Finite Group Databasebeta

← #14289591

Subgroups — #14289591

Order 1920.

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

normal subgroups only

This group has 436 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#11756493C211yesmaximal, characteristic
2#11751193C211yesmaximal, characteristic, complemented
3#11750943C212yesmaximal, complemented
4C3×C5×#333C211yesmaximal, characteristic, complemented
5#11746304C212yesmaximal, complemented
6#10599286—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8#91836—22no—
9C2×#6718—22no—
10#91784—22no—
11#91781—22no—
12C4×D60C2212yes—
13#91758C2211yescharacteristic
14C3×C5×C4⋊C8C2212yes—
15#91105—22no—
16#91101—22no—
17C4×C3⋊#168C2211yescharacteristic
18#68493—51nomaximal, Hall
19#66068—31no—
20#65381—31no—
21#65131—32no—
22C5×#333D311yescharacteristic, complemented
23#64703—32no—
24C2×C3×C5×Q8D412yes—
25C2×D60—22no—
26C2×D60D412yes—
27C2×C4×D15—22no—
28C2×Dic30—21no—
29C2×C3×C5×C8—22no—
30C3×C5×C4⋊C4—22no—
31C3×C42×C5C2311yescharacteristic
32#6718—44no—
33#6714—24no—
34#6714—22no—
35C4⋊Dic15—22no—
36C4⋊Dic15D412yes—
37C4×Dic15—22no—
38C2×C3⋊#168—21no—
39#5734—51no—
40#5092—51no—
41#4842—52no—
42C3×#333D511yescharacteristic, complemented
43#4483—52no—
44C5×C4⋊Q8C2×D311yescharacteristic
45#4093—62no—
46C2×#689—62no—
47#4041—62no—
48#4038—62no—
49C4×D20—32no—
50#4015—31no—
51C5×C4⋊C8C2×D312yes—
52#3953—62no—
53#3949—62no—
54C4×#168—31no—
55#1634—151noSylow
56C22×D15—22no—
57C3×C5×Q8—42no—
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5C2×D411yescharacteristic
60C2×C3×C4×C5C2×D412yes—
61C2×Dic15—22no—
62C2×Dic15—41no—
63D60—22no—
64D60—22no—
65D60—82no—
66C4×D15—42no—
67C4×D15—42no—
68Dic30—42no—
69C3×C5×C8—42no—
70C3⋊#168—22no—
71C3×C4⋊Q8C2×D511yescharacteristic
72#947—102no—
73C2×#216—102no—
74#895—102no—
75#892—102no—
76C4×D12—52no—
77#869—51no—
78C3×C4⋊C8C2×D512yes—
79#821—102no—
80#817—102no—
81C4×C3⋊C8—51no—
82C2×C5×Q8D1212yes—
83C2×D20—32no—
84C2×D20—62no—
85C2×C4×D5—62no—
86C2×Dic10—61no—
87C2×C5×C8—22no—
88C5×C4⋊C4—22no—
89C42×C5C22×D311yescharacteristic
90#689—124no—
91#685—64no—
92#685—62no—
93C4⋊Dic5—32no—
94C4⋊Dic5—62no—
95C4×Dic5—62no—
96C2×#168—61no—
97#555—151no—
98#494—151no—
99#476—152no—
100#333D1511yescharacteristic, complemented
101D4⋊C8—152no—
102C22×C3×C5#12011yescharacteristic
103C2×D15—42no—
104C2×D15—42no—
105C2×D15—42no—
106C3×C4×C5—21no—
107C3×C4×C5—42no—
108C3×C4×C5#13512yes—
109C3×C4×C5#13712yes—
110Dic15—42no—
111Dic15—81no—
112C2×C3×Q8D2012yes—
113C2×D12—52no—
114C2×D12—102no—
115C2×C4×D3—102no—
116C2×Dic6—101no—
117C2×C3×C8—22no—
118C3×C4⋊C4—22no—
119C3×C42C22×D511yescharacteristic
120#216—204no—
121(C2×D3)⋊C4—104no—
122(C2×D3)⋊C4—102no—
123C4⋊Dic3—52no—
124C4⋊Dic3—102no—
125C4×Dic3—102no—
126C2×C3⋊C8—101no—
127C22×D5—62no—
128C5×Q8—42no—
129C2×C4×C5—22no—
130C2×C4×C5C2×D1211yescharacteristic
131C2×C4×C5D3×D412yes—
132C2×Dic5—62no—
133C2×Dic5—121no—
134D20—62no—
135D20—62no—
136D20—242no—
137C4×D5—122no—
138C4×D5—122no—
139Dic10—122no—
140C5×C8—42no—
141#168—62no—
142C2×Q16—302no—
143C4⋊Q8—151no—
144C4⋊Q8C2×D1511yescharacteristic
145#124—302no—
146#121—302no—
147C4×D4—152no—
148#117—302no—
149#106—302no—
150C4⋊C8C2×D1512yes—
151#102—302no—
152C4×C8—151no—
153C2×C3×C5#45212yes—
154C2×C3×C5#45311yescharacteristic
155D15—82no—
156C22×D3—102no—
157C3×Q8—42no—
158C2×C3×C4—22no—
159C2×C3×C4C2×D2011yescharacteristic
160C2×C3×C4D4×D512yes—
161C2×Dic3—102no—
162C2×Dic3—201no—
163D12—102no—
164D12—102no—
165D12—402no—
166C4×D3—202no—
167C4×D3—202no—
168Dic6—202no—
169C3×C8—42no—
170C3⋊C8—102no—
171C22×C5#88211yescharacteristic
172C2×D5—122no—
173C2×D5—122no—
174C2×D5—122no—
175C4×C5—21no—
176C4×C5—42no—
177C4×C5#91612yes—
178C4×C5#91812yes—
179Dic5—122no—
180Dic5—241no—
181C2×Q8—301no—
182C2×Q8D6012yes—
183C2×D4—152no—
184C2×D4—302no—
185C22×C4—302no—
186Q16—604no—
187C2×C8—22no—
188C2×C8—301no—
189C4⋊C4—22no—
190C4⋊C4—152no—
191C4⋊C4—302no—
192C22⋊C4—304no—
193C22⋊C4—302no—
194C42—302no—
195C42C22×D1511yescharacteristic
196C3×C5#163411yescharacteristic, complemented, Hall
197C22×C3#402811yescharacteristic
198C2×D3—202no—
199C2×D3—202no—
200C2×D3—202no—
201C3×C4—21no—
202C3×C4—42no—
203C3×C4#406212yes—
204C3×C4#406412yes—
205Dic3—202no—
206Dic3—401no—
207C2×C5#474711yescharacteristic
208C2×C5#480812yes—
209D5—242no—
210C23—302no—
211Q8—42no—
212Q8—602no—
213D4—302no—
214D4—302no—
215D4—1202no—
216C2×C4—22no—
217C2×C4—302no—
218C2×C4—602no—
219C2×C4—602no—
220C2×C4—601no—
221C2×C4C2×D6011yescharacteristic
222C2×C4D4×D1512yes—
223C8—42no—
224C8—302no—
225C2×C3#6503611yescharacteristic
226C2×C3#6509912yes—
227D3—402no—
228C5#6849311yescharacteristic, complemented, Sylow
229C22—602no—
230C22—602no—
231C22—602no—
232C22#9177111yescharacteristic
233C4—21no—
234C4—42no—
235C4—602no—
236C4—1201no—
237C4#9180512yes—
238C4#9180712yes—
239C3#1059928611yescharacteristic, complemented, Sylow
240C2—1202no—
241C2#1175084811yescharacteristic
242C2#1175090912yes—
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#333C2
socleC22×C3×C5#120
prime radical#11756493C2
hypercenter#333D15
hypocenterC3×C5#1634
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #11751193C2semidirect
3. #11750943C2semidirect
4. C3×C5×#333C2semidirect
5. #11746304C2semidirect
22. C5×#333D3semidirect
42. C3×#333D5semidirect
100. #333D15semidirect
196. C3×C5#1634semidirect
228. C5#68493semidirect
239. C3#10599286semidirect

Maximal subgroups

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

subgroupindex
#117564932
#117511932
#117509432
C3×C5×#3332
#117463042
#105992863
#684935