Finite Group Databasebeta

← #14288853

Subgroups — #14288853

Order 1920.

480 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 91 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
2#11751174C211yesmaximal, characteristic
3#11750949C212yesmaximal, complemented
4C3×C5×#331C211yesmaximal, characteristic, complemented
5#11746305C212yesmaximal, complemented
6#10599195—31nomaximal, Hall
7C3×C5×#127C2211yescharacteristic
8#91825—22no—
9#91824—22no—
10D4×Dic15—22no—
11C2×#6715—22no—
12C2×#6706—22no—
13#91763C2211yescharacteristic
14C4×Dic30C2212yes—
15C3×C5×C4⋊C8C2212yes—
16#91105—22no—
17C4×C3⋊#168C2211yescharacteristic
18#68402—51nomaximal, Hall
19#66047—31no—
20#65362—31no—
21#65137—32no—
22C5×#331D311yescharacteristic, complemented
23#64704—32no—
24C2×C3×C5×D4—22no—
25C2×C3×C5×D4D412yes—
26C22×Dic15—22no—
27C2×D60—22no—
28C2×D60—21no—
29C2×Dic30D412yes—
30C2×C3×C5×C8—22no—
31C3×C42×C5C2311yescharacteristic
32#6719—24no—
33#6719—22no—
34#6715—44no—
35C4⋊Dic15D412yes—
36#6712—22no—
37C4×Dic15—22no—
38C2×C3⋊#168—21no—
39#6706—44no—
40#5713—51no—
41#5073—51no—
42#4848—52no—
43C3×#331D511yescharacteristic, complemented
44#4484—52no—
45C5×#127C2×D311yescharacteristic
46#4082—62no—
47#4081—62no—
48D4×Dic5—62no—
49C2×#686—62no—
50C2×#677—62no—
51#4020—31no—
52C4×Dic10—32no—
53C5×C4⋊C8C2×D312yes—
54#3953—62no—
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—
64C2×Dic15—22no—
65C2×Dic15—22no—
66C2×Dic15—82no—
67D60—42no—
68D60—42no—
69D60—42no—
70Dic30—22no—
71Dic30—22no—
72C3×C5×C8—42no—
73C3⋊#168—22no—
74C3×#127C2×D511yescharacteristic
75#936—102no—
76#935—102no—
77D4×Dic3—102no—
78C2×#213—102no—
79C2×#204—102no—
80#874—51no—
81C4×Dic6—52no—
82C3×C4⋊C8C2×D512yes—
83#821—102no—
84C4×C3⋊C8—51no—
85C2×C5×D4—22no—
86C2×C5×D4D1212yes—
87C22×Dic5—62no—
88C2×D20—61no—
89C2×D20—62no—
90C2×Dic10—32no—
91C2×C5×C8—22no—
92C42×C5C22×D311yescharacteristic
93C22⋊Dic5—64no—
94C22⋊Dic5—62no—
95#686—124no—
96C4⋊Dic5—32no—
97#683—62no—
98C4×Dic5—62no—
99C2×#168—61no—
100#677—124no—
101#559—151no—
102#493—151no—
103#460—152no—
104#331D1511yescharacteristic, complemented
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—
114Dic15—42no—
115Dic15—42no—
116C2×C3×D4—22no—
117C2×C3×D4D2012yes—
118C22×Dic3—102no—
119C2×D12—101no—
120C2×D12—102no—
121C2×Dic6—52no—
122C2×C3×C8—22no—
123C3×C42C22×D511yescharacteristic
124#217—104no—
125#217—102no—
126#213—204no—
127C4⋊Dic3—52no—
128Dic3⋊C4—102no—
129C4×Dic3—102no—
130C2×C3⋊C8—101no—
131#204—204no—
132C23×C5—22no—
133C22×D5—121no—
134C5×D4—42no—
135C5×D4—42no—
136C5×D4—42no—
137C2×C4×C5C2×D1211yescharacteristic
138C2×C4×C5D3×D412yes—
139C2×Dic5—62no—
140C2×Dic5—62no—
141C2×Dic5—242no—
142D20—122no—
143D20—122no—
144D20—122no—
145Dic10—62no—
146Dic10—62no—
147C5×C8—42no—
148#168—62no—
149C2×SD16—302no—
150C2×D8—302no—
151#127—151no—
152#127C2×D1511yescharacteristic
153#124—302no—
154#123—302no—
155C4×Q8—152no—
156C4×D4—302no—
157C4⋊C8C2×D1512yes—
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×D2011yescharacteristic
170C2×C3×C4D4×D512yes—
171C2×Dic3—102no—
172C2×Dic3—102no—
173C2×Dic3—402no—
174D12—202no—
175D12—202no—
176D12—202no—
177Dic6—102no—
178Dic6—102no—
179C3×C8—42no—
180C3⋊C8—102no—
181C22×C5—42no—
182C22×C5—44no—
183C22×C5#88211yescharacteristic
184C2×D5—241no—
185C2×D5—242no—
186C4×C5—21no—
187C4×C5#91112yes—
188C4×C5#91612yes—
189Dic5—122no—
190Dic5—122no—
191C2×Q8—152no—
192C2×D4—22no—
193C2×D4—301no—
194C2×D4—302no—
195C2×D4D6012yes—
196C22×C4—302no—
197SD16—604no—
198D8—604no—
199C2×C8—22no—
200C2×C8—301no—
201C4⋊C4—152no—
202C4⋊C4—302no—
203C22⋊C4—304no—
204C22⋊C4—302no—
205C42—302no—
206C42C22×D1511yescharacteristic
207C3×C5#162011yescharacteristic, complemented, Hall
208C22×C3—42no—
209C22×C3—44no—
210C22×C3#402811yescharacteristic
211C2×D3—401no—
212C2×D3—402no—
213C3×C4—21no—
214C3×C4#405712yes—
215C3×C4#406212yes—
216Dic3—202no—
217Dic3—202no—
218C2×C5—82no—
219C2×C5#474711yescharacteristic
220C2×C5#478112yes—
221D5—481no—
222C23—22no—
223C23—601no—
224Q8—302no—
225Q8—302no—
226D4—42no—
227D4—42no—
228D4—42no—
229D4—602no—
230D4—602no—
231D4—602no—
232C2×C4—302no—
233C2×C4—302no—
234C2×C4—1202no—
235C2×C4C2×D6011yescharacteristic
236C2×C4D4×D1512yes—
237C8—42no—
238C8—302no—
239C2×C3—82no—
240C2×C3#6503611yescharacteristic
241C2×C3#6507012yes—
242D3—801no—
243C5#6840211yescharacteristic, complemented, Sylow
244C22—42no—
245C22—44no—
246C22—1201no—
247C22—1202no—
248C22#9177111yescharacteristic
249C4—21no—
250C4—602no—
251C4—602no—
252C4#9180012yes—
253C4#9180512yes—
254C3#1059919511yescharacteristic, complemented, Sylow
255C2—82no—
256C2—2401no—
257C2#1175084811yescharacteristic
258C2#1175088212yes—
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#331C2
socleC22×C3×C5#120
prime radical#11751174C2
hypercenter#331D15
hypocenterC3×C5#1620
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
1. #11756472C2semidirect
3. #11750949C2semidirect
4. C3×C5×#331C2semidirect
5. #11746305C2semidirect
22. C5×#331D3semidirect
43. C3×#331D5semidirect
104. #331D15semidirect
207. C3×C5#1620semidirect
243. C5#68402semidirect
254. C3#10599195semidirect

Maximal subgroups

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

subgroupindex
#117564722
#117511742
#117509492
C3×C5×#3312
#117463052
#105991953
#684025