Finite Group Databasebeta

← #14288861

Subgroups — #14288861

Order 1920.

480 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 88 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
1#11756472C211yesmaximal, characteristic, complemented
2C5×#5073C211yesmaximal, characteristic
3#11747086C212yesmaximal, complemented
4C3×#64764C211yesmaximal, characteristic, complemented
5#11745844C212yesmaximal, complemented
6#10602077—31nomaximal, Hall
7C3×C5×#127C2211yescharacteristic
8#91825—22no—
9#91824—22no—
10D4×Dic15—22no—
11C4×Dic30C2212yes—
12C2×C5×#213—22no—
13C5×#874C2211yescharacteristic
14C2×#6659—22no—
15C4×C5×C3⋊C8C2211yescharacteristic
16C3×C4⋊#168C2212yes—
17#90967—22no—
18#68402—51nomaximal, Hall
19#66047—31no—
20C5×#493—31no—
21#65364—32no—
22#64764D311yescharacteristic, complemented
23#64676—32no—
24C2×C3×C5×D4—22no—
25C2×C3×C5×D4D412yes—
26C22×Dic15—22no—
27C2×Dic30D412yes—
28C2×C5×D12—21no—
29C2×C5×D12—22no—
30C3×C42×C5C2311yescharacteristic
31#6719—24no—
32#6719—22no—
33C4⋊Dic15D412yes—
34#6712—22no—
35C4×Dic15—22no—
36C5×#213—44no—
37C2×C5×C3⋊C8—21no—
38C2×C3×#168—22no—
39#6659—44no—
40#5713—51no—
41#5073D511yescharacteristic
42#4848—52no—
43C3×#331—51no—
44#4484—52no—
45C2×C5×D8—62no—
46C5×#127—31no—
47C5×#127C2×D311yescharacteristic
48#4082—62no—
49#4081—62no—
50D4×Dic5—62no—
51C2×#687—62no—
52C4×Dic10—32no—
53C4×C5×C8—31no—
54#3964—62no—
55C4⋊#168C2×D312yes—
56#1620—151noSylow
57C23×C3×C5—22no—
58C22×C5×D3—41no—
59C3×C5×D4—42no—
60C3×C5×D4—42no—
61C3×C5×D4—42no—
62C2×C3×C4×C5C2×D411yescharacteristic
63C2×C3×C4×C5C2×D412yes—
64C2×Dic15—22no—
65C2×Dic15—22no—
66C2×Dic15—82no—
67Dic30—22no—
68Dic30—22no—
69C5×D12—42no—
70C5×D12—42no—
71C5×D12—42no—
72C3×#168—42no—
73C5×C3⋊C8—22no—
74C3×#127C2×D511yescharacteristic
75#936—102no—
76#935—102no—
77D4×Dic3—102no—
78C2×#213—22no—
79C2×#204—102no—
80#874C2×D511yescharacteristic
81C4×Dic6—52no—
82C3×C4⋊C8—52no—
83#821—102no—
84C4×C3⋊C8C2×D511yescharacteristic
85C2×C5×D4—22no—
86C2×C5×D4—61no—
87C2×C5×D4—62no—
88C2×C5×D4D1212yes—
89C22×Dic5—62no—
90C2×Dic10—32no—
91C5×D8—124no—
92C2×C5×C8—61no—
93C42×C5C22×D311yescharacteristic
94C22⋊Dic5—64no—
95C22⋊Dic5—62no—
96#687—124no—
97C4⋊Dic5—32no—
98#683—62no—
99C4×Dic5—62no—
100C2×#168—22no—
101#559—151no—
102#493—31no—
103#460—152no—
104#331—51no—
105Q8⋊C8—152no—
106C22×C3×C5—44no—
107C22×C3×C5—42no—
108C22×C3×C5#12011yescharacteristic
109C2×C5×D3—82no—
110C2×C5×D3—81no—
111C3×C4×C5—21no—
112C3×C4×C5#13512yes—
113C3×C4×C5AGL(1,ℤ/8)12yes—
114Dic15—42no—
115Dic15—42no—
116C2×C3×D4—22no—
117C2×C3×D4C22⋊D512yes—
118C22×Dic3—102no—
119C2×D12—22no—
120C2×D12—21no—
121C2×Dic6—52no—
122C2×C3×C8—102no—
123C3×C42C22×D511yescharacteristic
124#217—104no—
125#217—102no—
126#213—44no—
127C4⋊Dic3—52no—
128Dic3⋊C4—102no—
129C4×Dic3—102no—
130C2×C3⋊C8—21no—
131#204—204no—
132C23×C5—22no—
133C23×C5—121no—
134C5×D4—42no—
135C5×D4—42no—
136C5×D4—42no—
137C5×D4—122no—
138C5×D4—122no—
139C5×D4—122no—
140C2×C4×C5C2×D1211yescharacteristic
141C2×C4×C5D3×D412yes—
142C2×Dic5—62no—
143C2×Dic5—62no—
144C2×Dic5—242no—
145Dic10—62no—
146Dic10—62no—
147C5×C8—62no—
148#168—42no—
149C2×SD16—302no—
150C2×D8—62no—
151#127—31no—
152#127D3×D511yescharacteristic
153#124—302no—
154#123—302no—
155C4×Q8—152no—
156C4×D4—302no—
157C4⋊C8—52no—
158#102—302no—
159C4×C8—31no—
160C2×C3×C5—82no—
161C2×C3×C5#44912yes—
162C2×C3×C5#45311yescharacteristic
163C5×D3—161no—
164C23×C3—22no—
165C22×D3—41no—
166C3×D4—42no—
167C3×D4—42no—
168C3×D4—42no—
169C2×C3×C4D4×D512yes—
170C2×C3×C4C2×C22⋊D511yescharacteristic
171C2×Dic3—102no—
172C2×Dic3—102no—
173C2×Dic3—402no—
174D12—42no—
175D12—42no—
176D12—42no—
177Dic6—102no—
178Dic6—102no—
179C3×C8—202no—
180C3⋊C8—22no—
181C22×C5—42no—
182C22×C5—44no—
183C22×C5—241no—
184C22×C5—242no—
185C22×C5#88211yescharacteristic
186C4×C5—21no—
187C4×C5#91112yes—
188C4×C5#91612yes—
189Dic5—122no—
190Dic5—122no—
191C2×Q8—152no—
192C2×D4—22no—
193C2×D4—61no—
194C2×D4—62no—
195C2×D4#120312yes—
196C22×C4—302no—
197SD16—604no—
198D8—124no—
199C2×C8—61no—
200C2×C8—102no—
201C4⋊C4—152no—
202C4⋊C4—302no—
203C22⋊C4—304no—
204C22⋊C4—302no—
205C42—302no—
206C42C2×D3×D511yescharacteristic
207C3×C5#162011yescharacteristic, complemented, Hall
208C22×C3—42no—
209C22×C3—44no—
210C22×C3#408311yescharacteristic
211C2×D3—81no—
212C2×D3—82no—
213C3×C4—21no—
214C3×C4#405712yes—
215C3×C4#405812yes—
216Dic3—202no—
217Dic3—202no—
218C2×C5—82no—
219C2×C5—481no—
220C2×C5#474711yescharacteristic
221C2×C5#478112yes—
222C23—22no—
223C23—121no—
224Q8—302no—
225Q8—302no—
226D4—42no—
227D4—42no—
228D4—42no—
229D4—122no—
230D4—122no—
231D4—122no—
232C2×C4—302no—
233C2×C4—302no—
234C2×C4—1202no—
235C2×C4C2×#120311yescharacteristic
236C2×C4#679012yes—
237C8—62no—
238C8—202no—
239C2×C3—82no—
240C2×C3#6536611yescharacteristic
241C2×C3#6544712yes—
242D3—161no—
243C5#6840211yescharacteristic, complemented, Sylow
244C22—42no—
245C22—44no—
246C22—241no—
247C22—242no—
248C22#9157311yescharacteristic
249C4—21no—
250C4—602no—
251C4—602no—
252C4#9148212yes—
253C4#9149912yes—
254C3#1060207711yescharacteristic, complemented, Sylow
255C2—82no—
256C2—481no—
257C2#1174904312yes—
258C2#1174914311yescharacteristic
subgroupG/H
centerC22#91573
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5#120
prime radicalC5×#5073C2
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. #11756472C2semidirect
3. #11747086C2semidirect
4. C3×#64764C2semidirect
5. #11745844C2semidirect
22. #64764D3semidirect
207. C3×C5#1620semidirect
243. C5#68402semidirect
254. C3#10602077semidirect

Maximal subgroups

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

subgroupindex
#117564722
C5×#50732
#117470862
C3×#647642
#117458442
#106020773
#684025