Finite Group Databasebeta

← #14291056

Subgroups — #14291056

Order 1920.

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

normal subgroups only

This group has 392 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
2C3×#65349C211yesmaximal, characteristic
3#11746952C212yesmaximal, complemented
4C5×#4540C211yesmaximal, characteristic
5#11745851C212yesmaximal, complemented
6#10599148—31nomaximal, Hall
7C3×C5×#124C2211yescharacteristic
8#91833—21no—
9#91824—21no—
10#91768—22no—
11#91767—22no—
12#91759C2212yes—
13C2×C3×#689—21no—
14C2×C3×#687—21no—
15C3×#4015C2211yescharacteristic
16C5×#803C2212yes—
17C3×#3935C2211yescharacteristic
18#90990—22no—
19#90987—22no—
20#71330—51nomaximal, Hall
21#66006—31no—
22#65349D311yescharacteristic
23#64991—32no—
24C5×#329—31no—
25#64685—32no—
26C2×C3×C5×Q8D411yescharacteristic
27C2×C3×C5×D4D411yescharacteristic
28C22×Dic15—21no—
29C2×Dic30—21no—
30C2×C3×Dic10—21no—
31C3×C5×C22⋊C4—22no—
32C3×C42×C5C2311yescharacteristic
33#6719—22no—
34#6719—21no—
35C4⋊Dic15D412yes—
36C4⋊Dic15D412yes—
37#6712—22no—
38#6712—22no—
39#6712—22no—
40C4×Dic15—21no—
41C2×C5×C3⋊C8—22no—
42C3×#689—42no—
43C3×#687—42no—
44C3×C4⋊Dic5—22no—
45C2×C3×#168—21no—
46#5672—51no—
47C3×#497—51no—
48#5081—52no—
49#4540D511yescharacteristic
50#4465—52no—
51C5×#124C2×D311yescharacteristic
52#4090—61no—
53C2×#689—21no—
54#4081—61no—
55C2×#687—21no—
56#4025—62no—
57#4024—62no—
58#4016—32no—
59#4015C2×D311yescharacteristic
60C5×#97—32no—
61#3950—62no—
62#3949—62no—
63#3935C2×D311yescharacteristic
64#1660—151noSylow
65C23×C3×C5—21no—
66C3×C5×Q8—41no—
67C3×C5×D4—41no—
68C2×C3×C4×C5—21no—
69C2×C3×C4×C5C2×D411yescharacteristic
70C2×C3×C4×C5C2×D412yes—
71C2×Dic15—22no—
72C2×Dic15—22no—
73C2×Dic15—81no—
74Dic30—81no—
75C2×C3×Dic5—41no—
76C3×Dic10—41no—
77C3×Dic10—41no—
78C3×#168—22no—
79C5×C3⋊C8—24no—
80C2×C3×Q16—101no—
81C2×C3×SD16—101no—
82C3×C4⋊Q8—51no—
83C3×#124C2×D511yescharacteristic
84#944—101no—
85#935—101no—
86#879—102no—
87#878—102no—
88#870—52no—
89C3×#97—51no—
90#808—102no—
91#807—102no—
92#803C2×D512yes—
93C2×C5×Q8#6711yescharacteristic
94C2×C5×D4#6711yescharacteristic
95C22×Dic5—61no—
96C2×Dic10—21no—
97C2×Dic10—61no—
98C2×C5×C8—62no—
99C5×C22⋊C4—22no—
100C42×C5C22×D311yescharacteristic
101C22⋊Dic5—62no—
102C22⋊Dic5—61no—
103#689—42no—
104#687—42no—
105C4⋊Dic5—22no—
106C4⋊Dic5—32no—
107C4⋊Dic5—32no—
108#683—62no—
109#683—62no—
110#683—62no—
111C4×Dic5—61no—
112C2×#168—21no—
113#563—151no—
114#501—152no—
115#497—51no—
116#330—152no—
117#329—31no—
118C22×C3×C5—41no—
119C22×C3×C5—42no—
120C22×C3×C5#12011yescharacteristic
121C3×C4×C5—21no—
122C3×C4×C5—22no—
123C3×C4×C5—41no—
124Dic15—42no—
125Dic15—42no—
126C3×Dic5—81no—
127C2×C3×Q8—101no—
128C2×C3×Q8D2011yescharacteristic
129C2×C3×D4D2011yescharacteristic
130C22×Dic3—101no—
131C2×Dic6—101no—
132C3×Q16—202no—
133C3×SD16—202no—
134C2×C3×C8—101no—
135C3×C4⋊C4—102no—
136C3×C22⋊C4—22no—
137C3×C42C22×D511yescharacteristic
138#217—102no—
139#217—101no—
140C4⋊Dic3—52no—
141C4⋊Dic3—52no—
142Dic3⋊C4—102no—
143Dic3⋊C4—102no—
144Dic3⋊C4—102no—
145C4×Dic3—101no—
146C2×C3⋊C8—22no—
147C23×C5—21no—
148C5×Q8—41no—
149C5×D4—41no—
150C2×C4×C5—21no—
151C2×C4×C5D3×D412yes—
152C2×C4×C5C2×#6711yescharacteristic
153C2×Dic5—41no—
154C2×Dic5—62no—
155C2×Dic5—62no—
156C2×Dic5—241no—
157Dic10—41no—
158Dic10—41no—
159Dic10—241no—
160C5×C8—64no—
161#168—22no—
162C2×Q16—101no—
163C2×SD16—101no—
164C4⋊Q8—51no—
165C4⋊Q8—301no—
166#126—302no—
167#125—152no—
168#124D3×D511yescharacteristic
169#123—301no—
170C22⋊Q8—302no—
171#107—302no—
172#106—302no—
173#97—32no—
174#97—51no—
175C2×C3×C5—81no—
176C2×C3×C5#45311yescharacteristic
177C2×C3×C5#45612yes—
178C23×C3—21no—
179C3×Q8—41no—
180C3×Q8—201no—
181C3×Q8—201no—
182C3×D4—41no—
183C2×C3×C4—21no—
184C2×C3×C4—201no—
185C2×C3×C4C2×D2011yescharacteristic
186C2×C3×C4D4×D512yes—
187C2×Dic3—102no—
188C2×Dic3—102no—
189C2×Dic3—401no—
190Dic6—401no—
191C3×C8—102no—
192C3⋊C8—24no—
193C22×C5—42no—
194C22×C5—41no—
195C22×C5#93711yescharacteristic
196C4×C5—22no—
197C4×C5—21no—
198C4×C5—41no—
199Dic5—81no—
200Dic5—122no—
201Dic5—122no—
202C2×Q8—101no—
203C2×Q8—301no—
204C2×Q8#120211yescharacteristic
205C2×D4#120211yescharacteristic
206C22×C4—301no—
207Q16—202no—
208SD16—202no—
209C2×C8—62no—
210C2×C8—101no—
211C4⋊C4—102no—
212C4⋊C4—152no—
213C4⋊C4—152no—
214C4⋊C4—302no—
215C4⋊C4—302no—
216C4⋊C4—302no—
217C22⋊C4—22no—
218C22⋊C4—302no—
219C22⋊C4—301no—
220C42—301no—
221C42C2×D3×D511yescharacteristic
222C3×C5#166011yescharacteristic, complemented, Hall
223C22×C3—41no—
224C22×C3—42no—
225C22×C3#402811yescharacteristic
226C3×C4—21no—
227C3×C4—22no—
228C3×C4—41no—
229C3×C4—401no—
230Dic3—202no—
231Dic3—202no—
232C2×C5—81no—
233C2×C5#507711yescharacteristic
234C2×C5#520512yes—
235C23—21no—
236Q8—41no—
237Q8—201no—
238Q8—201no—
239Q8—1201no—
240D4—41no—
241C2×C4—21no—
242C2×C4—201no—
243C2×C4—302no—
244C2×C4—302no—
245C2×C4—1201no—
246C2×C4C2×#120211yescharacteristic
247C2×C4#679012yes—
248C8—64no—
249C8—102no—
250C2×C3—81no—
251C2×C3#6503611yescharacteristic
252C2×C3#6511512yes—
253C5#7133011yescharacteristic, complemented, Sylow
254C22—41no—
255C22—42no—
256C22#9157211yescharacteristic
257C4—21no—
258C4—22no—
259C4—41no—
260C4—401no—
261C4—602no—
262C4—602no—
263C3#1059914811yescharacteristic, complemented, Sylow
264C2—81no—
265C2#1174914211yescharacteristic
266C2#1174942412yes—
subgroupG/H
centerC22#91572
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenter#124D3×D5
hypocenterC3×C5#1660
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
3. #11746952C2semidirect
5. #11745851C2semidirect
222. C3×C5#1660semidirect
253. C5#71330semidirect
263. C3#10599148semidirect

Maximal subgroups

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

subgroupindex
#117564312
C3×#653492
#117469522
C5×#45402
#117458512
#105991483
#713305