Finite Group Databasebeta

← #14291057

Subgroups — #14291057

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
2#11751161C211yesmaximal, characteristic
3#11746953C212yesmaximal, complemented
4C5×#4540C211yesmaximal, characteristic
5#11745849C212yesmaximal, complemented
6#10599148—31nomaximal, Hall
7C3×C5×#124C2211yescharacteristic
8C2×#6718—21no—
9C2×#6716—21no—
10#91758C2211yescharacteristic
11C3×#4090—21no—
12C3×#4081—21no—
13C3×#4025—22no—
14C3×#4024—22no—
15C3×#4016C2212yes—
16#91087C2211yescharacteristic
17C5×#803C2212yes—
18#90990—22no—
19#90987—22no—
20#71956—51nomaximal, Hall
21#66006D311yescharacteristic
22#65349—31no—
23#64991—32no—
24C5×#329—31no—
25#64685—32no—
26C2×C3×C5×Q8D411yescharacteristic
27C2×C3×C5×D4D411yescharacteristic
28C2×Dic30—21no—
29C22×C3×Dic5—21no—
30C2×C3×Dic10—21no—
31C3×C5×C22⋊C4—22no—
32C3×C42×C5C2311yescharacteristic
33#6718—42no—
34#6716—42no—
35C4⋊Dic15—22no—
36C2×C3⋊#168—21no—
37C2×C5×C3⋊C8—22no—
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#5060—51no—
49#4543—52no—
50#4540D511yescharacteristic
51C5×#124C2×D311yescharacteristic
52#4090—21no—
53C2×#689—61no—
54#4081—21no—
55C2×#687—61no—
56#4025—22no—
57#4024—22no—
58#4016C2×D312yes—
59#4015—31no—
60C5×#97—32no—
61#3950—62no—
62#3949—62no—
63#3935—31no—
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—41no—
72Dic30—41no—
73Dic30—41no—
74C2×C3×Dic5—22no—
75C2×C3×Dic5—22no—
76C2×C3×Dic5—81no—
77C3×Dic10—81no—
78C3⋊#168—22no—
79C5×C3⋊C8—24no—
80C3×C4⋊Q8—101no—
81C3×#126—102no—
82C3×#125—52no—
83C3×#124C2×D511yescharacteristic
84C3×#123—101no—
85C3×C22⋊Q8—102no—
86C2×#216—101no—
87C2×#214—101no—
88#869—51no—
89#808—102no—
90#807—102no—
91#803—51no—
92#803C2×D512yes—
93C2×C5×Q8#6711yescharacteristic
94C2×C5×D4#6711yescharacteristic
95C22×Dic5—21no—
96C2×Dic10—21no—
97C2×Dic10—61no—
98C2×C5×C8—62no—
99C5×C22⋊C4—22no—
100C42×C5C22×D311yescharacteristic
101C22⋊Dic5—22no—
102C22⋊Dic5—21no—
103#689—122no—
104#687—122no—
105C4⋊Dic5—62no—
106C4⋊Dic5#6712yes—
107C4⋊Dic5#6712yes—
108#683—22no—
109#683—22no—
110#683—22no—
111C4×Dic5—21no—
112C2×#168—61no—
113#563—51no—
114#501—152no—
115#497—151no—
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—81no—
125C3×Dic5—42no—
126C3×Dic5—42no—
127C2×C3×Q8—101no—
128C2×C3×Q8D2011yescharacteristic
129C2×C3×D4D2011yescharacteristic
130C22×C3×C4—101no—
131C2×Dic6—101no—
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—202no—
143#214—202no—
144C4⋊Dic3—102no—
145C2×C3⋊C8—22no—
146C2×C3⋊C8—101no—
147C23×C5—21no—
148C5×Q8—41no—
149C5×D4—41no—
150C2×C4×C5—21no—
151C2×C4×C5C2×#6711yescharacteristic
152C2×C4×C5C2×#6712yes—
153C2×Dic5—22no—
154C2×Dic5—22no—
155C2×Dic5—81no—
156C2×Dic5—121no—
157Dic10—81no—
158Dic10—121no—
159Dic10—121no—
160C5×C8—64no—
161#168—62no—
162C2×Q16—301no—
163C2×SD16—301no—
164C4⋊Q8—101no—
165C4⋊Q8—151no—
166#126—102no—
167#125—52no—
168#124D3×D511yescharacteristic
169#123—101no—
170C22⋊Q8—102no—
171#107—302no—
172#106—302no—
173#97—32no—
174#97—151no—
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×C4C2×D2011yescharacteristic
187C2×C3×C4D4×D512yes—
188C2×Dic3—201no—
189Dic6—201no—
190Dic6—201no—
191C3⋊C8—24no—
192C3⋊C8—102no—
193C22×C5—41no—
194C22×C5—42no—
195C22×C5#95311yescharacteristic
196C4×C5—21no—
197C4×C5—22no—
198C4×C5—41no—
199Dic5—42no—
200Dic5—42no—
201Dic5—241no—
202C2×Q8—101no—
203C2×Q8—301no—
204C2×Q8#120211yescharacteristic
205C2×D4#120211yescharacteristic
206C22×C4—101no—
207Q16—602no—
208SD16—602no—
209C2×C8—62no—
210C2×C8—301no—
211C4⋊C4—52no—
212C4⋊C4—52no—
213C4⋊C4—102no—
214C4⋊C4—102no—
215C4⋊C4—102no—
216C4⋊C4—302no—
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#402811yescharacteristic
226C3×C4—21no—
227C3×C4—22no—
228C3×C4—41no—
229C3×C4—202no—
230C3×C4—202no—
231Dic3—401no—
232C2×C5—81no—
233C2×C5#524111yescharacteristic
234C2×C5#524612yes—
235C23—21no—
236Q8—41no—
237Q8—401no—
238Q8—601no—
239Q8—601no—
240D4—41no—
241C2×C4—21no—
242C2×C4—102no—
243C2×C4—102no—
244C2×C4—401no—
245C2×C4—601no—
246C2×C4C2×#120211yescharacteristic
247C2×C4D5×#6712yes—
248C8—64no—
249C8—302no—
250C2×C3—81no—
251C2×C3#6503611yescharacteristic
252C2×C3#6511512yes—
253C5#7195611yescharacteristic, complemented, Sylow
254C22—41no—
255C22—42no—
256C22#9156411yescharacteristic
257C4—21no—
258C4—22no—
259C4—41no—
260C4—202no—
261C4—202no—
262C4—1201no—
263C3#1059914811yescharacteristic, complemented, Sylow
264C2—81no—
265C2#1174913811yescharacteristic
266C2#1174946412yes—
subgroupG/H
centerC22#91564
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. #11746953C2semidirect
5. #11745849C2semidirect
222. C3×C5#1660semidirect
253. C5#71956semidirect
263. C3#10599148semidirect

Maximal subgroups

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

subgroupindex
C3×#660062
#117511612
#117469532
C5×#45402
#117458492
#105991483
#719565