Finite Group Databasebeta

← #14318054

Subgroups — #14318054

Order 1920.

272 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 76 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#11747809C211yesmaximal, characteristic
3C5×#4490C211yesmaximal, characteristic, complemented
4C3×#64711C211yesmaximal, characteristic
5#11745939C211yesmaximal, characteristic, complemented
6#11745928C211yesmaximal, characteristic, complemented
7#11745892C211yesmaximal, characteristic
8#10600147—31nomaximal, Hall
9#91779—21no—
10C2×C3×D40C2211yescharacteristic
11#91434—21no—
12C3×C5×#107C2211yescharacteristic
13#91102C2211yescharacteristic
14C8×Dic15C2211yescharacteristic
15#91092—21no—
16C5×#818C2211yescharacteristic
17C2×C5×C3⋊C16C2211yescharacteristic
18C2×C3×#672C2211yescharacteristic
19#90964—21no—
20#69180—51nomaximal, Hall
21#65167—31no—
22#65161—31no—
23C5×#367—31no—
24#64729—31no—
25#64721—31no—
26#64711D311yescharacteristic
27#64709—31no—
28C2×C3×D20—21no—
29C2×D5×Dic3—41no—
30C2×C3×C5×C8C2311yescharacteristic
31C3×C5×C4⋊C4—21no—
32C4⋊Dic15—21no—
33C4⋊Dic15—41no—
34#6712—41no—
35C4×Dic15D411yescharacteristic
36C2×C3⋊#168D411yescharacteristic
37C5×C4⋊Dic3—21no—
38C3×D40—21no—
39C3×D40Q812yes—
40#6665—41no—
41C3×#672—21no—
42C5×C3⋊C16—21no—
43Dic3×D8—51no—
44#4878—51no—
45C3×#357—51no—
46#4562—51no—
47#4504—51no—
48Dic3⋊C16—51no—
49#4490D511yescharacteristic, complemented
50C2×D40C2×D311yescharacteristic
51#4039—61no—
52#4036—61no—
53C2×C5×C16—31no—
54C5×#107—31no—
55C5×#107C2×D311yescharacteristic
56#3950—31no—
57C8×Dic5—31no—
58C2×#672C2×D311yescharacteristic
59#3941—61no—
60#3940—61no—
61#2228—151noSylow
62C22×C3×D5—41no—
63C2×C3×C4×C5—41no—
64C2×C3×C4×C5C2×D411yescharacteristic
65C2×Dic15—41no—
66C2×Dic15D811yescharacteristic
67C2×Dic15D811yescharacteristic
68C2×C5×Dic3—41no—
69C3×D20—22no—
70C3×D20—41no—
71D5×Dic3—82no—
72C3×C5×C8C2×Q811yescharacteristic
73C3×C5×C8#4111yescharacteristic
74C3⋊#168—21no—
75C2×C3×D8—51no—
76D4×Dic3—101no—
77#890—101no—
78C2×C3×C16—51no—
79C3×#107C2×D511yescharacteristic
80#832—101no—
81#818—51no—
82#818C2×D511yescharacteristic
83C8×Dic3—51no—
84C2×C3⋊C16C2×D511yescharacteristic
85#808—101no—
86C2×D20—21no—
87C2×C4×D5—121no—
88C2×C5×C8C22×D311yescharacteristic
89C5×C4⋊C4—21no—
90C5×C4⋊C4—61no—
91#685—121no—
92C4⋊Dic5—61no—
93C4⋊Dic5—121no—
94#683—121no—
95C4×Dic5—31no—
96C2×#168—31no—
97D40—21no—
98D40Dic612yes—
99C5×C16—61no—
100#672—21no—
101#499—151no—
102C4×D8—151no—
103#367—31no—
104#366—151no—
105C4⋊C16—151no—
106#357—51no—
107#357—151no—
108C22×C3×C5C2×D811yescharacteristic
109C2×C3×D5—42no—
110C2×C3×D5—81no—
111C2×C3×D5—81no—
112C3×C4×C5—81no—
113C3×C4×C5C22⋊Q811yescharacteristic
114C3×C4×C5#13711yescharacteristic
115Dic15—21no—
116Dic15—21no—
117Dic15—81no—
118C5×Dic3—81no—
119C2×C3×D4—101no—
120C22×Dic3—201no—
121C3×D8—52no—
122C3×D8—101no—
123C2×C3×C8C22×D511yescharacteristic
124C3×C4⋊C4—21no—
125#217—201no—
126C4⋊Dic3—21no—
127C4⋊Dic3—101no—
128C4⋊Dic3—201no—
129Dic3⋊C4—201no—
130C4×Dic3—51no—
131C2×C3⋊C8—51no—
132C3×C16—101no—
133C3⋊C16—21no—
134C22×D5—41no—
135C2×C4×C5—41no—
136C2×C4×C5—121no—
137C2×C4×C5D3×D411yescharacteristic
138C2×Dic5—31no—
139C2×Dic5—31no—
140C2×Dic5—121no—
141D20—22no—
142D20—41no—
143C4×D5—242no—
144C5×C8C2×Dic611yescharacteristic
145C5×C8#23711yescharacteristic
146#168—61no—
147C2×D8—51no—
148#125—301no—
149C4×D4—301no—
150C2×C16—31no—
151C2×C16—51no—
152#107—31no—
153#107—151no—
154#107D3×D511yescharacteristic
155#106—301no—
156#102—301no—
157C4×C8—151no—
158C2×C3×C5#47411yescharacteristic
159C2×C3×C5#50811yescharacteristic
160C2×C3×C5#50911yescharacteristic
161C3×D5—82no—
162C23×C3—201no—
163C3×D4—102no—
164C3×D4—201no—
165C2×C3×C4—41no—
166C2×C3×C4D4×D511yescharacteristic
167C2×Dic3—41no—
168C2×Dic3—51no—
169C2×Dic3—51no—
170C2×Dic3—201no—
171C2×Dic3—402no—
172C3×C8#70911yescharacteristic
173C3×C8Q8×D511yescharacteristic
174C3⋊C8—101no—
175C22×C5D3×D811yescharacteristic
176C2×D5—42no—
177C2×D5—81no—
178C2×D5—81no—
179C4×C5—81no—
180C4×C5—241no—
181C4×C5#87811yescharacteristic
182C4×C5#91511yescharacteristic
183Dic5—61no—
184Dic5—61no—
185Dic5—241no—
186C2×D4—101no—
187C22×C4—601no—
188D8—52no—
189D8—101no—
190C2×C8—151no—
191C2×C8C2×D3×D511yescharacteristic
192C4⋊C4—21no—
193C4⋊C4—61no—
194C4⋊C4—301no—
195C4⋊C4—601no—
196C4⋊C4—601no—
197C22⋊C4—601no—
198C42—151no—
199C16—61no—
200C16—101no—
201C3×C5#222811yescharacteristic, complemented, Hall
202C22×C3—202no—
203C22×C3—401no—
204C22×C3—401no—
205C22×C3D5×D811yescharacteristic
206C3×C4—81no—
207C3×C4#404211yescharacteristic
208C3×C4#406411yescharacteristic
209Dic3—81no—
210Dic3—101no—
211Dic3—101no—
212Dic3—401no—
213C2×C5#475911yescharacteristic
214C2×C5#491211yescharacteristic
215C2×C5#491411yescharacteristic
216D5—82no—
217C23—201no—
218D4—102no—
219D4—201no—
220C2×C4—41no—
221C2×C4—121no—
222C2×C4—151no—
223C2×C4—151no—
224C2×C4—601no—
225C2×C4—1202no—
226C2×C4#679011yescharacteristic
227C8—301no—
228C8D5×Dic611yescharacteristic
229C8#676511yescharacteristic
230C2×C3—402no—
231C2×C3#6517911yescharacteristic
232C2×C3#6520311yescharacteristic
233C2×C3#6520511yescharacteristic
234C5#6918011yescharacteristic, complemented, Sylow
235C22—202no—
236C22—401no—
237C22—401no—
238C22#9148111yescharacteristic
239C4—81no—
240C4—241no—
241C4—301no—
242C4—301no—
243C4—1201no—
244C4#9143111yescharacteristic
245C4#9152211yescharacteristic
246C3#1060014711yescharacteristic, complemented, Sylow
247C2—402no—
248C2#1174725311yescharacteristic
249C2#1174828411yescharacteristic
250C2#1174829311yescharacteristic
subgroupG/H
centerC22#91481
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C2×D8
prime radicalC2×C3×D40C22
hypercenter#107D3×D5
hypocenterC3×C5#2228
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
1. #11750979C2semidirect
3. C5×#4490C2semidirect
5. #11745939C2semidirect
6. #11745928C2semidirect
49. #4490D5semidirect
201. C3×C5#2228semidirect
234. C5#69180semidirect
246. C3#10600147semidirect

Maximal subgroups

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

subgroupindex
#117509792
#117478092
C5×#44902
C3×#647112
#117459392
#117459282
#117458922
#106001473
#691805