Finite Group Databasebeta

← #14313514

Subgroups — #14313514

Order 1920.

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

normal subgroups only

This group has 540 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×#66049C211yesmaximal, characteristic
2#11749172C212yesmaximal, complemented
3#11746366C211yesmaximal, characteristic, complemented
4C5×#4545C211yesmaximal, characteristic, complemented
5#11746006C212yesmaximal, complemented
6#10599945—31nomaximal, Hall
7C2×C3×#711C2211yescharacteristic
8C2×C3×D4×D5C411yescharacteristic, complemented
9C3×C5×#127C2211yescharacteristic
10C3×#4086C2211yescharacteristic
11C3×#4085—22no—
12C3×#4083—22no—
13C3×#4082C411yescharacteristic, complemented
14C3×#4021C411yescharacteristic, complemented
15C3×#4018C411yescharacteristic, complemented
16#91528—22no—
17#91118C2212yescomplemented
18C5×#834C2212yescomplemented
19#90995—22no—
20#71861—51nomaximal, Hall
21#66049D311yescharacteristic
22#65029—32no—
23C5×#353—31no—
24#64765—31no—
25#64694—32no—
26C23×C3×D5—21no—
27C2×C3×C5×D4—22no—
28C2×C3×C5×D4C2×C411yescharacteristic
29C2×C3×C5×D4C2311yescharacteristic
30C2×C3×C22⋊D5—22no—
31C2×C3×C22⋊D5—21no—
32C2×C3×C22⋊D5D412yes—
33C22×C3×Dic5D412yes—
34C3×#711—42no—
35C3×D4×D5—42no—
36C2×C3×D20C2×C411yescharacteristic
37C2×C3×C4×D5C2×C411yescharacteristic
38C2×C3×Dic10C2×C411yescharacteristic
39C3×C42×C5C2×C411yescharacteristic
40#6719—22no—
41C5×#217—22no—
42C3×C22⋊Dic5—22no—
43C3×#685—21no—
44C3×#685—22no—
45C3×#683—21no—
46C3×C4×Dic5C2×C411yescharacteristic
47#6668—42no—
48Dic3×Dic5—42no—
49C3×#535—51no—
50#5240—52no—
51#4545—51no—
52#4545—52no—
53#4545D511yescharacteristic, complemented
54C2×#711C2×D311yescharacteristic
55C2×D4×D5Dic311yescharacteristic, complemented
56C5×#127C2×D311yescharacteristic
57#4086C2×D311yescharacteristic
58#4085—22no—
59#4083—22no—
60#4082Dic311yescharacteristic, complemented
61#4023—62no—
62#4021Dic311yescharacteristic, complemented
63#4018Dic311yescharacteristic, complemented
64C5×#99—32no—
65#3966—32no—
66#3938—62no—
67#2128—151noSylow
68C23×C3×C5—21no—
69C23×C3×C5C2×D412yes—
70C22×C3×D5—21no—
71C22×C3×D5—42no—
72C22×C3×D5—82no—
73C22×C3×D5C22⋊C411yescharacteristic
74C3×C5×D4—41no—
75C3×C5×D4—41no—
76C3×C5×D4—82no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5C22×C411yescharacteristic
79C2×Dic15—42no—
80C2×C5×Dic3—42no—
81C3×C22⋊D5—42no—
82C3×C22⋊D5—42no—
83C3×C22⋊D5—82no—
84C2×C3×Dic5—22no—
85C2×C3×Dic5—22no—
86C2×C3×Dic5—21no—
87C2×C3×Dic5C22⋊C412yes—
88C2×C3×Dic5C22⋊C411yescharacteristic
89C3×D20—41no—
90C3×C4×D5—22no—
91C3×Dic10—41no—
92C2×C3×#41—51no—
93C22×C3×D4—51no—
94C3×#127—51no—
95C3×#127C2×D511yescharacteristic
96C3×#124—51no—
97C3×#124—51no—
98C3×#121—102no—
99C3×#120—102no—
100C3×#117—51no—
101#926—102no—
102#834—52no—
103#834—102no—
104#834C2×D512yescomplemented
105C23×D5—21no—
106C2×C5×D4—22no—
107C2×C5×D4C2×Dic311yescharacteristic
108C2×C5×D4C22×D311yescharacteristic
109C2×C22⋊D5—22no—
110C2×C22⋊D5—21no—
111C2×C22⋊D5#6712yes—
112C22×Dic5#6712yes—
113#711—42no—
114D4×D5—42no—
115C2×D20C2×Dic311yescharacteristic
116C2×C4×D5C2×Dic311yescharacteristic
117C2×Dic10C2×Dic311yescharacteristic
118C5×C22⋊C4—62no—
119C42×C5C2×Dic311yescharacteristic
120C22⋊Dic5—22no—
121C22⋊Dic5—62no—
122#685—21no—
123#685—22no—
124#683—21no—
125#683—122no—
126C4×Dic5—122no—
127C4×Dic5C2×Dic311yescharacteristic
128#535—51no—
129#410—152no—
130#353—31no—
131#353—152no—
132#353—151no—
133C22×C3×C5—22no—
134C22×C3×C5—42no—
135C22×C3×C5—42no—
136C22×C3×C5—41no—
137C22×C3×C5C2×C22⋊C411yescharacteristic
138C2×C3×D5—21no—
139C2×C3×D5—41no—
140C2×C3×D5—42no—
141C2×C3×D5—41no—
142C2×C3×D5—84no—
143C3×C4×C5—21no—
144C3×C4×C5—41no—
145Dic15—82no—
146C3×Dic5—22no—
147C3×Dic5—41no—
148C3×Dic5#9912yes—
149C5×Dic3—82no—
150C24×C3—101no—
151C3×#41—202no—
152C2×C3×Q8—51no—
153C2×C3×D4—22no—
154C2×C3×D4—52no—
155C2×C3×D4—51no—
156C2×C3×D4—101no—
157C2×C3×D4—102no—
158C2×C3×D4—202no—
159C2×C3×D4C4×D511yescharacteristic
160C2×C3×D4C22×D511yescharacteristic
161C22×C3×C4—52no—
162C22×C3×C4—51no—
163C3×C4⋊C4—101no—
164C3×C22⋊C4—102no—
165C3×C22⋊C4—101no—
166C3×C22⋊C4—102no—
167C3×C42—51no—
168C3×C42C4×D511yescharacteristic
169#217—22no—
170#217—102no—
171C4⋊Dic3—202no—
172C4×Dic3—202no—
173C23×C5—21no—
174C23×C5C2×#6712yes—
175C22×D5—21no—
176C22×D5—42no—
177C22×D5—82no—
178C22×D5#21711yescharacteristic
179C5×D4—41no—
180C5×D4—41no—
181C5×D4—82no—
182C2×C4×C5—21no—
183C2×C4×C5—122no—
184C2×C4×C5C22×Dic311yescharacteristic
185C22⋊D5—42no—
186C22⋊D5—42no—
187C22⋊D5—82no—
188C2×Dic5—22no—
189C2×Dic5—22no—
190C2×Dic5—21no—
191C2×Dic5—122no—
192C2×Dic5#21712yes—
193C2×Dic5#21711yescharacteristic
194D20—41no—
195C4×D5—22no—
196Dic10—41no—
197C2×#41—51no—
198C22×D4—51no—
199#127—51no—
200#127D3×D511yescharacteristic
201#124—51no—
202#124—51no—
203#121—102no—
204#120—102no—
205#117—51no—
206#117—302no—
207#99—32no—
208#99—152no—
209#99—302no—
210C2×C3×C5—21no—
211C2×C3×C5—42no—
212C2×C3×C5—81no—
213C2×C3×C5C2×#9911yescharacteristic
214C3×D5—41no—
215C3×D5—81no—
216C23×C3—21no—
217C23×C3—51no—
218C23×C3—101no—
219C23×C3—202no—
220C23×C3—402no—
221C23×C3D4×D512yes—
222C3×Q8—201no—
223C3×D4—41no—
224C3×D4—41no—
225C3×D4—82no—
226C3×D4—201no—
227C3×D4—202no—
228C3×D4—202no—
229C3×D4—402no—
230C2×C3×C4—21no—
231C2×C3×C4—51no—
232C2×C3×C4—52no—
233C2×C3×C4—102no—
234C2×C3×C4—102no—
235C2×C3×C4—102no—
236C2×C3×C4—101no—
237C2×C3×C4C2×C4×D511yescharacteristic
238C2×Dic3—42no—
239C2×Dic3—202no—
240C22×C5—22no—
241C22×C5—42no—
242C22×C5—42no—
243C22×C5—41no—
244C22×C5C2×#21711yescharacteristic
245C2×D5—21no—
246C2×D5—41no—
247C2×D5—42no—
248C2×D5—41no—
249C2×D5—84no—
250C4×C5—21no—
251C4×C5—41no—
252C4×C5—242no—
253Dic5—22no—
254Dic5—41no—
255Dic5—242no—
256Dic5#83412yes—
257C24—101no—
258#41—202no—
259C2×Q8—51no—
260C2×D4—22no—
261C2×D4—52no—
262C2×D4—51no—
263C2×D4—101no—
264C2×D4—102no—
265C2×D4—202no—
266C2×D4D5×Dic311yescharacteristic
267C2×D4C2×D3×D511yescharacteristic
268C22×C4—52no—
269C22×C4—51no—
270C4⋊C4—101no—
271C4⋊C4—602no—
272C22⋊C4—62no—
273C22⋊C4—102no—
274C22⋊C4—101no—
275C22⋊C4—102no—
276C22⋊C4—302no—
277C42—51no—
278C42—602no—
279C42D5×Dic311yescharacteristic
280C3×C5#212811yescharacteristic, complemented, Hall
281C22×C3—22no—
282C22×C3—42no—
283C22×C3—42no—
284C22×C3—41no—
285C22×C3—101no—
286C22×C3—201no—
287C22×C3—202no—
288C22×C3—201no—
289C22×C3—404no—
290C22×C3D5×C22⋊C411yescharacteristic
291C3×C4—21no—
292C3×C4—41no—
293C3×C4—52no—
294C3×C4—102no—
295C3×C4—201no—
296Dic3—82no—
297Dic3—402no—
298C2×C5—21no—
299C2×C5—42no—
300C2×C5—81no—
301C2×C5C2×#83411yescharacteristic
302D5—41no—
303D5—81no—
304C23—21no—
305C23—51no—
306C23—101no—
307C23—202no—
308C23—402no—
309C23D5×#6712yes—
310Q8—201no—
311D4—41no—
312D4—41no—
313D4—82no—
314D4—201no—
315D4—202no—
316D4—202no—
317D4—402no—
318C2×C4—21no—
319C2×C4—51no—
320C2×C4—52no—
321C2×C4—102no—
322C2×C4—102no—
323C2×C4—102no—
324C2×C4—101no—
325C2×C4—122no—
326C2×C4—602no—
327C2×C4C2×D5×Dic311yescharacteristic
328C2×C3—21no—
329C2×C3—42no—
330C2×C3—81no—
331C2×C3—201no—
332C2×C3—401no—
333C2×C3D5×#9911yescharacteristic
334C5#7186111yescharacteristic, complemented, Sylow
335C22—22no—
336C22—42no—
337C22—42no—
338C22—41no—
339C22—101no—
340C22—201no—
341C22—202no—
342C22—201no—
343C22—404no—
344C22D5×#21711yescharacteristic
345C4—21no—
346C4—41no—
347C4—52no—
348C4—102no—
349C4—201no—
350C4—242no—
351C4—1202no—
352C3#1059994511yescharacteristic, complemented, Sylow
353C2—21no—
354C2—42no—
355C2—81no—
356C2—201no—
357C2—401no—
358C2D5×#83411yescharacteristic
subgroupG/H
centerC2D5×#834
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC3×C5×#127C22
socleC2×C3×C5C2×#99
prime radicalC3×#66049C2
cosocleC2×C3×C5×D4C23
hypercenter#127D3×D5
hypocenterC3×C5#2128
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #11749172C2semidirect
3. #11746366C2semidirect
4. C5×#4545C2semidirect
5. #11746006C2semidirect
8. C2×C3×D4×D5C4semidirect
13. C3×#4082C4semidirect
14. C3×#4021C4semidirect
15. C3×#4018C4semidirect
17. #91118C22semidirect
18. C5×#834C22semidirect
53. #4545D5semidirect
55. C2×D4×D5Dic3semidirect
60. #4082Dic3semidirect
62. #4021Dic3semidirect
63. #4018Dic3semidirect
104. #834C2×D5semidirect
280. C3×C5#2128semidirect
334. C5#71861semidirect
352. C3#10599945semidirect

Maximal subgroups

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

subgroupindex
C3×#660492
#117491722
#117463662
C5×#45452
#117460062
#105999453
#718615