Finite Group Databasebeta

← #14290959

Subgroups — #14290959

Order 1920.

412 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 412 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#11756431C211yesmaximal, characteristic, complemented
2C3×#65347C211yesmaximal, characteristic
3#11746892C212yesmaximal, complemented
4C5×#4540C211yesmaximal, characteristic, complemented
5#11745851C212yesmaximal, complemented
6#10599147—31nomaximal, Hall
7C3×C5×#124C2211yescharacteristic
8#91833—21no—
9#91824—21no—
10#91768—22no—
11#91767—22no—
12#91759C2212yes—
13C2×C3×#688—21no—
14C2×C3×#686—21no—
15C3×#4020C2211yescharacteristic
16C5×#803C2212yes—
17C3×#3935C2211yescharacteristic
18#90965—22no—
19#90965—22no—
20#71328—51nomaximal, Hall
21#66006—31no—
22#65347D311yescharacteristic
23#65002—32no—
24C5×#329—31no—
25#64685—32no—
26C2×C3×C5×Q8D411yescharacteristic
27C2×C3×C5×D4D411yescharacteristic
28C22×Dic15—21no—
29C2×Dic30—21no—
30C2×C3×D20—21no—
31C2×C3×D20—22no—
32C3×C5×C22⋊C4—22no—
33C3×C42×C5C2311yescharacteristic
34#6719—22no—
35#6719—21no—
36C4⋊Dic15D412yes—
37C4⋊Dic15D412yes—
38#6712—22no—
39#6712—22no—
40#6712—22no—
41C4×Dic15—21no—
42C2×C5×C3⋊C8—22no—
43C3×#688—42no—
44C3×#686—42no—
45C2×C3×#168—21no—
46#5672—51no—
47C3×#496—51no—
48#5071—52no—
49#4540D511yescharacteristic, complemented
50#4465—52no—
51C5×#124C2×D311yescharacteristic
52#4090—61no—
53C2×#688—21no—
54#4081—61no—
55C2×#686—21no—
56#4025—62no—
57#4024—62no—
58#4020C2×D311yescharacteristic
59#4016—32no—
60C5×#97—32no—
61#3953—62no—
62#3953—62no—
63#3935C2×D311yescharacteristic
64#1657—151noSylow
65C23×C3×C5—21no—
66C22×C3×D5—41no—
67C3×C5×Q8—41no—
68C3×C5×D4—41no—
69C2×C3×C4×C5—21no—
70C2×C3×C4×C5C2×D411yescharacteristic
71C2×C3×C4×C5C2×D412yes—
72C2×Dic15—22no—
73C2×Dic15—22no—
74C2×Dic15—81no—
75Dic30—81no—
76C3×D20—41no—
77C3×D20—41no—
78C3×D20—44no—
79C3×#168—22no—
80C5×C3⋊C8—42no—
81C2×C3×SD16—101no—
82C2×C3×D8—101no—
83C3×#127—51no—
84C3×#124C2×D511yescharacteristic
85#944—101no—
86#935—101no—
87#879—102no—
88#878—102no—
89#870—52no—
90C3×#97—51no—
91#832—102no—
92#832—102no—
93#803C2×D512yes—
94C2×C5×Q8#6711yescharacteristic
95C2×C5×D4#6711yescharacteristic
96C22×Dic5—61no—
97C2×D20—22no—
98C2×D20—21no—
99C2×Dic10—61no—
100C2×C5×C8—62no—
101C5×C22⋊C4—22no—
102C42×C5C22×D311yescharacteristic
103C22⋊Dic5—62no—
104C22⋊Dic5—61no—
105#688—42no—
106#686—42no—
107C4⋊Dic5—32no—
108C4⋊Dic5—32no—
109#683—62no—
110#683—62no—
111#683—62no—
112C4×Dic5—61no—
113C2×#168—21no—
114#563—151no—
115#496—51no—
116#490—152no—
117#330—152no—
118#329—31no—
119C22×C3×C5—41no—
120C22×C3×C5—42no—
121C22×C3×C5#12011yescharacteristic
122C2×C3×D5—81no—
123C2×C3×D5—82no—
124C3×C4×C5—21no—
125C3×C4×C5—22no—
126C3×C4×C5—41no—
127Dic15—42no—
128Dic15—42no—
129C2×C3×Q8D2011yescharacteristic
130C2×C3×D4—101no—
131C2×C3×D4—102no—
132C2×C3×D4D2011yescharacteristic
133C22×Dic3—101no—
134C2×Dic6—101no—
135C3×SD16—202no—
136C3×D8—202no—
137C2×C3×C8—101no—
138C3×C22⋊C4—22no—
139C3×C42C22×D511yescharacteristic
140#217—102no—
141#217—101no—
142C4⋊Dic3—52no—
143C4⋊Dic3—52no—
144Dic3⋊C4—102no—
145Dic3⋊C4—102no—
146Dic3⋊C4—102no—
147C4×Dic3—101no—
148C2×C3⋊C8—22no—
149C23×C5—21no—
150C22×D5—41no—
151C5×Q8—41no—
152C5×D4—41no—
153C2×C4×C5—21no—
154C2×C4×C5D3×D412yes—
155C2×C4×C5C2×#6711yescharacteristic
156C2×Dic5—62no—
157C2×Dic5—62no—
158C2×Dic5—241no—
159D20—41no—
160D20—41no—
161D20—44no—
162Dic10—241no—
163C5×C8—122no—
164#168—22no—
165C2×SD16—101no—
166C2×D8—101no—
167C4⋊Q8—301no—
168#127—51no—
169#126—302no—
170#125—152no—
171#124D3×D511yescharacteristic
172#123—301no—
173C22⋊Q8—302no—
174#102—302no—
175#102—302no—
176#97—32no—
177#97—51no—
178C2×C3×C5—81no—
179C2×C3×C5#45311yescharacteristic
180C2×C3×C5#45412yes—
181C3×D5—161no—
182C23×C3—21no—
183C23×C3—201no—
184C3×Q8—41no—
185C3×D4—41no—
186C3×D4—201no—
187C3×D4—201no—
188C3×D4—204no—
189C2×C3×C4—21no—
190C2×C3×C4C2×D2011yescharacteristic
191C2×C3×C4D4×D512yes—
192C2×Dic3—102no—
193C2×Dic3—102no—
194C2×Dic3—401no—
195Dic6—401no—
196C3×C8—102no—
197C3⋊C8—42no—
198C22×C5—42no—
199C22×C5—41no—
200C22×C5#93711yescharacteristic
201C2×D5—82no—
202C2×D5—81no—
203C4×C5—22no—
204C4×C5—21no—
205C4×C5—41no—
206Dic5—122no—
207Dic5—122no—
208C2×Q8—301no—
209C2×Q8#120211yescharacteristic
210C2×D4—101no—
211C2×D4—102no—
212C2×D4#120211yescharacteristic
213C22×C4—301no—
214SD16—202no—
215D8—202no—
216C2×C8—62no—
217C2×C8—101no—
218C4⋊C4—152no—
219C4⋊C4—152no—
220C4⋊C4—302no—
221C4⋊C4—302no—
222C4⋊C4—302no—
223C22⋊C4—22no—
224C22⋊C4—302no—
225C22⋊C4—301no—
226C42—301no—
227C42C2×D3×D511yescharacteristic
228C3×C5#165711yescharacteristic, complemented, Hall
229C22×C3—41no—
230C22×C3—42no—
231C22×C3—401no—
232C22×C3—402no—
233C22×C3#402811yescharacteristic
234C3×C4—21no—
235C3×C4—22no—
236C3×C4—41no—
237Dic3—202no—
238Dic3—202no—
239C2×C5—81no—
240C2×C5#507711yescharacteristic
241C2×C5#520112yes—
242D5—161no—
243C23—21no—
244C23—201no—
245Q8—41no—
246Q8—1201no—
247D4—41no—
248D4—201no—
249D4—201no—
250D4—204no—
251C2×C4—21no—
252C2×C4—302no—
253C2×C4—302no—
254C2×C4—1201no—
255C2×C4C2×#120211yescharacteristic
256C2×C4#679012yes—
257C8—102no—
258C8—122no—
259C2×C3—81no—
260C2×C3—801no—
261C2×C3#6503611yescharacteristic
262C2×C3#6511612yes—
263C5#7132811yescharacteristic, complemented, Sylow
264C22—41no—
265C22—42no—
266C22—401no—
267C22—402no—
268C22#9157211yescharacteristic
269C4—21no—
270C4—22no—
271C4—41no—
272C4—602no—
273C4—602no—
274C3#1059914711yescharacteristic, complemented, Sylow
275C2—81no—
276C2—801no—
277C2#1174914211yescharacteristic
278C2#1174946012yes—
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5#120
prime radicalC3×#65347C2
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. #11756431C2semidirect
3. #11746892C2semidirect
4. C5×#4540C2semidirect
5. #11745851C2semidirect
49. #4540D5semidirect
228. C3×C5#1657semidirect
263. C5#71328semidirect
274. C3#10599147semidirect

Maximal subgroups

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

subgroupindex
#117564312
C3×#653472
#117468922
C5×#45402
#117458512
#105991473
#713285