Finite Group Databasebeta

← #14280995

Subgroups — #14280995

Order 1920.

624 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 129 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#11746785C214yesmaximal, complemented
4#10604882—31nomaximal, Hall
5C23×C3×C4×C5C411yescharacteristic
6C23×C3×Dic5C411yescharacteristic
7C23×C3×Dic5C2211yescharacteristic
8C2×#6762—22no—
9C2×C3×#683—22no—
10C2×C3×#683—22no—
11C2×C3×#683C412yes—
12C2×C3×#683C2212yes—
13#91241—22no—
14#91241C2214yes—
15#71552—51nomaximal, Hall
16C22×#683D311yescharacteristic
17#65798—32no—
18#64914—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—21no—
25C22×C3×Dic5—21no—
26C22×C3×Dic5—24no—
27C22×C3×Dic5—42no—
28C22×C3×Dic5C2×C412yes—
29C22×C3×Dic5C2×C411yescharacteristic
30C22×C3×Dic5D412yes—
31C22×C3×Dic5D412yes—
32C22×C3×Dic5C2311yescharacteristic
33#6762—44no—
34C2×C3⋊#170—24no—
35C3×#683—24no—
36C3×#683—24no—
37C22×C3×C4⋊C4—51no—
38#5207—52no—
39#4528—54no—
40C23×C4×C5Dic311yescharacteristic
41C23×Dic5Dic311yescharacteristic
42C23×Dic5C2×D311yescharacteristic
43C2×#704—62no—
44C2×#683—22no—
45C2×#683—22no—
46C2×#683Dic312yes—
47C2×#683C2×D312yes—
48C22⋊#170—34no—
49C22⋊#170—62no—
50#1463—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—24no—
62C2×C3×Dic5—24no—
63C2×C3×Dic5—24no—
64C2×C3×Dic5—22no—
65C2×C3×Dic5—22no—
66C2×C3×Dic5—41no—
67C2×C3×Dic5—42no—
68C2×C3×Dic5—41no—
69C2×C3×Dic5C22⋊C412yes—
70C2×C3×Dic5M1614yescomplemented
71C2×C3×Dic5C2×D412yes—
72C3⋊#170—44no—
73C23×C3×C4—51no—
74C23×C3×C4—51no—
75C23×C3×C4AGL(1,𝔽5)11yescharacteristic
76C2×C3×C4⋊C4—52no—
77C2×C3×C4⋊C4—52no—
78C2×C3×C4⋊C4—102no—
79C2×C3×C4⋊C4—102no—
80C2×#208—102no—
81#830—54no—
82#830—102no—
83C24×C5C2×Dic311yescharacteristic
84C22×C4×C5—21no—
85C22×C4×C5—21no—
86C22×C4×C5—42no—
87C22×C4×C5C2×Dic312yes—
88C22×Dic5—21no—
89C22×Dic5—21no—
90C22×Dic5—24no—
91C22×Dic5—42no—
92C22×Dic5C2×Dic312yes—
93C22×Dic5C2×Dic311yescharacteristic
94C22×Dic5#6712yes—
95C22×Dic5#6712yes—
96C22×Dic5C22×D311yescharacteristic
97#704—124no—
98C2×#170—64no—
99#683—24no—
100#683—24no—
101C22×C4⋊C4—51no—
102#407—152no—
103#324—154no—
104C22×C3×C5—28no—
105C22×C3×C5—21no—
106C22×C3×C5—21no—
107C22×C3×C5—21no—
108C22×C3×C5—21no—
109C22×C3×C5—21no—
110C22×C3×C5—21no—
111C22×C3×C5#9912yes—
112C22×C3×C5#10112yes—
113C22×C3×C5C2×C22⋊C411yescharacteristic
114C22×C3×C5C2×M1612yes—
115C3×C4×C5—42no—
116C3×Dic5—24no—
117C3×Dic5—22no—
118C3×Dic5—22no—
119C24×C3C2×AGL(1,𝔽5)11yescharacteristic
120C22×C3×C4—21no—
121C22×C3×C4—21no—
122C22×C3×C4—42no—
123C22×C3×C4—52no—
124C22×C3×C4—52no—
125C22×C3×C4—52no—
126C22×C3×C4—51no—
127C22×C3×C4—51no—
128C22×C3×C4—104no—
129C22×C3×C4—101no—
130C22×C3×C4—101no—
131C22×C3×C4—202no—
132C22×C3×C4C2×AGL(1,𝔽5)12yes—
133C3×C4⋊C4—104no—
134C3×C4⋊C4—104no—
135#208—204no—
136C2×C3⋊C8—104no—
137C23×C5—22no—
138C23×C5—22no—
139C23×C5—22no—
140C23×C5#21711yescharacteristic
141C23×C5#21711yescharacteristic
142C23×C5C22×Dic311yescharacteristic
143C2×C4×C5—22no—
144C2×C4×C5—42no—
145C2×C4×C5—42no—
146C2×C4×C5—42no—
147C2×Dic5—24no—
148C2×Dic5—24no—
149C2×Dic5—24no—
150C2×Dic5—22no—
151C2×Dic5—22no—
152C2×Dic5—41no—
153C2×Dic5—42no—
154C2×Dic5—41no—
155C2×Dic5#20814yescomplemented
156C2×Dic5#21712yes—
157C2×Dic5C2×#6712yes—
158#170—124no—
159C23×C4—51no—
160C23×C4—51no—
161C23×C4ΓL(1,𝔽16)11yescharacteristic
162C2×M16—302no—
163C2×C4⋊C4—52no—
164C2×C4⋊C4—52no—
165C2×C4⋊C4—102no—
166C2×C4⋊C4—102no—
167C22⋊C8—154no—
168C22⋊C8—302no—
169C2×C3×C5—22no—
170C2×C3×C5—22no—
171C2×C3×C5—22no—
172C2×C3×C5#40711yescharacteristic
173C2×C3×C5C2×#9911yescharacteristic
174C2×C3×C5C2×#10111yescharacteristic
175C23×C3—22no—
176C23×C3—22no—
177C23×C3—22no—
178C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
179C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
180C23×C3C22×AGL(1,𝔽5)11yescharacteristic
181C2×C3×C4—22no—
182C2×C3×C4—42no—
183C2×C3×C4—42no—
184C2×C3×C4—42no—
185C2×C3×C4—54no—
186C2×C3×C4—52no—
187C2×C3×C4—52no—
188C2×C3×C4—104no—
189C2×C3×C4—104no—
190C2×C3×C4—102no—
191C2×C3×C4—102no—
192C2×C3×C4—104no—
193C2×C3×C4—201no—
194C2×C3×C4—202no—
195C2×C3×C4—201no—
196C3⋊C8—204no—
197C22×C5—28no—
198C22×C5—21no—
199C22×C5—21no—
200C22×C5—21no—
201C22×C5—21no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5#83412yes—
205C22×C5#83612yes—
206C22×C5C2×#20812yes—
207C22×C5C2×#21711yescharacteristic
208C4×C5—42no—
209Dic5—24no—
210Dic5—22no—
211Dic5—22no—
212C24C2×ΓL(1,𝔽16)11yescharacteristic
213C22×C4—21no—
214C22×C4—21no—
215C22×C4—42no—
216C22×C4—52no—
217C22×C4—52no—
218C22×C4—52no—
219C22×C4—51no—
220C22×C4—51no—
221C22×C4—104no—
222C22×C4—101no—
223C22×C4—101no—
224C22×C4—202no—
225C22×C4C2×ΓL(1,𝔽16)12yes—
226M16—604no—
227C2×C8—304no—
228C4⋊C4—104no—
229C4⋊C4—104no—
230C3×C5#146311yescharacteristic, complemented, Hall
231C22×C3—28no—
232C22×C3—21no—
233C22×C3—21no—
234C22×C3—21no—
235C22×C3—21no—
236C22×C3—21no—
237C22×C3—21no—
238C22×C3#400512yes—
239C22×C3#401112yes—
240C22×C3D5⋊M1612yes—
241C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
242C3×C4—42no—
243C3×C4—102no—
244C3×C4—102no—
245C3×C4—104no—
246C2×C5—22no—
247C2×C5—22no—
248C2×C5—22no—
249C2×C5#520711yescharacteristic
250C2×C5C2×#83411yescharacteristic
251C2×C5C2×#83611yescharacteristic
252C23—22no—
253C23—22no—
254C23—22no—
255C23#676311yescharacteristic
256C23#676311yescharacteristic
257C23C22×ΓL(1,𝔽16)11yescharacteristic
258C2×C4—22no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—54no—
263C2×C4—52no—
264C2×C4—52no—
265C2×C4—104no—
266C2×C4—104no—
267C2×C4—102no—
268C2×C4—102no—
269C2×C4—104no—
270C2×C4—201no—
271C2×C4—202no—
272C2×C4—201no—
273C8—604no—
274C2×C3—22no—
275C2×C3—22no—
276C2×C3—22no—
277C2×C3#6575511yescharacteristic
278C2×C3C2×#400511yescharacteristic
279C2×C3C2×#401111yescharacteristic
280C5#7155211yescharacteristic, complemented, Sylow
281C22—28no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22#9123412yes—
289C22#9124012yes—
290C22D5⋊#20812yes—
291C22C2×#676311yescharacteristic
292C4—42no—
293C4—102no—
294C4—102no—
295C4—104no—
296C3#1060488211yescharacteristic, complemented, Sylow
297C2—22no—
298C2—22no—
299C2—22no—
300C2#1175241411yescharacteristic
301C2C2×#9123411yescharacteristic
302C2C2×#9124011yescharacteristic
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#1463
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. #11746785C2semidirect
70. C2×C3×Dic5M16semidirect
155. C2×Dic5#208semidirect
230. C3×C5#1463semidirect
280. C5#71552semidirect
296. C3#10604882semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#6832
#117524572
#117467852
#106048823
#715525