Finite Group Databasebeta

← #14296933

Subgroups — #14296933

Order 1920.

1128 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 1128 conjugacy classes of subgroups — too many to draw. Only its 180 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
1C23×Dic30C211yesmaximal, characteristic
2C5×#5207C211yesmaximal, characteristic
3C3×#65496C211yesmaximal, characteristic
4C2×#90963C214yesmaximal, complemented
5#10600783—31nomaximal, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C23×Dic15C412yes—
8C22×Dic30—22no—
9C22×Dic30—22no—
10C22×Dic30—28no—
11C22×Dic30C412yes—
12C22×Dic30C2212yes—
13C2×C5×#208C2212yes—
14C2×C3×#681C2212yes—
15C5×#830—22no—
16C3×C22⋊#168—22no—
17#90963—28no—
18#69990—51nomaximal, Hall
19C23×Dic10—31no—
20C5×#407—31no—
21#65496D311yescharacteristic
22C2×#3956—34no—
23C24×C3×C5C2×C411yescharacteristic
24C22×C3×C4×C5—24no—
25C22×C3×C4×C5C2×C411yescharacteristic
26C22×C3×C4×C5D412yes—
27C22×C3×C4×C5D412yes—
28C22×C3×C4×C5C2311yescharacteristic
29C22×Dic15—24no—
30C22×Dic15—28no—
31C22×Dic15C2×C414yes—
32C2×Dic30—216no—
33C2×Dic30—216no—
34C2×Dic30—24no—
35C2×Dic30—22no—
36C2×Dic30—24no—
37C2×Dic30—22no—
38C2×Dic30—28no—
39C2×Dic30D418yes—
40C5×#208—24no—
41C2×C5×C3⋊C8—22no—
42C3×#681—24no—
43C2×C3×#168—22no—
44C23×Dic6—51no—
45C3×#407—51no—
46#5207D511yescharacteristic
47C2×#824—54no—
48C23×C4×C5C2×D311yescharacteristic
49C23×Dic5—32no—
50C22×Dic10—32no—
51C22×Dic10—32no—
52C22×Dic10—68no—
53C22×Dic10—62no—
54C22×Dic10—62no—
55C2×C5×M16—32no—
56C2×#681C2×D312yes—
57C5×C22⋊C8—62no—
58C22⋊#168—22no—
59#3956—68no—
60#1784—151noSylow
61C23×C3×C5—24no—
62C23×C3×C5—22no—
63C23×C3×C5C22⋊C412yes—
64C23×C3×C5C22×C411yescharacteristic
65C2×C3×C4×C5—22no—
66C2×C3×C4×C5—24no—
67C2×C3×C4×C5—24no—
68C2×C3×C4×C5C22⋊C412yes—
69C2×C3×C4×C5C2×D411yescharacteristic
70C2×C3×C4×C5C2×D414yes—
71C2×C3×C4×C5C2×D411yescharacteristic
72C2×Dic15—216no—
73C2×Dic15—24no—
74C2×Dic15—24no—
75C2×Dic15C22⋊C418yes—
76Dic30—216no—
77Dic30—28no—
78Dic30—28no—
79C3×#168—42no—
80C5×C3⋊C8—42no—
81C23×C3×C4C2×D511yescharacteristic
82C23×Dic3—52no—
83C22×Dic6—52no—
84C22×Dic6—52no—
85C22×Dic6—108no—
86C22×Dic6—102no—
87C22×Dic6—102no—
88C2×C3×M16—52no—
89C2×#208C2×D512yes—
90C3×C22⋊C8—102no—
91#830—22no—
92#824—108no—
93C24×C5C4×D311yescharacteristic
94C22×C4×C5—24no—
95C22×C4×C5C4×D311yescharacteristic
96C22×C4×C5D1212yes—
97C22×C4×C5#6712yes—
98C22×C4×C5C22×D311yescharacteristic
99C22×Dic5—34no—
100C22×Dic5—68no—
101C22×Dic5—64no—
102C2×Dic10—38no—
103C2×Dic10—68no—
104C2×Dic10—616no—
105C2×Dic10—616no—
106C2×Dic10—64no—
107C2×Dic10—62no—
108C2×Dic10—64no—
109C2×Dic10—62no—
110C5×M16—64no—
111C2×C5×C8—62no—
112#681—24no—
113C2×#168—22no—
114C23×Q8—151no—
115C2×#101—154no—
116#407—31no—
117#407—51no—
118C22×C3×C5—28no—
119C22×C3×C5—22no—
120C22×C3×C5—22no—
121C22×C3×C5—22no—
122C22×C3×C5#10114yescomplemented
123C22×C3×C5C2×C22⋊C412yes—
124C22×C3×C5C2×C22⋊C411yescharacteristic
125C3×C4×C5—22no—
126C3×C4×C5#12012yes—
127C3×C4×C5#12012yes—
128Dic15—28no—
129C24×C3C4×D511yescharacteristic
130C22×C3×C4—24no—
131C22×C3×C4C4×D511yescharacteristic
132C22×C3×C4D2012yes—
133C22×C3×C4C22⋊D512yes—
134C22×C3×C4C22×D511yescharacteristic
135C22×Dic3—54no—
136C22×Dic3—108no—
137C22×Dic3—104no—
138C2×Dic6—58no—
139C2×Dic6—108no—
140C2×Dic6—1016no—
141C2×Dic6—1016no—
142C2×Dic6—104no—
143C2×Dic6—102no—
144C2×Dic6—104no—
145C2×Dic6—102no—
146C3×M16—104no—
147C2×C3×C8—102no—
148#208—24no—
149C2×C3⋊C8—22no—
150C23×C5—24no—
151C23×C5—22no—
152C23×C5(C2×D3)⋊C412yes—
153C23×C5C2×C4×D311yescharacteristic
154C2×C4×C5—22no—
155C2×C4×C5—24no—
156C2×C4×C5—24no—
157C2×C4×C5(C2×D3)⋊C412yes—
158C2×C4×C5C2×D1211yescharacteristic
159C2×C4×C5D3×D414yes—
160C2×C4×C5C2×#6711yescharacteristic
161C2×Dic5—38no—
162C2×Dic5—616no—
163C2×Dic5—64no—
164C2×Dic5—64no—
165Dic10—616no—
166Dic10—68no—
167Dic10—68no—
168C5×C8—122no—
169#168—42no—
170C22×Q8—152no—
171C22×Q8—152no—
172C22×Q8—308no—
173C22×Q8—302no—
174C22×Q8—302no—
175C23×C4—152no—
176C23×C4D3×D511yescharacteristic
177C2×M16—32no—
178C2×M16—52no—
179#101—308no—
180C22⋊C8—62no—
181C22⋊C8—102no—
182C2×C3×C5—24no—
183C2×C3×C5—22no—
184C2×C3×C5#37911yescharacteristic
185C2×C3×C5C2×#10112yes—
186C23×C3—24no—
187C23×C3—22no—
188C23×C3#68512yes—
189C23×C3C2×C4×D511yescharacteristic
190C2×C3×C4—22no—
191C2×C3×C4—24no—
192C2×C3×C4—24no—
193C2×C3×C4#68512yes—
194C2×C3×C4C2×D2011yescharacteristic
195C2×C3×C4D4×D514yes—
196C2×C3×C4C2×C22⋊D511yescharacteristic
197C2×Dic3—58no—
198C2×Dic3—1016no—
199C2×Dic3—104no—
200C2×Dic3—104no—
201Dic6—1016no—
202Dic6—108no—
203Dic6—108no—
204C3×C8—202no—
205C3⋊C8—42no—
206C22×C5—28no—
207C22×C5—22no—
208C22×C5—22no—
209C22×C5—22no—
210C22×C5#82414yescomplemented
211C22×C5D3×C22⋊C412yes—
212C22×C5C2×(C2×D3)⋊C411yescharacteristic
213C4×C5—22no—
214C4×C5#88212yes—
215C4×C5#93712yes—
216Dic5—68no—
217C24#120011yescharacteristic
218C2×Q8—158no—
219C2×Q8—308no—
220C2×Q8—3016no—
221C2×Q8—3016no—
222C2×Q8—304no—
223C2×Q8—302no—
224C2×Q8—302no—
225C2×Q8—304no—
226C22×C4—24no—
227C22×C4—154no—
228C22×C4—308no—
229C22×C4—304no—
230C22×C4#120011yescharacteristic
231C22×C4#120212yes—
232C22×C4#120312yes—
233C22×C4C2×D3×D511yescharacteristic
234M16—64no—
235M16—104no—
236C2×C8—62no—
237C2×C8—102no—
238C3×C5#178411yescharacteristic, complemented, Hall
239C22×C3—28no—
240C22×C3—22no—
241C22×C3—22no—
242C22×C3—22no—
243C22×C3#395614yescomplemented
244C22×C3D5×C22⋊C412yes—
245C22×C3C2×#68511yescharacteristic
246C3×C4—22no—
247C3×C4#402812yes—
248C3×C4#408312yes—
249Dic3—108no—
250C2×C5—24no—
251C2×C5—22no—
252C2×C5#495511yescharacteristic
253C2×C5C2×#82412yes—
254C23—24no—
255C23—22no—
256C23#666712yes—
257C23C2×#120011yescharacteristic
258Q8—3016no—
259Q8—308no—
260Q8—308no—
261C2×C4—22no—
262C2×C4—24no—
263C2×C4—24no—
264C2×C4—158no—
265C2×C4—3016no—
266C2×C4—304no—
267C2×C4—304no—
268C2×C4#666712yes—
269C2×C4C2×#120211yescharacteristic
270C2×C4C2×#120311yescharacteristic
271C2×C4#679014yes—
272C8—122no—
273C8—202no—
274C2×C3—24no—
275C2×C3—22no—
276C2×C3#6524411yescharacteristic
277C2×C3C2×#395612yes—
278C5#6999011yescharacteristic, complemented, Sylow
279C22—28no—
280C22—22no—
281C22—22no—
282C22—22no—
283C22#9096314yescomplemented
284C22C2×#666711yescharacteristic
285C22#9156112yes—
286C4—22no—
287C4—308no—
288C4#9157212yes—
289C4#9157312yes—
290C3#1060078311yescharacteristic, complemented, Sylow
291C2—24no—
292C2—22no—
293C2C2×#9096312yes—
294C2#1174950211yescharacteristic
subgroupG/H
centerC22C2×#6667
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5C2×C4
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1784
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C2×#90963C2semidirect
122. C22×C3×C5#101semidirect
210. C22×C5#824semidirect
238. C3×C5#1784semidirect
243. C22×C3#3956semidirect
278. C5#69990semidirect
283. C22#90963semidirect
290. C3#10600783semidirect

Maximal subgroups

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

subgroupindex
C23×Dic302
C5×#52072
C3×#654962
C2×#909632
#106007833
#699905