Finite Group Databasebeta

← #14291013

Subgroups — #14291013

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
2C5×#5060C211yesmaximal, characteristic, complemented
3#11746898C212yesmaximal, complemented
4#11746361C211yesmaximal, characteristic, complemented
5#11745846C212yesmaximal, complemented
6#10602122—31nomaximal, Hall
7C3×C5×#124C2211yescharacteristic
8C2×C5×#216—21no—
9C2×C5×#214—21no—
10C5×#869C2211yescharacteristic, complemented
11C3×#4093—21no—
12C3×#4083—21no—
13C3×#4031—22no—
14C3×#4028—22no—
15C3×#4021C2212yes—
16#91087C2212yescomplemented
17C5×#803C2211yescharacteristic, complemented
18#90970—22no—
19#90964—22no—
20#71949—51nomaximal, Hall
21#66017D311yescharacteristic
22C5×#497—31no—
23#65378—32no—
24#64760—31no—
25#64684—32no—
26C23×C3×D5—21no—
27C2×C3×C5×Q8D411yescharacteristic
28C2×C3×C5×D4D411yescharacteristic
29C2×C5×Dic6—21no—
30C2×C3×C22⋊D5—22no—
31C2×C3×D20—21no—
32C2×C3×D20D412yes—
33C2×C3×Dic10D412yes—
34C3×C5×C22⋊C4—22no—
35C3×C42×C5C2311yescharacteristic
36C2×C3⋊#168—22no—
37C5×#216—42no—
38C5×#214—42no—
39C5×C4⋊Dic3—22no—
40C2×C5×C3⋊C8—21no—
41C3×C22⋊Dic5—21no—
42C3×#685—22no—
43C3×#685—22no—
44C3×#685—22no—
45C3×C4×Dic5—21no—
46C3×H(3,𝔽4)—51no—
47#5060D511yescharacteristic, complemented
48#5055—52no—
49#4540—51no—
50#4540—52no—
51C2×C5×Q16—61no—
52C2×C5×SD16—61no—
53C5×C4⋊Q8—31no—
54C5×#124C2×D311yescharacteristic
55#4093—21no—
56#4083—21no—
57#4031—22no—
58#4028—22no—
59#4021C2×D312yes—
60C5×#97—31no—
61#3942—62no—
62#3941—62no—
63#3935—32no—
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×D412yes—
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×C5×Dic3—41no—
75C5×Dic6—41no—
76C5×Dic6—41no—
77C3×C22⋊D5—82no—
78C2×C3×Dic5—22no—
79C3×D20—42no—
80C3×D20—81no—
81C3×Dic10—42no—
82C3⋊#168—42no—
83C5×C3⋊C8—22no—
84C3×#124—52no—
85C3×#124—102no—
86C3×#124—101no—
87C3×#124C2×D511yescharacteristic
88C3×#120—102no—
89C3×#120—101no—
90C2×#216—21no—
91C2×#214—21no—
92#869C2×D511yescharacteristic, complemented
93#835—102no—
94#832—102no—
95#803—52no—
96#803C2×D511yescharacteristic, complemented
97C23×D5—21no—
98C2×C5×Q8—61no—
99C2×C5×Q8#6711yescharacteristic
100C2×C5×D4#6711yescharacteristic
101C2×C22⋊D5—22no—
102C2×D20—21no—
103C2×D20#6712yes—
104C2×Dic10#6712yes—
105C5×Q16—122no—
106C5×SD16—122no—
107C2×C5×C8—61no—
108C5×C4⋊C4—62no—
109C5×C22⋊C4—22no—
110C42×C5C22×D311yescharacteristic
111C22⋊Dic5—21no—
112#685—22no—
113#685—22no—
114#685—22no—
115C4×Dic5—21no—
116C2×#168—62no—
117H(3,𝔽4)—51no—
118#497—31no—
119#489—152no—
120#329—152no—
121#329—151no—
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—
132C3×Dic5—42no—
133C5×Dic3—81no—
134C24×C3—101no—
135C2×C3×Q8—52no—
136C2×C3×Q8C22⋊D511yescharacteristic
137C2×C3×D4—52no—
138C2×C3×D4—101no—
139C2×C3×D4—102no—
140C2×C3×D4C22⋊D511yescharacteristic
141C2×Dic6—21no—
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—42no—
150#214—42no—
151C4⋊Dic3—22no—
152C2×C3⋊C8—21no—
153C2×C3⋊C8—102no—
154C23×C5—21no—
155C22×D5—22no—
156C22×D5—81no—
157C22×D5—82no—
158C5×Q8—41no—
159C5×Q8—121no—
160C5×Q8—121no—
161C5×D4—41no—
162C2×C4×C5—21no—
163C2×C4×C5—121no—
164C2×C4×C5C2×#6711yescharacteristic
165C2×C4×C5C2×#6712yes—
166C22⋊D5—82no—
167C2×Dic5—22no—
168D20—42no—
169D20—81no—
170Dic10—42no—
171C5×C8—62no—
172#168—122no—
173C2×Q16—61no—
174C2×SD16—61no—
175C4⋊Q8—31no—
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—31no—
185#97—152no—
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×C4D4×D512yes—
203C2×C3×C4C2×C22⋊D511yescharacteristic
204C2×Dic3—41no—
205Dic6—41no—
206Dic6—41no—
207C3⋊C8—22no—
208C3⋊C8—202no—
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—
219C4×C5—241no—
220Dic5—42no—
221C24—101no—
222C2×Q8—52no—
223C2×Q8—61no—
224C2×Q8#120111yescharacteristic
225C2×D4—52no—
226C2×D4—101no—
227C2×D4—102no—
228C2×D4#120111yescharacteristic
229Q16—122no—
230SD16—122no—
231C2×C8—61no—
232C2×C8—302no—
233C4⋊C4—62no—
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#408311yescharacteristic
249C3×C4—21no—
250C3×C4—22no—
251C3×C4—41no—
252C3×C4—202no—
253Dic3—81no—
254C2×C5—81no—
255C2×C5#524111yescharacteristic
256C2×C5#524212yes—
257D5—82no—
258C23—21no—
259C23—102no—
260C23—401no—
261C23—402no—
262Q8—41no—
263Q8—121no—
264Q8—121no—
265Q8—202no—
266D4—41no—
267D4—202no—
268D4—401no—
269D4—402no—
270C2×C4—21no—
271C2×C4—102no—
272C2×C4—121no—
273C2×C4C2×#120111yescharacteristic
274C2×C4D5×#6712yes—
275C8—62no—
276C8—602no—
277C2×C3—81no—
278C2×C3—402no—
279C2×C3#6536611yescharacteristic
280C2×C3#6549112yes—
281C5#7194911yescharacteristic, complemented, Sylow
282C22—41no—
283C22—42no—
284C22—202no—
285C22—202no—
286C22—202no—
287C22—404no—
288C22#9156311yescharacteristic
289C4—21no—
290C4—22no—
291C4—41no—
292C4—202no—
293C4—241no—
294C3#1060212211yescharacteristic, complemented, Sylow
295C2—81no—
296C2—402no—
297C2#1174913711yescharacteristic
298C2#1174941512yes—
subgroupG/H
centerC22#91563
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. C5×#5060C2semidirect
3. #11746898C2semidirect
4. #11746361C2semidirect
5. #11745846C2semidirect
10. C5×#869C22semidirect
16. #91087C22semidirect
17. C5×#803C22semidirect
47. #5060D5semidirect
92. #869C2×D5semidirect
96. #803C2×D5semidirect
241. C3×C5#1659semidirect
281. C5#71949semidirect
294. C3#10602122semidirect

Maximal subgroups

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

subgroupindex
C3×#660172
C5×#50602
#117468982
#117463612
#117458462
#106021223
#719495