Finite Group Databasebeta

← #14290958

Subgroups — #14290958

Order 1920.

412 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 412 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
1C5×#5672C211yesmaximal, characteristic, complemented
2#11751159C211yesmaximal, characteristic
3#11746915C212yesmaximal, complemented
4C3×#64760C211yesmaximal, characteristic, complemented
5#11745850C212yesmaximal, complemented
6#10602748—31nomaximal, Hall
7C3×C5×#124C2211yescharacteristic
8C2×#6717—21no—
9C2×#6715—21no—
10#91763C2211yescharacteristic
11C5×#944—21no—
12C5×#935—21no—
13C5×#879—22no—
14C5×#878—22no—
15C5×#870C2212yes—
16#91087C2211yescharacteristic
17C3×#3935C2212yes—
18#90969—22no—
19#90969—22no—
20#68354—51nomaximal, Hall
21C5×#563—31no—
22#65356—32no—
23#65347—31no—
24#64763—32no—
25#64760D311yescharacteristic, complemented
26C2×C3×C5×Q8D411yescharacteristic
27C2×C3×C5×D4D411yescharacteristic
28C2×D60—22no—
29C2×D60—21no—
30C22×C5×Dic3—21no—
31C2×C5×Dic6—21no—
32C3×C5×C22⋊C4—22no—
33C3×C42×C5C2311yescharacteristic
34#6717—42no—
35#6715—42no—
36C2×C3⋊#168—21no—
37C5×#217—22no—
38C5×#217—21no—
39C5×C4⋊Dic3D412yes—
40C5×C4⋊Dic3D412yes—
41C5×Dic3⋊C4—22no—
42C5×Dic3⋊C4—22no—
43C5×Dic3⋊C4—22no—
44C4×C5×Dic3—21no—
45C2×C3×#168—22no—
46#5672D511yescharacteristic, complemented
47#5058—51no—
48#4713—52no—
49C3×#329—51no—
50#4465—52no—
51C5×C4⋊Q8—61no—
52C5×#126—62no—
53C5×#125—32no—
54C5×#124C2×D311yescharacteristic
55C5×#123—61no—
56C5×C22⋊Q8—62no—
57C2×#688—61no—
58C2×#686—61no—
59#4020—31no—
60#3941—62no—
61#3941—62no—
62#3935—31no—
63#3935C2×D312yes—
64#1657—151noSylow
65C23×C3×C5—21no—
66C22×D15—41no—
67C3×C5×Q8—41no—
68C3×C5×D4—41no—
69C2×C3×C4×C5—21no—
70C2×C3×C4×C5C2×D411yescharacteristic
71C2×C3×C4×C5C2×D412yes—
72D60—41no—
73D60—41no—
74D60—44no—
75C2×C5×Dic3—22no—
76C2×C5×Dic3—22no—
77C2×C5×Dic3—81no—
78C5×Dic6—81no—
79C3⋊#168—22no—
80C3×#168—42no—
81C3×#124C2×D511yescharacteristic
82#944—21no—
83C2×#215—101no—
84#935—21no—
85C2×#213—101no—
86#879—22no—
87#878—22no—
88#874—51no—
89#870C2×D512yes—
90C3×#97—52no—
91#821—102no—
92#821—102no—
93#803—51no—
94C2×C5×Q8—61no—
95C2×C5×Q8D1211yescharacteristic
96C2×C5×D4D1211yescharacteristic
97C22×C4×C5—61no—
98C2×D20—61no—
99C2×D20—62no—
100C5×C4⋊C4—32no—
101C5×C4⋊C4—32no—
102C5×C4⋊C4—62no—
103C5×C4⋊C4—62no—
104C5×C4⋊C4—62no—
105C5×C22⋊C4—22no—
106C5×C22⋊C4—62no—
107C5×C22⋊C4—61no—
108C42×C5—61no—
109C42×C5C22×D311yescharacteristic
110#688—122no—
111#686—122no—
112C2×#168—22no—
113C2×#168—61no—
114#563—31no—
115#496—151no—
116#490—152no—
117#330—152no—
118#329—51no—
119C22×C3×C5—41no—
120C22×C3×C5—42no—
121C22×C3×C5#12011yescharacteristic
122C2×D15—81no—
123C2×D15—82no—
124C3×C4×C5—21no—
125C3×C4×C5—22no—
126C3×C4×C5—41no—
127C5×Dic3—42no—
128C5×Dic3—42no—
129C2×C3×Q8C22⋊D511yescharacteristic
130C2×C3×D4C22⋊D511yescharacteristic
131C22×Dic3—21no—
132C2×D12—102no—
133C2×D12—101no—
134C2×Dic6—21no—
135C2×C3×C8—102no—
136C3×C22⋊C4—22no—
137C3×C42C22×D511yescharacteristic
138#217—22no—
139#217—21no—
140#215—202no—
141#213—202no—
142C4⋊Dic3C22⋊D512yes—
143C4⋊Dic3C22⋊D512yes—
144Dic3⋊C4—22no—
145Dic3⋊C4—22no—
146Dic3⋊C4—22no—
147C4×Dic3—21no—
148C2×C3⋊C8—101no—
149C23×C5—21no—
150C22×D5—121no—
151C5×Q8—41no—
152C5×Q8—241no—
153C5×D4—41no—
154C2×C4×C5—21no—
155C2×C4×C5—62no—
156C2×C4×C5—62no—
157C2×C4×C5—241no—
158C2×C4×C5C2×D1211yescharacteristic
159C2×C4×C5D3×D412yes—
160D20—121no—
161D20—121no—
162D20—124no—
163#168—42no—
164#168—62no—
165C2×SD16—301no—
166C2×D8—301no—
167C4⋊Q8—61no—
168#127—151no—
169#126—62no—
170#125—32no—
171#124D3×D511yescharacteristic
172#123—61no—
173C22⋊Q8—62no—
174#102—302no—
175#102—302no—
176#97—52no—
177#97—151no—
178C2×C3×C5—81no—
179C2×C3×C5#45311yescharacteristic
180C2×C3×C5#45412yes—
181D15—161no—
182C23×C3—21no—
183C22×D3—201no—
184C3×Q8—41no—
185C3×D4—41no—
186C2×C3×C4—21no—
187C2×C3×C4C2×C22⋊D511yescharacteristic
188C2×C3×C4C2×C22⋊D512yes—
189C2×Dic3—22no—
190C2×Dic3—22no—
191C2×Dic3—81no—
192D12—201no—
193D12—201no—
194D12—204no—
195Dic6—81no—
196C3×C8—202no—
197C3⋊C8—102no—
198C22×C5—41no—
199C22×C5—42no—
200C22×C5#88211yescharacteristic
201C2×D5—241no—
202C2×D5—242no—
203C4×C5—21no—
204C4×C5—22no—
205C4×C5—41no—
206C4×C5—122no—
207C4×C5—122no—
208C2×Q8—61no—
209C2×Q8#120311yescharacteristic
210C2×D4—301no—
211C2×D4—302no—
212C2×D4#120311yescharacteristic
213C22×C4—61no—
214SD16—602no—
215D8—602no—
216C2×C8—102no—
217C2×C8—301no—
218C4⋊C4—32no—
219C4⋊C4—32no—
220C4⋊C4—62no—
221C4⋊C4—62no—
222C4⋊C4—62no—
223C22⋊C4—22no—
224C22⋊C4—62no—
225C22⋊C4—61no—
226C42—61no—
227C42C2×D3×D511yescharacteristic
228C3×C5#165711yescharacteristic, complemented, Hall
229C22×C3—41no—
230C22×C3—42no—
231C22×C3#409911yescharacteristic
232C2×D3—401no—
233C2×D3—402no—
234C3×C4—21no—
235C3×C4—22no—
236C3×C4—41no—
237Dic3—42no—
238Dic3—42no—
239C2×C5—81no—
240C2×C5#474711yescharacteristic
241C2×C5#482712yes—
242D5—481no—
243C23—21no—
244C23—601no—
245Q8—41no—
246Q8—241no—
247D4—41no—
248D4—601no—
249D4—601no—
250D4—604no—
251C2×C4—21no—
252C2×C4—62no—
253C2×C4—62no—
254C2×C4—241no—
255C2×C4C2×#120311yescharacteristic
256C2×C4D3×C22⋊D512yes—
257C8—202no—
258C8—302no—
259C2×C3—81no—
260C2×C3#6553011yescharacteristic
261C2×C3#6553412yes—
262D3—801no—
263C5#6835411yescharacteristic, complemented, Sylow
264C22—41no—
265C22—42no—
266C22—1201no—
267C22—1202no—
268C22#9157011yescharacteristic
269C4—21no—
270C4—22no—
271C4—41no—
272C4—122no—
273C4—122no—
274C3#1060274811yescharacteristic, complemented, Sylow
275C2—81no—
276C2—2401no—
277C2#1174914111yescharacteristic
278C2#1174945912yes—
subgroupG/H
centerC22#91570
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5#120
prime radical#11751159C2
hypercenter#124D3×D5
hypocenterC3×C5#1657
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
1. C5×#5672C2semidirect
3. #11746915C2semidirect
4. C3×#64760C2semidirect
5. #11745850C2semidirect
25. #64760D3semidirect
46. #5672D5semidirect
228. C3×C5#1657semidirect
263. C5#68354semidirect
274. C3#10602748semidirect

Maximal subgroups

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

subgroupindex
C5×#56722
#117511592
#117469152
C3×#647602
#117458502
#106027483
#683545