Finite Group Databasebeta

← #14514620

Subgroups — #14514620

Order 1920.

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

normal subgroups only

This group has 694 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
1C4×C5×C22⋊A4C211yesmaximal, characteristic
2#11756927C212yesmaximal
3#10615762—31nomaximal, Hall
4C2×C5×C22⋊A4C2211yescharacteristic
5#91948—43nomaximal
6#87502—51nomaximal, Hall
7C24×C4×C5D311yescharacteristic
8C2×#4070—33no—
9#65536—32no—
10#65501—33no—
11#65499—36no—
12C5×C22⋊A4Q811yescharacteristic, complemented
13C4×C5×A4—43no—
14C4×C5×A4—81no—
15A4⋊Dic5—46no—
16C4×C22⋊A4D511yescharacteristic
17#5936—52no—
18C25×C5C2×D311yescharacteristic
19C23×C4×C5—33no—
20C23×C4×C5—33no—
21C23×C4×C5—61no—
22C23×C4×C5—61no—
23C22×Dic10—31no—
24C2×C22⋊Dic5—36no—
25C2×C22⋊Dic5—36no—
26C2×C4⋊Dic5—33no—
27#4070—63no—
28#4070—63no—
29#4070—63no—
30#4070—63no—
31C2×#683—36no—
32#3963—36no—
33#2848—151noSylow
34C2×C5×A4—43no—
35C2×C5×A4—81no—
36Dic30—161no—
37C2×C22⋊A4C2×D511yescharacteristic
38A4⋊Q8—203no—
39C24×C5—33no—
40C24×C5—33no—
41C24×C5—61no—
42C24×C5—61no—
43C24×C5Dic611yescharacteristic, complemented
44C22×C4×C5—21no—
45C22×C4×C5—31no—
46C22×C4×C5—33no—
47C22×C4×C5—33no—
48C22×C4×C5—33no—
49C22×C4×C5—33no—
50C22×C4×C5—66no—
51C22×C4×C5—63no—
52C22×C4×C5—63no—
53C22×C4×C5—61no—
54C22×C4×C5—63no—
55C22×C4×C5S413yes—
56C22×Dic5—32no—
57C22×Dic5—36no—
58C2×Dic10—63no—
59C2×Dic10—63no—
60C22⋊Dic5—66no—
61C22⋊Dic5—66no—
62C22⋊Dic5—66no—
63C22⋊Dic5—66no—
64C4⋊Dic5—63no—
65C4⋊Dic5—63no—
66#683—66no—
67#683—66no—
68C24×C4D1511yescharacteristic
69C2×C22⋊Q8—153no—
70#385—156no—
71#380—153no—
72#379—152no—
73C5×A4—43no—
74C5×A4—81no—
75C3×C4×C5—161no—
76Dic15—162no—
77C22⋊A4Dic1011yescharacteristic, complemented
78C4×A4—43no—
79C4×A4—81no—
80SL(2,ℤ/4)—206no—
81C23×C5—21no—
82C23×C5—31no—
83C23×C5—33no—
84C23×C5—33no—
85C23×C5—33no—
86C23×C5—33no—
87C23×C5—33no—
88C23×C5—61no—
89C23×C5—61no—
90C23×C5—63no—
91C23×C5—66no—
92C23×C5—63no—
93C23×C5—63no—
94C23×C5C2×S413yes—
95C2×C4×C5—33no—
96C2×C4×C5—33no—
97C2×C4×C5—33no—
98C2×C4×C5—33no—
99C2×C4×C5—63no—
100C2×C4×C5—66no—
101C2×C4×C5—63no—
102C2×C4×C5—61no—
103C2×C4×C5—61no—
104C2×Dic5—66no—
105C2×Dic5—66no—
106C2×Dic5—612no—
107Dic10—123no—
108Dic10—121no—
109C25C2×D1511yescharacteristic
110C22×Q8—151no—
111C23×C4—33no—
112C23×C4—33no—
113C23×C4—61no—
114C23×C4—61no—
115C22⋊Q8—303no—
116C22⋊Q8—303no—
117C22⋊Q8—303no—
118C22⋊Q8—303no—
119C2×C4⋊C4—153no—
120C2×C4⋊C4—156no—
121C2×C22⋊C4—156no—
122C2×C22⋊C4—156no—
123#95—156no—
124C2×C3×C5—161no—
125C2×A4—43no—
126C2×A4—81no—
127Dic6—801no—
128C22×C5—21no—
129C22×C5—33no—
130C22×C5—33no—
131C22×C5—31no—
132C22×C5—33no—
133C22×C5—33no—
134C22×C5—33no—
135C22×C5—63no—
136C22×C5—66no—
137C22×C5—63no—
138C22×C5—63no—
139C22×C5—61no—
140C22×C5—61no—
141C22×C5A4⋊Q813yescomplemented
142C4×C5—33no—
143C4×C5—61no—
144C4×C5#102011yescharacteristic
145Dic5—126no—
146Dic5—122no—
147C24—33no—
148C24—33no—
149C24—61no—
150C24—61no—
151C24Dic3011yescharacteristic, complemented
152C2×Q8—303no—
153C2×Q8—303no—
154C22×C4—21no—
155C22×C4—31no—
156C22×C4—33no—
157C22×C4—33no—
158C22×C4—33no—
159C22×C4—33no—
160C22×C4—66no—
161C22×C4—63no—
162C22×C4—63no—
163C22×C4—61no—
164C22×C4—63no—
165C22×C4—156no—
166C22×C4—152no—
167C22×C4C5⋊S413yes—
168C4⋊C4—306no—
169C4⋊C4—306no—
170C4⋊C4—303no—
171C4⋊C4—303no—
172C22⋊C4—306no—
173C22⋊C4—306no—
174C22⋊C4—306no—
175C22⋊C4—306no—
176C3×C5—161noHall
177A4—43no—
178A4—81no—
179C3×C4—161no—
180Dic3—802no—
181C2×C5—33no—
182C2×C5—33no—
183C2×C5—61no—
184C2×C5—61no—
185C2×C5C2×#102011yescharacteristic
186C23—21no—
187C23—31no—
188C23—33no—
189C23—33no—
190C23—33no—
191C23—33no—
192C23—33no—
193C23—61no—
194C23—61no—
195C23—63no—
196C23—66no—
197C23—63no—
198C23—63no—
199C23C2×C5⋊S413yes—
200Q8—603no—
201Q8—601no—
202C2×C4—33no—
203C2×C4—33no—
204C2×C4—33no—
205C2×C4—33no—
206C2×C4—63no—
207C2×C4—66no—
208C2×C4—63no—
209C2×C4—61no—
210C2×C4—61no—
211C2×C4—306no—
212C2×C4—306no—
213C2×C4—3012no—
214C2×C3—161no—
215C5#8750211yescharacteristic, complemented, Sylow
216C22—21no—
217C22—33no—
218C22—33no—
219C22—31no—
220C22—33no—
221C22—33no—
222C22—33no—
223C22—63no—
224C22—66no—
225C22—63no—
226C22—63no—
227C22—61no—
228C22—61no—
229C22#9194813yescomplemented
230C4—33no—
231C4—61no—
232C4—606no—
233C4—602no—
234C4C5⋊#102011yescharacteristic
235C3—161noSylow
236C2—33no—
237C2—33no—
238C2—61no—
239C2—61no—
240C2C2×C5⋊#102011yescharacteristic
subgroupG/H
center, FrattiniC2C2×C5⋊#1020
commutator, prime radical, cosocleC2×C5×C22⋊A4C22
FittingC24×C4×C5D3
socleC25×C5C2×D3
hypercenterC4C5⋊#1020
hypocenterC5×C22⋊A4Q8
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
12. C5×C22⋊A4Q8semidirect
43. C24×C5Dic6semidirect
77. C22⋊A4Dic10semidirect
141. C22×C5A4⋊Q8semidirect
151. C24Dic30semidirect
215. C5#87502semidirect
229. C22#91948semidirect

Maximal subgroups

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

subgroupindex
C4×C5×C22⋊A42
#117569272
#106157623
#919484
#875025