Finite Group Databasebeta

← #14289009

Subgroups — #14289009

Order 1920.

456 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 95 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#11756481C211yesmaximal, characteristic, complemented
2C3×C5×#492C211yesmaximal, characteristic
3#11751176C212yesmaximal
4#11746367C211yesmaximal, characteristic, complemented
5#11746277C212yesmaximal, complemented
6#10602062—31nomaximal, Hall
7C2×C3×C5×SD16—22no—
8C3×C5×C4⋊Q8C2211yescharacteristic
9C3×C5×#127C2211yescharacteristic
10#91833—22no—
11C2×#6716—22no—
12#91777—22no—
13#91776—22no—
14C4×Dic30C2212yes—
15C3×C4×C5×C8C2211yescharacteristic
16#91116—22no—
17C4⋊(C3⋊#168)C2212yes—
18#71269—51nomaximal, Hall
19#66056—31no—
20C5×#492D311yescharacteristic
21#65364—32no—
22#64766—31no—
23#64676—32no—
24C2×C3×C5×Q8D412yes—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4—21no—
27C2×Dic30—22no—
28C2×Dic30D412yes—
29C3×C5×SD16—44no—
30C2×C3×C5×C8—21no—
31C3×C5×C4⋊C4—22no—
32C3×C42×C5C2311yescharacteristic
33#6716—44no—
34C4⋊Dic15D412yes—
35#6712—24no—
36#6712—22no—
37C4×Dic15—22no—
38C4×Dic15—22no—
39C2×C3⋊#168—22no—
40#5722—51no—
41C3×#492D511yescharacteristic
42#5075—52no—
43#4546—51no—
44#4456—52no—
45C2×C5×SD16—22no—
46C5×C4⋊Q8C2×D311yescharacteristic
47C5×#127C2×D311yescharacteristic
48#4090—62no—
49C2×#687—62no—
50#4034—62no—
51#4033—62no—
52C4×Dic10—32no—
53C4×C5×C8C2×D311yescharacteristic
54#3964—62no—
55C4⋊#168—32no—
56#1623—151noSylow
57C23×C3×C5—41no—
58C3×C5×Q8—42no—
59C3×C5×D4—42no—
60C3×C5×D4—42no—
61C3×C5×D4—42no—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5C2×D411yescharacteristic
64C2×C3×C4×C5C2×D412yes—
65C2×Dic15—22no—
66C2×Dic15—22no—
67Dic30—22no—
68Dic30—82no—
69Dic30SD1614yescomplemented
70C3×C5×C8—22no—
71C3⋊#168—42no—
72C2×C3×SD16—22no—
73C3×C4⋊Q8C2×D511yescharacteristic
74C3×#127C2×D511yescharacteristic
75#944—102no—
76C2×#214—102no—
77#888—102no—
78#887—102no—
79C4×Dic6—52no—
80C3×C4×C8C2×D511yescharacteristic
81#832—102no—
82C4⋊(C3⋊C8)—52no—
83C2×C5×Q8#6712yes—
84C2×C5×D4—22no—
85C2×C5×D4—21no—
86C2×Dic10—32no—
87C2×Dic10—62no—
88C5×SD16—44no—
89C2×C5×C8—21no—
90C5×C4⋊C4—22no—
91C42×C5C22×D311yescharacteristic
92#687—124no—
93C4⋊Dic5—32no—
94#683—64no—
95#683—62no—
96C4×Dic5—62no—
97C4×Dic5—62no—
98C2×#168—62no—
99Q82—151no—
100#492D1511yescharacteristic
101#460—152no—
102#333—151no—
103Q8⋊C8—152no—
104C22×C3×C5—82no—
105C22×C3×C5—81no—
106C22×C3×C5#12011yescharacteristic
107C3×C4×C5—21no—
108C3×C4×C5—42no—
109C3×C4×C5C2×SD1612yes—
110C3×C4×C5#13712yes—
111Dic15—24no—
112Dic15—42no—
113C2×C3×Q8C22⋊D512yes—
114C2×C3×D4—22no—
115C2×C3×D4—21no—
116C2×Dic6—52no—
117C2×Dic6—102no—
118C3×SD16—44no—
119C2×C3×C8—21no—
120C3×C4⋊C4—22no—
121C3×C42C22×D511yescharacteristic
122#214—204no—
123C4⋊Dic3—52no—
124Dic3⋊C4—104no—
125Dic3⋊C4—102no—
126C4×Dic3—102no—
127C4×Dic3—102no—
128C2×C3⋊C8—102no—
129C23×C5—41no—
130C5×Q8—42no—
131C5×D4—42no—
132C5×D4—42no—
133C5×D4—42no—
134C2×C4×C5—22no—
135C2×C4×C5D3×D412yes—
136C2×C4×C5C2×#6711yescharacteristic
137C2×Dic5—62no—
138C2×Dic5—62no—
139Dic10—34no—
140Dic10—62no—
141Dic10—242no—
142C5×C8—22no—
143#168—122no—
144C2×SD16—22no—
145C2×SD16—302no—
146C4⋊Q8—302no—
147C4⋊Q8—302no—
148C4⋊Q8C2×D1511yescharacteristic
149#127C2×D1511yescharacteristic
150C4×Q8—152no—
151C4×Q8—302no—
152C4⋊C8—152no—
153#102—302no—
154C4×C8C2×D1511yescharacteristic
155C2×C3×C5—161no—
156C2×C3×C5#44812yes—
157C2×C3×C5#45311yescharacteristic
158C23×C3—41no—
159C3×Q8—42no—
160C3×D4—42no—
161C3×D4—42no—
162C3×D4—42no—
163C2×C3×C4—22no—
164C2×C3×C4D4×D512yes—
165C2×C3×C4C2×C22⋊D511yescharacteristic
166C2×Dic3—102no—
167C2×Dic3—102no—
168Dic6—54no—
169Dic6—102no—
170Dic6—402no—
171C3×C8—22no—
172C3⋊C8—202no—
173C22×C5—82no—
174C22×C5—81no—
175C22×C5#93711yescharacteristic
176C4×C5—21no—
177C4×C5—42no—
178C4×C5D3×SD1612yes—
179C4×C5#91512yes—
180Dic5—64no—
181Dic5—122no—
182C2×Q8—152no—
183C2×Q8—302no—
184C2×Q8#122012yes—
185C2×D4—22no—
186C2×D4—21no—
187SD16—44no—
188SD16—604no—
189C2×C8—21no—
190C2×C8—302no—
191C4⋊C4—22no—
192C4⋊C4—152no—
193C4⋊C4—304no—
194C4⋊C4—302no—
195C42—302no—
196C42—302no—
197C42C22×D1511yescharacteristic
198C3×C5#162311yescharacteristic, complemented, Hall
199C22×C3—81no—
200C22×C3—82no—
201C22×C3#408311yescharacteristic
202C3×C4—21no—
203C3×C4—42no—
204C3×C4D5×SD1612yes—
205C3×C4#406112yes—
206Dic3—104no—
207Dic3—202no—
208C2×C5—161no—
209C2×C5#507711yescharacteristic
210C2×C5#517012yes—
211C23—41no—
212Q8—42no—
213Q8—154no—
214Q8—302no—
215Q8—1202no—
216D4—42no—
217D4—42no—
218D4—42no—
219C2×C4—22no—
220C2×C4—302no—
221C2×C4—302no—
222C2×C4D4×D1512yes—
223C2×C4C2×#122011yescharacteristic
224C8—22no—
225C8—602no—
226C2×C3—161no—
227C2×C3#6536611yescharacteristic
228C2×C3#6545912yes—
229C5#7126911yescharacteristic, complemented, Sylow
230C22—81no—
231C22—82no—
232C22#9182611yescharacteristic
233C4—21no—
234C4—42no—
235C4—304no—
236C4—602no—
237C4SD16×D1512yes—
238C4#9180412yes—
239C3#1060206211yescharacteristic, complemented, Sylow
240C2—161no—
241C2#1175117811yescharacteristic
242C2#1175127112yes—
subgroupG/H
centerC22#91826
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#492C2
socleC22×C3×C5#120
prime radicalC3×C5×#127C22
hypercenter#492D15
hypocenterC3×C5#1623
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
1. #11756481C2semidirect
4. #11746367C2semidirect
5. #11746277C2semidirect
69. Dic30SD16semidirect
198. C3×C5#1623semidirect
229. C5#71269semidirect
239. C3#10602062semidirect

Maximal subgroups

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

subgroupindex
#117564812
C3×C5×#4922
#117511762
#117463672
#117462772
#106020623
#712695