Finite Group Databasebeta

← #14291036

Subgroups — #14291036

Order 1920.

392 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 75 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×C5×#497C211yesmaximal, characteristic
3#11751182C212yesmaximal, complemented
4#11746361C211yesmaximal, characteristic
5#11746286C212yesmaximal, complemented
6#10602123—31nomaximal, Hall
7C2×C3×C5×Q16—21no—
8C2×C3×C5×SD16—21no—
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C5×#124C2211yescharacteristic
11#91833—21no—
12#91824—21no—
13#91768—22no—
14#91767—22no—
15#91759C2212yes—
16C3×C5×#97C2211yescharacteristic
17#91092—22no—
18#91091—22no—
19#91087C2212yes—
20#71330—51nomaximal, Hall
21#66006—31no—
22C5×#497D311yescharacteristic
23#65369—32no—
24#64760—31no—
25#64685—32no—
26C2×C3×C5×Q8—21no—
27C2×C3×C5×Q8D411yescharacteristic
28C2×C3×C5×D4D411yescharacteristic
29C22×Dic15—21no—
30C2×Dic30—21no—
31C3×C5×Q16—42no—
32C3×C5×SD16—42no—
33C2×C3×C5×C8—21no—
34C3×C5×C4⋊C4—22no—
35C3×C5×C22⋊C4—22no—
36C3×C42×C5C2311yescharacteristic
37#6719—22no—
38#6719—21no—
39C4⋊Dic15D412yes—
40C4⋊Dic15D412yes—
41#6712—22no—
42#6712—22no—
43#6712—22no—
44C4×Dic15—21no—
45C2×C3⋊#168—22no—
46#5672—51no—
47C3×#497D511yescharacteristic
48#5081—52no—
49#4540—51no—
50#4465—52no—
51C2×C5×Q16—21no—
52C2×C5×SD16—21no—
53C5×C4⋊Q8C2×D311yescharacteristic
54C5×#124C2×D311yescharacteristic
55#4090—61no—
56#4081—61no—
57#4025—62no—
58#4024—62no—
59#4016—32no—
60C5×#97C2×D311yescharacteristic
61#3940—62no—
62#3939—62no—
63#3935—32no—
64#1660—151noSylow
65C23×C3×C5—21no—
66C3×C5×Q8—41no—
67C3×C5×Q8—41no—
68C3×C5×Q8—41no—
69C3×C5×D4—41no—
70C2×C3×C4×C5—21no—
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5C2×D412yes—
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×Dic15—22no—
75C2×Dic15—22no—
76C2×Dic15—81no—
77Dic30—81no—
78C3×C5×C8—22no—
79C3⋊#168—24no—
80C2×C3×Q16—21no—
81C2×C3×SD16—21no—
82C3×C4⋊Q8C2×D511yescharacteristic
83C3×#124C2×D511yescharacteristic
84#944—101no—
85#935—101no—
86#879—102no—
87#878—102no—
88#870—52no—
89C3×#97C2×D511yescharacteristic
90#808—102no—
91#807—102no—
92#803—52no—
93C2×C5×Q8—21no—
94C2×C5×Q8#6711yescharacteristic
95C2×C5×D4#6711yescharacteristic
96C22×Dic5—61no—
97C2×Dic10—61no—
98C5×Q16—42no—
99C5×SD16—42no—
100C2×C5×C8—21no—
101C5×C4⋊C4—22no—
102C5×C22⋊C4—22no—
103C42×C5C22×D311yescharacteristic
104C22⋊Dic5—62no—
105C22⋊Dic5—61no—
106C4⋊Dic5—32no—
107C4⋊Dic5—32no—
108#683—62no—
109#683—62no—
110#683—62no—
111C4×Dic5—61no—
112C2×#168—62no—
113#563—151no—
114#501—152no—
115#497D1511yescharacteristic
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×C4×C5—81no—
125Dic15—42no—
126Dic15—42no—
127C2×C3×Q8—21no—
128C2×C3×Q8C22⋊D511yescharacteristic
129C2×C3×D4C22⋊D511yescharacteristic
130C22×Dic3—101no—
131C2×Dic6—101no—
132C3×Q16—42no—
133C3×SD16—42no—
134C2×C3×C8—21no—
135C3×C4⋊C4—22no—
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—102no—
147C23×C5—21no—
148C5×Q8—41no—
149C5×Q8—41no—
150C5×Q8—41no—
151C5×D4—41no—
152C2×C4×C5—21no—
153C2×C4×C5—41no—
154C2×C4×C5D3×D412yes—
155C2×C4×C5C2×#6711yescharacteristic
156C2×Dic5—62no—
157C2×Dic5—62no—
158C2×Dic5—241no—
159Dic10—241no—
160C5×C8—22no—
161#168—64no—
162C2×Q16—21no—
163C2×SD16—21no—
164C4⋊Q8—301no—
165C4⋊Q8C2×D1511yescharacteristic
166#126—302no—
167#125—152no—
168#124C2×D1511yescharacteristic
169#123—301no—
170C22⋊Q8—302no—
171#107—302no—
172#106—302no—
173#97—152no—
174#97C2×D1511yescharacteristic
175C2×C3×C5—81no—
176C2×C3×C5#45311yescharacteristic
177C2×C3×C5#45612yes—
178C23×C3—21no—
179C3×Q8—41no—
180C3×Q8—41no—
181C3×Q8—41no—
182C3×D4—41no—
183C2×C3×C4—21no—
184C2×C3×C4—41no—
185C2×C3×C4D4×D512yes—
186C2×C3×C4C2×C22⋊D511yescharacteristic
187C2×Dic3—102no—
188C2×Dic3—102no—
189C2×Dic3—401no—
190Dic6—401no—
191C3×C8—22no—
192C3⋊C8—104no—
193C22×C5—42no—
194C22×C5—41no—
195C22×C5#93711yescharacteristic
196C4×C5—22no—
197C4×C5—21no—
198C4×C5—41no—
199C4×C5—81no—
200Dic5—122no—
201Dic5—122no—
202C2×Q8—21no—
203C2×Q8—301no—
204C2×Q8#122011yescharacteristic
205C2×D4#122011yescharacteristic
206C22×C4—301no—
207Q16—42no—
208SD16—42no—
209C2×C8—21no—
210C2×C8—302no—
211C4⋊C4—22no—
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—
221C42C22×D1511yescharacteristic
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—81no—
230Dic3—202no—
231Dic3—202no—
232C2×C5—81no—
233C2×C5#507711yescharacteristic
234C2×C5#520512yes—
235C23—21no—
236Q8—41no—
237Q8—41no—
238Q8—41no—
239Q8—1201no—
240D4—41no—
241C2×C4—21no—
242C2×C4—41no—
243C2×C4—302no—
244C2×C4—302no—
245C2×C4—1201no—
246C2×C4D4×D1512yes—
247C2×C4C2×#122011yescharacteristic
248C8—22no—
249C8—304no—
250C2×C3—81no—
251C2×C3#6536611yescharacteristic
252C2×C3#6549412yes—
253C5#7133011yescharacteristic, complemented, Sylow
254C22—41no—
255C22—42no—
256C22#9182611yescharacteristic
257C4—21no—
258C4—22no—
259C4—41no—
260C4—81no—
261C4—602no—
262C4—602no—
263C3#1060212311yescharacteristic, complemented, Sylow
264C2—81no—
265C2#1175117811yescharacteristic
266C2#1175130612yes—
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#497C2
socleC22×C3×C5#120
prime radicalC2×C3×C5×D4D4
hypercenter#497D15
hypocenterC3×C5#1660
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
3. #11751182C2semidirect
5. #11746286C2semidirect
222. C3×C5#1660semidirect
253. C5#71330semidirect
263. C3#10602123semidirect

Maximal subgroups

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

subgroupindex
#117564312
C3×C5×#4972
#117511822
#117463612
#117462862
#106021233
#713305