Finite Group Databasebeta

← #14290939

Subgroups — #14290939

Order 1920.

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

normal subgroups only

This group has 412 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#11756431C211yesmaximal, characteristic, complemented
2C3×C5×#496C211yesmaximal, characteristic
3#11751172C212yesmaximal, complemented
4#11746361C211yesmaximal, characteristic, complemented
5#11746286C212yesmaximal, complemented
6#10602121—31nomaximal, Hall
7C2×C3×C5×SD16—21no—
8C2×C3×C5×D8—21no—
9C3×C5×#127C2211yescharacteristic
10C3×C5×#124C2211yescharacteristic
11#91833—21no—
12#91824—21no—
13#91768—22no—
14#91767—22no—
15#91759C2212yes—
16C3×C5×#97C2211yescharacteristic
17#91116—22no—
18#91116—22no—
19#91087C2212yes—
20#71328—51nomaximal, Hall
21#66006—31no—
22C5×#496D311yescharacteristic
23#65360—32no—
24#64760—31no—
25#64685—32no—
26C2×C3×C5×Q8D411yescharacteristic
27C2×C3×C5×D4—21no—
28C2×C3×C5×D4—22no—
29C2×C3×C5×D4D411yescharacteristic
30C22×Dic15—21no—
31C2×Dic30—21no—
32C3×C5×SD16—42no—
33C3×C5×D8—42no—
34C2×C3×C5×C8—21no—
35C3×C5×C22⋊C4—22no—
36C3×C42×C5C2311yescharacteristic
37#6719—22no—
38#6719—21no—
39C4⋊Dic15D412yes—
40C4⋊Dic15D412yes—
41#6712—22no—
42#6712—22no—
43#6712—22no—
44C4×Dic15—21no—
45C2×C3⋊#168—22no—
46#5672—51no—
47C3×#496D511yescharacteristic
48#5071—52no—
49#4540—51no—
50#4465—52no—
51C2×C5×SD16—21no—
52C2×C5×D8—21no—
53C5×#127C2×D311yescharacteristic
54C5×#124C2×D311yescharacteristic
55#4090—61no—
56#4081—61no—
57#4025—62no—
58#4024—62no—
59#4016—32no—
60C5×#97C2×D311yescharacteristic
61#3964—62no—
62#3964—62no—
63#3935—32no—
64#1657—151noSylow
65C23×C3×C5—21no—
66C23×C3×C5—41no—
67C3×C5×Q8—41no—
68C3×C5×D4—41no—
69C3×C5×D4—41no—
70C3×C5×D4—41no—
71C3×C5×D4—44no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5C2×D412yes—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×Dic15—22no—
76C2×Dic15—22no—
77C2×Dic15—81no—
78Dic30—81no—
79C3×C5×C8—22no—
80C3⋊#168—42no—
81C2×C3×SD16—21no—
82C2×C3×D8—21no—
83C3×#127C2×D511yescharacteristic
84C3×#124C2×D511yescharacteristic
85#944—101no—
86#935—101no—
87#879—102no—
88#878—102no—
89#870—52no—
90C3×#97C2×D511yescharacteristic
91#832—102no—
92#832—102no—
93#803—52no—
94C2×C5×Q8#6711yescharacteristic
95C2×C5×D4—22no—
96C2×C5×D4—21no—
97C2×C5×D4#6711yescharacteristic
98C22×Dic5—61no—
99C2×Dic10—61no—
100C5×SD16—42no—
101C5×D8—42no—
102C2×C5×C8—21no—
103C5×C22⋊C4—22no—
104C42×C5C22×D311yescharacteristic
105C22⋊Dic5—62no—
106C22⋊Dic5—61no—
107C4⋊Dic5—32no—
108C4⋊Dic5—32no—
109#683—62no—
110#683—62no—
111#683—62no—
112C4×Dic5—61no—
113C2×#168—62no—
114#563—151no—
115#496D1511yescharacteristic
116#490—152no—
117#330—152no—
118#329—151no—
119C22×C3×C5—41no—
120C22×C3×C5—42no—
121C22×C3×C5—81no—
122C22×C3×C5—82no—
123C22×C3×C5#12011yescharacteristic
124C3×C4×C5—21no—
125C3×C4×C5—22no—
126C3×C4×C5—41no—
127Dic15—42no—
128Dic15—42no—
129C2×C3×Q8C22⋊D511yescharacteristic
130C2×C3×D4—22no—
131C2×C3×D4—21no—
132C2×C3×D4C22⋊D511yescharacteristic
133C22×Dic3—101no—
134C2×Dic6—101no—
135C3×SD16—42no—
136C3×D8—42no—
137C2×C3×C8—21no—
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—102no—
149C23×C5—21no—
150C23×C5—41no—
151C5×Q8—41no—
152C5×D4—41no—
153C5×D4—41no—
154C5×D4—41no—
155C5×D4—44no—
156C2×C4×C5—21no—
157C2×C4×C5D3×D412yes—
158C2×C4×C5C2×#6711yescharacteristic
159C2×Dic5—62no—
160C2×Dic5—62no—
161C2×Dic5—241no—
162Dic10—241no—
163C5×C8—22no—
164#168—122no—
165C2×SD16—21no—
166C2×D8—21no—
167C4⋊Q8—301no—
168#127C2×D1511yescharacteristic
169#126—302no—
170#125—152no—
171#124C2×D1511yescharacteristic
172#123—301no—
173C22⋊Q8—302no—
174#102—302no—
175#102—302no—
176#97—152no—
177#97C2×D1511yescharacteristic
178C2×C3×C5—81no—
179C2×C3×C5—161no—
180C2×C3×C5#45311yescharacteristic
181C2×C3×C5#45412yes—
182C23×C3—21no—
183C23×C3—41no—
184C3×Q8—41no—
185C3×D4—41no—
186C3×D4—41no—
187C3×D4—41no—
188C3×D4—44no—
189C2×C3×C4—21no—
190C2×C3×C4D4×D512yes—
191C2×C3×C4C2×C22⋊D511yescharacteristic
192C2×Dic3—102no—
193C2×Dic3—102no—
194C2×Dic3—401no—
195Dic6—401no—
196C3×C8—22no—
197C3⋊C8—202no—
198C22×C5—42no—
199C22×C5—41no—
200C22×C5—82no—
201C22×C5—81no—
202C22×C5#93711yescharacteristic
203C4×C5—22no—
204C4×C5—21no—
205C4×C5—41no—
206Dic5—122no—
207Dic5—122no—
208C2×Q8—301no—
209C2×Q8#122011yescharacteristic
210C2×D4—22no—
211C2×D4—21no—
212C2×D4#122011yescharacteristic
213C22×C4—301no—
214SD16—42no—
215D8—42no—
216C2×C8—21no—
217C2×C8—302no—
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—
227C42C22×D1511yescharacteristic
228C3×C5#165711yescharacteristic, complemented, Hall
229C22×C3—41no—
230C22×C3—42no—
231C22×C3—81no—
232C22×C3—82no—
233C22×C3#408311yescharacteristic
234C3×C4—21no—
235C3×C4—22no—
236C3×C4—41no—
237Dic3—202no—
238Dic3—202no—
239C2×C5—81no—
240C2×C5—161no—
241C2×C5#507711yescharacteristic
242C2×C5#520112yes—
243C23—21no—
244C23—41no—
245Q8—41no—
246Q8—1201no—
247D4—41no—
248D4—41no—
249D4—41no—
250D4—44no—
251C2×C4—21no—
252C2×C4—302no—
253C2×C4—302no—
254C2×C4—1201no—
255C2×C4D4×D1512yes—
256C2×C4C2×#122011yescharacteristic
257C8—22no—
258C8—602no—
259C2×C3—81no—
260C2×C3—161no—
261C2×C3#6536611yescharacteristic
262C2×C3#6549012yes—
263C5#7132811yescharacteristic, complemented, Sylow
264C22—41no—
265C22—42no—
266C22—81no—
267C22—82no—
268C22#9182611yescharacteristic
269C4—21no—
270C4—22no—
271C4—41no—
272C4—602no—
273C4—602no—
274C3#1060212111yescharacteristic, complemented, Sylow
275C2—81no—
276C2—161no—
277C2#1175117811yescharacteristic
278C2#1175130212yes—
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
Fitting, prime radicalC3×C5×#496C2
socleC22×C3×C5#120
hypercenter#496D15
hypocenterC3×C5#1657
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. #11756431C2semidirect
3. #11751172C2semidirect
4. #11746361C2semidirect
5. #11746286C2semidirect
228. C3×C5#1657semidirect
263. C5#71328semidirect
274. C3#10602121semidirect

Maximal subgroups

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

subgroupindex
#117564312
C3×C5×#4962
#117511722
#117463612
#117462862
#106021213
#713285