Finite Group Databasebeta

← #14291018

Subgroups — #14291018

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
1C3×#66017C211yesmaximal, characteristic
2#11751161C211yesmaximal, characteristic, complemented
3#11746893C212yesmaximal, complemented
4C5×#4540C211yesmaximal, characteristic, complemented
5#11745846C212yesmaximal, complemented
6#10599146—31nomaximal, Hall
7C3×C5×#124C2211yescharacteristic
8C2×#6718—21no—
9C2×#6716—21no—
10#91758C2211yescharacteristic, complemented
11C3×#4093—21no—
12C3×#4083—21no—
13C3×#4031—22no—
14C3×#4028—22no—
15C3×#4021C2212yes—
16#91087C2211yescharacteristic, complemented
17C5×#803C2212yescomplemented
18#90971—22no—
19#90965—22no—
20#71949—51nomaximal, Hall
21#66017D311yescharacteristic
22#65349—31no—
23#65003—32no—
24C5×#329—31no—
25#64684—32no—
26C23×C3×D5—21no—
27C2×C3×C5×Q8D411yescharacteristic
28C2×C3×C5×D4D411yescharacteristic
29C2×Dic30—21no—
30C2×C3×C22⋊D5—22no—
31C2×C3×D20—21no—
32C2×C3×D20D412yes—
33C2×C3×Dic10D412yes—
34C3×C5×C22⋊C4—22no—
35C3×C42×C5C2311yescharacteristic
36#6718—42no—
37#6716—42no—
38C4⋊Dic15—22no—
39C2×C3⋊#168—21no—
40C2×C5×C3⋊C8—22no—
41C3×C22⋊Dic5—21no—
42C3×#685—22no—
43C3×#685—22no—
44C3×#685—22no—
45C3×C4×Dic5—21no—
46C3×H(3,𝔽4)—51no—
47#5060—51no—
48#5055—52no—
49#4540—52no—
50#4540D511yescharacteristic, complemented
51C5×#124C2×D311yescharacteristic
52#4093—21no—
53C2×#689—61no—
54#4083—21no—
55C2×#687—61no—
56#4031—22no—
57#4028—22no—
58#4021C2×D312yes—
59#4015—31no—
60C5×#97—32no—
61#3953—62no—
62#3948—62no—
63#3935—31no—
64#1659—151noSylow
65C23×C3×C5—21no—
66C22×C3×D5—22no—
67C22×C3×D5—81no—
68C22×C3×D5—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—
77C3×C22⋊D5—82no—
78C2×C3×Dic5—22no—
79C3×D20—42no—
80C3×D20—81no—
81C3×Dic10—42no—
82C3⋊#168—22no—
83C5×C3⋊C8—42no—
84C3×#124—52no—
85C3×#124—102no—
86C3×#124—101no—
87C3×#124C2×D511yescharacteristic
88C3×#120—102no—
89C3×#120—101no—
90C2×#216—101no—
91C2×#214—101no—
92#869—51no—
93#835—102no—
94#832—102no—
95#803—51no—
96#803C2×D512yescomplemented
97C23×D5—21no—
98C2×C5×Q8#6711yescharacteristic
99C2×C5×D4#6711yescharacteristic
100C2×C22⋊D5—22no—
101C2×D20—21no—
102C2×D20#6712yes—
103C2×Dic10—61no—
104C2×Dic10#6712yes—
105C2×C5×C8—62no—
106C5×C22⋊C4—22no—
107C42×C5C22×D311yescharacteristic
108C22⋊Dic5—21no—
109#689—122no—
110#687—122no—
111#685—22no—
112#685—22no—
113#685—22no—
114C4⋊Dic5—62no—
115C4×Dic5—21no—
116C2×#168—61no—
117H(3,𝔽4)—51no—
118#497—151no—
119#489—152no—
120#329—31no—
121#329—152no—
122C22×C3×C5—41no—
123C22×C3×C5—42no—
124C22×C3×C5#12011yescharacteristic
125C2×C3×D5—42no—
126C2×C3×D5—42no—
127C2×C3×D5—42no—
128C2×C3×D5—84no—
129C3×C4×C5—21no—
130C3×C4×C5—22no—
131C3×C4×C5—41no—
132Dic15—81no—
133C3×Dic5—42no—
134C24×C3—101no—
135C2×C3×Q8—52no—
136C2×C3×Q8D2011yescharacteristic
137C2×C3×D4—52no—
138C2×C3×D4—101no—
139C2×C3×D4—102no—
140C2×C3×D4D2011yescharacteristic
141C2×Dic6—101no—
142C3×C22⋊C4—22no—
143C3×C22⋊C4—102no—
144C3×C22⋊C4—101no—
145C3×C22⋊C4—102no—
146C3×C22⋊C4—102no—
147C3×C42—101no—
148C3×C42C22×D511yescharacteristic
149#216—202no—
150#214—202no—
151C4⋊Dic3—102no—
152C2×C3⋊C8—22no—
153C2×C3⋊C8—101no—
154C23×C5—21no—
155C22×D5—22no—
156C22×D5—81no—
157C22×D5—82no—
158C5×Q8—41no—
159C5×D4—41no—
160C2×C4×C5—21no—
161C2×C4×C5C2×#6711yescharacteristic
162C2×C4×C5C2×#6712yes—
163C22⋊D5—82no—
164C2×Dic5—22no—
165C2×Dic5—121no—
166D20—42no—
167D20—81no—
168Dic10—42no—
169Dic10—121no—
170Dic10—121no—
171C5×C8—122no—
172#168—62no—
173C2×Q16—301no—
174C2×SD16—301no—
175C4⋊Q8—151no—
176#124—52no—
177#124—102no—
178#124—101no—
179#124D3×D511yescharacteristic
180#120—102no—
181#120—101no—
182#103—302no—
183#102—302no—
184#97—32no—
185#97—151no—
186C2×C3×C5—81no—
187C2×C3×C5#45311yescharacteristic
188C2×C3×C5#45512yes—
189C3×D5—82no—
190C23×C3—21no—
191C23×C3—102no—
192C23×C3—401no—
193C23×C3—402no—
194C3×Q8—41no—
195C3×Q8—202no—
196C3×D4—41no—
197C3×D4—202no—
198C3×D4—401no—
199C3×D4—402no—
200C2×C3×C4—21no—
201C2×C3×C4—102no—
202C2×C3×C4C2×D2011yescharacteristic
203C2×C3×C4D4×D512yes—
204C2×Dic3—201no—
205Dic6—201no—
206Dic6—201no—
207C3⋊C8—42no—
208C3⋊C8—102no—
209C22×C5—41no—
210C22×C5—42no—
211C22×C5#95311yescharacteristic
212C2×D5—42no—
213C2×D5—42no—
214C2×D5—42no—
215C2×D5—84no—
216C4×C5—21no—
217C4×C5—22no—
218C4×C5—41no—
219Dic5—42no—
220Dic5—241no—
221C24—101no—
222C2×Q8—52no—
223C2×Q8—301no—
224C2×Q8#120211yescharacteristic
225C2×D4—52no—
226C2×D4—101no—
227C2×D4—102no—
228C2×D4#120211yescharacteristic
229Q16—602no—
230SD16—602no—
231C2×C8—62no—
232C2×C8—301no—
233C4⋊C4—302no—
234C22⋊C4—22no—
235C22⋊C4—102no—
236C22⋊C4—101no—
237C22⋊C4—102no—
238C22⋊C4—102no—
239C42—101no—
240C42C2×D3×D511yescharacteristic
241C3×C5#165911yescharacteristic, complemented, Hall
242C22×C3—41no—
243C22×C3—42no—
244C22×C3—202no—
245C22×C3—202no—
246C22×C3—202no—
247C22×C3—404no—
248C22×C3#402811yescharacteristic
249C3×C4—21no—
250C3×C4—22no—
251C3×C4—41no—
252C3×C4—202no—
253Dic3—401no—
254C2×C5—81no—
255C2×C5#524111yescharacteristic
256C2×C5#524212yes—
257D5—82no—
258C23—21no—
259C23—102no—
260C23—401no—
261C23—402no—
262Q8—41no—
263Q8—202no—
264Q8—601no—
265Q8—601no—
266D4—41no—
267D4—202no—
268D4—401no—
269D4—402no—
270C2×C4—21no—
271C2×C4—102no—
272C2×C4—601no—
273C2×C4C2×#120211yescharacteristic
274C2×C4D5×#6712yes—
275C8—122no—
276C8—302no—
277C2×C3—81no—
278C2×C3—402no—
279C2×C3#6503611yescharacteristic
280C2×C3#6511412yes—
281C5#7194911yescharacteristic, complemented, Sylow
282C22—41no—
283C22—42no—
284C22—202no—
285C22—202no—
286C22—202no—
287C22—404no—
288C22#9156411yescharacteristic
289C4—21no—
290C4—22no—
291C4—41no—
292C4—202no—
293C4—1201no—
294C3#1059914611yescharacteristic, complemented, Sylow
295C2—81no—
296C2—402no—
297C2#1174913811yescharacteristic
298C2#1174946312yes—
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5#120
prime radicalC3×#66017C2
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. #11746893C2semidirect
4. C5×#4540C2semidirect
5. #11745846C2semidirect
10. #91758C22semidirect
16. #91087C22semidirect
17. C5×#803C22semidirect
50. #4540D5semidirect
96. #803C2×D5semidirect
241. C3×C5#1659semidirect
281. C5#71949semidirect
294. C3#10599146semidirect

Maximal subgroups

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

subgroupindex
C3×#660172
#117511612
#117468932
C5×#45402
#117458462
#105991463
#719495