Finite Group Databasebeta

← #14289068

Subgroups — #14289068

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#11756493C211yesmaximal, characteristic, complemented
2C3×#65374C211yesmaximal, characteristic, complemented
3#11747043C212yesmaximal, complemented
4C5×#4546C211yesmaximal, characteristic, complemented
5#11745839C212yesmaximal, complemented
6#10599284—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8#91836—22no—
9#91784—22no—
10#91781—22no—
11C4×D60C2212yes—
12C2×C3×#688—22no—
13C3×#4020C2211yescharacteristic
14C2×#6653—22no—
15C5×C4⋊(C3⋊C8)C2212yes—
16C3×C4×#168C2211yescharacteristic
17#90965—22no—
18#71265—51nomaximal, Hall
19#66068—31no—
20#65374D311yescharacteristic, complemented
21#65132—32no—
22C5×#333—31no—
23#64703—32no—
24C2×C3×C5×Q8D412yes—
25C2×D60—22no—
26C2×D60D412yes—
27C2×C4×D15—22no—
28C2×C3×D20—21no—
29C2×C3×D20—22no—
30C3×C5×C4⋊C4—22no—
31C3×C42×C5C2311yescharacteristic
32#6714—24no—
33#6714—22no—
34C4⋊Dic15D412yes—
35C4×Dic15—22no—
36C2×C5×C3⋊C8—22no—
37C3×#688—44no—
38C2×C3×#168—21no—
39#6653—44no—
40#5734—51no—
41C3×#492—51no—
42#5072—52no—
43#4546D511yescharacteristic, complemented
44#4459—52no—
45C5×C4⋊Q8C2×D311yescharacteristic
46#4093—62no—
47C2×#688—22no—
48C2×D40—62no—
49#4041—62no—
50#4038—62no—
51#4020C2×D311yescharacteristic
52C4×D20—32no—
53C5×C4⋊C8—32no—
54#3953—62no—
55C4×#168C2×D311yescharacteristic
56#1624—151noSylow
57C22×D15—22no—
58C22×C3×D5—41no—
59C3×C5×Q8—42no—
60C2×C3×C4×C5—22no—
61C2×C3×C4×C5C2×D411yescharacteristic
62C2×C3×C4×C5C2×D412yes—
63C2×Dic15—22no—
64D60—22no—
65D60—22no—
66D60—82no—
67C4×D15—42no—
68C4×D15—42no—
69C3×D20—42no—
70C3×D20—42no—
71C3×D20—42no—
72C3×#168—22no—
73C5×C3⋊C8—42no—
74C2×C3×SD16—102no—
75C3×C4⋊Q8C2×D511yescharacteristic
76C3×#127—51no—
77#947—102no—
78C2×#213—102no—
79#895—102no—
80#892—102no—
81C4×D12—52no—
82C3×C4×C8—51no—
83#832—102no—
84C4⋊(C3⋊C8)C2×D512yes—
85C2×C5×Q8#6712yes—
86C2×D20—22no—
87C2×D20—21no—
88C2×D20—32no—
89C2×D20—62no—
90C2×C4×D5—62no—
91C2×C5×C8—62no—
92C5×C4⋊C4—22no—
93C42×C5C22×D311yescharacteristic
94#688—44no—
95#685—64no—
96#685—62no—
97C4⋊Dic5—32no—
98C4×Dic5—62no—
99C2×#168—21no—
100D40—124no—
101#555—151no—
102#492—51no—
103#459—152no—
104#333—31no—
105D4⋊C8—152no—
106C22×C3×C5#12011yescharacteristic
107C2×D15—42no—
108C2×D15—42no—
109C2×D15—42no—
110C2×C3×D5—82no—
111C2×C3×D5—81no—
112C3×C4×C5—21no—
113C3×C4×C5—42no—
114C3×C4×C5#13512yes—
115C3×C4×C5AGL(1,ℤ/8)12yes—
116Dic15—42no—
117C2×C3×Q8D2012yes—
118C2×C3×D4—101no—
119C2×C3×D4—102no—
120C2×D12—52no—
121C2×D12—102no—
122C2×C4×D3—102no—
123C3×SD16—204no—
124C2×C3×C8—101no—
125C3×C4⋊C4—22no—
126C3×C42C22×D511yescharacteristic
127#213—204no—
128(C2×D3)⋊C4—104no—
129(C2×D3)⋊C4—102no—
130C4⋊Dic3—52no—
131C4×Dic3—102no—
132C2×C3⋊C8—22no—
133C22×D5—41no—
134C22×D5—62no—
135C5×Q8—42no—
136C2×C4×C5—22no—
137C2×C4×C5D3×D412yes—
138C2×C4×C5C2×#6711yescharacteristic
139C2×Dic5—62no—
140D20—42no—
141D20—42no—
142D20—42no—
143D20—62no—
144D20—62no—
145D20—242no—
146C4×D5—122no—
147C4×D5—122no—
148C5×C8—122no—
149#168—22no—
150C2×SD16—102no—
151C2×D8—302no—
152C4⋊Q8D3×D511yescharacteristic
153#127—51no—
154#124—302no—
155#121—302no—
156C4×D4—152no—
157#117—302no—
158C4⋊C8—32no—
159#102—302no—
160C4×C8—51no—
161C2×C3×C5#44912yes—
162C2×C3×C5#45311yescharacteristic
163D15—82no—
164C3×D5—161no—
165C23×C3—201no—
166C22×D3—102no—
167C3×Q8—42no—
168C3×D4—202no—
169C3×D4—202no—
170C3×D4—202no—
171C2×C3×C4—22no—
172C2×C3×C4C2×D2011yescharacteristic
173C2×C3×C4D4×D512yes—
174C2×Dic3—102no—
175D12—102no—
176D12—102no—
177D12—402no—
178C4×D3—202no—
179C4×D3—202no—
180C3×C8—102no—
181C3⋊C8—42no—
182C22×C5#93711yescharacteristic
183C2×D5—82no—
184C2×D5—81no—
185C2×D5—122no—
186C2×D5—122no—
187C2×D5—122no—
188C4×C5—21no—
189C4×C5—42no—
190C4×C5#91412yes—
191C4×C5#91612yes—
192Dic5—122no—
193C2×Q8#120212yes—
194C2×D4—101no—
195C2×D4—102no—
196C2×D4—152no—
197C2×D4—302no—
198C22×C4—302no—
199SD16—204no—
200D8—604no—
201C2×C8—62no—
202C2×C8—101no—
203C4⋊C4—22no—
204C4⋊C4—152no—
205C22⋊C4—304no—
206C22⋊C4—302no—
207C42—302no—
208C42C2×D3×D511yescharacteristic
209C3×C5#162411yescharacteristic, complemented, Hall
210C22×C3—401no—
211C22×C3—402no—
212C22×C3#402811yescharacteristic
213C2×D3—202no—
214C2×D3—202no—
215C2×D3—202no—
216C3×C4—21no—
217C3×C4—42no—
218C3×C4#406012yes—
219C3×C4#406512yes—
220Dic3—202no—
221C2×C5#507711yescharacteristic
222C2×C5#517212yes—
223D5—161no—
224D5—242no—
225C23—201no—
226C23—302no—
227Q8—42no—
228D4—202no—
229D4—202no—
230D4—202no—
231D4—302no—
232D4—302no—
233D4—1202no—
234C2×C4—22no—
235C2×C4—302no—
236C2×C4—602no—
237C2×C4—602no—
238C2×C4C2×#120211yescharacteristic
239C2×C4#679012yes—
240C8—102no—
241C8—122no—
242C2×C3—801no—
243C2×C3#6503611yescharacteristic
244C2×C3#6510012yes—
245D3—402no—
246C5#7126511yescharacteristic, complemented, Sylow
247C22—401no—
248C22—402no—
249C22—602no—
250C22—602no—
251C22—602no—
252C22#9157211yescharacteristic
253C4—21no—
254C4—42no—
255C4—602no—
256C4#9150612yes—
257C4#9152112yes—
258C3#1059928411yescharacteristic, complemented, Sylow
259C2—801no—
260C2—1202no—
261C2#1174914211yescharacteristic
262C2#1174928812yes—
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1624
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #11756493C2semidirect
2. C3×#65374C2semidirect
3. #11747043C2semidirect
4. C5×#4546C2semidirect
5. #11745839C2semidirect
20. #65374D3semidirect
43. #4546D5semidirect
209. C3×C5#1624semidirect
246. C5#71265semidirect
258. C3#10599284semidirect

Maximal subgroups

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

subgroupindex
#117564932
C3×#653742
#117470432
C5×#45462
#117458392
#105992843
#712655