Finite Group Databasebeta

← #14288863

Subgroups — #14288863

Order 1920.

480 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 92 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
1C5×#5713C211yesmaximal, characteristic, complemented
2#11751174C211yesmaximal, characteristic
3#11747078C212yesmaximal, complemented
4C3×#64764C211yesmaximal, characteristic, complemented
5#11745842C212yesmaximal, complemented
6#10602736—31nomaximal, Hall
7C3×C5×#127C2211yescharacteristic
8C2×#6715—22no—
9#91763C2211yescharacteristic
10C5×#936—22no—
11C5×#935—22no—
12C5×D4×Dic3—22no—
13C4×C5×Dic6C2212yes—
14C2×#6660—22no—
15C4×C3⋊#168C2211yescharacteristic
16C3×C4⋊#168C2212yes—
17#90969—22no—
18#68402—51nomaximal, Hall
19C5×#559—31no—
20#65362—31no—
21#65316—32no—
22#64764D311yescharacteristic, complemented
23Q8⋊#168—32no—
24C2×C3×C5×D4—22no—
25C2×C3×C5×D4D412yes—
26C2×D60—22no—
27C2×D60—21no—
28C22×C5×Dic3—22no—
29C2×C5×Dic6D412yes—
30C3×C42×C5C2311yescharacteristic
31#6715—44no—
32C2×C3⋊#168—21no—
33C5×#217—24no—
34C5×#217—22no—
35C5×C4⋊Dic3D412yes—
36C5×Dic3⋊C4—22no—
37C4×C5×Dic3—22no—
38C2×C3×#168—22no—
39#6660—44no—
40#5713D511yescharacteristic, complemented
41#5073—51no—
42#4848—52no—
43C3×#331—51no—
44#4484—52no—
45C5×#127C2×D311yescharacteristic
46C5×#124—62no—
47C5×#123—62no—
48C4×C5×Q8—32no—
49C4×C5×D4—62no—
50C2×#688—62no—
51C2×#686—62no—
52#4020—31no—
53#3941—62no—
54C4⋊#168C2×D312yes—
55C4×#168—31no—
56#1620—151noSylow
57C23×C3×C5—22no—
58C22×D15—41no—
59C3×C5×D4—42no—
60C3×C5×D4—42no—
61C3×C5×D4—42no—
62C2×C3×C4×C5C2×D411yescharacteristic
63C2×C3×C4×C5C2×D412yes—
64D60—42no—
65D60—42no—
66D60—42no—
67C2×C5×Dic3—22no—
68C2×C5×Dic3—22no—
69C2×C5×Dic3—82no—
70C5×Dic6—22no—
71C5×Dic6—22no—
72C3⋊#168—22no—
73C3×#168—42no—
74C3×#127C2×D511yescharacteristic
75#936—22no—
76#935—22no—
77D4×Dic3—22no—
78C2×#213—102no—
79C2×#204—102no—
80#874—51no—
81C4×Dic6C2×D512yes—
82C3×C4⋊C8—52no—
83#821—102no—
84C4×C3⋊C8—51no—
85C2×C5×Q8—32no—
86C2×C5×D4—22no—
87C2×C5×D4D1212yes—
88C22×C4×C5—62no—
89C2×D20—61no—
90C2×D20—62no—
91C5×C4⋊C4—32no—
92C5×C4⋊C4—62no—
93C5×C22⋊C4—64no—
94C5×C22⋊C4—62no—
95C42×C5—62no—
96C42×C5C22×D311yescharacteristic
97#688—124no—
98#686—124no—
99C2×#168—22no—
100C2×#168—61no—
101#559—31no—
102#493—151no—
103#460—152no—
104#331—51no—
105Q8⋊C8—152no—
106C22×C3×C5—44no—
107C22×C3×C5—42no—
108C22×C3×C5#12011yescharacteristic
109C2×D15—82no—
110C2×D15—81no—
111C3×C4×C5—21no—
112C3×C4×C5#13512yes—
113C3×C4×C5AGL(1,ℤ/8)12yes—
114C5×Dic3—42no—
115C5×Dic3—42no—
116C2×C3×D4—22no—
117C2×C3×D4C22⋊D512yes—
118C22×Dic3—22no—
119C2×D12—102no—
120C2×D12—101no—
121C2×Dic6C22⋊D512yes—
122C2×C3×C8—102no—
123C3×C42C22×D511yescharacteristic
124#217—24no—
125#217—22no—
126#213—204no—
127C4⋊Dic3C22⋊D512yes—
128Dic3⋊C4—22no—
129C4×Dic3—22no—
130C2×C3⋊C8—101no—
131#204—204no—
132C23×C5—22no—
133C22×D5—121no—
134C5×Q8—62no—
135C5×Q8—62no—
136C5×D4—42no—
137C5×D4—42no—
138C5×D4—42no—
139C2×C4×C5—62no—
140C2×C4×C5—62no—
141C2×C4×C5—242no—
142C2×C4×C5C2×D1211yescharacteristic
143C2×C4×C5D3×D412yes—
144D20—122no—
145D20—122no—
146D20—122no—
147#168—42no—
148#168—62no—
149C2×SD16—302no—
150C2×D8—302no—
151#127—151no—
152#127D3×D511yescharacteristic
153#124—62no—
154#123—62no—
155C4×Q8—32no—
156C4×D4—62no—
157C4⋊C8—52no—
158#102—302no—
159C4×C8—151no—
160C2×C3×C5—82no—
161C2×C3×C5#44912yes—
162C2×C3×C5#45311yescharacteristic
163D15—161no—
164C23×C3—22no—
165C22×D3—201no—
166C3×D4—42no—
167C3×D4—42no—
168C3×D4—42no—
169C2×C3×C4C2×C22⋊D511yescharacteristic
170C2×C3×C4C2×C22⋊D512yes—
171C2×Dic3—22no—
172C2×Dic3—22no—
173C2×Dic3—82no—
174D12—202no—
175D12—202no—
176D12—202no—
177Dic6—22no—
178Dic6—22no—
179C3×C8—202no—
180C3⋊C8—102no—
181C22×C5—42no—
182C22×C5—44no—
183C22×C5#88211yescharacteristic
184C2×D5—241no—
185C2×D5—242no—
186C4×C5—21no—
187C4×C5—122no—
188C4×C5—122no—
189C4×C5#91112yes—
190C4×C5#91612yes—
191C2×Q8—32no—
192C2×D4—22no—
193C2×D4—301no—
194C2×D4—302no—
195C2×D4#120312yes—
196C22×C4—62no—
197SD16—604no—
198D8—604no—
199C2×C8—102no—
200C2×C8—301no—
201C4⋊C4—32no—
202C4⋊C4—62no—
203C22⋊C4—64no—
204C22⋊C4—62no—
205C42—62no—
206C42C2×D3×D511yescharacteristic
207C3×C5#162011yescharacteristic, complemented, Hall
208C22×C3—44no—
209C22×C3—42no—
210C22×C3#409911yescharacteristic
211C2×D3—402no—
212C2×D3—401no—
213C3×C4—21no—
214C3×C4#409512yes—
215C3×C4#409612yes—
216Dic3—42no—
217Dic3—42no—
218C2×C5—82no—
219C2×C5#474711yescharacteristic
220C2×C5#478112yes—
221D5—481no—
222C23—22no—
223C23—601no—
224Q8—62no—
225Q8—62no—
226D4—42no—
227D4—42no—
228D4—42no—
229D4—602no—
230D4—602no—
231D4—602no—
232C2×C4—62no—
233C2×C4—62no—
234C2×C4—242no—
235C2×C4C2×#120311yescharacteristic
236C2×C4D3×C22⋊D512yes—
237C8—202no—
238C8—302no—
239C2×C3—82no—
240C2×C3#6552712yes—
241C2×C3#6553011yescharacteristic
242D3—801no—
243C5#6840211yescharacteristic, complemented, Sylow
244C22—42no—
245C22—44no—
246C22—1201no—
247C22—1202no—
248C22#9157011yescharacteristic
249C4—21no—
250C4—122no—
251C4—122no—
252C4#9148012yes—
253C4#9149512yes—
254C3#1060273611yescharacteristic, complemented, Sylow
255C2—82no—
256C2—2401no—
257C2#1174903612yes—
258C2#1174914111yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5#120
prime radical#11751174C2
hypercenter#127D3×D5
hypocenterC3×C5#1620
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
1. C5×#5713C2semidirect
3. #11747078C2semidirect
4. C3×#64764C2semidirect
5. #11745842C2semidirect
22. #64764D3semidirect
40. #5713D5semidirect
207. C3×C5#1620semidirect
243. C5#68402semidirect
254. C3#10602736semidirect

Maximal subgroups

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

subgroupindex
C5×#57132
#117511742
#117470782
C3×#647642
#117458422
#106027363
#684025