Finite Group Databasebeta

← #14298381

Subgroups — #14298381

Order 1920.

632 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 632 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C22×C3×#683C211yesmaximal, characteristic
2#11752457C212yesmaximal
3#11746790C214yesmaximal, complemented
4#10604908—31nomaximal, Hall
5C23×C3×C4×C5C411yescharacteristic
6C23×C3×Dic5C411yescharacteristic
7C23×C3×Dic5C2211yescharacteristic
8C2×#6762C2214yes—
9C2×C3×#683—22no—
10C2×C3×#683—22no—
11C2×C3×#683C412yes—
12C2×C3×#683C2212yes—
13#91241—22no—
14#91241—22no—
15#71562—51nomaximal, Hall
16C22×#683D311yescharacteristic
17#65798—32no—
18#64919—34no—
19C24×C3×C5C2×C411yescharacteristic
20C22×C3×C4×C5—21no—
21C22×C3×C4×C5—21no—
22C22×C3×C4×C5—42no—
23C22×C3×C4×C5C2×C412yes—
24C22×C3×Dic5—24no—
25C22×C3×Dic5—21no—
26C22×C3×Dic5—21no—
27C22×C3×Dic5—42no—
28C22×C3×Dic5C2×C411yescharacteristic
29C22×C3×Dic5C2×C412yes—
30C22×C3×Dic5D412yes—
31C22×C3×Dic5D412yes—
32C22×C3×Dic5C2311yescharacteristic
33#6762—28no—
34C2×C3⋊#170—24no—
35C3×#683—24no—
36C3×#683—24no—
37C22×C3×C4⋊C4—51no—
38#5207—52no—
39#4530—54no—
40C23×C4×C5Dic311yescharacteristic
41C23×Dic5Dic311yescharacteristic
42C23×Dic5C2×D311yescharacteristic
43C2×#704—34no—
44C2×#683—22no—
45C2×#683—22no—
46C2×#683Dic312yes—
47C2×#683C2×D312yes—
48C22⋊#170—62no—
49C22⋊#170—62no—
50#1821—151noSylow
51C23×C3×C5—22no—
52C23×C3×C5—22no—
53C23×C3×C5—22no—
54C23×C3×C5C22⋊C411yescharacteristic
55C23×C3×C5C22⋊C411yescharacteristic
56C23×C3×C5C22×C411yescharacteristic
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5—42no—
59C2×C3×C4×C5—42no—
60C2×C3×C4×C5—42no—
61C2×C3×Dic5—22no—
62C2×C3×Dic5—24no—
63C2×C3×Dic5—24no—
64C2×C3×Dic5—22no—
65C2×C3×Dic5—42no—
66C2×C3×Dic5—42no—
67C2×C3×Dic5—42no—
68C2×C3×Dic5C22⋊C412yes—
69C2×C3×Dic5C2×D412yes—
70C2×C3×Dic5#4114yes—
71C3⋊#170—44no—
72C23×C3×C4—51no—
73C23×C3×C4—51no—
74C23×C3×C4AGL(1,𝔽5)11yescharacteristic
75C2×C3×C4⋊C4—52no—
76C2×C3×C4⋊C4—52no—
77C2×C3×C4⋊C4—102no—
78C2×C3×C4⋊C4—102no—
79C2×#208—54no—
80#830—102no—
81#830—102no—
82C24×C5C2×Dic311yescharacteristic
83C22×C4×C5—21no—
84C22×C4×C5—21no—
85C22×C4×C5—42no—
86C22×C4×C5C2×Dic312yes—
87C22×Dic5—24no—
88C22×Dic5—21no—
89C22×Dic5—21no—
90C22×Dic5—42no—
91C22×Dic5C2×Dic311yescharacteristic
92C22×Dic5C2×Dic312yes—
93C22×Dic5#6712yes—
94C22×Dic5#6712yes—
95C22×Dic5C22×D311yescharacteristic
96#704—68no—
97C2×#170—64no—
98#683—24no—
99#683—24no—
100C22×C4⋊C4—51no—
101#407—152no—
102#343—154no—
103C22×C3×C5—28no—
104C22×C3×C5—21no—
105C22×C3×C5—21no—
106C22×C3×C5—21no—
107C22×C3×C5—21no—
108C22×C3×C5—21no—
109C22×C3×C5—21no—
110C22×C3×C5#10012yes—
111C22×C3×C5#10112yes—
112C22×C3×C5C2×C22⋊C411yescharacteristic
113C22×C3×C5#11712yes—
114C3×C4×C5—42no—
115C3×Dic5—22no—
116C3×Dic5—42no—
117C3×Dic5#12314yes—
118C24×C3C2×AGL(1,𝔽5)11yescharacteristic
119C22×C3×C4—21no—
120C22×C3×C4—21no—
121C22×C3×C4—42no—
122C22×C3×C4—51no—
123C22×C3×C4—52no—
124C22×C3×C4—52no—
125C22×C3×C4—51no—
126C22×C3×C4—52no—
127C22×C3×C4—104no—
128C22×C3×C4—101no—
129C22×C3×C4—101no—
130C22×C3×C4—202no—
131C22×C3×C4C2×AGL(1,𝔽5)12yes—
132C3×C4⋊C4—104no—
133C3×C4⋊C4—104no—
134#208—108no—
135C2×C3⋊C8—104no—
136C23×C5—22no—
137C23×C5—22no—
138C23×C5—22no—
139C23×C5#21711yescharacteristic
140C23×C5#21711yescharacteristic
141C23×C5C22×Dic311yescharacteristic
142C2×C4×C5—22no—
143C2×C4×C5—42no—
144C2×C4×C5—42no—
145C2×C4×C5—42no—
146C2×Dic5—22no—
147C2×Dic5—24no—
148C2×Dic5—24no—
149C2×Dic5—22no—
150C2×Dic5—42no—
151C2×Dic5—42no—
152C2×Dic5—42no—
153C2×Dic5#21712yes—
154C2×Dic5#23514yes—
155C2×Dic5C2×#6712yes—
156#170—124no—
157C23×C4—51no—
158C23×C4—51no—
159C23×C4ΓL(1,𝔽16)11yescharacteristic
160C2×M16—154no—
161C2×C4⋊C4—52no—
162C2×C4⋊C4—52no—
163C2×C4⋊C4—102no—
164C2×C4⋊C4—102no—
165C22⋊C8—302no—
166C22⋊C8—302no—
167C2×C3×C5—22no—
168C2×C3×C5—22no—
169C2×C3×C5—22no—
170C2×C3×C5#38111yescharacteristic
171C2×C3×C5C2×#10011yescharacteristic
172C2×C3×C5C2×#10111yescharacteristic
173C23×C3—22no—
174C23×C3—22no—
175C23×C3—22no—
176C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
177C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
178C23×C3C22×AGL(1,𝔽5)11yescharacteristic
179C2×C3×C4—22no—
180C2×C3×C4—42no—
181C2×C3×C4—42no—
182C2×C3×C4—42no—
183C2×C3×C4—54no—
184C2×C3×C4—52no—
185C2×C3×C4—52no—
186C2×C3×C4—104no—
187C2×C3×C4—104no—
188C2×C3×C4—102no—
189C2×C3×C4—102no—
190C2×C3×C4—202no—
191C2×C3×C4—202no—
192C2×C3×C4—202no—
193C3⋊C8—204no—
194C22×C5—28no—
195C22×C5—21no—
196C22×C5—21no—
197C22×C5—21no—
198C22×C5—21no—
199C22×C5—21no—
200C22×C5—21no—
201C22×C5#83312yes—
202C22×C5#83612yes—
203C22×C5#92612yes—
204C22×C5C2×#21711yescharacteristic
205C4×C5—42no—
206Dic5—22no—
207Dic5—42no—
208Dic5#92914yes—
209C24C2×ΓL(1,𝔽16)11yescharacteristic
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—42no—
213C22×C4—51no—
214C22×C4—52no—
215C22×C4—52no—
216C22×C4—51no—
217C22×C4—52no—
218C22×C4—104no—
219C22×C4—101no—
220C22×C4—101no—
221C22×C4—202no—
222C22×C4C2×ΓL(1,𝔽16)12yes—
223M16—308no—
224C2×C8—304no—
225C4⋊C4—104no—
226C4⋊C4—104no—
227C3×C5#182111yescharacteristic, complemented, Hall
228C22×C3—28no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3—21no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3#400512yes—
236C22×C3#401312yes—
237C22×C3#413012yes—
238C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
239C3×C4—42no—
240C3×C4—54no—
241C3×C4—102no—
242C3×C4—202no—
243C2×C5—22no—
244C2×C5—22no—
245C2×C5—22no—
246C2×C5#521111yescharacteristic
247C2×C5C2×#83311yescharacteristic
248C2×C5C2×#83611yescharacteristic
249C23—22no—
250C23—22no—
251C23—22no—
252C23#676311yescharacteristic
253C23#676311yescharacteristic
254C23C22×ΓL(1,𝔽16)11yescharacteristic
255C2×C4—22no—
256C2×C4—42no—
257C2×C4—42no—
258C2×C4—42no—
259C2×C4—54no—
260C2×C4—52no—
261C2×C4—52no—
262C2×C4—104no—
263C2×C4—104no—
264C2×C4—102no—
265C2×C4—102no—
266C2×C4—202no—
267C2×C4—202no—
268C2×C4—202no—
269C8—604no—
270C2×C3—22no—
271C2×C3—22no—
272C2×C3—22no—
273C2×C3C2×#400511yescharacteristic
274C2×C3#6576411yescharacteristic
275C2×C3C2×#401311yescharacteristic
276C5#7156211yescharacteristic, complemented, Sylow
277C22—28no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22#9123412yes—
285C22#9124212yes—
286C22#9198912yes—
287C22C2×#676311yescharacteristic
288C4—42no—
289C4—54no—
290C4—102no—
291C4—202no—
292C3#1060490811yescharacteristic, complemented, Sylow
293C2—22no—
294C2—22no—
295C2—22no—
296C2C2×#9123411yescharacteristic
297C2#1175242311yescharacteristic
298C2C2×#9124211yescharacteristic
subgroupG/H
centerC22C2×#6763
commutatorC23×C3×C5C22×C4
FrattiniC23C22×ΓL(1,𝔽16)
FittingC23×C3×C4×C5C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5C2×C4
cosocleC22×C3×Dic5C23
hypercenterC23×C4ΓL(1,𝔽16)
hypocenterC3×C5#1821
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. #11746790C2semidirect
227. C3×C5#1821semidirect
276. C5#71562semidirect
292. C3#10604908semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6832
#117524572
#117467902
#106049083
#715625