Finite Group Databasebeta

← #14289582

Subgroups — #14289582

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
2C3×C5×#494C211yesmaximal, characteristic, complemented
3#11751185C212yesmaximal, complemented
4#11746367C211yesmaximal, characteristic, complemented
5#11746280C212yesmaximal, complemented
6#10602097—31nomaximal, Hall
7C2×C3×C5×Q16—22no—
8C3×C5×C4⋊Q8C2211yescharacteristic
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91836—22no—
11#91784—22no—
12#91781—22no—
13C4×D60C2212yes—
14C3×C4×C5×C8C2211yescharacteristic
15#91093—22no—
16#91092—22no—
17C4⋊(C3⋊#168)C2212yes—
18#71304—51nomaximal, Hall
19#66068—31no—
20C5×#494D311yescharacteristic, complemented
21#65373—32no—
22#64766—31no—
23#64679—32no—
24C2×C3×C5×Q8—21no—
25C2×C3×C5×Q8D412yes—
26C2×D60—22no—
27C2×D60D412yes—
28C2×C4×D15—22no—
29C3×C5×Q16—44no—
30C2×C3×C5×C8—21no—
31C3×C5×C4⋊C4—22no—
32C3×C5×C4⋊C4—22no—
33C3×C42×C5C2311yescharacteristic
34#6714—24no—
35#6714—22no—
36C4⋊Dic15D412yes—
37C4×Dic15—22no—
38C2×C3⋊#168—22no—
39#5734—51no—
40C3×#494D511yescharacteristic, complemented
41#5084—52no—
42#4546—51no—
43#4459—52no—
44C2×C5×Q16—22no—
45C5×C4⋊Q8C2×D311yescharacteristic
46C5×C4⋊Q8C2×D311yescharacteristic
47#4093—62no—
48#4041—62no—
49#4038—62no—
50C4×D20—32no—
51C4×C5×C8C2×D311yescharacteristic
52#3941—62no—
53#3940—62no—
54C4⋊#168—32no—
55#1634—151noSylow
56C22×D15—22no—
57C3×C5×Q8—42no—
58C3×C5×Q8—42no—
59C2×C3×C4×C5—22no—
60C2×C3×C4×C5—41no—
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×C5×C8—22no—
70C3⋊#168—42no—
71C2×C3×Q16—22no—
72C3×C4⋊Q8C2×D511yescharacteristic
73C3×C4⋊Q8C2×D511yescharacteristic
74#947—102no—
75#895—102no—
76#892—102no—
77C4×D12—52no—
78C3×C4×C8C2×D511yescharacteristic
79#809—102no—
80#808—102no—
81C4⋊(C3⋊C8)—52no—
82C2×C5×Q8—21no—
83C2×C5×Q8#6712yes—
84C2×D20—32no—
85C2×D20—62no—
86C2×C4×D5—62no—
87C5×Q16—44no—
88C2×C5×C8—21no—
89C5×C4⋊C4—22no—
90C5×C4⋊C4—22no—
91C42×C5C22×D311yescharacteristic
92#685—64no—
93#685—62no—
94C4⋊Dic5—32no—
95C4×Dic5—62no—
96C2×#168—62no—
97#555—151no—
98#494D1511yescharacteristic, complemented
99#476—152no—
100#333—151no—
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—81no—
109C3×C4×C5#13512yes—
110C3×C4×C5#13712yes—
111Dic15—42no—
112C2×C3×Q8—21no—
113C2×C3×Q8C22⋊D512yes—
114C2×D12—52no—
115C2×D12—102no—
116C2×C4×D3—102no—
117C3×Q16—44no—
118C2×C3×C8—21no—
119C3×C4⋊C4—22no—
120C3×C4⋊C4—22no—
121C3×C42C22×D511yescharacteristic
122(C2×D3)⋊C4—104no—
123(C2×D3)⋊C4—102no—
124C4⋊Dic3—52no—
125C4×Dic3—102no—
126C2×C3⋊C8—102no—
127C22×D5—62no—
128C5×Q8—42no—
129C5×Q8—42no—
130C2×C4×C5—22no—
131C2×C4×C5—41no—
132C2×C4×C5D3×D412yes—
133C2×C4×C5C2×#6711yescharacteristic
134C2×Dic5—62no—
135D20—62no—
136D20—62no—
137D20—242no—
138C4×D5—122no—
139C4×D5—122no—
140C5×C8—22no—
141#168—122no—
142C2×Q16—22no—
143C4⋊Q8C2×D1511yescharacteristic
144C4⋊Q8C2×D1511yescharacteristic
145#124—302no—
146#121—302no—
147C4×D4—152no—
148#117—302no—
149#106—302no—
150C4⋊C8—152no—
151#102—302no—
152C4×C8C2×D1511yescharacteristic
153C2×C3×C5#45212yes—
154C2×C3×C5#45311yescharacteristic
155D15—82no—
156C22×D3—102no—
157C3×Q8—42no—
158C3×Q8—42no—
159C2×C3×C4—22no—
160C2×C3×C4—41no—
161C2×C3×C4D4×D512yes—
162C2×C3×C4C2×C22⋊D511yescharacteristic
163C2×Dic3—102no—
164D12—102no—
165D12—102no—
166D12—402no—
167C4×D3—202no—
168C4×D3—202no—
169C3×C8—22no—
170C3⋊C8—202no—
171C22×C5#93711yescharacteristic
172C2×D5—122no—
173C2×D5—122no—
174C2×D5—122no—
175C4×C5—21no—
176C4×C5—42no—
177C4×C5—81no—
178C4×C5#91812yes—
179C4×C5#91912yes—
180Dic5—122no—
181C2×Q8—21no—
182C2×Q8#122012yes—
183C2×D4—152no—
184C2×D4—302no—
185C22×C4—302no—
186Q16—44no—
187C2×C8—21no—
188C2×C8—302no—
189C4⋊C4—22no—
190C4⋊C4—22no—
191C4⋊C4—152no—
192C22⋊C4—304no—
193C22⋊C4—302no—
194C42—302no—
195C42C22×D1511yescharacteristic
196C3×C5#163411yescharacteristic, complemented, Hall
197C22×C3#408311yescharacteristic
198C2×D3—202no—
199C2×D3—202no—
200C2×D3—202no—
201C3×C4—21no—
202C3×C4—42no—
203C3×C4—81no—
204C3×C4#406412yes—
205C3×C4#406512yes—
206Dic3—202no—
207C2×C5#507711yescharacteristic
208C2×C5#518712yes—
209D5—242no—
210C23—302no—
211Q8—42no—
212Q8—42no—
213D4—302no—
214D4—302no—
215D4—1202no—
216C2×C4—22no—
217C2×C4—41no—
218C2×C4—302no—
219C2×C4—602no—
220C2×C4—602no—
221C2×C4D4×D1512yes—
222C2×C4C2×#122011yescharacteristic
223C8—22no—
224C8—602no—
225C2×C3#6536611yescharacteristic
226C2×C3#6547612yes—
227D3—402no—
228C5#7130411yescharacteristic, complemented, Sylow
229C22—602no—
230C22—602no—
231C22—602no—
232C22#9182611yescharacteristic
233C4—21no—
234C4—42no—
235C4—81no—
236C4—602no—
237C4#9180712yes—
238C4#9180812yes—
239C3#1060209711yescharacteristic, complemented, Sylow
240C2—1202no—
241C2#1175117811yescharacteristic
242C2#1175128812yes—
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#494C2
socleC22×C3×C5#120
prime radical#11756493C2
hypercenter#494D15
hypocenterC3×C5#1634
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
2. C3×C5×#494C2semidirect
3. #11751185C2semidirect
4. #11746367C2semidirect
5. #11746280C2semidirect
20. C5×#494D3semidirect
40. C3×#494D5semidirect
98. #494D15semidirect
196. C3×C5#1634semidirect
228. C5#71304semidirect
239. C3#10602097semidirect

Maximal subgroups

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

subgroupindex
#117564932
C3×C5×#4942
#117511852
#117463672
#117462802
#106020973
#713045