Finite Group Databasebeta

← #14291006

Subgroups — #14291006

Order 1920.

456 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 75 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
2#11751161C211yesmaximal, characteristic, complemented
3#11750815C212yesmaximal, complemented
4C3×C5×#329C211yesmaximal, characteristic, complemented
5#11746285C212yesmaximal, complemented
6#10599146—31nomaximal, Hall
7C3×C5×#124C2211yescharacteristic
8#91836—21no—
9C2×#6718—21no—
10#91826—21no—
11C2×#6716—21no—
12#91774—22no—
13#91771—22no—
14#91764C2212yes—
15#91758C2211yescharacteristic, complemented
16C3×C5×#97C2212yescomplemented
17#91105—22no—
18#91100—22no—
19#91087C2211yescharacteristic, complemented
20#68353—51nomaximal, Hall
21#66017—31no—
22#65349—31no—
23#65003—32no—
24C5×#329D311yescharacteristic, complemented
25#64684—32no—
26C23×D15—21no—
27C2×C3×C5×Q8D411yescharacteristic
28C2×C3×C5×D4D411yescharacteristic
29C2×#1220—22no—
30C2×D60—21no—
31C2×D60D412yes—
32C2×Dic30—21no—
33C2×Dic30D412yes—
34C2×C3×C5×C8—22no—
35C3×C5×C22⋊C4—22no—
36C3×C42×C5C2311yescharacteristic
37#6719—21no—
38#6718—42no—
39#6716—42no—
40#6714—22no—
41#6714—22no—
42#6714—22no—
43C4⋊Dic15—22no—
44C4×Dic15—21no—
45C2×C3⋊#168—21no—
46#5683—51no—
47#5060—51no—
48#4714—52no—
49C3×#329D511yescharacteristic, complemented
50#4464—52no—
51C5×#124C2×D311yescharacteristic
52#4093—61no—
53C2×#689—61no—
54#4083—61no—
55C2×#687—61no—
56#4031—62no—
57#4028—62no—
58#4021—32no—
59#4015—31no—
60C5×#97C2×D312yescomplemented
61#3953—62no—
62#3948—62no—
63#3935—31no—
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—
76C2×Dic15—41no—
77D60—42no—
78D60—81no—
79Dic30—42no—
80Dic30—41no—
81Dic30—41no—
82C3×C5×C8—42no—
83C3⋊#168—22no—
84C3×#124C2×D511yescharacteristic
85#947—101no—
86C2×#216—101no—
87#937—101no—
88C2×#214—101no—
89#885—102no—
90#882—102no—
91#875—52no—
92#869—51no—
93C3×#97C2×D512yescomplemented
94#821—102no—
95#816—102no—
96#803—51no—
97C23×D5—61no—
98C2×C5×Q8D1211yescharacteristic
99C2×C5×D4D1211yescharacteristic
100C2×C22⋊D5—62no—
101C2×D20—32no—
102C2×D20—61no—
103C2×Dic10—32no—
104C2×Dic10—61no—
105C2×C5×C8—22no—
106C5×C22⋊C4—22no—
107C42×C5C22×D311yescharacteristic
108C22⋊Dic5—61no—
109#689—122no—
110#687—122no—
111#685—62no—
112#685—62no—
113#685—62no—
114C4⋊Dic5—62no—
115C4×Dic5—61no—
116C2×#168—61no—
117H(3,𝔽4)—151no—
118#497—151no—
119#489—152no—
120#329—152no—
121#329D1511yescharacteristic, complemented
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—
133Dic15—81no—
134C23×D3—101no—
135C2×C3×Q8D2011yescharacteristic
136C2×C3×D4D2011yescharacteristic
137C2×#67—102no—
138C2×D12—52no—
139C2×D12—101no—
140C2×Dic6—52no—
141C2×Dic6—101no—
142C2×C3×C8—22no—
143C3×C22⋊C4—22no—
144C3×C42C22×D511yescharacteristic
145#217—101no—
146#216—202no—
147#214—202no—
148(C2×D3)⋊C4—102no—
149(C2×D3)⋊C4—102no—
150(C2×D3)⋊C4—102no—
151C4⋊Dic3—102no—
152C4×Dic3—101no—
153C2×C3⋊C8—101no—
154C23×C5—21no—
155C22×D5—62no—
156C22×D5—241no—
157C22×D5—242no—
158C5×Q8—41no—
159C5×D4—41no—
160C2×C4×C5—21no—
161C2×C4×C5C2×D1211yescharacteristic
162C2×C4×C5D3×D412yes—
163C22⋊D5—242no—
164C2×Dic5—62no—
165C2×Dic5—121no—
166D20—122no—
167D20—241no—
168Dic10—122no—
169Dic10—121no—
170Dic10—121no—
171C5×C8—42no—
172#168—62no—
173C2×Q16—301no—
174C2×SD16—301no—
175C4⋊Q8—151no—
176#124—152no—
177#124—302no—
178#124—301no—
179#124C2×D1511yescharacteristic
180#120—302no—
181#120—301no—
182#103—302no—
183#102—302no—
184#97—151no—
185#97C2×D1512yescomplemented
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×C4C2×D2011yescharacteristic
198C2×C3×C4D4×D512yes—
199#67—402no—
200C2×Dic3—102no—
201C2×Dic3—201no—
202D12—202no—
203D12—401no—
204Dic6—202no—
205Dic6—201no—
206Dic6—201no—
207C3×C8—42no—
208C3⋊C8—102no—
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—
219Dic5—122no—
220Dic5—241no—
221C24—301no—
222C2×Q8—152no—
223C2×Q8—301no—
224C2×Q8D6011yescharacteristic
225C2×D4—152no—
226C2×D4—301no—
227C2×D4—302no—
228C2×D4D6011yescharacteristic
229Q16—602no—
230SD16—602no—
231C2×C8—22no—
232C2×C8—301no—
233C4⋊C4—302no—
234C22⋊C4—22no—
235C22⋊C4—302no—
236C22⋊C4—301no—
237C22⋊C4—302no—
238C22⋊C4—302no—
239C42—301no—
240C42C22×D1511yescharacteristic
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—
252Dic3—202no—
253Dic3—401no—
254C2×C5—81no—
255C2×C5#474711yescharacteristic
256C2×C5#482512yes—
257D5—242no—
258C23—21no—
259C23—302no—
260C23—1202no—
261C23—1201no—
262Q8—41no—
263Q8—602no—
264Q8—601no—
265Q8—601no—
266D4—41no—
267D4—602no—
268D4—1201no—
269D4—1202no—
270C2×C4—21no—
271C2×C4—302no—
272C2×C4—601no—
273C2×C4C2×D6011yescharacteristic
274C2×C4D4×D1512yes—
275C8—42no—
276C8—302no—
277C2×C3—81no—
278C2×C3#6503611yescharacteristic
279C2×C3#6511412yes—
280D3—402no—
281C5#6835311yescharacteristic, complemented, Sylow
282C22—42no—
283C22—41no—
284C22—602no—
285C22—602no—
286C22—602no—
287C22—1204no—
288C22#9177111yescharacteristic
289C4—22no—
290C4—21no—
291C4—41no—
292C4—602no—
293C4—1201no—
294C3#1059914611yescharacteristic, complemented, Sylow
295C2—81no—
296C2—1202no—
297C2#1175084811yescharacteristic
298C2#1175092612yes—
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#329C2
socleC22×C3×C5#120
prime radical#11756442C2
hypercenter#329D15
hypocenterC3×C5#1659
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #11751161C2semidirect
3. #11750815C2semidirect
4. C3×C5×#329C2semidirect
5. #11746285C2semidirect
15. #91758C22semidirect
16. C3×C5×#97C22semidirect
19. #91087C22semidirect
24. C5×#329D3semidirect
49. C3×#329D5semidirect
60. C5×#97C2×D3semidirect
93. C3×#97C2×D5semidirect
121. #329D15semidirect
185. #97C2×D15semidirect
241. C3×C5#1659semidirect
281. C5#68353semidirect
294. C3#10599146semidirect

Maximal subgroups

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

subgroupindex
#117564422
#117511612
#117508152
C3×C5×#3292
#117462852
#105991463
#683535