Finite Group Databasebeta

← #14290948

Subgroups — #14290948

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
2#11751159C211yesmaximal, characteristic
3#11750814C212yesmaximal, complemented
4C3×C5×#329C211yesmaximal, characteristic, complemented
5#11746286C212yesmaximal, complemented
6#10599147—31nomaximal, Hall
7C3×C5×#124C2211yescharacteristic
8#91833—21no—
9C2×#6717—21no—
10#91824—21no—
11C2×#6715—21no—
12#91768—22no—
13#91767—22no—
14#91763C2211yescharacteristic
15#91759C2212yes—
16C3×C5×#97C2212yes—
17#91105—22no—
18#91105—22no—
19#91087C2211yescharacteristic
20#68354—51nomaximal, Hall
21#66006—31no—
22#65347—31no—
23#65002—32no—
24C5×#329D311yescharacteristic, complemented
25#64685—32no—
26C2×C3×C5×Q8D411yescharacteristic
27C2×C3×C5×D4D411yescharacteristic
28C22×Dic15—21no—
29C2×D60—21no—
30C2×D60—22no—
31C2×Dic30—21no—
32C2×C3×C5×C8—22no—
33C3×C5×C22⋊C4—22no—
34C3×C42×C5C2311yescharacteristic
35#6719—22no—
36#6719—21no—
37#6717—42no—
38#6715—42no—
39C4⋊Dic15D412yes—
40C4⋊Dic15D412yes—
41#6712—22no—
42#6712—22no—
43#6712—22no—
44C4×Dic15—21no—
45C2×C3⋊#168—21no—
46#5672—51no—
47#5058—51no—
48#4713—52no—
49C3×#329D511yescharacteristic, complemented
50#4465—52no—
51C5×#124C2×D311yescharacteristic
52#4090—61no—
53C2×#688—61no—
54#4081—61no—
55C2×#686—61no—
56#4025—62no—
57#4024—62no—
58#4020—31no—
59#4016—32no—
60C5×#97C2×D312yes—
61#3953—62no—
62#3953—62no—
63#3935—31no—
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—
72C2×Dic15—22no—
73C2×Dic15—22no—
74C2×Dic15—81no—
75D60—41no—
76D60—41no—
77D60—44no—
78Dic30—81no—
79C3×C5×C8—42no—
80C3⋊#168—22no—
81C3×#124C2×D511yescharacteristic
82#944—101no—
83C2×#215—101no—
84#935—101no—
85C2×#213—101no—
86#879—102no—
87#878—102no—
88#874—51no—
89#870—52no—
90C3×#97C2×D512yes—
91#821—102no—
92#821—102no—
93#803—51no—
94C2×C5×Q8D1211yescharacteristic
95C2×C5×D4D1211yescharacteristic
96C22×Dic5—61no—
97C2×D20—61no—
98C2×D20—62no—
99C2×Dic10—61no—
100C2×C5×C8—22no—
101C5×C22⋊C4—22no—
102C42×C5C22×D311yescharacteristic
103C22⋊Dic5—62no—
104C22⋊Dic5—61no—
105#688—122no—
106#686—122no—
107C4⋊Dic5—32no—
108C4⋊Dic5—32no—
109#683—62no—
110#683—62no—
111#683—62no—
112C4×Dic5—61no—
113C2×#168—61no—
114#563—151no—
115#496—151no—
116#490—152no—
117#330—152no—
118#329D1511yescharacteristic, complemented
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—
127Dic15—42no—
128Dic15—42no—
129C2×C3×Q8D2011yescharacteristic
130C2×C3×D4D2011yescharacteristic
131C22×Dic3—101no—
132C2×D12—101no—
133C2×D12—102no—
134C2×Dic6—101no—
135C2×C3×C8—22no—
136C3×C22⋊C4—22no—
137C3×C42C22×D511yescharacteristic
138#217—102no—
139#217—101no—
140#215—202no—
141#213—202no—
142C4⋊Dic3—52no—
143C4⋊Dic3—52no—
144Dic3⋊C4—102no—
145Dic3⋊C4—102no—
146Dic3⋊C4—102no—
147C4×Dic3—101no—
148C2×C3⋊C8—101no—
149C23×C5—21no—
150C22×D5—121no—
151C5×Q8—41no—
152C5×D4—41no—
153C2×C4×C5—21no—
154C2×C4×C5C2×D1211yescharacteristic
155C2×C4×C5D3×D412yes—
156C2×Dic5—62no—
157C2×Dic5—62no—
158C2×Dic5—241no—
159D20—121no—
160D20—121no—
161D20—124no—
162Dic10—241no—
163C5×C8—42no—
164#168—62no—
165C2×SD16—301no—
166C2×D8—301no—
167C4⋊Q8—301no—
168#127—151no—
169#126—302no—
170#125—152no—
171#124C2×D1511yescharacteristic
172#123—301no—
173C22⋊Q8—302no—
174#102—302no—
175#102—302no—
176#97—151no—
177#97C2×D1512yes—
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×D2011yescharacteristic
188C2×C3×C4D4×D512yes—
189C2×Dic3—102no—
190C2×Dic3—102no—
191C2×Dic3—401no—
192D12—201no—
193D12—201no—
194D12—204no—
195Dic6—401no—
196C3×C8—42no—
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—
206Dic5—122no—
207Dic5—122no—
208C2×Q8—301no—
209C2×Q8D6011yescharacteristic
210C2×D4—301no—
211C2×D4—302no—
212C2×D4D6011yescharacteristic
213C22×C4—301no—
214SD16—602no—
215D8—602no—
216C2×C8—22no—
217C2×C8—301no—
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#402811yescharacteristic
232C2×D3—401no—
233C2×D3—402no—
234C3×C4—21no—
235C3×C4—22no—
236C3×C4—41no—
237Dic3—202no—
238Dic3—202no—
239C2×C5—81no—
240C2×C5#474711yescharacteristic
241C2×C5#482712yes—
242D5—481no—
243C23—21no—
244C23—601no—
245Q8—41no—
246Q8—1201no—
247D4—41no—
248D4—601no—
249D4—601no—
250D4—604no—
251C2×C4—21no—
252C2×C4—302no—
253C2×C4—302no—
254C2×C4—1201no—
255C2×C4C2×D6011yescharacteristic
256C2×C4D4×D1512yes—
257C8—42no—
258C8—302no—
259C2×C3—81no—
260C2×C3#6503611yescharacteristic
261C2×C3#6511612yes—
262D3—801no—
263C5#6835411yescharacteristic, complemented, Sylow
264C22—42no—
265C22—41no—
266C22—1202no—
267C22—1201no—
268C22#9177111yescharacteristic
269C4—22no—
270C4—21no—
271C4—41no—
272C4—602no—
273C4—602no—
274C3#1059914711yescharacteristic, complemented, Sylow
275C2—81no—
276C2—2401no—
277C2#1175084811yescharacteristic
278C2#1175092812yes—
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#329C2
socleC22×C3×C5#120
prime radical#11751159C2
hypercenter#329D15
hypocenterC3×C5#1657
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
1. #11756431C2semidirect
3. #11750814C2semidirect
4. C3×C5×#329C2semidirect
5. #11746286C2semidirect
24. C5×#329D3semidirect
49. C3×#329D5semidirect
118. #329D15semidirect
228. C3×C5#1657semidirect
263. C5#68354semidirect
274. C3#10599147semidirect

Maximal subgroups

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

subgroupindex
#117564312
#117511592
#117508142
C3×C5×#3292
#117462862
#105991473
#683545