Finite Group Databasebeta

← #14291055

Subgroups — #14291055

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
1C5×#5672C211yesmaximal, characteristic
2#11751161C211yesmaximal, characteristic
3#11746958C212yesmaximal, complemented
4C3×#64760C211yesmaximal, characteristic
5#11745850C212yesmaximal, complemented
6#10602749—31nomaximal, Hall
7C3×C5×#124C2211yescharacteristic
8C2×#6718—21no—
9C2×#6716—21no—
10#91758C2211yescharacteristic
11C5×#944—21no—
12C5×#935—21no—
13C5×#879—22no—
14C5×#878—22no—
15C5×#870C2212yes—
16#91087C2211yescharacteristic
17C3×#3935C2212yes—
18#90988—22no—
19#90985—22no—
20#68355—51nomaximal, Hall
21C5×#563—31no—
22#65354—32no—
23#65349—31no—
24#64763—32no—
25#64760D311yescharacteristic
26C2×C3×C5×Q8D411yescharacteristic
27C2×C3×C5×D4D411yescharacteristic
28C2×Dic30—21no—
29C22×C5×Dic3—21no—
30C2×C5×Dic6—21no—
31C3×C5×C22⋊C4—22no—
32C3×C42×C5C2311yescharacteristic
33#6718—42no—
34#6716—42no—
35C4⋊Dic15—22no—
36C2×C3⋊#168—21no—
37C5×#217—22no—
38C5×#217—21no—
39C5×C4⋊Dic3D412yes—
40C5×C4⋊Dic3D412yes—
41C5×Dic3⋊C4—22no—
42C5×Dic3⋊C4—22no—
43C5×Dic3⋊C4—22no—
44C4×C5×Dic3—21no—
45C2×C3×#168—22no—
46#5672D511yescharacteristic
47#5060—51no—
48#4702—52no—
49C3×#329—51no—
50#4465—52no—
51C5×C4⋊Q8—61no—
52C5×#126—62no—
53C5×#125—32no—
54C5×#124C2×D311yescharacteristic
55C5×#123—61no—
56C5×C22⋊Q8—62no—
57C2×#689—61no—
58C2×#687—61no—
59#4015—31no—
60#3940—62no—
61#3939—62no—
62#3935—31no—
63#3935C2×D312yes—
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×C5×Dic3—22no—
75C2×C5×Dic3—22no—
76C2×C5×Dic3—81no—
77C5×Dic6—81no—
78C3⋊#168—22no—
79C3×#168—24no—
80C3×#124C2×D511yescharacteristic
81#944—21no—
82C2×#216—101no—
83#935—21no—
84C2×#214—101no—
85#879—22no—
86#878—22no—
87#870C2×D512yes—
88#869—51no—
89C3×#97—52no—
90#818—102no—
91#817—102no—
92#803—51no—
93C2×C5×Q8—61no—
94C2×C5×Q8D1211yescharacteristic
95C2×C5×D4D1211yescharacteristic
96C22×C4×C5—61no—
97C2×Dic10—61no—
98C5×C4⋊C4—32no—
99C5×C4⋊C4—32no—
100C5×C4⋊C4—62no—
101C5×C4⋊C4—62no—
102C5×C4⋊C4—62no—
103C5×C22⋊C4—22no—
104C5×C22⋊C4—62no—
105C5×C22⋊C4—61no—
106C42×C5—61no—
107C42×C5C22×D311yescharacteristic
108#689—122no—
109#687—122no—
110C4⋊Dic5—62no—
111C2×#168—22no—
112C2×#168—61no—
113#563—31no—
114#501—152no—
115#497—151no—
116#330—152no—
117#329—51no—
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—
125C5×Dic3—42no—
126C5×Dic3—42no—
127C2×C3×Q8C22⋊D511yescharacteristic
128C2×C3×D4C22⋊D511yescharacteristic
129C22×Dic3—21no—
130C2×Dic6—21no—
131C2×Dic6—101no—
132C2×C3×C8—102no—
133C3×C22⋊C4—22no—
134C3×C42C22×D511yescharacteristic
135#217—22no—
136#217—21no—
137#216—202no—
138#214—202no—
139C4⋊Dic3—102no—
140C4⋊Dic3C22⋊D512yes—
141C4⋊Dic3C22⋊D512yes—
142Dic3⋊C4—22no—
143Dic3⋊C4—22no—
144Dic3⋊C4—22no—
145C4×Dic3—21no—
146C2×C3⋊C8—101no—
147C23×C5—21no—
148C5×Q8—41no—
149C5×Q8—241no—
150C5×D4—41no—
151C2×C4×C5—21no—
152C2×C4×C5—62no—
153C2×C4×C5—62no—
154C2×C4×C5—241no—
155C2×C4×C5C2×D1211yescharacteristic
156C2×C4×C5D3×D412yes—
157C2×Dic5—121no—
158Dic10—121no—
159Dic10—121no—
160#168—24no—
161#168—62no—
162C2×Q16—301no—
163C2×SD16—301no—
164C4⋊Q8—61no—
165C4⋊Q8—151no—
166#126—62no—
167#125—32no—
168#124D3×D511yescharacteristic
169#123—61no—
170C22⋊Q8—62no—
171#107—302no—
172#106—302no—
173#97—52no—
174#97—151no—
175C2×C3×C5—81no—
176C2×C3×C5#45311yescharacteristic
177C2×C3×C5#45612yes—
178C23×C3—21no—
179C3×Q8—41no—
180C3×D4—41no—
181C2×C3×C4—21no—
182C2×C3×C4C2×C22⋊D511yescharacteristic
183C2×C3×C4C2×C22⋊D512yes—
184C2×Dic3—22no—
185C2×Dic3—22no—
186C2×Dic3—81no—
187C2×Dic3—201no—
188Dic6—81no—
189Dic6—201no—
190Dic6—201no—
191C3×C8—104no—
192C3⋊C8—102no—
193C22×C5—41no—
194C22×C5—42no—
195C22×C5#88211yescharacteristic
196C4×C5—21no—
197C4×C5—22no—
198C4×C5—41no—
199C4×C5—122no—
200C4×C5—122no—
201Dic5—241no—
202C2×Q8—61no—
203C2×Q8—301no—
204C2×Q8#120311yescharacteristic
205C2×D4#120311yescharacteristic
206C22×C4—61no—
207Q16—602no—
208SD16—602no—
209C2×C8—102no—
210C2×C8—301no—
211C4⋊C4—32no—
212C4⋊C4—32no—
213C4⋊C4—62no—
214C4⋊C4—62no—
215C4⋊C4—62no—
216C4⋊C4—302no—
217C22⋊C4—22no—
218C22⋊C4—62no—
219C22⋊C4—61no—
220C42—61no—
221C42C2×D3×D511yescharacteristic
222C3×C5#166011yescharacteristic, complemented, Hall
223C22×C3—41no—
224C22×C3—42no—
225C22×C3#409911yescharacteristic
226C3×C4—21no—
227C3×C4—22no—
228C3×C4—41no—
229Dic3—42no—
230Dic3—42no—
231Dic3—401no—
232C2×C5—81no—
233C2×C5#474711yescharacteristic
234C2×C5#482612yes—
235C23—21no—
236Q8—41no—
237Q8—241no—
238Q8—601no—
239Q8—601no—
240D4—41no—
241C2×C4—21no—
242C2×C4—62no—
243C2×C4—62no—
244C2×C4—241no—
245C2×C4—601no—
246C2×C4C2×#120311yescharacteristic
247C2×C4D3×C22⋊D512yes—
248C8—104no—
249C8—302no—
250C2×C3—81no—
251C2×C3#6553011yescharacteristic
252C2×C3#6553512yes—
253C5#6835511yescharacteristic, complemented, Sylow
254C22—41no—
255C22—42no—
256C22#9157011yescharacteristic
257C4—21no—
258C4—22no—
259C4—41no—
260C4—122no—
261C4—122no—
262C4—1201no—
263C3#1060274911yescharacteristic, complemented, Sylow
264C2—81no—
265C2#1174914111yescharacteristic
266C2#1174942312yes—
subgroupG/H
centerC22#91570
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. #11746958C2semidirect
5. #11745850C2semidirect
222. C3×C5#1660semidirect
253. C5#68355semidirect
263. C3#10602749semidirect

Maximal subgroups

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

subgroupindex
C5×#56722
#117511612
#117469582
C3×#647602
#117458502
#106027493
#683555