Finite Group Databasebeta

← #14318048

Subgroups — #14318048

Order 1920.

272 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 77 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#11750979C211yesmaximal, characteristic, complemented
2#11750973C211yesmaximal, characteristic
3C3×C5×#366C211yesmaximal, characteristic, complemented
4#11746330C211yesmaximal, characteristic
5#11746322C211yesmaximal, characteristic, complemented
6#11746312C211yesmaximal, characteristic
7#11746311C211yesmaximal, characteristic, complemented
8#10600127—31nomaximal, Hall
9C2×D120C2211yescharacteristic
10#91782—21no—
11#91779—21no—
12C2×C3×C5×C16C2211yescharacteristic
13C3×C5×#107C2211yescharacteristic
14C3×C5×#107C2211yescharacteristic
15#91102C2211yescharacteristic
16C8×Dic15C2211yescharacteristic
17C2×C3⋊#672C2211yescharacteristic
18#91093—21no—
19#91092—21no—
20#69334—51nomaximal, Hall
21#65167—31no—
22#65161—31no—
23C5×#366D311yescharacteristic, complemented
24#64729—31no—
25#64721—31no—
26#64711—31no—
27#64710—31no—
28C2×D60—21no—
29C2×C4×D15—41no—
30C2×C3×C5×C8C2311yescharacteristic
31C3×C5×C4⋊C4—21no—
32C3×C5×C4⋊C4—21no—
33#6714—41no—
34C4⋊Dic15—21no—
35C4⋊Dic15—41no—
36#6712—41no—
37C4×Dic15D411yescharacteristic
38C2×C3⋊#168D411yescharacteristic
39D120—21no—
40D120Q812yes—
41C3×C5×C16—21no—
42C3⋊#672—21no—
43#4878—51no—
44#4872—51no—
45C3×#366D511yescharacteristic, complemented
46#4509—51no—
47Dic3⋊C16—51no—
48#4491—51no—
49#4490—51no—
50C2×D40—31no—
51#4039—61no—
52#4036—61no—
53C2×C5×C16C2×D311yescharacteristic
54C5×#107C2×D311yescharacteristic
55C5×#107C2×D311yescharacteristic
56#3950—31no—
57C8×Dic5—31no—
58C2×#672—31no—
59#3941—61no—
60#3940—61no—
61#2228—151noSylow
62C22×D15—41no—
63C2×C3×C4×C5—41no—
64C2×C3×C4×C5—41no—
65C2×C3×C4×C5C2×D411yescharacteristic
66C2×Dic15—41no—
67C2×Dic15D811yescharacteristic
68C2×Dic15D811yescharacteristic
69D60—22no—
70D60—41no—
71C4×D15—82no—
72C3×C5×C8C2×Q811yescharacteristic
73C3×C5×C8#4111yescharacteristic
74C3⋊#168—21no—
75C2×D24—51no—
76#893—101no—
77#890—101no—
78C2×C3×C16C2×D511yescharacteristic
79C3×#107C2×D511yescharacteristic
80C3×#107C2×D511yescharacteristic
81#818—51no—
82C8×Dic3—51no—
83C2×C3⋊C16—51no—
84#809—101no—
85#808—101no—
86C2×D20—61no—
87C2×C4×D5—121no—
88C2×C5×C8C22×D311yescharacteristic
89C5×C4⋊C4—21no—
90C5×C4⋊C4—21no—
91#685—121no—
92C4⋊Dic5—61no—
93C4⋊Dic5—121no—
94#683—121no—
95C4×Dic5—31no—
96C2×#168—31no—
97D40—32no—
98D40—61no—
99C5×C16—21no—
100#672—61no—
101#499—151no—
102C4×D8—151no—
103#367—151no—
104#366D1511yescharacteristic, complemented
105C4⋊C16—151no—
106#357—151no—
107#357—151no—
108C22×C3×C5C2×D811yescharacteristic
109C2×D15—42no—
110C2×D15—81no—
111C2×D15—81no—
112C3×C4×C5—81no—
113C3×C4×C5—81no—
114C3×C4×C5C22⋊Q811yescharacteristic
115C3×C4×C5#13711yescharacteristic
116Dic15—21no—
117Dic15—21no—
118Dic15—81no—
119C2×D12—101no—
120C2×C4×D3—201no—
121C2×C3×C8C22×D511yescharacteristic
122C3×C4⋊C4—21no—
123C3×C4⋊C4—21no—
124(C2×D3)⋊C4—201no—
125C4⋊Dic3—101no—
126C4⋊Dic3—201no—
127Dic3⋊C4—201no—
128C4×Dic3—51no—
129C2×C3⋊C8—51no—
130D24—52no—
131D24—101no—
132C3×C16—21no—
133C3⋊C16—101no—
134C22×D5—121no—
135C2×C4×C5—41no—
136C2×C4×C5—41no—
137C2×C4×C5D3×D411yescharacteristic
138C2×Dic5—31no—
139C2×Dic5—31no—
140C2×Dic5—121no—
141D20—62no—
142D20—121no—
143C4×D5—242no—
144C5×C8#23511yescharacteristic
145C5×C8D3×Q811yescharacteristic
146#168—61no—
147C2×D8—151no—
148#125—301no—
149C4×D4—301no—
150C2×C16—151no—
151C2×C16C2×D1511yescharacteristic
152#107—151no—
153#107C2×D1511yescharacteristic
154#107C2×D1511yescharacteristic
155#106—301no—
156#102—301no—
157C4×C8—151no—
158C2×C3×C5#47411yescharacteristic
159C2×C3×C5#50811yescharacteristic
160C2×C3×C5#50911yescharacteristic
161D15—82no—
162C22×D3—201no—
163C2×C3×C4—41no—
164C2×C3×C4—41no—
165C2×C3×C4D4×D511yescharacteristic
166C2×Dic3—51no—
167C2×Dic3—51no—
168C2×Dic3—201no—
169D12—102no—
170D12—201no—
171C4×D3—402no—
172C3×C8#70911yescharacteristic
173C3×C8Q8×D511yescharacteristic
174C3⋊C8—101no—
175C22×C5D3×D811yescharacteristic
176C2×D5—122no—
177C2×D5—241no—
178C2×D5—241no—
179C4×C5—81no—
180C4×C5—81no—
181C4×C5#89611yescharacteristic
182C4×C5#91811yescharacteristic
183Dic5—61no—
184Dic5—61no—
185Dic5—241no—
186C2×D4—301no—
187C22×C4—601no—
188D8—152no—
189D8—301no—
190C2×C8—151no—
191C2×C8C22×D1511yescharacteristic
192C4⋊C4—21no—
193C4⋊C4—21no—
194C4⋊C4—301no—
195C4⋊C4—601no—
196C4⋊C4—601no—
197C22⋊C4—601no—
198C42—151no—
199C16—21no—
200C16—301no—
201C3×C5#222811yescharacteristic, complemented, Hall
202C22×C3D5×D811yescharacteristic
203C2×D3—202no—
204C2×D3—401no—
205C2×D3—401no—
206C3×C4—81no—
207C3×C4—81no—
208C3×C4#404211yescharacteristic
209C3×C4#406411yescharacteristic
210Dic3—101no—
211Dic3—101no—
212Dic3—401no—
213C2×C5#489011yescharacteristic
214C2×C5#491111yescharacteristic
215C2×C5#491911yescharacteristic
216D5—242no—
217C23—601no—
218D4—302no—
219D4—601no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—151no—
223C2×C4—151no—
224C2×C4—601no—
225C2×C4—1202no—
226C2×C4D4×D1511yescharacteristic
227C8—301no—
228C8#681711yescharacteristic
229C8Q8×D1511yescharacteristic
230C2×C3#6517911yescharacteristic
231C2×C3#6520011yescharacteristic
232C2×C3#6520811yescharacteristic
233D3—402no—
234C5#6933411yescharacteristic, complemented, Sylow
235C22—602no—
236C22—1201no—
237C22—1201no—
238C22D8×D1511yescharacteristic
239C4—81no—
240C4—81no—
241C4—301no—
242C4—301no—
243C4—1201no—
244C4#9178511yescharacteristic
245C4#9180711yescharacteristic
246C3#1060012711yescharacteristic, complemented, Sylow
247C2—1202no—
248C2#1175099111yescharacteristic
249C2#1175101211yescharacteristic
250C2#1175102011yescharacteristic
subgroupG/H
centerC22D8×D15
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#366C2
socleC22×C3×C5C2×D8
prime radicalC2×D120C22
hypercenter#366D15
hypocenterC3×C5#2228
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #366

Complements

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

NH ≅ G/Ntype
1. #11750979C2semidirect
3. C3×C5×#366C2semidirect
5. #11746322C2semidirect
7. #11746311C2semidirect
23. C5×#366D3semidirect
45. C3×#366D5semidirect
104. #366D15semidirect
201. C3×C5#2228semidirect
234. C5#69334semidirect
246. C3#10600127semidirect

Maximal subgroups

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

subgroupindex
#117509792
#117509732
C3×C5×#3662
#117463302
#117463222
#117463122
#117463112
#106001273
#693345