Finite Group Databasebeta

← C4⋊(C5⋊#1020) #14514622

Subgroups — C4⋊(C5⋊#1020) #14514622

Order 1920.

870 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 870 conjugacy classes of subgroups — too many to draw. Only its 39 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×C5⋊#1020C212yesmaximal, complemented
2C4×C5×C22⋊A4C211yesmaximal, characteristic, complemented
3#10615763—31nomaximal, Hall
4C2×C5×C22⋊A4C2211yescharacteristic
5C5⋊#1020—22no—
6C4⋊(C5⋊S4)—43nomaximal
7C4⋊#1020—51nomaximal, Hall
8C24×C4×C5D311yescharacteristic, complemented
9C2×#4099—32no—
10C2×#4076—33no—
11#65502—36no—
12#65501—33no—
13C5×C22⋊A4D411yescharacteristic, complemented
14C2×C5⋊S4—46no—
15C4×C5×A4—43no—
16C4×C5×A4—81no—
17C2×#1020—52no—
18C4×C22⋊A4D511yescharacteristic, complemented
19C25×C5C2×D311yescharacteristic
20C23×C4×C5—33no—
21C23×C4×C5—33no—
22C23×C4×C5—61no—
23C23×C4×C5—61no—
24C22×C22⋊D5—36no—
25C22×D20—31no—
26#4099—66no—
27#4099—62no—
28C2×C22⋊Dic5—36no—
29#4076—63no—
30#4076—63no—
31#4076—63no—
32#4076—63no—
33C2×#685—36no—
34C2×C4⋊Dic5—33no—
35#3963—36no—
36#2847—151noSylow
37C2×C5×A4—43no—
38C2×C5×A4—81no—
39C5⋊S4—86no—
40D60—161no—
41C2×C22⋊A4C2×D511yescharacteristic
42#1020—102no—
43C4⋊S4—203no—
44C24×C5—33no—
45C24×C5—33no—
46C24×C5—61no—
47C24×C5—61no—
48C24×C5D1211yescharacteristic, complemented
49C23×D5—32no—
50C22×C4×C5—21no—
51C22×C4×C5—31no—
52C22×C4×C5—33no—
53C22×C4×C5—33no—
54C22×C4×C5—33no—
55C22×C4×C5—33no—
56C22×C4×C5—66no—
57C22×C4×C5—63no—
58C22×C4×C5—63no—
59C22×C4×C5—61no—
60C22×C4×C5—63no—
61C22×C4×C5S413yescomplemented
62C2×C22⋊D5—66no—
63C2×C22⋊D5—66no—
64C2×C22⋊D5—66no—
65C2×C22⋊D5—66no—
66C2×C22⋊D5—66no—
67C2×C22⋊D5—66no—
68C22×Dic5—36no—
69C2×D20—63no—
70C2×D20—63no—
71C22⋊Dic5—66no—
72C22⋊Dic5—66no—
73#685—66no—
74#685—66no—
75C4⋊Dic5—63no—
76C4⋊Dic5—63no—
77C24×C4D1511yescharacteristic, complemented
78C2×#121—153no—
79C2×#120—152no—
80#386—156no—
81#380—153no—
82C2×D15—162no—
83C5×A4—43no—
84C5×A4—81no—
85C3×C4×C5—161no—
86C22⋊A4D2011yescharacteristic, complemented
87C2×S4—206no—
88C4×A4—43no—
89C4×A4—81no—
90C23×C5—21no—
91C23×C5—31no—
92C23×C5—33no—
93C23×C5—33no—
94C23×C5—33no—
95C23×C5—33no—
96C23×C5—33no—
97C23×C5—61no—
98C23×C5—61no—
99C23×C5—63no—
100C23×C5—66no—
101C23×C5—63no—
102C23×C5—63no—
103C23×C5C2×S413yes—
104C22×D5—66no—
105C22×D5—62no—
106C22×D5—66no—
107C2×C4×C5—33no—
108C2×C4×C5—33no—
109C2×C4×C5—33no—
110C2×C4×C5—33no—
111C2×C4×C5—63no—
112C2×C4×C5—66no—
113C2×C4×C5—63no—
114C2×C4×C5—61no—
115C2×C4×C5—61no—
116C22⋊D5—126no—
117C22⋊D5—126no—
118C22⋊D5—126no—
119C22⋊D5—126no—
120C2×Dic5—66no—
121C2×Dic5—66no—
122C2×Dic5—66no—
123D20—123no—
124D20—121no—
125C25C2×D1511yescharacteristic
126C22×D4—151no—
127C22×D4—156no—
128C23×C4—33no—
129C23×C4—33no—
130C23×C4—61no—
131C23×C4—61no—
132#121—303no—
133#121—303no—
134#121—303no—
135#121—303no—
136#120—306no—
137#120—302no—
138C2×C4⋊C4—153no—
139C2×C22⋊C4—156no—
140C2×C22⋊C4—156no—
141#95—156no—
142C2×C3×C5—161no—
143D15—322no—
144C2×A4—43no—
145C2×A4—81no—
146S4—406no—
147D12—801no—
148C22×C5—21no—
149C22×C5—33no—
150C22×C5—31no—
151C22×C5—33no—
152C22×C5—33no—
153C22×C5—33no—
154C22×C5—33no—
155C22×C5—63no—
156C22×C5—66no—
157C22×C5—63no—
158C22×C5—63no—
159C22×C5—61no—
160C22×C5—61no—
161C22×C5C4⋊S413yescomplemented
162C2×D5—126no—
163C2×D5—126no—
164C2×D5—122no—
165C4×C5—33no—
166C4×C5—61no—
167C4×C5#102011yescharacteristic, complemented
168Dic5—126no—
169C24—33no—
170C24—33no—
171C24—61no—
172C24—61no—
173C24—152no—
174C24D6011yescharacteristic, complemented
175C2×D4—303no—
176C2×D4—303no—
177C2×D4—306no—
178C2×D4—306no—
179C2×D4—306no—
180C2×D4—306no—
181C2×D4—306no—
182C2×D4—306no—
183C22×C4—21no—
184C22×C4—31no—
185C22×C4—33no—
186C22×C4—33no—
187C22×C4—33no—
188C22×C4—33no—
189C22×C4—66no—
190C22×C4—63no—
191C22×C4—63no—
192C22×C4—61no—
193C22×C4—63no—
194C22×C4—156no—
195C22×C4C5⋊S413yescomplemented
196C4⋊C4—303no—
197C4⋊C4—303no—
198C22⋊C4—306no—
199C22⋊C4—306no—
200C22⋊C4—306no—
201C22⋊C4—306no—
202C3×C5—161noHall
203C2×D3—802no—
204A4—43no—
205A4—81no—
206C3×C4—161no—
207C2×C5—33no—
208C2×C5—33no—
209C2×C5—61no—
210C2×C5—61no—
211C2×C5C2×#102011yescharacteristic
212D5—242no—
213C23—21no—
214C23—31no—
215C23—33no—
216C23—33no—
217C23—33no—
218C23—33no—
219C23—33no—
220C23—61no—
221C23—61no—
222C23—63no—
223C23—66no—
224C23—63no—
225C23—63no—
226C23—306no—
227C23—302no—
228C23—306no—
229C23C2×C5⋊S413yes—
230D4—603no—
231D4—606no—
232D4—606no—
233D4—606no—
234D4—606no—
235D4—601no—
236C2×C4—33no—
237C2×C4—33no—
238C2×C4—33no—
239C2×C4—33no—
240C2×C4—63no—
241C2×C4—66no—
242C2×C4—63no—
243C2×C4—61no—
244C2×C4—61no—
245C2×C4—306no—
246C2×C4—306no—
247C2×C4—306no—
248C2×C3—161no—
249D3—1602no—
250C5C4⋊#102011yescharacteristic, complemented, Sylow
251C22—21no—
252C22—33no—
253C22—31no—
254C22—33no—
255C22—33no—
256C22—33no—
257C22—33no—
258C22—63no—
259C22—66no—
260C22—63no—
261C22—63no—
262C22—61no—
263C22—61no—
264C22—606no—
265C22—606no—
266C22—602no—
267C22C4⋊(C5⋊S4)13yescomplemented
268C4—33no—
269C4—61no—
270C4—606no—
271C4C5⋊#102011yescharacteristic, complemented
272C3—161noSylow
273C2—33no—
274C2—33no—
275C2—61no—
276C2—61no—
277C2—1202no—
278C2C2×C5⋊#102011yescharacteristic
subgroupG/H
center, FrattiniC2C2×C5⋊#1020
commutator, cosocleC2×C5×C22⋊A4C22
FittingC24×C4×C5D3
socleC25×C5C2×D3
hypercenterC4C5⋊#1020
hypocenterC5×C22⋊A4D4
LCSG ▷ C2×C5×C22⋊A4 ▷ C5×C22⋊A4
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
1. C2×C5⋊#1020C2semidirect
2. C4×C5×C22⋊A4C2semidirect
8. C24×C4×C5D3semidirect
13. C5×C22⋊A4D4semidirect
18. C4×C22⋊A4D5semidirect
48. C24×C5D12semidirect
61. C22×C4×C5S4semidirect
77. C24×C4D15semidirect
86. C22⋊A4D20semidirect
161. C22×C5C4⋊S4semidirect
167. C4×C5#1020semidirect
174. C24D60semidirect
195. C22×C4C5⋊S4semidirect
250. C5C4⋊#1020semidirect
267. C22C4⋊(C5⋊S4)semidirect
271. C4C5⋊#1020semidirect

Maximal subgroups

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

subgroupindex
C2×C5⋊#10202
C4×C5×C22⋊A42
#106157633
C4⋊(C5⋊S4)4
C4⋊#10205