Finite Group Databasebeta

← #14313475

Subgroups — #14313475

Order 1920.

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

normal subgroups only

This group has 572 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
2D5×#834C212yesmaximal, complemented
3#11746366C211yesmaximal, characteristic, complemented
4C5×#4545C211yesmaximal, characteristic, complemented
5#11746009C212yesmaximal, complemented
6#10599943—31nomaximal, Hall
7C2×C3×#711C411yescharacteristic, complemented
8C2×C3×D4×D5C2211yescharacteristic
9C3×C5×#127C2211yescharacteristic
10C3×#4086C411yescharacteristic, complemented
11C3×#4085—22no—
12C3×#4083—22no—
13C3×#4082C2211yescharacteristic
14C3×#4021C411yescharacteristic, complemented
15C3×#4018C411yescharacteristic, complemented
16D5×#217—22no—
17#91118C2212yes—
18C5×#834C2212yes—
19#90995—22no—
20#71860—51nomaximal, Hall
21#66049D311yescharacteristic
22D5×#99—32no—
23C5×#353—31no—
24#64765—31no—
25#64693—32no—
26C23×C3×D5D412yes—
27C2×C3×C5×D4—22no—
28C2×C3×C5×D4C2×C411yescharacteristic, complemented
29C2×C3×C5×D4C2311yescharacteristic
30C2×C3×C22⋊D5—21no—
31C2×C3×C22⋊D5—22no—
32C2×C3×C22⋊D5D412yes—
33C22×C3×Dic5—21no—
34C3×#711—42no—
35C3×D4×D5—42no—
36C2×C3×D20C2×C411yescharacteristic
37C2×C3×C4×D5C2×C411yescharacteristic
38C2×C3×Dic10C2×C411yescharacteristic, complemented
39C2×D5×Dic3—42no—
40C3×C42×C5C2×C411yescharacteristic, complemented
41#6719—22no—
42C5×#217—22no—
43C3×C22⋊Dic5—22no—
44C3×#685—21no—
45C3×#685—22no—
46C3×#683—21no—
47C3×C4×Dic5C2×C411yescharacteristic, complemented
48#6665—42no—
49C3×#535—51no—
50C2×#834—52no—
51#4545—51no—
52#4545D511yescharacteristic, complemented
53#4541—52no—
54C2×#711Dic311yescharacteristic, complemented
55C2×D4×D5C2×D311yescharacteristic
56C5×#127C2×D311yescharacteristic
57#4086Dic311yescharacteristic, complemented
58#4085—22no—
59#4083—22no—
60#4082C2×D311yescharacteristic
61D5×C22⋊C4—62no—
62#4021Dic311yescharacteristic, complemented
63#4018Dic311yescharacteristic, complemented
64C5×#99—32no—
65#3966—32no—
66#3938—62no—
67#2127—151noSylow
68C23×C3×C5—21no—
69C23×C3×C5C2×D412yes—
70C22×C3×D5—22no—
71C22×C3×D5—22no—
72C22×C3×D5—82no—
73C22×C3×D5C22⋊C412yes—
74C22×C3×D5C22⋊C411yescharacteristic
75C3×C5×D4—41no—
76C3×C5×D4—41no—
77C3×C5×D4—82no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5C22×C411yescharacteristic
80C2×Dic15—42no—
81C2×C5×Dic3—42no—
82C3×C22⋊D5—42no—
83C3×C22⋊D5—42no—
84C3×C22⋊D5—82no—
85C2×C3×Dic5—21no—
86C2×C3×Dic5—21no—
87C2×C3×Dic5—42no—
88C2×C3×Dic5C22⋊C411yescharacteristic
89C3×D20—41no—
90C3×C4×D5—22no—
91C3×Dic10—41no—
92D5×Dic3—84no—
93C2×C3×#41—51no—
94C22×C3×D4—51no—
95C3×#127—51no—
96C3×#127C2×D511yescharacteristic
97C3×#124—51no—
98C3×#124—51no—
99C3×#121—102no—
100C3×#120—102no—
101C3×#117—51no—
102C2×#217—102no—
103#834—52no—
104#834—102no—
105#834C2×D512yes—
106C23×D5#6712yes—
107C2×C5×D4—22no—
108C2×C5×D4C2×Dic311yescharacteristic, complemented
109C2×C5×D4C22×D311yescharacteristic
110C2×C22⋊D5—21no—
111C2×C22⋊D5—22no—
112C2×C22⋊D5#6712yes—
113C22×Dic5—21no—
114#711—42no—
115D4×D5—42no—
116C2×D20C2×Dic311yescharacteristic
117C2×C4×D5—122no—
118C2×C4×D5C2×Dic311yescharacteristic
119C2×Dic10C2×Dic311yescharacteristic, complemented
120C5×C22⋊C4—62no—
121C42×C5C2×Dic311yescharacteristic, complemented
122C22⋊Dic5—22no—
123C22⋊Dic5—62no—
124#685—21no—
125#685—22no—
126#685—122no—
127#683—21no—
128C4×Dic5C2×Dic311yescharacteristic, complemented
129#535—51no—
130C2×#99—152no—
131#354—152no—
132#353—31no—
133#353—151no—
134C22×C3×C5—22no—
135C22×C3×C5—42no—
136C22×C3×C5—42no—
137C22×C3×C5—41no—
138C22×C3×C5C2×C22⋊C411yescharacteristic
139C2×C3×D5—22no—
140C2×C3×D5—41no—
141C2×C3×D5—44no—
142C2×C3×D5—42no—
143C2×C3×D5—82no—
144C2×C3×D5#9912yes—
145C3×C4×C5—21no—
146C3×C4×C5—41no—
147Dic15—82no—
148C3×Dic5—21no—
149C3×Dic5—41no—
150C3×Dic5—41no—
151C5×Dic3—82no—
152C24×C3—52no—
153C3×#41—202no—
154C2×C3×Q8—51no—
155C2×C3×D4—22no—
156C2×C3×D4—52no—
157C2×C3×D4—51no—
158C2×C3×D4—101no—
159C2×C3×D4—102no—
160C2×C3×D4—202no—
161C2×C3×D4C4×D511yescharacteristic, complemented
162C2×C3×D4C22×D511yescharacteristic
163C22×C3×C4—51no—
164C22×C3×C4—101no—
165C22×Dic3—202no—
166C3×C4⋊C4—101no—
167C3×C22⋊C4—101no—
168C3×C22⋊C4—102no—
169C3×C22⋊C4—102no—
170C3×C42—51no—
171C3×C42C4×D511yescharacteristic, complemented
172#217—22no—
173#217—102no—
174#217—202no—
175C23×C5—21no—
176C23×C5C2×#6712yes—
177C22×D5—22no—
178C22×D5—22no—
179C22×D5—82no—
180C22×D5#21712yes—
181C22×D5#21711yescharacteristic
182C5×D4—41no—
183C5×D4—41no—
184C5×D4—82no—
185C2×C4×C5—21no—
186C2×C4×C5—122no—
187C2×C4×C5C22×Dic311yescharacteristic
188C22⋊D5—42no—
189C22⋊D5—42no—
190C22⋊D5—82no—
191C2×Dic5—21no—
192C2×Dic5—21no—
193C2×Dic5—42no—
194C2×Dic5—122no—
195C2×Dic5#21711yescharacteristic
196D20—41no—
197C4×D5—22no—
198C4×D5—244no—
199Dic10—41no—
200C2×#41—51no—
201C22×D4—51no—
202#127—51no—
203#127D3×D511yescharacteristic
204#124—51no—
205#124—51no—
206#121—102no—
207#120—102no—
208#117—51no—
209C2×C22⋊C4—302no—
210#99—32no—
211#99—152no—
212#99—302no—
213C2×C3×C5—21no—
214C2×C3×C5—42no—
215C2×C3×C5—81no—
216C2×C3×C5C2×#9911yescharacteristic
217C3×D5—22no—
218C3×D5—42no—
219C23×C3—21no—
220C23×C3—51no—
221C23×C3—52no—
222C23×C3—102no—
223C23×C3—102no—
224C23×C3—402no—
225C23×C3D4×D512yes—
226C3×Q8—201no—
227C3×D4—41no—
228C3×D4—41no—
229C3×D4—82no—
230C3×D4—201no—
231C3×D4—202no—
232C3×D4—202no—
233C3×D4—402no—
234C2×C3×C4—21no—
235C2×C3×C4—51no—
236C2×C3×C4—102no—
237C2×C3×C4—101no—
238C2×C3×C4—101no—
239C2×C3×C4—202no—
240C2×C3×C4C2×C4×D511yescharacteristic
241C2×Dic3—42no—
242C2×Dic3—202no—
243C2×Dic3—404no—
244C22×C5—22no—
245C22×C5—42no—
246C22×C5—42no—
247C22×C5—41no—
248C22×C5C2×#21711yescharacteristic
249C2×D5—22no—
250C2×D5—41no—
251C2×D5—44no—
252C2×D5—42no—
253C2×D5—82no—
254C2×D5#83412yes—
255C4×C5—21no—
256C4×C5—41no—
257C4×C5—242no—
258Dic5—21no—
259Dic5—41no—
260Dic5—41no—
261Dic5—242no—
262C24—52no—
263#41—202no—
264C2×Q8—51no—
265C2×D4—22no—
266C2×D4—52no—
267C2×D4—51no—
268C2×D4—101no—
269C2×D4—102no—
270C2×D4—202no—
271C2×D4D5×Dic311yescharacteristic, complemented
272C2×D4C2×D3×D511yescharacteristic
273C22×C4—51no—
274C22×C4—101no—
275C22×C4—602no—
276C4⋊C4—101no—
277C22⋊C4—62no—
278C22⋊C4—101no—
279C22⋊C4—102no—
280C22⋊C4—102no—
281C22⋊C4—302no—
282C22⋊C4—602no—
283C42—51no—
284C42D5×Dic311yescharacteristic, complemented
285C3×C5#212711yescharacteristic, complemented, Hall
286C22×C3—22no—
287C22×C3—42no—
288C22×C3—42no—
289C22×C3—41no—
290C22×C3—52no—
291C22×C3—102no—
292C22×C3—201no—
293C22×C3—202no—
294C22×C3—204no—
295C22×C3—402no—
296C22×C3D5×C22⋊C411yescharacteristic
297C3×C4—21no—
298C3×C4—41no—
299C3×C4—101no—
300C3×C4—201no—
301C3×C4—201no—
302Dic3—82no—
303Dic3—402no—
304C2×C5—21no—
305C2×C5—42no—
306C2×C5—81no—
307C2×C5C2×#83411yescharacteristic
308D5—22no—
309D5—42no—
310C23—21no—
311C23—51no—
312C23—52no—
313C23—102no—
314C23—102no—
315C23—402no—
316C23D5×#6712yes—
317Q8—201no—
318D4—41no—
319D4—41no—
320D4—82no—
321D4—201no—
322D4—202no—
323D4—202no—
324D4—402no—
325C2×C4—21no—
326C2×C4—51no—
327C2×C4—102no—
328C2×C4—101no—
329C2×C4—101no—
330C2×C4—122no—
331C2×C4—202no—
332C2×C4—602no—
333C2×C4—1204no—
334C2×C4C2×D5×Dic311yescharacteristic
335C2×C3—21no—
336C2×C3—42no—
337C2×C3—81no—
338C2×C3—102no—
339C2×C3—202no—
340C2×C3D5×#9911yescharacteristic
341C5#7186011yescharacteristic, complemented, Sylow
342C22—22no—
343C22—42no—
344C22—42no—
345C22—41no—
346C22—52no—
347C22—102no—
348C22—201no—
349C22—202no—
350C22—204no—
351C22—402no—
352C22D5×#21711yescharacteristic
353C4—21no—
354C4—41no—
355C4—101no—
356C4—201no—
357C4—201no—
358C4—242no—
359C4—1202no—
360C3#1059994311yescharacteristic, complemented, Sylow
361C2—21no—
362C2—42no—
363C2—81no—
364C2—102no—
365C2—202no—
366C2D5×#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#2127
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. D5×#834C2semidirect
3. #11746366C2semidirect
4. C5×#4545C2semidirect
5. #11746009C2semidirect
7. C2×C3×#711C4semidirect
10. C3×#4086C4semidirect
14. C3×#4021C4semidirect
15. C3×#4018C4semidirect
28. C2×C3×C5×D4C2×C4semidirect
38. C2×C3×Dic10C2×C4semidirect
40. C3×C42×C5C2×C4semidirect
47. C3×C4×Dic5C2×C4semidirect
52. #4545D5semidirect
54. C2×#711Dic3semidirect
57. #4086Dic3semidirect
62. #4021Dic3semidirect
63. #4018Dic3semidirect
108. C2×C5×D4C2×Dic3semidirect
119. C2×Dic10C2×Dic3semidirect
121. C42×C5C2×Dic3semidirect
128. C4×Dic5C2×Dic3semidirect
161. C2×C3×D4C4×D5semidirect
171. C3×C42C4×D5semidirect
271. C2×D4D5×Dic3semidirect
284. C42D5×Dic3semidirect
285. C3×C5#2127semidirect
341. C5#71860semidirect
360. C3#10599943semidirect

Maximal subgroups

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

subgroupindex
C3×#660492
D5×#8342
#117463662
C5×#45452
#117460092
#105999433
#718605