Finite Group Databasebeta

← #14313732

Subgroups — #14313732

Order 1920.

524 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 96 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
1C3×#66008C211yesmaximal, characteristic
2#11749369C212yesmaximal, complemented
3#11746363C211yesmaximal, characteristic, complemented
4C5×#4542C211yesmaximal, characteristic, complemented
5#11746012C212yesmaximal, complemented
6#10599959—31nomaximal, Hall
7C2×C3×#713C2211yescharacteristic
8C2×C3×D4×D5C411yescharacteristic
9C3×C5×#124C2211yescharacteristic
10C3×#4093C2211yescharacteristic
11C3×#4086C411yescharacteristic
12C3×#4030—22no—
13C3×#4028—22no—
14C3×#4020C411yescharacteristic
15C3×#4018C411yescharacteristic
16D5×#208—22no—
17#91120C2212yescomplemented
18C5×#836C2212yescomplemented
19#90958—22no—
20#71862—51nomaximal, Hall
21#66008D311yescharacteristic
22#65040—32no—
23C5×#355—31no—
24#64762—31no—
25#64697—32no—
26C23×C3×D5—21no—
27C2×C3×C5×Q8C2311yescharacteristic
28C2×C3×C5×D4C2×C411yescharacteristic
29C2×C3×C22⋊D5—22no—
30C2×C3×C22⋊D5—21no—
31C3×#713—42no—
32C3×D4×D5—42no—
33C2×C3×D20—22no—
34C2×C3×D20C2×C411yescharacteristic
35C2×C3×D20C2×C411yescharacteristic
36C2×C3×D20D412yes—
37C2×C3×C4×D5C2×C411yescharacteristic
38C2×C3×C4×D5D412yes—
39C3×C5×C22⋊C4—22no—
40C3×C42×C5C2×C411yescharacteristic
41#6710—22no—
42C5×#208—22no—
43C3×#685—21no—
44C3×#685—22no—
45C3×#683—21no—
46C3×C4×Dic5C2×C411yescharacteristic
47#6649—42no—
48D5×C3⋊C8—42no—
49C3×#535—51no—
50#5237—52no—
51#4542—51no—
52#4542—52no—
53#4542D511yescharacteristic, complemented
54C2×#713C2×D311yescharacteristic
55C2×D4×D5Dic311yescharacteristic
56C5×#124C2×D311yescharacteristic
57#4093C2×D311yescharacteristic
58#4086Dic311yescharacteristic
59D5×M16—62no—
60#4030—22no—
61#4028—22no—
62#4020Dic311yescharacteristic
63#4018Dic311yescharacteristic
64C5×#101—32no—
65#3968—32no—
66#3955—62no—
67#2134—151noSylow
68C23×C3×C5—21no—
69C22×C3×D5—21no—
70C22×C3×D5—42no—
71C22×C3×D5—82no—
72C22×C3×D5C22⋊C411yescharacteristic
73C22×C3×D5C22⋊C412yes—
74C3×C5×Q8—41no—
75C3×C5×D4—41no—
76C2×C3×C4×C5—21no—
77C2×C3×C4×C5C22×C411yescharacteristic
78C2×C3×C4×C5C2×D412yes—
79C3×C22⋊D5—42no—
80C3×C22⋊D5—82no—
81C2×C3×Dic5—21no—
82C2×C3×Dic5C22⋊C411yescharacteristic
83C3×D20—41no—
84C3×D20—42no—
85C3×D20—41no—
86C3×D20—82no—
87C3×C4×D5—22no—
88C3×C4×D5—22no—
89C3×C4×D5—22no—
90C3⋊#168—42no—
91C5×C3⋊C8—42no—
92C2×C3×#41—51no—
93C22×C3×D4—51no—
94C3×#127—51no—
95C3×#127—51no—
96C3×#124—51no—
97C3×#124C2×D511yescharacteristic
98C3×#121—102no—
99C3×#120—102no—
100C3×#117—51no—
101C2×#208—102no—
102#836—52no—
103#836C2×D512yescomplemented
104#833—102no—
105C23×D5—21no—
106C2×C5×Q8C22×D311yescharacteristic
107C2×C5×D4C2×Dic311yescharacteristic
108C2×C22⋊D5—22no—
109C2×C22⋊D5—21no—
110#713—42no—
111D4×D5—42no—
112C2×D20—22no—
113C2×D20C2×Dic311yescharacteristic
114C2×D20C2×Dic311yescharacteristic
115C2×D20#6712yes—
116C2×C4×D5C2×Dic311yescharacteristic
117C2×C4×D5#6712yes—
118C5×M16—62no—
119C5×C22⋊C4—22no—
120C42×C5C2×Dic311yescharacteristic
121#685—21no—
122#685—22no—
123#683—21no—
124C4×Dic5C2×Dic311yescharacteristic
125#681—62no—
126#676—122no—
127C8×D5—122no—
128#535—51no—
129#413—152no—
130#355—31no—
131#355—152no—
132#355—151no—
133C22×C3×C5—42no—
134C22×C3×C5—41no—
135C22×C3×C5C2×C22⋊C411yescharacteristic
136C2×C3×D5—21no—
137C2×C3×D5—22no—
138C2×C3×D5—42no—
139C2×C3×D5—41no—
140C2×C3×D5—42no—
141C2×C3×D5—41no—
142C2×C3×D5—84no—
143C3×C4×C5—22no—
144C3×C4×C5—21no—
145C3×C4×C5—41no—
146C3×Dic5—41no—
147C3×Dic5#9912yes—
148C24×C3—101no—
149C3×#41—202no—
150C2×C3×Q8C22×D511yescharacteristic
151C2×C3×D4—51no—
152C2×C3×D4—51no—
153C2×C3×D4—52no—
154C2×C3×D4—102no—
155C2×C3×D4—101no—
156C2×C3×D4—102no—
157C2×C3×D4—202no—
158C2×C3×D4C4×D511yescharacteristic
159C22×C3×C4—51no—
160C22×C3×C4—52no—
161C3×C4⋊C4—101no—
162C3×C22⋊C4—22no—
163C3×C22⋊C4—101no—
164C3×C22⋊C4—102no—
165C3×C42—51no—
166C3×C42C4×D511yescharacteristic
167#208—22no—
168#208—102no—
169#208—202no—
170C2×C3⋊C8—202no—
171C23×C5—21no—
172C22×D5—21no—
173C22×D5—42no—
174C22×D5—82no—
175C22×D5#21711yescharacteristic
176C22×D5#21712yes—
177C5×Q8—41no—
178C5×D4—41no—
179C2×C4×C5—21no—
180C2×C4×C5C22×Dic311yescharacteristic
181C2×C4×C5C2×#6712yes—
182C22⋊D5—42no—
183C22⋊D5—82no—
184C2×Dic5—21no—
185C2×Dic5#21711yescharacteristic
186D20—41no—
187D20—42no—
188D20—41no—
189D20—82no—
190C4×D5—22no—
191C4×D5—22no—
192C4×D5—22no—
193C5×C8—122no—
194#168—122no—
195C2×#41—51no—
196C22×D4—51no—
197C2×M16—302no—
198#127—51no—
199#127—51no—
200#124—51no—
201#124D3×D511yescharacteristic
202#121—102no—
203#120—102no—
204#117—51no—
205#101—32no—
206#101—152no—
207#100—302no—
208C2×C3×C5—21no—
209C2×C3×C5—81no—
210C2×C3×C5C2×#9911yescharacteristic
211C3×D5—42no—
212C3×D5—41no—
213C3×D5—81no—
214C23×C3—21no—
215C23×C3—51no—
216C23×C3—52no—
217C23×C3—101no—
218C23×C3—202no—
219C23×C3—402no—
220C3×Q8—41no—
221C3×D4—41no—
222C3×D4—202no—
223C3×D4—201no—
224C3×D4—201no—
225C3×D4—202no—
226C3×D4—402no—
227C3×D4—402no—
228C2×C3×C4—21no—
229C2×C3×C4—51no—
230C2×C3×C4—102no—
231C2×C3×C4—102no—
232C2×C3×C4—102no—
233C2×C3×C4—101no—
234C2×C3×C4C2×C4×D511yescharacteristic
235C2×C3×C4D4×D512yes—
236C3⋊C8—42no—
237C3⋊C8—202no—
238C22×C5—42no—
239C22×C5—41no—
240C22×C5C2×#21711yescharacteristic
241C2×D5—21no—
242C2×D5—22no—
243C2×D5—42no—
244C2×D5—41no—
245C2×D5—42no—
246C2×D5—41no—
247C2×D5—84no—
248C4×C5—22no—
249C4×C5—21no—
250C4×C5—41no—
251Dic5—41no—
252Dic5#83412yes—
253C24—101no—
254#41—202no—
255C2×Q8C2×D3×D511yescharacteristic
256C2×D4—51no—
257C2×D4—51no—
258C2×D4—52no—
259C2×D4—102no—
260C2×D4—101no—
261C2×D4—102no—
262C2×D4—202no—
263C2×D4D5×Dic311yescharacteristic
264C22×C4—51no—
265C22×C4—52no—
266M16—62no—
267M16—302no—
268M16—602no—
269C2×C8—602no—
270C4⋊C4—101no—
271C22⋊C4—22no—
272C22⋊C4—101no—
273C22⋊C4—102no—
274C42—51no—
275C42D5×Dic311yescharacteristic
276C3×C5#213411yescharacteristic, complemented, Hall
277C22×C3—42no—
278C22×C3—41no—
279C22×C3—102no—
280C22×C3—101no—
281C22×C3—202no—
282C22×C3—201no—
283C22×C3—202no—
284C22×C3—201no—
285C22×C3—404no—
286C22×C3D5×C22⋊C411yescharacteristic
287C3×C4—22no—
288C3×C4—21no—
289C3×C4—41no—
290C3×C4—52no—
291C3×C4—201no—
292C2×C5—21no—
293C2×C5—81no—
294C2×C5C2×#83411yescharacteristic
295D5—41no—
296D5—42no—
297D5—81no—
298C23—21no—
299C23—51no—
300C23—52no—
301C23—101no—
302C23—202no—
303C23—402no—
304Q8—41no—
305D4—41no—
306D4—202no—
307D4—201no—
308D4—201no—
309D4—202no—
310D4—402no—
311D4—402no—
312C2×C4—21no—
313C2×C4—51no—
314C2×C4—102no—
315C2×C4—102no—
316C2×C4—102no—
317C2×C4—101no—
318C2×C4C2×D5×Dic311yescharacteristic
319C2×C4D5×#6712yes—
320C8—122no—
321C8—602no—
322C2×C3—21no—
323C2×C3—81no—
324C2×C3—201no—
325C2×C3—202no—
326C2×C3—401no—
327C2×C3D5×#9911yescharacteristic
328C5#7186211yescharacteristic, complemented, Sylow
329C22—42no—
330C22—41no—
331C22—101no—
332C22—102no—
333C22—202no—
334C22—201no—
335C22—202no—
336C22—201no—
337C22—404no—
338C22D5×#21711yescharacteristic
339C4—22no—
340C4—21no—
341C4—41no—
342C4—52no—
343C4—201no—
344C3#1059995911yescharacteristic, complemented, Sylow
345C2—21no—
346C2—81no—
347C2—201no—
348C2—202no—
349C2—401no—
350C2D5×#83411yescharacteristic
subgroupG/H
centerC2D5×#834
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×Q8C2×D3×D5
FittingC3×C5×#124C22
socleC2×C3×C5C2×#99
prime radicalC3×#66008C2
cosocleC2×C3×C5×Q8C23
hypercenter#124D3×D5
hypocenterC3×C5#2134
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11749369C2semidirect
3. #11746363C2semidirect
4. C5×#4542C2semidirect
5. #11746012C2semidirect
17. #91120C22semidirect
18. C5×#836C22semidirect
53. #4542D5semidirect
103. #836C2×D5semidirect
276. C3×C5#2134semidirect
328. C5#71862semidirect
344. C3#10599959semidirect

Maximal subgroups

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

subgroupindex
C3×#660082
#117493692
#117463632
C5×#45422
#117460122
#105999593
#718625