomaximal, Hall
8C2×(C24⋊C5)⋊C2—31no—
9C4×C24⋊C5D311yescharacteristic, complemented
10#66245—31no—
11C3×C24⋊C5C2×C411yescharacteristic, complemented
12C24×C3×C4D511yescharacteristic, complemented
13C2×#953—51no—
14C2×C4×#67—53no—
15#5247—51no—
16#5213—53no—
17#5210—53no—
18C4×#217—53no—
19C2×C24⋊C5C2×D311yescharacteristic
20(C24⋊C5)⋊C2—32no—
21C4×#120—151noSylow
22C4×D15—161nomaximal
23C25×C3C2×D511yescharacteristic
24C23×C3×C4—53no—
25C23×C3×C4—53no—
26C22×#67—53no—
27C22×C4×D3—51no—
28#953—56no—
29#953—52no—
30C2×#217—53no—
31C2×#217—53no—
32C2×#217—53no—
33C4×#67—106no—
34C4×#67—106no—
35C2×(C2×D3)⋊C4—53no—
36C2×Dic3⋊C4—53no—
37C2×C4×Dic3—53no—
38C3⋊#95—56no—
39C24⋊C5C4×D311yescharacteristic, complemented
40C24×C4D1511yescharacteristic, complemented
41C2×#120—151no—
42C2×C4×D4—153no—
43#386—153no—
44#385—153no—
45#379—151no—
46C4×C22⋊C4—153no—
47C2×D15—161no—
48C3×C4×C5—161no—
49Dic15—161no—
50C24×C3—53no—
51C24×C3—53no—
52C24×C3C4×D511yescharacteristic, complemented
53C23×D3—51no—
54C22×C3×C4—51no—
55C22×C3×C4—56no—
56C22×C3×C4—56no—
57C22×C3×C4—53no—
58C22×C3×C4—106no—
59C2×#67—56no—
60C2×#67—56no—
61C2×#67—106no—
62C2×#67—106no—
63C22×Dic3—53no—
64C22×Dic3—53no—
65C22×Dic3—51no—
66C2×C4×D3—103no—
67C2×C4×D3—103no—
68#217—56no—
69#217—56no—
70#217—106no—
71#217—106no—
72(C2×D3)⋊C4—106no—
73Dic3⋊C4—106no—
74C4×Dic3—103no—
75C4×Dic3—103no—
76C4×D5—481no—
77C25C2×D1511yescharacteristic
78C22×D4—153no—
79C23×C4—53no—
80C23×C4—53no—
81C23×C4—151no—
82#120—156no—
83#120—152no—
84C4×D4—306no—
85C4×D4—306no—
86C2×C4⋊C4—153no—
87C2×C22⋊C4—153no—
88C2×C22⋊C4—153no—
89C2×C22⋊C4—153no—
90C2×C22⋊C4—153no—
91C2×C42—153no—
92#95—156no—
93C2×C3×C5—161no—
94D15—162no—
95C23×C3—53no—
96C23×C3—51no—
97C23×C3—56no—
98C23×C3—56no—
99C23×C3—53no—
100C23×C3—106no—
101C22×D3—52no—
102C22×D3—103no—
103C22×D3—103no—
104C2×C3×C4—53no—
105C2×C3×C4—53no—
106C2×C3×C4—56no—
107C2×C3×C4—106no—
108#67—1012no—
109#67—1012no—
110C2×Dic3—56no—
111C2×Dic3—103no—
112C2×Dic3—103no—
113C2×Dic3—103no—
114C2×Dic3—103no—
115C2×Dic3—106no—
116C4×D3—203no—
117C4×D3—201no—
118C2×D5—481no—
119C4×C5—161no—
120Dic5—481no—
121C24—53no—
122C24—53no—
123C24—151no—
124C24C4×D1511yescharacteristic, complemented
125C2×D4—156no—
126C2×D4—156no—
127C2×D4—306no—
128C2×D4—306no—
129C22×C4—51no—
130C22×C4—56no—
131C22×C4—56no—
132C22×C4—53no—
133C22×C4—106no—
134C22×C4—153no—
135C22×C4—153no—
136C22×C4—151no—
137C22×C4—303no—
138C22×C4—303no—
139C4⋊C4—306no—
140C22⋊C4—156no—
141C22⋊C4—156no—
142C22⋊C4—306no—
143C22⋊C4—306no—
144C22⋊C4—306no—
145C42—303no—
146C42—303no—
147C3×C5—161noHall
148C22×C3—56no—
149C22×C3—56no—
150C22×C3—51no—
151C22×C3—53no—
152C22×C3—53no—
153C22×C3—106no—
154C2×D3—106no—
155C2×D3—203no—
156C2×D3—201no—
157C3×C4—53no—
158C3×C4(C24⋊C5)⋊C211yescharacteristic, complemented
159Dic3—106no—
160Dic3—203no—
161Dic3—201no—
162C2×C5—161no—
163D5—482no—
164C23—53no—
165C23—51no—
166C23—56no—
167C23—56no—
168C23—53no—
169C23—106no—
170C23—152no—
171C23—303no—
172C23—303no—
173D4—3012no—
174D4—3012no—
175C2×C4—53no—
176C2×C4—53no—
177C2×C4—56no—
178C2×C4—106no—
179C2×C4—156no—
180C2×C4—303no—
181C2×C4—303no—
182C2×C4—303no—
183C2×C4—303no—
184C2×C4—306no—
185C2×C4—603no—
186C2×C4—601no—
187C2×C3—53no—
188C2×C3—53no—
189C2×C3C2×(C24⋊C5)⋊C211yescharacteristic
190D3—202no—
191C5—161noSylow
192C22—56no—
193C22—56no—
194C22—51no—
195C22—53no—
196C22—53no—
197C22—106no—
198C22—306no—
199C22—603no—
200C22—601no—
201C4—53no—
202C4—306no—
203C4—603no—
204C4—601no—
205C4C3⋊((C24⋊C5)⋊C2)11yescharacteristic, direct product factor
206C3C4×(C24⋊C5)⋊C211yescharacteristic, complemented, Sylow
207C2—53no—
208C2—53no—
209C2—602no—
210C2C2×C3⋊((C24⋊C5)⋊C2)11yescharacteristic
subgroupG/H
center, hypercenterC4C3⋊((C24⋊C5)⋊C2)
commutator, hypocenterC3×C24⋊C5C2×C4
FrattiniC2C2×C3⋊((C24⋊C5)⋊C2)
FittingC24×C3×C4D5
socleC25×C3C2×D5
prime radicalC2×C3⋊((C24⋊C5)⋊C2)C2
cosocleC2×C3×C24⋊C5C22
LCSG ▷ C3×C24⋊C5
UCSC1 ◁ C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×C24⋊C5C2semidirect
3. C3⋊#66245C2semidirect
6. C3⋊((C24⋊C5)⋊C2)C4direct (N × H)
9. C4×C24⋊C5D3semidirect
11. C3×C24⋊C5C2×C4semidirect
12. C24×C3×C4D5semidirect
39. C24⋊C5C4×D3semidirect
40. C24×C4D15semidirect
52. C24×C3C4×D5semidirect
124. C24C4×D15semidirect
158. C3×C4(C24⋊C5)⋊C2semidirect
205. C4C3⋊((C24⋊C5)⋊C2)direct (N × H)
206. C3C4×(C24⋊C5)⋊C2semidirect

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
C3⋊#662452
C4×(C24⋊C5)⋊C23
C4×#9535
C4×D1516