Finite Group Databasebeta

← #14291052

Subgroups — #14291052

Order 1920.

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

normal subgroups only

This group has 392 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
1C3×#66006C211yesmaximal, characteristic
2C5×#5060C211yesmaximal, characteristic
3#11746970C212yesmaximal, complemented
4#11746361C211yesmaximal, characteristic
5#11745849C212yesmaximal, complemented
6#10602123—31nomaximal, Hall
7C3×C5×#124C2211yescharacteristic
8C2×C5×#216—21no—
9C2×C5×#214—21no—
10C5×#869C2211yescharacteristic
11C3×#4090—21no—
12C3×#4081—21no—
13C3×#4025—22no—
14C3×#4024—22no—
15C3×#4016C2212yes—
16#91087C2212yes—
17C5×#803C2211yescharacteristic
18#90989—22no—
19#90986—22no—
20#71956—51nomaximal, Hall
21#66006D311yescharacteristic
22C5×#497—31no—
23#65369—32no—
24#64760—31no—
25#64685—32no—
26C2×C3×C5×Q8D411yescharacteristic
27C2×C3×C5×D4D411yescharacteristic
28C2×C5×Dic6—21no—
29C22×C3×Dic5—21no—
30C2×C3×Dic10—21no—
31C3×C5×C22⋊C4—22no—
32C3×C42×C5C2311yescharacteristic
33C2×C3⋊#168—22no—
34C5×#216—42no—
35C5×#214—42no—
36C5×C4⋊Dic3—22no—
37C2×C5×C3⋊C8—21no—
38C3×C22⋊Dic5—22no—
39C3×C22⋊Dic5—21no—
40C3×C4⋊Dic5D412yes—
41C3×C4⋊Dic5D412yes—
42C3×#683—22no—
43C3×#683—22no—
44C3×#683—22no—
45C3×C4×Dic5—21no—
46C3×#563—51no—
47#5064—52no—
48#5060D511yescharacteristic
49#4543—52no—
50#4540—51no—
51C2×C5×Q16—61no—
52C2×C5×SD16—61no—
53C5×C4⋊Q8—31no—
54C5×#124C2×D311yescharacteristic
55#4090—21no—
56#4081—21no—
57#4025—22no—
58#4024—22no—
59#4016C2×D312yes—
60C5×#97—31no—
61#3940—62no—
62#3939—62no—
63#3935—32no—
64#1660—151noSylow
65C23×C3×C5—21no—
66C3×C5×Q8—41no—
67C3×C5×D4—41no—
68C2×C3×C4×C5—21no—
69C2×C3×C4×C5C2×D412yes—
70C2×C3×C4×C5C2×D411yescharacteristic
71C2×C5×Dic3—41no—
72C5×Dic6—41no—
73C5×Dic6—41no—
74C2×C3×Dic5—22no—
75C2×C3×Dic5—22no—
76C2×C3×Dic5—81no—
77C3×Dic10—81no—
78C3⋊#168—24no—
79C5×C3⋊C8—22no—
80C3×C4⋊Q8—101no—
81C3×#126—102no—
82C3×#125—52no—
83C3×#124C2×D511yescharacteristic
84C3×#123—101no—
85C3×C22⋊Q8—102no—
86C2×#216—21no—
87C2×#214—21no—
88#869C2×D511yescharacteristic
89#808—102no—
90#807—102no—
91#803—52no—
92#803C2×D511yescharacteristic
93C2×C5×Q8—61no—
94C2×C5×Q8#6711yescharacteristic
95C2×C5×D4#6711yescharacteristic
96C22×Dic5—21no—
97C2×Dic10—21no—
98C5×Q16—122no—
99C5×SD16—122no—
100C2×C5×C8—61no—
101C5×C4⋊C4—62no—
102C5×C22⋊C4—22no—
103C42×C5C22×D311yescharacteristic
104C22⋊Dic5—22no—
105C22⋊Dic5—21no—
106C4⋊Dic5#6712yes—
107C4⋊Dic5#6712yes—
108#683—22no—
109#683—22no—
110#683—22no—
111C4×Dic5—21no—
112C2×#168—62no—
113#563—51no—
114#501—152no—
115#497—31no—
116#330—152no—
117#329—151no—
118C22×C3×C5—41no—
119C22×C3×C5—42no—
120C22×C3×C5#12011yescharacteristic
121C3×C4×C5—21no—
122C3×C4×C5—22no—
123C3×C4×C5—41no—
124C3×Dic5—42no—
125C3×Dic5—42no—
126C5×Dic3—81no—
127C2×C3×Q8—101no—
128C2×C3×Q8C22⋊D511yescharacteristic
129C2×C3×D4C22⋊D511yescharacteristic
130C22×C3×C4—101no—
131C2×Dic6—21no—
132C3×C4⋊C4—52no—
133C3×C4⋊C4—52no—
134C3×C4⋊C4—102no—
135C3×C4⋊C4—102no—
136C3×C4⋊C4—102no—
137C3×C22⋊C4—22no—
138C3×C22⋊C4—102no—
139C3×C22⋊C4—101no—
140C3×C42—101no—
141C3×C42C22×D511yescharacteristic
142#216—42no—
143#214—42no—
144C4⋊Dic3—22no—
145C2×C3⋊C8—21no—
146C2×C3⋊C8—102no—
147C23×C5—21no—
148C5×Q8—41no—
149C5×Q8—121no—
150C5×Q8—121no—
151C5×D4—41no—
152C2×C4×C5—21no—
153C2×C4×C5—121no—
154C2×C4×C5C2×#6711yescharacteristic
155C2×C4×C5C2×#6712yes—
156C2×Dic5—22no—
157C2×Dic5—22no—
158C2×Dic5—81no—
159Dic10—81no—
160C5×C8—62no—
161#168—64no—
162C2×Q16—61no—
163C2×SD16—61no—
164C4⋊Q8—31no—
165C4⋊Q8—101no—
166#126—102no—
167#125—52no—
168#124D3×D511yescharacteristic
169#123—101no—
170C22⋊Q8—102no—
171#107—302no—
172#106—302no—
173#97—31no—
174#97—152no—
175C2×C3×C5—81no—
176C2×C3×C5#45311yescharacteristic
177C2×C3×C5#45612yes—
178C23×C3—21no—
179C3×Q8—41no—
180C3×Q8—401no—
181C3×D4—41no—
182C2×C3×C4—21no—
183C2×C3×C4—102no—
184C2×C3×C4—102no—
185C2×C3×C4—401no—
186C2×C3×C4D4×D512yes—
187C2×C3×C4C2×C22⋊D511yescharacteristic
188C2×Dic3—41no—
189Dic6—41no—
190Dic6—41no—
191C3⋊C8—22no—
192C3⋊C8—104no—
193C22×C5—41no—
194C22×C5—42no—
195C22×C5#95311yescharacteristic
196C4×C5—21no—
197C4×C5—22no—
198C4×C5—41no—
199C4×C5—241no—
200Dic5—42no—
201Dic5—42no—
202C2×Q8—61no—
203C2×Q8—101no—
204C2×Q8#120111yescharacteristic
205C2×D4#120111yescharacteristic
206C22×C4—101no—
207Q16—122no—
208SD16—122no—
209C2×C8—61no—
210C2×C8—302no—
211C4⋊C4—52no—
212C4⋊C4—52no—
213C4⋊C4—62no—
214C4⋊C4—102no—
215C4⋊C4—102no—
216C4⋊C4—102no—
217C22⋊C4—22no—
218C22⋊C4—102no—
219C22⋊C4—101no—
220C42—101no—
221C42C2×D3×D511yescharacteristic
222C3×C5#166011yescharacteristic, complemented, Hall
223C22×C3—41no—
224C22×C3—42no—
225C22×C3#408311yescharacteristic
226C3×C4—21no—
227C3×C4—22no—
228C3×C4—41no—
229C3×C4—202no—
230C3×C4—202no—
231Dic3—81no—
232C2×C5—81no—
233C2×C5#524111yescharacteristic
234C2×C5#524612yes—
235C23—21no—
236Q8—41no—
237Q8—121no—
238Q8—121no—
239Q8—401no—
240D4—41no—
241C2×C4—21no—
242C2×C4—102no—
243C2×C4—102no—
244C2×C4—121no—
245C2×C4—401no—
246C2×C4C2×#120111yescharacteristic
247C2×C4D5×#6712yes—
248C8—62no—
249C8—304no—
250C2×C3—81no—
251C2×C3#6536611yescharacteristic
252C2×C3#6549412yes—
253C5#7195611yescharacteristic, complemented, Sylow
254C22—41no—
255C22—42no—
256C22#9156311yescharacteristic
257C4—21no—
258C4—22no—
259C4—41no—
260C4—202no—
261C4—202no—
262C4—241no—
263C3#1060212311yescharacteristic, complemented, Sylow
264C2—81no—
265C2#1174913711yescharacteristic
266C2#1174946212yes—
subgroupG/H
centerC22#91563
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. #11746970C2semidirect
5. #11745849C2semidirect
222. C3×C5#1660semidirect
253. C5#71956semidirect
263. C3#10602123semidirect

Maximal subgroups

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

subgroupindex
C3×#660062
C5×#50602
#117469702
#117463612
#117458492
#106021233
#719565