Finite Group Databasebeta

← #14291014

Subgroups — #14291014

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
2C5×#5060C211yesmaximal, characteristic, complemented
3#11746914C212yesmaximal, complemented
4C3×#64760C211yesmaximal, characteristic, complemented
5#11745848C212yesmaximal, complemented
6#10602122—31nomaximal, Hall
7C3×C5×#124C2211yescharacteristic
8#91836—21no—
9#91826—21no—
10#91774—22no—
11#91771—22no—
12#91764C2212yes—
13C2×C5×#216—21no—
14C2×C5×#214—21no—
15C5×#869C2211yescharacteristic, complemented
16C5×#803C2211yescharacteristic, complemented
17C3×#3935C2212yescomplemented
18#90975—22no—
19#90969—22no—
20#68353—51nomaximal, Hall
21#66017—31no—
22C5×#497—31no—
23#65378—32no—
24#64760D311yescharacteristic, complemented
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×C5×Dic6—21no—
34C3×C5×C22⋊C4—22no—
35C3×C42×C5C2311yescharacteristic
36#6719—21no—
37#6714—22no—
38#6714—22no—
39#6714—22no—
40C4×Dic15—21no—
41C5×#216—42no—
42C5×#214—42no—
43C5×C4⋊Dic3—22no—
44C2×C5×C3⋊C8—21no—
45C2×C3×#168—22no—
46#5683—51no—
47#5060D511yescharacteristic, complemented
48#4714—52no—
49C3×#329—51no—
50#4464—52no—
51C2×C5×Q16—61no—
52C2×C5×SD16—61no—
53C5×C4⋊Q8—31no—
54C5×#124C2×D311yescharacteristic
55#4093—61no—
56#4083—61no—
57#4031—62no—
58#4028—62no—
59#4021—32no—
60C5×#97—31no—
61#3942—62no—
62#3941—62no—
63#3935C2×D312yescomplemented
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×D412yes—
73C2×C3×C4×C5C2×D411yescharacteristic
74#1220—82no—
75C2×Dic15—22no—
76D60—42no—
77D60—81no—
78Dic30—42no—
79C2×C5×Dic3—41no—
80C5×Dic6—41no—
81C5×Dic6—41no—
82C3×#168—42no—
83C5×C3⋊C8—22no—
84C3×#124C2×D511yescharacteristic
85#947—101no—
86C2×#216—21no—
87#937—101no—
88C2×#214—21no—
89#885—102no—
90#882—102no—
91#875—52no—
92#869C2×D511yescharacteristic, complemented
93C3×#97—52no—
94#821—102no—
95#816—102no—
96#803C2×D511yescharacteristic, complemented
97C23×D5—61no—
98C2×C5×Q8—61no—
99C2×C5×Q8D1211yescharacteristic
100C2×C5×D4D1211yescharacteristic
101C2×C22⋊D5—62no—
102C2×D20—32no—
103C2×D20—61no—
104C2×Dic10—32no—
105C5×Q16—122no—
106C5×SD16—122no—
107C2×C5×C8—61no—
108C5×C4⋊C4—62no—
109C5×C22⋊C4—22no—
110C42×C5C22×D311yescharacteristic
111C22⋊Dic5—61no—
112#685—62no—
113#685—62no—
114#685—62no—
115C4×Dic5—61no—
116C2×#168—22no—
117H(3,𝔽4)—151no—
118#497—31no—
119#489—152no—
120#329—51no—
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—
133C5×Dic3—81no—
134C23×D3—101no—
135C2×C3×Q8C22⋊D511yescharacteristic
136C2×C3×D4C22⋊D511yescharacteristic
137C2×#67—102no—
138C2×D12—52no—
139C2×D12—101no—
140C2×Dic6—21no—
141C2×Dic6—52no—
142C2×C3×C8—102no—
143C3×C22⋊C4—22no—
144C3×C42C22×D511yescharacteristic
145#217—101no—
146#216—42no—
147#214—42no—
148(C2×D3)⋊C4—102no—
149(C2×D3)⋊C4—102no—
150(C2×D3)⋊C4—102no—
151C4⋊Dic3—22no—
152C4×Dic3—101no—
153C2×C3⋊C8—21no—
154C23×C5—21no—
155C22×D5—62no—
156C22×D5—241no—
157C22×D5—242no—
158C5×Q8—41no—
159C5×Q8—121no—
160C5×Q8—121no—
161C5×D4—41no—
162C2×C4×C5—21no—
163C2×C4×C5—121no—
164C2×C4×C5C2×D1211yescharacteristic
165C2×C4×C5D3×D412yes—
166C22⋊D5—242no—
167C2×Dic5—62no—
168D20—122no—
169D20—241no—
170Dic10—122no—
171C5×C8—62no—
172#168—42no—
173C2×Q16—61no—
174C2×SD16—61no—
175C4⋊Q8—31no—
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—31no—
185#97—52no—
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×D4—41no—
196C2×C3×C4—21no—
197C2×C3×C4D4×D512yes—
198C2×C3×C4C2×C22⋊D511yescharacteristic
199#67—402no—
200C2×Dic3—41no—
201C2×Dic3—102no—
202D12—202no—
203D12—401no—
204Dic6—41no—
205Dic6—41no—
206Dic6—202no—
207C3×C8—202no—
208C3⋊C8—22no—
209C22×C5—41no—
210C22×C5—42no—
211C22×C5#88211yescharacteristic
212C2×D5—122no—
213C2×D5—122no—
214C2×D5—122no—
215C2×D5—244no—
216C4×C5—21no—
217C4×C5—22no—
218C4×C5—41no—
219C4×C5—241no—
220Dic5—122no—
221C24—301no—
222C2×Q8—61no—
223C2×Q8—152no—
224C2×Q8#120311yescharacteristic
225C2×D4—152no—
226C2×D4—301no—
227C2×D4—302no—
228C2×D4#120311yescharacteristic
229Q16—122no—
230SD16—122no—
231C2×C8—61no—
232C2×C8—102no—
233C4⋊C4—62no—
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#408311yescharacteristic
245C2×D3—202no—
246C2×D3—202no—
247C2×D3—202no—
248C2×D3—404no—
249C3×C4—21no—
250C3×C4—22no—
251C3×C4—41no—
252Dic3—81no—
253Dic3—202no—
254C2×C5—81no—
255C2×C5#474711yescharacteristic
256C2×C5#482512yes—
257D5—242no—
258C23—21no—
259C23—302no—
260C23—1201no—
261C23—1202no—
262Q8—41no—
263Q8—121no—
264Q8—121no—
265Q8—602no—
266D4—41no—
267D4—602no—
268D4—1201no—
269D4—1202no—
270C2×C4—21no—
271C2×C4—121no—
272C2×C4—302no—
273C2×C4C2×#120311yescharacteristic
274C2×C4#679012yes—
275C8—62no—
276C8—202no—
277C2×C3—81no—
278C2×C3#6536611yescharacteristic
279C2×C3#6549112yes—
280D3—402no—
281C5#6835311yescharacteristic, complemented, Sylow
282C22—41no—
283C22—42no—
284C22—602no—
285C22—602no—
286C22—602no—
287C22—1204no—
288C22#9157311yescharacteristic
289C4—21no—
290C4—22no—
291C4—41no—
292C4—241no—
293C4—602no—
294C3#1060212211yescharacteristic, complemented, Sylow
295C2—81no—
296C2—1202no—
297C2#1174914311yescharacteristic
298C2#1174946812yes—
subgroupG/H
centerC22#91573
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. C5×#5060C2semidirect
3. #11746914C2semidirect
4. C3×#64760C2semidirect
5. #11745848C2semidirect
15. C5×#869C22semidirect
16. C5×#803C22semidirect
17. C3×#3935C22semidirect
24. #64760D3semidirect
47. #5060D5semidirect
63. #3935C2×D3semidirect
92. #869C2×D5semidirect
96. #803C2×D5semidirect
241. C3×C5#1659semidirect
281. C5#68353semidirect
294. C3#10602122semidirect

Maximal subgroups

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

subgroupindex
#117564422
C5×#50602
#117469142
C3×#647602
#117458482
#106021223
#683535