Finite Group Databasebeta

← #14289026

Subgroups — #14289026

Order 1920.

456 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 92 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#11756481C211yesmaximal, characteristic, complemented
2C5×#5085C211yesmaximal, characteristic
3#11747086C212yesmaximal
4C3×#64766C211yesmaximal, characteristic, complemented
5#11745844C212yesmaximal, complemented
6#10602062—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8#91833—22no—
9#91777—22no—
10#91776—22no—
11C4×Dic30C2212yes—
12C2×C5×#215—22no—
13C5×#874C2211yescharacteristic
14C2×#6659—22no—
15C4×C5×C3⋊C8C2211yescharacteristic
16C3×C4⋊#168C2212yes—
17#90967—22no—
18#68504—51nomaximal, Hall
19#66056—31no—
20C5×#492—31no—
21#65364—32no—
22#64766D311yescharacteristic, complemented
23#64676—32no—
24C2×C3×C5×Q8D412yes—
25C2×Dic30—22no—
26C2×Dic30D412yes—
27C2×C5×D12—22no—
28C2×C5×D12—21no—
29C3×C5×C4⋊C4—22no—
30C3×C42×C5C2311yescharacteristic
31C4⋊Dic15D412yes—
32#6712—24no—
33#6712—22no—
34C4×Dic15—22no—
35C4×Dic15—22no—
36C5×#215—44no—
37C2×C5×C3⋊C8—21no—
38C2×C3×#168—22no—
39#6659—44no—
40#5722—51no—
41#5085D511yescharacteristic
42#4848—52no—
43C3×#333—51no—
44#4484—52no—
45C2×C5×SD16—62no—
46C5×C4⋊Q8C2×D311yescharacteristic
47C5×#127—31no—
48#4090—62no—
49C2×#687—62no—
50#4034—62no—
51#4033—62no—
52C4×Dic10—32no—
53C4×C5×C8—31no—
54#3964—62no—
55C4⋊#168C2×D312yes—
56#1623—151noSylow
57C22×C5×D3—41no—
58C3×C5×Q8—42no—
59C2×C3×C4×C5—22no—
60C2×C3×C4×C5C2×D411yescharacteristic
61C2×C3×C4×C5C2×D412yes—
62C2×Dic15—22no—
63C2×Dic15—22no—
64Dic30—22no—
65Dic30—82no—
66Dic30SD1614yescomplemented
67C5×D12—42no—
68C5×D12—42no—
69C5×D12—42no—
70C3×#168—42no—
71C5×C3⋊C8—22no—
72C3×C4⋊Q8C2×D511yescharacteristic
73#944—102no—
74C2×#215—22no—
75C2×#204—102no—
76#888—102no—
77#887—102no—
78#874C2×D511yescharacteristic
79C4×Dic6—52no—
80C3×C4⋊C8—52no—
81#821—102no—
82C4×C3⋊C8C2×D511yescharacteristic
83C2×C5×Q8D1212yes—
84C2×C5×D4—61no—
85C2×C5×D4—62no—
86C2×Dic10—32no—
87C2×Dic10—62no—
88C5×SD16—124no—
89C2×C5×C8—61no—
90C5×C4⋊C4—22no—
91C42×C5C22×D311yescharacteristic
92#687—124no—
93C4⋊Dic5—32no—
94#683—64no—
95#683—62no—
96C4×Dic5—62no—
97C4×Dic5—62no—
98C2×#168—22no—
99Q82—151no—
100#492—31no—
101#460—152no—
102#333—51no—
103Q8⋊C8—152no—
104C22×C3×C5#12011yescharacteristic
105C2×C5×D3—82no—
106C2×C5×D3—81no—
107C3×C4×C5—21no—
108C3×C4×C5—42no—
109C3×C4×C5C2×SD1612yes—
110C3×C4×C5#13712yes—
111Dic15—24no—
112Dic15—42no—
113C2×C3×Q8C22⋊D512yes—
114C2×D12—22no—
115C2×D12—21no—
116C2×Dic6—52no—
117C2×Dic6—102no—
118C2×C3×C8—102no—
119C3×C4⋊C4—22no—
120C3×C42C22×D511yescharacteristic
121#215—44no—
122C4⋊Dic3—52no—
123Dic3⋊C4—104no—
124Dic3⋊C4—102no—
125C4×Dic3—102no—
126C4×Dic3—102no—
127C2×C3⋊C8—21no—
128#204—204no—
129C23×C5—121no—
130C5×Q8—42no—
131C5×D4—122no—
132C5×D4—122no—
133C5×D4—122no—
134C2×C4×C5—22no—
135C2×C4×C5C2×D1211yescharacteristic
136C2×C4×C5D3×D412yes—
137C2×Dic5—62no—
138C2×Dic5—62no—
139Dic10—34no—
140Dic10—62no—
141Dic10—242no—
142C5×C8—62no—
143#168—42no—
144C2×SD16—62no—
145C2×SD16—302no—
146C4⋊Q8—302no—
147C4⋊Q8—302no—
148C4⋊Q8D3×D511yescharacteristic
149#127—31no—
150C4×Q8—152no—
151C4×Q8—302no—
152C4⋊C8—52no—
153#102—302no—
154C4×C8—31no—
155C2×C3×C5#44812yes—
156C2×C3×C5#45311yescharacteristic
157C5×D3—161no—
158C22×D3—41no—
159C3×Q8—42no—
160C2×C3×C4—22no—
161C2×C3×C4D4×D512yes—
162C2×C3×C4C2×C22⋊D511yescharacteristic
163C2×Dic3—102no—
164C2×Dic3—102no—
165D12—42no—
166D12—42no—
167D12—42no—
168Dic6—54no—
169Dic6—102no—
170Dic6—402no—
171C3×C8—202no—
172C3⋊C8—22no—
173C22×C5—241no—
174C22×C5—242no—
175C22×C5#88211yescharacteristic
176C4×C5—21no—
177C4×C5—42no—
178C4×C5D3×SD1612yes—
179C4×C5#91812yes—
180Dic5—64no—
181Dic5—122no—
182C2×Q8—152no—
183C2×Q8—302no—
184C2×Q8#120312yes—
185C2×D4—61no—
186C2×D4—62no—
187SD16—124no—
188SD16—604no—
189C2×C8—61no—
190C2×C8—102no—
191C4⋊C4—22no—
192C4⋊C4—152no—
193C4⋊C4—304no—
194C4⋊C4—302no—
195C42—302no—
196C42—302no—
197C42C2×D3×D511yescharacteristic
198C3×C5#162311yescharacteristic, complemented, Hall
199C22×C3#408311yescharacteristic
200C2×D3—81no—
201C2×D3—82no—
202C3×C4—21no—
203C3×C4—42no—
204C3×C4D5×SD1612yes—
205C3×C4#406112yes—
206Dic3—104no—
207Dic3—202no—
208C2×C5—481no—
209C2×C5#474711yescharacteristic
210C2×C5#480612yes—
211C23—121no—
212Q8—42no—
213Q8—154no—
214Q8—302no—
215Q8—1202no—
216D4—122no—
217D4—122no—
218D4—122no—
219C2×C4—22no—
220C2×C4—302no—
221C2×C4—302no—
222C2×C4C2×#120311yescharacteristic
223C2×C4#679012yes—
224C8—62no—
225C8—202no—
226C2×C3#6536611yescharacteristic
227C2×C3#6545912yes—
228D3—161no—
229C5#6850411yescharacteristic, complemented, Sylow
230C22—241no—
231C22—242no—
232C22#9157311yescharacteristic
233C4—21no—
234C4—42no—
235C4—304no—
236C4—602no—
237C4#9150512yes—
238C4#9152412yes—
239C3#1060206211yescharacteristic, complemented, Sylow
240C2—481no—
241C2#1174914311yescharacteristic
242C2#1174928712yes—
subgroupG/H
centerC22#91573
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC5×#874C22
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1623
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
1. #11756481C2semidirect
4. C3×#64766C2semidirect
5. #11745844C2semidirect
22. #64766D3semidirect
66. Dic30SD16semidirect
198. C3×C5#1623semidirect
229. C5#68504semidirect
239. C3#10602062semidirect

Maximal subgroups

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

subgroupindex
#117564812
C5×#50852
#117470862
C3×#647662
#117458442
#106020623
#685045