Finite Group Databasebeta

← #14458229

Subgroups — #14458229

Order 1920.

888 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 888 conjugacy classes of subgroups — too many to draw. Only its 167 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#11756525C214yesmaximal, complemented
2C3×C5×#494C211yesmaximal, characteristic, complemented
3#11751293C214yesmaximal, complemented
4#11751196C214yesmaximal, complemented
5#11750801C212yesmaximal, complemented
6#10613539—31nomaximal, Hall
7#92098C2214yes—
8C2×C3×C5×Q16C2214yes—
9C3×C5×C4⋊Q8C2212yes—
10#91831C2218yes—
11#91808—24no—
12#91807—28no—
13Q16×D15—24no—
14#91793C2212yes—
15#91790C2214yes—
16C3×C4×C5×C8C2211yescharacteristic
17#91120C2214yes—
18#91103C2212yes—
19#91089C2214yes—
20#81808—51nomaximal, Hall
21#66100—34no—
22C5×#494D311yescharacteristic, complemented
23#65481—34no—
24#65384—34no—
25#64989—32no—
26C2×C3×C5×Q8C2314yes—
27#6821—28no—
28Q8×D15—28no—
29#6817—44no—
30#6817C2314yes—
31C3×C5×Q16—24no—
32C3×C5×Q16—24no—
33C2×C3×C5×C8C2312yes—
34C3×C5×C4⋊C4—42no—
35C3×C42×C5C2311yescharacteristic
36#6718—28no—
37#6717—28no—
38#6710C2314yes—
39Dic60D412yes—
40D120D412yes—
41#6706D414yes—
42#6705—24no—
43C8×D15—24no—
44#5766—54no—
45C3×#494D511yescharacteristic, complemented
46#5192—54no—
47#5095—54no—
48#4700—52no—
49#4147—34no—
50C2×C5×Q16C2×D314yes—
51C5×C4⋊Q8C2×D312yes—
52#4088—38no—
53#4065—64no—
54#4064—68no—
55D5×Q16—64no—
56#4050—32no—
57#4047—34no—
58C4×C5×C8C2×D311yescharacteristic
59#3968—34no—
60#3951—32no—
61#3937—34no—
62#3293—151noSylow
63C3×C5×Q8—28no—
64C2×C3×C4×C5—21no—
65C2×C3×C4×C5—24no—
66C2×C3×C4×C5C2411yescharacteristic
67#1220—24no—
68D60—44no—
69D60C2×D414yes—
70C4×D15—24no—
71C4×D15—48no—
72Dic30—44no—
73Dic30C2×D414yes—
74C3×C5×C8C2×D412yes—
75C3×C5×C8C2×D412yes—
76C3⋊#168—24no—
77#1007—54no—
78C2×C3×Q16C2×D514yes—
79C3×C4⋊Q8C2×D512yes—
80#942—58no—
81#919—104no—
82#918—108no—
83D3×Q16—104no—
84#904—52no—
85#901—54no—
86C3×C4×C8C2×D511yescharacteristic
87#836—54no—
88#819—52no—
89#805—54no—
90C2×C5×Q8C22×D314yes—
91#713—68no—
92Q8×D5—68no—
93#709—34no—
94#709—124no—
95C5×Q16—24no—
96C5×Q16—24no—
97C2×C5×C8C22×D312yes—
98C5×C4⋊C4—42no—
99C42×C5C22×D311yescharacteristic
100#689—68no—
101#688—68no—
102#681—34no—
103Dic20—32no—
104D40—32no—
105#677—34no—
106#676—64no—
107C8×D5—64no—
108#578—154no—
109#494D1511yescharacteristic, complemented
110#473—154no—
111#456—154no—
112#443—152no—
113C22×C3×C5H(5,𝔽2)11yescharacteristic
114C2×D15—24no—
115C3×C4×C5—22no—
116C3×C4×C5—44no—
117C3×C4×C5C22×D412yes—
118Dic15—24no—
119C2×C3×Q8C22×D514yes—
120#239—108no—
121D3×Q8—108no—
122#235—54no—
123#235—204no—
124C3×Q16—24no—
125C3×Q16—24no—
126C2×C3×C8C22×D512yes—
127C3×C4⋊C4—42no—
128C3×C42C22×D511yescharacteristic
129#216—108no—
130#215—108no—
131#208—54no—
132Dic12—52no—
133D24—52no—
134#204—54no—
135ΓL(1,𝔽25)—104no—
136D3×C8—104no—
137C5×Q8—28no—
138C2×C4×C5—21no—
139C2×C4×C5—24no—
140C2×C4×C5C23×D311yescharacteristic
141C22⋊D5—64no—
142D20—34no—
143D20—124no—
144C4×D5—64no—
145C4×D5—128no—
146Dic10—34no—
147Dic10—124no—
148C5×C8D3×D412yes—
149C5×C8D3×D412yes—
150#168—64no—
1512−1+4—154no—
152#137—158no—
153#137—308no—
154#135—152no—
155#135—304no—
156C2×Q16—304no—
157C2×Q16C2×D1514yes—
158#131—154no—
159C4⋊Q8C2×D1512yes—
160#108—152no—
161#104—154no—
162#101—154no—
163C4×C8C2×D1511yescharacteristic
164C2×C3×C5—21no—
165C2×C3×C5D4211yescharacteristic
166D15—44no—
167C3×Q8—28no—
168C2×C3×C4—21no—
169C2×C3×C4—24no—
170C2×C3×C4C23×D511yescharacteristic
171#67—104no—
172D12—54no—
173D12—204no—
174C4×D3—104no—
175C4×D3—208no—
176Dic6—54no—
177Dic6—204no—
178C3×C8D4×D512yes—
179C3×C8D4×D512yes—
180C3⋊C8—104no—
181C22×C5#100411yescharacteristic
182C2×D5—64no—
183C4×C5—22no—
184C4×C5—44no—
185C4×C5C2×D3×D412yes—
186Dic5—64no—
187#41—154no—
188#41—308no—
189#41—604no—
190C2×Q8—308no—
191C2×Q8C22×D1514yes—
192Q16—24no—
193Q16—24no—
194Q16—152no—
195Q16—308no—
196SD16—154no—
197SD16—308no—
198D8—152no—
199M16—154no—
200M16—304no—
201C2×C8—304no—
202C2×C8C22×D1512yes—
203C4⋊C4—42no—
204C42C22×D1511yescharacteristic
205C3×C5#329311yescharacteristic, complemented, Hall
206C22×C3#414411yescharacteristic
207C2×D3—104no—
208C3×C4—22no—
209C3×C4—44no—
210C3×C4C2×D4×D512yes—
211Dic3—104no—
212C2×C5—21no—
213C2×C5#571711yescharacteristic
214D5—124no—
215Q8—28no—
216Q8—154no—
217Q8—604no—
218D4—154no—
219D4—304no—
220D4—604no—
221C2×C4—21no—
222C2×C4—24no—
223C2×C4—304no—
224C2×C4—608no—
225C2×C4C23×D1511yescharacteristic
226C8—304no—
227C8D4×D1512yes—
228C8D4×D1512yes—
229C2×C3—21no—
230C2×C3#6605111yescharacteristic
231D3—204no—
232C5#8180811yescharacteristic, complemented, Sylow
233C22—304no—
234C22#9209511yescharacteristic
235C4—22no—
236C4—44no—
237C4—304no—
238C4C2×D4×D1512yes—
239C3#1061353911yescharacteristic, complemented, Sylow
240C2—21no—
241C2—604no—
242C2#1175647611yescharacteristic
subgroupG/H
centerC2#11756476
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#494C2
socleC2×C3×C5D42
hypercenter#494D15
hypocenterC3×C5#3293
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #11756525C2semidirect
2. C3×C5×#494C2semidirect
3. #11751293C2semidirect
4. #11751196C2semidirect
5. #11750801C2semidirect
22. C5×#494D3semidirect
45. C3×#494D5semidirect
109. #494D15semidirect
205. C3×C5#3293semidirect
232. C5#81808semidirect
239. C3#10613539semidirect

Maximal subgroups

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

subgroupindex
#117565252
C3×C5×#4942
#117512932
#117511962
#117508012
#106135393
#818085