Finite Group Databasebeta

← #14294176

Subgroups — #14294176

Order 1920.

352 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 102 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#11751179C211yesmaximal, characteristic
2C5×#5078C211yesmaximal, characteristic
3C3×#65370C211yesmaximal, characteristic
4#11747096C211yesmaximal, characteristic
5#11746948C211yesmaximal, characteristic
6#11746924C211yesmaximal, characteristic
7#11745832C211yesmaximal, characteristic
8#10602160—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91758C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13C2×#6663—22no—
14#91091—22no—
15C4×C3⋊#168C2211yescharacteristic
16C5×#807—22no—
17C4×C5×C3⋊C8C2211yescharacteristic
18C3×#3967—22no—
19C3×C4×#168C2211yescharacteristic
20#90987—22no—
21#90970—22no—
22#71226—51nomaximal, Hall
23C5×#500—31no—
24#65382—31no—
25#65381—31no—
26#65370D311yescharacteristic
27#65367—31no—
28#64969—31no—
29#64675—31no—
30C2×C3×C5×Q8—21no—
31C2×Dic30—21no—
32C2×C5×Dic6—21no—
33C2×C3×Dic10—21no—
34C3×C5×C4⋊C4—21no—
35C3×C5×C4⋊C4—21no—
36C3×C42×C5C2311yescharacteristic
37C4⋊Dic15—21no—
38C4⋊Dic15—21no—
39C2×C3⋊#168D412yes—
40C5×C4⋊Dic3—21no—
41C5×C4⋊Dic3—21no—
42C2×C5×C3⋊C8D412yes—
43C3×C4⋊Dic5—21no—
44C3×C4⋊Dic5—21no—
45C2×C3×#168D412yes—
46#6663—44no—
47C3×#487—51no—
48#5080—51no—
49#5079—51no—
50#5078—51no—
51#5078D511yescharacteristic
52#4699—51no—
53#4454—51no—
54C5×C4⋊Q8—31no—
55C5×C4⋊Q8C2×D311yescharacteristic
56C2×#689—62no—
57#4015—31no—
58#4015C2×D311yescharacteristic
59C5×#107—62no—
60C4×C5×C8—31no—
61#3967—22no—
62#3949—62no—
63#3942—62no—
64#3939—62no—
65C4×#168—31no—
66C4×#168C2×D311yescharacteristic
67#1723—151noSylow
68C3×C5×Q8—42no—
69C2×C3×C4×C5—41no—
70C2×C3×C4×C5C2×D411yescharacteristic
71C2×C3×C4×C5C2×D411yescharacteristic
72C2×C3×C4×C5C2×D411yescharacteristic
73C2×Dic15—41no—
74Dic30—42no—
75C2×C5×Dic3—41no—
76C5×Dic6—42no—
77C2×C3×Dic5—41no—
78C3×Dic10—42no—
79C3⋊#168—22no—
80C3×#168—22no—
81C5×C3⋊C8Q1614yescomplemented
82C3×C4⋊Q8—51no—
83C3×C4⋊Q8C2×D511yescharacteristic
84C2×Dic12—102no—
85#869—51no—
86#869C2×D511yescharacteristic
87C3×#103—102no—
88C3×C4×C8—51no—
89#835—102no—
90#808—102no—
91#807—22no—
92#807—102no—
93C4×C3⋊C8—51no—
94C4×C3⋊C8C2×D511yescharacteristic
95C2×C5×Q8—21no—
96C2×C5×Q8—61no—
97C2×Dic10—21no—
98C2×Dic10—61no—
99C2×C5×C8—32no—
100C5×C4⋊C4—21no—
101C5×C4⋊C4—21no—
102C5×C4⋊C4—61no—
103C5×C4⋊C4—61no—
104C42×C5C22×D311yescharacteristic
105#689—124no—
106C4⋊Dic5—21no—
107C4⋊Dic5—21no—
108C4⋊Dic5—61no—
109C4⋊Dic5—61no—
110C2×#168—32no—
111C2×#168#6712yes—
112#500—31no—
113#500—151no—
114#498—151no—
115#494—151no—
116#487—51no—
117#487—151no—
118#322—151no—
119C22×C3×C5#12711yescharacteristic
120C3×C4×C5—81no—
121C3×C4×C5C2×Q1612yes—
122C3×C4×C5AGL(1,ℤ/8)12yes—
123C3×C4×C5#13712yes—
124Dic15—81no—
125C3×Dic5—81no—
126C5×Dic3—81no—
127C2×C3×Q8—21no—
128C2×C3×Q8—101no—
129C2×Dic6—21no—
130C2×Dic6—101no—
131C2×C3×C8—52no—
132C3×C4⋊C4—21no—
133C3×C4⋊C4—21no—
134C3×C4⋊C4—101no—
135C3×C4⋊C4—101no—
136C3×C42C22×D511yescharacteristic
137C4⋊Dic3—21no—
138C4⋊Dic3—21no—
139C4⋊Dic3—101no—
140C4⋊Dic3—101no—
141C2×C3⋊C8—52no—
142C2×C3⋊C8C22⋊D512yes—
143Dic12—204no—
144C5×Q8—42no—
145C5×Q8—122no—
146C2×C4×C5—41no—
147C2×C4×C5—121no—
148C2×C4×C5D3×D411yescharacteristic
149C2×C4×C5D3×D411yescharacteristic
150C2×C4×C5C2×#6711yescharacteristic
151C2×Dic5—41no—
152C2×Dic5—121no—
153Dic10—42no—
154Dic10—122no—
155C5×C8—34no—
156#168—22no—
157#168—62no—
158C2×Q16—302no—
159C4⋊Q8—31no—
160C4⋊Q8—51no—
161C4⋊Q8—151no—
162C4⋊Q8D3×D511yescharacteristic
163#107—62no—
164#107—302no—
165#106—302no—
166#103—102no—
167#103—302no—
168C4×C8—31no—
169C4×C8—51no—
170C4×C8—151no—
171C2×C3×C5#49411yescharacteristic
172C2×C3×C5#49611yescharacteristic
173C2×C3×C5#49711yescharacteristic
174C3×Q8—42no—
175C3×Q8—202no—
176C2×C3×C4—41no—
177C2×C3×C4—201no—
178C2×C3×C4D4×D511yescharacteristic
179C2×C3×C4D4×D511yescharacteristic
180C2×C3×C4C2×C22⋊D511yescharacteristic
181C2×Dic3—41no—
182C2×Dic3—201no—
183Dic6—42no—
184Dic6—202no—
185C3×C8—102no—
186C3⋊C8—102no—
187C3⋊C8#68914yescomplemented
188C22×C5#94011yescharacteristic
189C4×C5—81no—
190C4×C5—241no—
191C4×C5#91512yes—
192C4×C5D3×Q1612yes—
193C4×C5#94912yes—
194Dic5—81no—
195Dic5—241no—
196C2×Q8—21no—
197C2×Q8—61no—
198C2×Q8—101no—
199C2×Q8—301no—
200Q16—604no—
201C2×C8—32no—
202C2×C8—52no—
203C2×C8—152no—
204C4⋊C4—21no—
205C4⋊C4—21no—
206C4⋊C4—61no—
207C4⋊C4—61no—
208C4⋊C4—101no—
209C4⋊C4—101no—
210C4⋊C4—301no—
211C4⋊C4—301no—
212C42C2×D3×D511yescharacteristic
213C3×C5#172311yescharacteristic, complemented, Hall
214C22×C3#408611yescharacteristic
215C3×C4—81no—
216C3×C4—401no—
217C3×C4#405712yes—
218C3×C4#406412yes—
219C3×C4C2×#68912yes—
220Dic3—81no—
221Dic3—401no—
222C2×C5#505811yescharacteristic
223C2×C5#516711yescharacteristic
224C2×C5#518311yescharacteristic
225Q8—42no—
226Q8—122no—
227Q8—202no—
228Q8—602no—
229C2×C4—41no—
230C2×C4—121no—
231C2×C4—201no—
232C2×C4—601no—
233C2×C4D5×#6711yescharacteristic
234C2×C4D3×C22⋊D511yescharacteristic
235C2×C4#679011yescharacteristic
236C8—34no—
237C8—102no—
238C8—302no—
239C2×C3#6538111yescharacteristic
240C2×C3#6544311yescharacteristic
241C2×C3#6547911yescharacteristic
242C5#7122611yescharacteristic, complemented, Sylow
243C22#9156711yescharacteristic
244C4—81no—
245C4—241no—
246C4—401no—
247C4—1201no—
248C4#9147812yes—
249C4D3×#68912yes—
250C4#9152212yes—
251C3#1060216011yescharacteristic, complemented, Sylow
252C2#1174909411yescharacteristic
253C2#1174932011yescharacteristic
254C2#1174935711yescharacteristic
subgroupG/H
centerC22#91567
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socle, prime radicalC22×C3×C5#127
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1723
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
81. C5×C3⋊C8Q16semidirect
187. C3⋊C8#689semidirect
213. C3×C5#1723semidirect
242. C5#71226semidirect
251. C3#10602160semidirect

Maximal subgroups

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

subgroupindex
#117511792
C5×#50782
C3×#653702
#117470962
#117469482
#117469242
#117458322
#106021603
#712265