Finite Group Databasebeta

← #14291016

Subgroups — #14291016

Order 1920.

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

normal subgroups only

This group has 456 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
1C5×#5683C211yesmaximal, characteristic
2#11751161C211yesmaximal, characteristic, complemented
3#11746909C212yesmaximal, complemented
4C3×#64760C211yesmaximal, characteristic, complemented
5#11745847C212yesmaximal, complemented
6#10602742—31nomaximal, Hall
7C3×C5×#124C2211yescharacteristic
8C2×#6718—21no—
9C2×#6716—21no—
10#91758C2211yescharacteristic, complemented
11C5×#947—21no—
12C5×#937—21no—
13C5×#885—22no—
14C5×#882—22no—
15C5×#875C2212yes—
16#91087C2211yescharacteristic, complemented
17C3×#3935C2212yescomplemented
18#90973—22no—
19#90967—22no—
20#68353—51nomaximal, Hall
21C5×H(3,𝔽4)—31no—
22#65349—31no—
23#65344—32no—
24#64760—32no—
25#64760D311yescharacteristic, complemented
26C23×C5×D3—21no—
27C2×C3×C5×Q8D411yescharacteristic
28C2×C3×C5×D4D411yescharacteristic
29C2×Dic30—21no—
30C2×C5×#67—22no—
31C2×C5×D12—21no—
32C2×C5×D12D412yes—
33C2×C5×Dic6D412yes—
34C3×C5×C22⋊C4—22no—
35C3×C42×C5C2311yescharacteristic
36#6718—42no—
37#6716—42no—
38C4⋊Dic15—22no—
39C2×C3⋊#168—21no—
40C5×#217—21no—
41C5×(C2×D3)⋊C4—22no—
42C5×(C2×D3)⋊C4—22no—
43C5×(C2×D3)⋊C4—22no—
44C4×C5×Dic3—21no—
45C2×C3×#168—22no—
46#5683D511yescharacteristic
47#5060—51no—
48#4714—52no—
49C3×#329—51no—
50#4464—52no—
51C5×#124—32no—
52C5×#124—62no—
53C5×#124—61no—
54C5×#124C2×D311yescharacteristic
55C5×#120—62no—
56C5×#120—61no—
57C2×#689—61no—
58C2×#687—61no—
59#4015—31no—
60#3967—62no—
61#3964—62no—
62#3935—31no—
63#3935C2×D312yescomplemented
64#1659—151noSylow
65C23×C3×C5—21no—
66C22×C5×D3—22no—
67C22×C5×D3—81no—
68C22×C5×D3—82no—
69C3×C5×Q8—41no—
70C3×C5×D4—41no—
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5C2×D411yescharacteristic
73C2×C3×C4×C5C2×D412yes—
74C2×Dic15—41no—
75Dic30—41no—
76Dic30—41no—
77C5×#67—82no—
78C2×C5×Dic3—22no—
79C5×D12—42no—
80C5×D12—81no—
81C5×Dic6—42no—
82C3⋊#168—22no—
83C3×#168—42no—
84C3×#124C2×D511yescharacteristic
85#947—21no—
86C2×#216—101no—
87#937—21no—
88C2×#214—101no—
89#885—22no—
90#882—22no—
91#875C2×D512yes—
92#869—51no—
93C3×#97—52no—
94#821—102no—
95#816—102no—
96#803—51no—
97C24×C5—61no—
98C2×C5×Q8—32no—
99C2×C5×Q8D1211yescharacteristic
100C2×C5×D4—32no—
101C2×C5×D4—61no—
102C2×C5×D4—62no—
103C2×C5×D4D1211yescharacteristic
104C2×Dic10—61no—
105C5×C22⋊C4—22no—
106C5×C22⋊C4—62no—
107C5×C22⋊C4—61no—
108C5×C22⋊C4—62no—
109C5×C22⋊C4—62no—
110C42×C5—61no—
111C42×C5C22×D311yescharacteristic
112#689—122no—
113#687—122no—
114C4⋊Dic5—62no—
115C2×#168—22no—
116C2×#168—61no—
117H(3,𝔽4)—31no—
118#497—151no—
119#489—152no—
120#329—51no—
121#329—152no—
122C22×C3×C5—41no—
123C22×C3×C5—42no—
124C22×C3×C5#12011yescharacteristic
125C2×C5×D3—42no—
126C2×C5×D3—42no—
127C2×C5×D3—42no—
128C2×C5×D3—84no—
129C3×C4×C5—21no—
130C3×C4×C5—22no—
131C3×C4×C5—41no—
132Dic15—81no—
133C5×Dic3—42no—
134C23×D3—21no—
135C2×C3×Q8C22⋊D511yescharacteristic
136C2×C3×D4C22⋊D511yescharacteristic
137C2×#67—22no—
138C2×D12—21no—
139C2×D12C22⋊D512yes—
140C2×Dic6—101no—
141C2×Dic6C22⋊D512yes—
142C2×C3×C8—102no—
143C3×C22⋊C4—22no—
144C3×C42C22×D511yescharacteristic
145#217—21no—
146#216—202no—
147#214—202no—
148(C2×D3)⋊C4—22no—
149(C2×D3)⋊C4—22no—
150(C2×D3)⋊C4—22no—
151C4⋊Dic3—102no—
152C4×Dic3—21no—
153C2×C3⋊C8—101no—
154C23×C5—21no—
155C23×C5—62no—
156C23×C5—241no—
157C23×C5—242no—
158C5×Q8—41no—
159C5×Q8—122no—
160C5×D4—41no—
161C5×D4—122no—
162C5×D4—241no—
163C5×D4—242no—
164C2×C4×C5—21no—
165C2×C4×C5—62no—
166C2×C4×C5C2×D1211yescharacteristic
167C2×C4×C5D3×D412yes—
168C2×Dic5—121no—
169Dic10—121no—
170Dic10—121no—
171#168—42no—
172#168—62no—
173C2×Q16—301no—
174C2×SD16—301no—
175C4⋊Q8—151no—
176#124—32no—
177#124—62no—
178#124—61no—
179#124D3×D511yescharacteristic
180#120—62no—
181#120—61no—
182#103—302no—
183#102—302no—
184#97—52no—
185#97—151no—
186C2×C3×C5—81no—
187C2×C3×C5#45311yescharacteristic
188C2×C3×C5#45512yes—
189C5×D3—82no—
190C23×C3—21no—
191C22×D3—22no—
192C22×D3—81no—
193C22×D3—82no—
194C3×Q8—41no—
195C3×D4—41no—
196C2×C3×C4—21no—
197C2×C3×C4C2×C22⋊D511yescharacteristic
198C2×C3×C4C2×C22⋊D512yes—
199#67—82no—
200C2×Dic3—22no—
201C2×Dic3—201no—
202D12—42no—
203D12—81no—
204Dic6—42no—
205Dic6—201no—
206Dic6—201no—
207C3×C8—202no—
208C3⋊C8—102no—
209C22×C5—41no—
210C22×C5—42no—
211C22×C5—122no—
212C22×C5—122no—
213C22×C5—122no—
214C22×C5—244no—
215C22×C5#88211yescharacteristic
216C4×C5—21no—
217C4×C5—22no—
218C4×C5—41no—
219C4×C5—122no—
220Dic5—241no—
221C24—61no—
222C2×Q8—32no—
223C2×Q8—301no—
224C2×Q8#120311yescharacteristic
225C2×D4—32no—
226C2×D4—61no—
227C2×D4—62no—
228C2×D4#120311yescharacteristic
229Q16—602no—
230SD16—602no—
231C2×C8—102no—
232C2×C8—301no—
233C4⋊C4—302no—
234C22⋊C4—22no—
235C22⋊C4—62no—
236C22⋊C4—61no—
237C22⋊C4—62no—
238C22⋊C4—62no—
239C42—61no—
240C42C2×D3×D511yescharacteristic
241C3×C5#165911yescharacteristic, complemented, Hall
242C22×C3—41no—
243C22×C3—42no—
244C22×C3#409911yescharacteristic
245C2×D3—42no—
246C2×D3—42no—
247C2×D3—42no—
248C2×D3—84no—
249C3×C4—21no—
250C3×C4—22no—
251C3×C4—41no—
252Dic3—42no—
253Dic3—401no—
254C2×C5—81no—
255C2×C5—242no—
256C2×C5#474711yescharacteristic
257C2×C5#482512yes—
258C23—21no—
259C23—62no—
260C23—241no—
261C23—242no—
262Q8—41no—
263Q8—122no—
264Q8—601no—
265Q8—601no—
266D4—41no—
267D4—122no—
268D4—241no—
269D4—242no—
270C2×C4—21no—
271C2×C4—62no—
272C2×C4—601no—
273C2×C4C2×#120311yescharacteristic
274C2×C4D3×C22⋊D512yes—
275C8—202no—
276C8—302no—
277C2×C3—81no—
278C2×C3#6553011yescharacteristic
279C2×C3#6553112yes—
280D3—82no—
281C5#6835311yescharacteristic, complemented, Sylow
282C22—41no—
283C22—42no—
284C22—122no—
285C22—122no—
286C22—122no—
287C22—244no—
288C22#9157011yescharacteristic
289C4—21no—
290C4—22no—
291C4—41no—
292C4—122no—
293C4—1201no—
294C3#1060274211yescharacteristic, complemented, Sylow
295C2—81no—
296C2—242no—
297C2#1174914111yescharacteristic
298C2#1174946612yes—
subgroupG/H
centerC22#91570
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5#120
prime radicalC5×#5683C2
hypercenter#124D3×D5
hypocenterC3×C5#1659
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11751161C2semidirect
3. #11746909C2semidirect
4. C3×#64760C2semidirect
5. #11745847C2semidirect
10. #91758C22semidirect
16. #91087C22semidirect
17. C3×#3935C22semidirect
25. #64760D3semidirect
63. #3935C2×D3semidirect
241. C3×C5#1659semidirect
281. C5#68353semidirect
294. C3#10602742semidirect

Maximal subgroups

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

subgroupindex
C5×#56832
#117511612
#117469092
C3×#647602
#117458472
#106027423
#683535