Finite Group Databasebeta

← #14291042

Subgroups — #14291042

Order 1920.

392 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 87 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×C5×#563C211yesmaximal, characteristic
2#11751165C212yesmaximal, complemented
3#11751161C211yesmaximal, characteristic
4#11746364C212yesmaximal, complemented
5#11746361C211yesmaximal, characteristic
6#10602749—31nomaximal, Hall
7C3×C5×C4⋊Q8—21no—
8C3×C5×#126—22no—
9C3×C5×#125C2212yes—
10C3×C5×#124C2211yescharacteristic
11C3×C5×#123—21no—
12C3×C5×C22⋊Q8—22no—
13C2×#6718—21no—
14C2×#6716—21no—
15#91758C2211yescharacteristic
16#91092—22no—
17#91091—22no—
18#91087C2212yes—
19#91087C2211yescharacteristic
20#71956—51nomaximal, Hall
21C5×#563D311yescharacteristic
22#65354—32no—
23#65349—31no—
24#64763—32no—
25#64760—31no—
26C2×C3×C5×Q8—21no—
27C2×C3×C5×Q8D411yescharacteristic
28C2×C3×C5×D4D411yescharacteristic
29C22×C3×C4×C5—21no—
30C2×Dic30—21no—
31C3×C5×C4⋊C4—22no—
32C3×C5×C4⋊C4—22no—
33C3×C5×C4⋊C4—22no—
34C3×C5×C4⋊C4D412yes—
35C3×C5×C4⋊C4D412yes—
36C3×C5×C22⋊C4—22no—
37C3×C5×C22⋊C4—21no—
38C3×C5×C22⋊C4—22no—
39C3×C42×C5—21no—
40C3×C42×C5C2311yescharacteristic
41#6718—42no—
42#6716—42no—
43C4⋊Dic15—22no—
44C2×C3⋊#168—21no—
45C2×C3⋊#168—22no—
46C3×#563D511yescharacteristic
47#5064—52no—
48#5060—51no—
49#4543—52no—
50#4540—51no—
51C5×C4⋊Q8—21no—
52C5×#126—22no—
53C5×#125C2×D312yes—
54C5×#124C2×D311yescharacteristic
55C5×#123—21no—
56C5×C22⋊Q8—22no—
57C2×#689—61no—
58C2×#687—61no—
59#4015—31no—
60#3940—62no—
61#3939—62no—
62#3935—31no—
63#3935—32no—
64#1660—151noSylow
65C23×C3×C5—21no—
66C3×C5×Q8—41no—
67C3×C5×Q8—81no—
68C3×C5×D4—41no—
69C2×C3×C4×C5—22no—
70C2×C3×C4×C5—21no—
71C2×C3×C4×C5—22no—
72C2×C3×C4×C5—81no—
73C2×C3×C4×C5C2×D412yes—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×Dic15—41no—
76Dic30—41no—
77Dic30—41no—
78C3⋊#168—24no—
79C3⋊#168—22no—
80C3×C4⋊Q8—21no—
81C3×#126—22no—
82C3×#125C2×D512yes—
83C3×#124C2×D511yescharacteristic
84C3×#123—21no—
85C3×C22⋊Q8—22no—
86C2×#216—101no—
87C2×#214—101no—
88#869—51no—
89#808—102no—
90#807—102no—
91#803—52no—
92#803—51no—
93C2×C5×Q8—21no—
94C2×C5×Q8#6711yescharacteristic
95C2×C5×D4#6711yescharacteristic
96C22×C4×C5—21no—
97C2×Dic10—61no—
98C5×C4⋊C4—22no—
99C5×C4⋊C4—22no—
100C5×C4⋊C4—22no—
101C5×C4⋊C4#6712yes—
102C5×C4⋊C4#6712yes—
103C5×C22⋊C4—22no—
104C5×C22⋊C4—21no—
105C5×C22⋊C4—22no—
106C42×C5—21no—
107C42×C5C22×D311yescharacteristic
108#689—122no—
109#687—122no—
110C4⋊Dic5—62no—
111C2×#168—62no—
112C2×#168—61no—
113#563D1511yescharacteristic
114#501—152no—
115#497—151no—
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—42no—
124C3×C4×C5—41no—
125C3×C4×C5—42no—
126Dic15—81no—
127C2×C3×Q8—21no—
128C2×C3×Q8C22⋊D511yescharacteristic
129C2×C3×D4C22⋊D511yescharacteristic
130C22×C3×C4—21no—
131C2×Dic6—101no—
132C3×C4⋊C4—22no—
133C3×C4⋊C4—22no—
134C3×C4⋊C4—22no—
135C3×C4⋊C4C22⋊D512yes—
136C3×C4⋊C4C22⋊D512yes—
137C3×C22⋊C4—22no—
138C3×C22⋊C4—21no—
139C3×C22⋊C4—22no—
140C3×C42—21no—
141C3×C42C22×D511yescharacteristic
142#216—202no—
143#214—202no—
144C4⋊Dic3—102no—
145C2×C3⋊C8—102no—
146C2×C3⋊C8—101no—
147C23×C5—21no—
148C5×Q8—41no—
149C5×Q8—81no—
150C5×D4—41no—
151C2×C4×C5—22no—
152C2×C4×C5—21no—
153C2×C4×C5—22no—
154C2×C4×C5—81no—
155C2×C4×C5C2×#6712yes—
156C2×C4×C5C2×#6711yescharacteristic
157C2×Dic5—121no—
158Dic10—121no—
159Dic10—121no—
160#168—64no—
161#168—62no—
162C2×Q16—301no—
163C2×SD16—301no—
164C4⋊Q8—21no—
165C4⋊Q8—151no—
166#126—22no—
167#125C2×D1512yes—
168#124C2×D1511yescharacteristic
169#123—21no—
170C22⋊Q8—22no—
171#107—302no—
172#106—302no—
173#97—152no—
174#97—151no—
175C2×C3×C5—81no—
176C2×C3×C5#45311yescharacteristic
177C2×C3×C5#45612yes—
178C23×C3—21no—
179C3×Q8—41no—
180C3×Q8—81no—
181C3×D4—41no—
182C2×C3×C4—22no—
183C2×C3×C4—21no—
184C2×C3×C4—22no—
185C2×C3×C4—81no—
186C2×C3×C4C2×C22⋊D512yes—
187C2×C3×C4C2×C22⋊D511yescharacteristic
188C2×Dic3—201no—
189Dic6—201no—
190Dic6—201no—
191C3⋊C8—104no—
192C3⋊C8—102no—
193C22×C5—41no—
194C22×C5—42no—
195C22×C5#95311yescharacteristic
196C4×C5—21no—
197C4×C5—22no—
198C4×C5—42no—
199C4×C5—41no—
200C4×C5—42no—
201Dic5—241no—
202C2×Q8—21no—
203C2×Q8—301no—
204C2×Q8#122011yescharacteristic
205C2×D4#122011yescharacteristic
206C22×C4—21no—
207Q16—602no—
208SD16—602no—
209C2×C8—302no—
210C2×C8—301no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—302no—
215C4⋊C4#122012yes—
216C4⋊C4#122012yes—
217C22⋊C4—22no—
218C22⋊C4—21no—
219C22⋊C4—22no—
220C42—21no—
221C42C22×D1511yescharacteristic
222C3×C5#166011yescharacteristic, complemented, Hall
223C22×C3—41no—
224C22×C3—42no—
225C22×C3#409911yescharacteristic
226C3×C4—21no—
227C3×C4—22no—
228C3×C4—42no—
229C3×C4—41no—
230C3×C4—42no—
231Dic3—401no—
232C2×C5—81no—
233C2×C5#524111yescharacteristic
234C2×C5#524612yes—
235C23—21no—
236Q8—41no—
237Q8—81no—
238Q8—601no—
239Q8—601no—
240D4—41no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—81no—
245C2×C4—601no—
246C2×C4C2×#122012yes—
247C2×C4C2×#122011yescharacteristic
248C8—302no—
249C8—304no—
250C2×C3—81no—
251C2×C3#6553011yescharacteristic
252C2×C3#6553512yes—
253C5#7195611yescharacteristic, complemented, Sylow
254C22—41no—
255C22—42no—
256C22#9184211yescharacteristic
257C4—21no—
258C4—22no—
259C4—42no—
260C4—41no—
261C4—42no—
262C4—1201no—
263C3#1060274911yescharacteristic, complemented, Sylow
264C2—81no—
265C2#1175134211yescharacteristic
266C2#1175134712yes—
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#563C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenter#563D15
hypocenterC3×C5#1660
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
2. #11751165C2semidirect
4. #11746364C2semidirect
222. C3×C5#1660semidirect
253. C5#71956semidirect
263. C3#10602749semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5632
#117511652
#117511612
#117463642
#117463612
#106027493
#719565