Finite Group Databasebeta

← #14291017

Subgroups — #14291017

Order 1920.

456 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 72 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#11756442C211yesmaximal, characteristic
2C3×#65349C211yesmaximal, characteristic, complemented
3#11746935C212yesmaximal, complemented
4C5×#4540C211yesmaximal, characteristic, complemented
5#11745848C212yesmaximal, complemented
6#10599146—31nomaximal, Hall
7C3×C5×#124C2211yescharacteristic
8#91836—21no—
9#91826—21no—
10#91774—22no—
11#91771—22no—
12#91764C2212yes—
13C2×C3×#689—21no—
14C2×C3×#687—21no—
15C3×#4015C2211yescharacteristic, complemented
16C5×#803C2212yescomplemented
17C3×#3935C2211yescharacteristic, complemented
18#90974—22no—
19#90968—22no—
20#71329—51nomaximal, Hall
21#66017—31no—
22#65349D311yescharacteristic, complemented
23#65003—32no—
24C5×#329—31no—
25#64684—32no—
26C23×D15—21no—
27C2×C3×C5×Q8D411yescharacteristic
28C2×C3×C5×D4D411yescharacteristic
29C2×#1220—22no—
30C2×D60—21no—
31C2×D60D412yes—
32C2×Dic30D412yes—
33C2×C3×Dic10—21no—
34C3×C5×C22⋊C4—22no—
35C3×C42×C5C2311yescharacteristic
36#6719—21no—
37#6714—22no—
38#6714—22no—
39#6714—22no—
40C4×Dic15—21no—
41C2×C5×C3⋊C8—22no—
42C3×#689—42no—
43C3×#687—42no—
44C3×C4⋊Dic5—22no—
45C2×C3×#168—21no—
46#5683—51no—
47C3×#497—51no—
48#5089—52no—
49#4540D511yescharacteristic, complemented
50#4464—52no—
51C5×#124C2×D311yescharacteristic
52#4093—61no—
53C2×#689—21no—
54#4083—61no—
55C2×#687—21no—
56#4031—62no—
57#4028—62no—
58#4021—32no—
59#4015C2×D311yescharacteristic, complemented
60C5×#97—32no—
61#3953—62no—
62#3948—62no—
63#3935C2×D311yescharacteristic, complemented
64#1659—151noSylow
65C23×C3×C5—21no—
66C22×D15—22no—
67C22×D15—81no—
68C22×D15—82no—
69C3×C5×Q8—41no—
70C3×C5×D4—41no—
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5C2×D411yescharacteristic
73C2×C3×C4×C5C2×D412yes—
74#1220—82no—
75C2×Dic15—22no—
76D60—42no—
77D60—81no—
78Dic30—42no—
79C2×C3×Dic5—41no—
80C3×Dic10—41no—
81C3×Dic10—41no—
82C3×#168—22no—
83C5×C3⋊C8—42no—
84C2×C3×Q16—101no—
85C2×C3×SD16—101no—
86C3×C4⋊Q8—51no—
87C3×#124C2×D511yescharacteristic
88#947—101no—
89#937—101no—
90#885—102no—
91#882—102no—
92#875—52no—
93C3×#97—51no—
94#810—102no—
95#809—102no—
96#803C2×D512yescomplemented
97C23×D5—61no—
98C2×C5×Q8#6711yescharacteristic
99C2×C5×D4#6711yescharacteristic
100C2×C22⋊D5—62no—
101C2×D20—32no—
102C2×D20—61no—
103C2×Dic10—21no—
104C2×Dic10—32no—
105C2×C5×C8—62no—
106C5×C22⋊C4—22no—
107C42×C5C22×D311yescharacteristic
108C22⋊Dic5—61no—
109#689—42no—
110#687—42no—
111#685—62no—
112#685—62no—
113#685—62no—
114C4⋊Dic5—22no—
115C4×Dic5—61no—
116C2×#168—21no—
117H(3,𝔽4)—151no—
118#497—51no—
119#489—152no—
120#329—31no—
121#329—152no—
122C22×C3×C5—41no—
123C22×C3×C5—42no—
124C22×C3×C5#12011yescharacteristic
125C2×D15—42no—
126C2×D15—42no—
127C2×D15—42no—
128C2×D15—84no—
129C3×C4×C5—21no—
130C3×C4×C5—22no—
131C3×C4×C5—41no—
132Dic15—42no—
133C3×Dic5—81no—
134C23×D3—101no—
135C2×C3×Q8—101no—
136C2×C3×Q8D2011yescharacteristic
137C2×C3×D4D2011yescharacteristic
138C2×#67—102no—
139C2×D12—52no—
140C2×D12—101no—
141C2×Dic6—52no—
142C3×Q16—202no—
143C3×SD16—202no—
144C2×C3×C8—101no—
145C3×C4⋊C4—102no—
146C3×C22⋊C4—22no—
147C3×C42C22×D511yescharacteristic
148#217—101no—
149(C2×D3)⋊C4—102no—
150(C2×D3)⋊C4—102no—
151(C2×D3)⋊C4—102no—
152C4×Dic3—101no—
153C2×C3⋊C8—22no—
154C23×C5—21no—
155C22×D5—62no—
156C22×D5—242no—
157C22×D5—241no—
158C5×Q8—41no—
159C5×D4—41no—
160C2×C4×C5—21no—
161C2×C4×C5D3×D412yes—
162C2×C4×C5C2×#6711yescharacteristic
163C22⋊D5—242no—
164C2×Dic5—41no—
165C2×Dic5—62no—
166D20—122no—
167D20—241no—
168Dic10—41no—
169Dic10—41no—
170Dic10—122no—
171C5×C8—122no—
172#168—22no—
173C2×Q16—101no—
174C2×SD16—101no—
175C4⋊Q8—51no—
176#124—152no—
177#124—302no—
178#124—301no—
179#124D3×D511yescharacteristic
180#120—302no—
181#120—301no—
182#103—302no—
183#102—302no—
184#97—32no—
185#97—51no—
186C2×C3×C5—81no—
187C2×C3×C5#45311yescharacteristic
188C2×C3×C5#45512yes—
189D15—82no—
190C23×C3—21no—
191C22×D3—102no—
192C22×D3—401no—
193C22×D3—402no—
194C3×Q8—41no—
195C3×Q8—201no—
196C3×Q8—201no—
197C3×D4—41no—
198C2×C3×C4—21no—
199C2×C3×C4—201no—
200C2×C3×C4C2×D2011yescharacteristic
201C2×C3×C4D4×D512yes—
202#67—402no—
203C2×Dic3—102no—
204D12—202no—
205D12—401no—
206Dic6—202no—
207C3×C8—102no—
208C3⋊C8—42no—
209C22×C5—42no—
210C22×C5—41no—
211C22×C5#93711yescharacteristic
212C2×D5—122no—
213C2×D5—122no—
214C2×D5—122no—
215C2×D5—244no—
216C4×C5—22no—
217C4×C5—21no—
218C4×C5—41no—
219Dic5—81no—
220Dic5—122no—
221C24—301no—
222C2×Q8—101no—
223C2×Q8—152no—
224C2×Q8#120211yescharacteristic
225C2×D4—152no—
226C2×D4—301no—
227C2×D4—302no—
228C2×D4#120211yescharacteristic
229Q16—202no—
230SD16—202no—
231C2×C8—62no—
232C2×C8—101no—
233C4⋊C4—102no—
234C22⋊C4—22no—
235C22⋊C4—302no—
236C22⋊C4—301no—
237C22⋊C4—302no—
238C22⋊C4—302no—
239C42—301no—
240C42C2×D3×D511yescharacteristic
241C3×C5#165911yescharacteristic, complemented, Hall
242C22×C3—41no—
243C22×C3—42no—
244C22×C3#402811yescharacteristic
245C2×D3—202no—
246C2×D3—202no—
247C2×D3—202no—
248C2×D3—404no—
249C3×C4—21no—
250C3×C4—22no—
251C3×C4—41no—
252C3×C4—401no—
253Dic3—202no—
254C2×C5—81no—
255C2×C5#507711yescharacteristic
256C2×C5#520212yes—
257D5—242no—
258C23—21no—
259C23—302no—
260C23—1201no—
261C23—1202no—
262Q8—41no—
263Q8—201no—
264Q8—201no—
265Q8—602no—
266D4—41no—
267D4—602no—
268D4—1201no—
269D4—1202no—
270C2×C4—21no—
271C2×C4—201no—
272C2×C4—302no—
273C2×C4C2×#120211yescharacteristic
274C2×C4#679012yes—
275C8—102no—
276C8—122no—
277C2×C3—81no—
278C2×C3#6503611yescharacteristic
279C2×C3#6511412yes—
280D3—402no—
281C5#7132911yescharacteristic, complemented, Sylow
282C22—41no—
283C22—42no—
284C22—602no—
285C22—602no—
286C22—602no—
287C22—1204no—
288C22#9157211yescharacteristic
289C4—21no—
290C4—22no—
291C4—41no—
292C4—401no—
293C4—602no—
294C3#1059914611yescharacteristic, complemented, Sylow
295C2—81no—
296C2—1202no—
297C2#1174914211yescharacteristic
298C2#1174946712yes—
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5#120
prime radical#11756442C2
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. C3×#65349C2semidirect
3. #11746935C2semidirect
4. C5×#4540C2semidirect
5. #11745848C2semidirect
15. C3×#4015C22semidirect
16. C5×#803C22semidirect
17. C3×#3935C22semidirect
22. #65349D3semidirect
49. #4540D5semidirect
59. #4015C2×D3semidirect
63. #3935C2×D3semidirect
96. #803C2×D5semidirect
241. C3×C5#1659semidirect
281. C5#71329semidirect
294. C3#10599146semidirect

Maximal subgroups

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

subgroupindex
#117564422
C3×#653492
#117469352
C5×#45402
#117458482
#105991463
#713295