Finite Group Databasebeta

← #14294174

Subgroups — #14294174

Order 1920.

352 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 100 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
1C5×#4681C211yesmaximal, characteristic
2C3×#64971C211yesmaximal, characteristic
3#11747103C211yesmaximal, characteristic
4#11746962C211yesmaximal, characteristic
5#11746947C211yesmaximal, characteristic
6#11746924C211yesmaximal, characteristic
7#11746275C211yesmaximal, characteristic
8#10602020—31nomaximal, Hall
9C5×#869C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×#4015C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13C2×#6661—22no—
14C3×C4×C5×C8C2211yescharacteristic
15C4×C3⋊#168C2211yescharacteristic
16C4×C3⋊#168C2211yescharacteristic
17C5×#816—22no—
18C3×#3950—22no—
19#90989—22no—
20#90986—22no—
21#90970—22no—
22#71368—51nomaximal, Hall
23C5×#487—31no—
24#65382—31no—
25#65381—31no—
26#65368—31no—
27#65367—31no—
28#64971D311yescharacteristic
29#64674—31no—
30C2×C5×Dic6—21no—
31C2×C5×Dic6—21no—
32C2×C3×Dic10—21no—
33C2×C3×Dic10—21no—
34C2×C3×C5×C8D412yes—
35C3×C42×C5C2311yescharacteristic
36C2×C3⋊#168D412yes—
37C2×C3⋊#168D412yes—
38C5×C4⋊Dic3—21no—
39C5×C4⋊Dic3—21no—
40C5×C4⋊Dic3—21no—
41C5×C4⋊Dic3—21no—
42C3×C4⋊Dic5—21no—
43C3×C4⋊Dic5—21no—
44C3×C4⋊Dic5—21no—
45C3×C4⋊Dic5—21no—
46#6661—44no—
47C3×#500—51no—
48#5092—51no—
49#5080—51no—
50#5079—51no—
51#5078—51no—
52#4681D511yescharacteristic
53#4454—51no—
54C5×C4⋊Q8—31no—
55C5×C4⋊Q8—31no—
56C2×#689—62no—
57#4015C2×D311yescharacteristic
58#4015C2×D311yescharacteristic
59C5×#103—62no—
60C4×C5×C8C2×D311yescharacteristic
61#3950—22no—
62#3942—62no—
63#3940—62no—
64#3939—62no—
65C4×#168—31no—
66C4×#168—31no—
67#1723—151noSylow
68C2×C3×C4×C5C2×D411yescharacteristic
69C2×C3×C4×C5C2×D411yescharacteristic
70C2×C3×C4×C5C2×D411yescharacteristic
71C2×C5×Dic3—41no—
72C2×C5×Dic3—41no—
73C5×Dic6—42no—
74C5×Dic6—42no—
75C2×C3×Dic5—41no—
76C2×C3×Dic5—41no—
77C3×Dic10—42no—
78C3×Dic10—42no—
79C3×C5×C8—22no—
80C3⋊#168—22no—
81C3⋊#168Q1614yescomplemented
82C3×C4⋊Q8—51no—
83C3×C4⋊Q8—51no—
84C2×#216—102no—
85#869C2×D511yescharacteristic
86#869C2×D511yescharacteristic
87C3×#107—102no—
88C3×C4×C8C2×D511yescharacteristic
89#835—102no—
90#816—22no—
91#808—102no—
92#807—102no—
93C4×C3⋊C8—51no—
94C4×C3⋊C8—51no—
95C2×C5×Q8—61no—
96C2×C5×Q8—61no—
97C2×Dic10—21no—
98C2×Dic10—21no—
99C2×C5×C8#6712yes—
100C5×C4⋊C4—61no—
101C5×C4⋊C4—61no—
102C5×C4⋊C4—61no—
103C5×C4⋊C4—61no—
104C42×C5C22×D311yescharacteristic
105#689—124no—
106C4⋊Dic5—21no—
107C4⋊Dic5—21no—
108C4⋊Dic5—21no—
109C4⋊Dic5—21no—
110C2×#168—32no—
111C2×#168—32no—
112#500—51no—
113#500—151no—
114#498—151no—
115#494—151no—
116#487—31no—
117#487—151no—
118#322—151no—
119C22×C3×C5#12711yescharacteristic
120C3×C4×C5C2×Q1612yes—
121C3×C4×C5AGL(1,ℤ/8)12yes—
122C3×C4×C5#13712yes—
123C3×Dic5—81no—
124C3×Dic5—81no—
125C5×Dic3—81no—
126C5×Dic3—81no—
127C2×C3×Q8—101no—
128C2×C3×Q8—101no—
129C2×Dic6—21no—
130C2×Dic6—21no—
131C2×C3×C8C22⋊D512yes—
132C3×C4⋊C4—101no—
133C3×C4⋊C4—101no—
134C3×C4⋊C4—101no—
135C3×C4⋊C4—101no—
136C3×C42C22×D511yescharacteristic
137#216—204no—
138C4⋊Dic3—21no—
139C4⋊Dic3—21no—
140C4⋊Dic3—21no—
141C4⋊Dic3—21no—
142C2×C3⋊C8—52no—
143C2×C3⋊C8—52no—
144C5×Q8—122no—
145C5×Q8—122no—
146C2×C4×C5—121no—
147C2×C4×C5—121no—
148C2×C4×C5D3×D411yescharacteristic
149C2×C4×C5D3×D411yescharacteristic
150C2×C4×C5C2×#6711yescharacteristic
151C2×Dic5—41no—
152C2×Dic5—41no—
153Dic10—42no—
154Dic10—42no—
155C5×C8—22no—
156#168—34no—
157#168—62no—
158C2×Q16—302no—
159C4⋊Q8—31no—
160C4⋊Q8—31no—
161C4⋊Q8—51no—
162C4⋊Q8—51no—
163#107—102no—
164#107—302no—
165#106—302no—
166#103—62no—
167#103—302no—
168C4×C8—151no—
169C4×C8—151no—
170C4×C8D3×D511yescharacteristic
171C2×C3×C5#49411yescharacteristic
172C2×C3×C5#49611yescharacteristic
173C2×C3×C5#49711yescharacteristic
174C3×Q8—202no—
175C3×Q8—202no—
176C2×C3×C4—201no—
177C2×C3×C4—201no—
178C2×C3×C4D4×D511yescharacteristic
179C2×C3×C4D4×D511yescharacteristic
180C2×C3×C4C2×C22⋊D511yescharacteristic
181C2×Dic3—41no—
182C2×Dic3—41no—
183Dic6—42no—
184Dic6—42no—
185C3×C8—22no—
186C3⋊C8—54no—
187C3⋊C8—102no—
188C22×C5#94011yescharacteristic
189C4×C5—241no—
190C4×C5—241no—
191C4×C5#91112yes—
192C4×C5D3×Q1612yes—
193C4×C5#94212yes—
194Dic5—81no—
195Dic5—81no—
196C2×Q8—61no—
197C2×Q8—61no—
198C2×Q8—101no—
199C2×Q8—101no—
200Q16—604no—
201C2×C8—152no—
202C2×C8—152no—
203C2×C8#120112yes—
204C4⋊C4—61no—
205C4⋊C4—61no—
206C4⋊C4—61no—
207C4⋊C4—61no—
208C4⋊C4—101no—
209C4⋊C4—101no—
210C4⋊C4—101no—
211C4⋊C4—101no—
212C42C2×D3×D511yescharacteristic
213C3×C5#172311yescharacteristic, complemented, Hall
214C22×C3#408611yescharacteristic
215C3×C4—401no—
216C3×C4—401no—
217C3×C4#406012yes—
218C3×C4D5×Q1612yes—
219C3×C4#409712yes—
220Dic3—81no—
221Dic3—81no—
222C2×C5#508611yescharacteristic
223C2×C5#515411yescharacteristic
224C2×C5#518311yescharacteristic
225Q8—122no—
226Q8—122no—
227Q8—202no—
228Q8—202no—
229C2×C4—121no—
230C2×C4—121no—
231C2×C4—201no—
232C2×C4—201no—
233C2×C4#677711yescharacteristic
234C2×C4#677711yescharacteristic
235C2×C4C2×#120111yescharacteristic
236C8—22no—
237C8—154no—
238C8—302no—
239C2×C3#6534911yescharacteristic
240C2×C3#6546511yescharacteristic
241C2×C3#6547011yescharacteristic
242C5#7136811yescharacteristic, complemented, Sylow
243C22#9146311yescharacteristic
244C4—241no—
245C4—241no—
246C4—401no—
247C4—401no—
248C4#9125812yes—
249C4#9126412yes—
250C4#9130912yes—
251C3#1060202011yescharacteristic, complemented, Sylow
252C2#1174708211yescharacteristic
253C2#1174801511yescharacteristic
254C2#1174804111yescharacteristic
subgroupG/H
centerC22#91463
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×C8C22
socle, prime radicalC22×C3×C5#127
hypercenterC4×C8D3×D5
hypocenterC3×C5#1723
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
81. C3⋊#168Q16semidirect
213. C3×C5#1723semidirect
242. C5#71368semidirect
251. C3#10602020semidirect

Maximal subgroups

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

subgroupindex
C5×#46812
C3×#649712
#117471032
#117469622
#117469472
#117469242
#117462752
#106020203
#713685