Finite Group Databasebeta

← #14284146

Subgroups — #14284146

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66014C211yesmaximal, characteristic
2#11747003C211yesmaximal, characteristic, complemented
3#11746870C211yesmaximal, characteristic, complemented
4#11746361C211yesmaximal, characteristic, complemented
5C5×#4540C211yesmaximal, characteristic, complemented
6#11745849C211yesmaximal, characteristic, complemented
7#11745849C211yesmaximal, characteristic, complemented
8#10599137—31nomaximal, Hall
9C3×C5×#124C2211yescharacteristic
10C3×#4092C411yescharacteristic
11C3×Q8×Dic5C411yescharacteristic
12C3×#4084C411yescharacteristic
13C3×D4×Dic5C411yescharacteristic
14C3×#4029—21no—
15C3×#4027—21no—
16C3×#4025—21no—
17C3×#4023—21no—
18C3×C42×D5C2211yescharacteristic
19C3×#4016C2211yescharacteristic
20C2×#6649—21no—
21#91087C2211yescharacteristic
22#91087C2211yescharacteristic
23C5×#803C2211yescharacteristic
24C5×#803C2211yescharacteristic
25#90982—21no—
26#90955—21no—
27Dic5×C3⋊C8—21no—
28#71747—51nomaximal, Hall
29#66014D311yescharacteristic
30#64996—31no—
31#64994—31no—
32C5×#329—31no—
33#64760—31no—
34#64685—31no—
35#64685—31no—
36C2×C3×C5×Q8C2×C411yescharacteristic
37C2×C3×C5×D4C2×C411yescharacteristic
38C2×C3×C22⋊D5—21no—
39C22×C3×Dic5—21no—
40C2×C3×C4×D5C2×C411yescharacteristic
41C2×C3×C4×D5D411yescharacteristic
42C2×C3×C4×D5D411yescharacteristic
43C3×C5×C22⋊C4—21no—
44C3×C5×C22⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C3×C22⋊Dic5—21no—
51C3×C22⋊Dic5—21no—
52C3×#685—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5C2×C411yescharacteristic
55C3×C4⋊Dic5C2×C411yescharacteristic
56C3×#683—21no—
57C3×#683—21no—
58C3×#683—21no—
59C3×C4×Dic5—21no—
60C3×C4×Dic5C2×C411yescharacteristic
61C3×C4×Dic5D411yescharacteristic
62C3×C4×Dic5D411yescharacteristic
63#6649—24no—
64C3×#529—51no—
65#4926—51no—
66C4×#208—51no—
67#4543—51no—
68#4543—51no—
69#4540—51no—
70#4540D511yescharacteristic, complemented
71C5×#124C2×D311yescharacteristic
72#4092Dic311yescharacteristic
73Q8×Dic5Dic311yescharacteristic
74#4084Dic311yescharacteristic
75D4×Dic5Dic311yescharacteristic
76C2×#676—61no—
77#4029—21no—
78#4027—21no—
79#4025—21no—
80#4023—21no—
81C42×D5C2×D311yescharacteristic
82#4016C2×D311yescharacteristic
83C5×#97—31no—
84C5×#97—31no—
85#3952—61no—
86#3946—61no—
87C8×Dic5—61no—
88#3935—31no—
89#3935—31no—
90#1529—151noSylow
91C23×C3×C5—21no—
92C22×C3×D5C22⋊C411yescharacteristic
93C3×C5×Q8—41no—
94C3×C5×D4—41no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C3×C22⋊D5—42no—
100C2×C3×Dic5—21no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—42no—
103C2×C3×Dic5C22⋊C411yescharacteristic
104C2×C3×Dic5C22⋊C411yescharacteristic
105C2×C3×Dic5C22⋊C411yescharacteristic
106C3×C4×D5—22no—
107C3×C4×D5—41no—
108C3×C4×D5—41no—
109C3⋊#168—22no—
110C3⋊#168—41no—
111C5×C3⋊C8—22no—
112C5×C3⋊C8—41no—
113C3×#126—101no—
114C3×#125—51no—
115C3×#124C2×D511yescharacteristic
116C3×#123—101no—
117C3×C22⋊Q8—51no—
118C3×#121—51no—
119C3×C4×Q8—51no—
120C3×C4×D4—51no—
121C3×C4×D4—101no—
122C3×#117—101no—
123C2×C3×C42—51no—
124C2×#208—101no—
125#830—101no—
126C4⋊(C3⋊C8)—101no—
127#803—51no—
128#803—51no—
129#803C2×D511yescharacteristic
130#803C2×D511yescharacteristic
131C4×C3⋊C8—101no—
132C2×C5×Q8C2×Dic311yescharacteristic
133C2×C5×D4C2×Dic311yescharacteristic
134C2×C22⋊D5—21no—
135C22×Dic5—21no—
136C2×C4×D5C2×Dic311yescharacteristic
137C2×C4×D5#6711yescharacteristic
138C2×C4×D5#6711yescharacteristic
139C2×C5×C8—61no—
140C2×C5×C8—61no—
141C5×C22⋊C4—21no—
142C5×C22⋊C4—21no—
143C42×C5C22×D311yescharacteristic
144C22⋊Dic5—21no—
145C22⋊Dic5—21no—
146#685—21no—
147C4⋊Dic5—21no—
148C4⋊Dic5C2×Dic311yescharacteristic
149C4⋊Dic5C2×Dic311yescharacteristic
150#683—21no—
151#683—21no—
152#683—21no—
153C4×Dic5—21no—
154C4×Dic5C2×Dic311yescharacteristic
155C4×Dic5#6711yescharacteristic
156C4×Dic5#6711yescharacteristic
157C2×#168—61no—
158C2×#168—61no—
159#676—64no—
160#529—51no—
161#432—151no—
162C4×M16—151no—
163#330—151no—
164#330—151no—
165#329—31no—
166#329—151no—
167C22×C3×C5—41no—
168C22×C3×C5—41no—
169C22×C3×C5—41no—
170C22×C3×C5C2×C22⋊C411yescharacteristic
171C2×C3×D5—21no—
172C2×C3×D5—21no—
173C2×C3×D5—21no—
174C3×C4×C5—21no—
175C3×C4×C5—21no—
176C3×C4×C5—21no—
177C3×C4×C5—41no—
178C3×Dic5—21no—
179C3×Dic5—21no—
180C3×Dic5—41no—
181C3×Dic5—41no—
182C3×Dic5#10412yes—
183C2×C3×Q8C4×D511yescharacteristic
184C2×C3×D4—101no—
185C2×C3×D4C4×D511yescharacteristic
186C22×C3×C4—51no—
187C22×C3×C4—51no—
188C22×C3×C4—51no—
189C22×C3×C4—101no—
190C3×C4⋊C4—51no—
191C3×C4⋊C4—51no—
192C3×C4⋊C4—101no—
193C3×C4⋊C4—101no—
194C3×C4⋊C4—101no—
195C3×C4⋊C4—101no—
196C3×C22⋊C4—21no—
197C3×C22⋊C4—21no—
198C3×C22⋊C4—101no—
199C3×C22⋊C4—101no—
200C3×C22⋊C4—101no—
201C3×C42—51no—
202C3×C42—51no—
203C3×C42—51no—
204C3×C42—101no—
205C3×C42C22×D511yescharacteristic
206#208—104no—
207C2×C3⋊C8—21no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8—101no—
210C2×C3⋊C8—101no—
211C23×C5—21no—
212C22×D5#21711yescharacteristic
213C5×Q8—41no—
214C5×D4—41no—
215C2×C4×C5—21no—
216C2×C4×C5C22×Dic311yescharacteristic
217C2×C4×C5C2×#6711yescharacteristic
218C2×C4×C5C2×#6711yescharacteristic
219C22⋊D5—42no—
220C2×Dic5—21no—
221C2×Dic5—21no—
222C2×Dic5—42no—
223C2×Dic5#21711yescharacteristic
224C2×Dic5#21711yescharacteristic
225C2×Dic5#21711yescharacteristic
226C4×D5—22no—
227C4×D5—41no—
228C4×D5—41no—
229C5×C8—62no—
230C5×C8—121no—
231#168—62no—
232#168—121no—
233C2×M16—301no—
234#126—101no—
235#125—51no—
236#124D3×D511yescharacteristic
237#123—101no—
238C22⋊Q8—51no—
239#121—51no—
240C4×Q8—51no—
241C4×D4—51no—
242C4×D4—101no—
243#117—101no—
244C2×C42—51no—
245C4⋊C8—301no—
246C22⋊C8—301no—
247#97—31no—
248#97—31no—
249#97—151no—
250#97—151no—
251C4×C8—301no—
252C2×C3×C5—81no—
253C2×C3×C5#41311yescharacteristic
254C2×C3×C5C2×#10411yescharacteristic
255C2×C3×C5#42111yescharacteristic
256C3×D5—41no—
257C23×C3—21no—
258C23×C3—51no—
259C3×Q8—41no—
260C3×D4—41no—
261C3×D4—202no—
262C2×C3×C4—21no—
263C2×C3×C4—51no—
264C2×C3×C4—51no—
265C2×C3×C4—51no—
266C2×C3×C4—102no—
267C2×C3×C4—101no—
268C2×C3×C4—101no—
269C2×C3×C4—201no—
270C2×C3×C4—201no—
271C2×C3×C4—202no—
272C2×C3×C4C2×C4×D511yescharacteristic
273C2×C3×C4D4×D511yescharacteristic
274C2×C3×C4D4×D511yescharacteristic
275C3⋊C8—22no—
276C3⋊C8—41no—
277C3⋊C8—102no—
278C3⋊C8—201no—
279C22×C5—41no—
280C22×C5—41no—
281C22×C5—41no—
282C22×C5C2×#21711yescharacteristic
283C2×D5—21no—
284C2×D5—21no—
285C2×D5—21no—
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—21no—
289C4×C5—41no—
290Dic5—21no—
291Dic5—21no—
292Dic5—41no—
293Dic5—41no—
294Dic5#83712yes—
295C2×Q8D5×Dic311yescharacteristic
296C2×D4—101no—
297C2×D4D5×Dic311yescharacteristic
298C22×C4—51no—
299C22×C4—51no—
300C22×C4—51no—
301C22×C4—101no—
302M16—304no—
303C2×C8—61no—
304C2×C8—61no—
305C2×C8—301no—
306C2×C8—301no—
307C4⋊C4—51no—
308C4⋊C4—51no—
309C4⋊C4—101no—
310C4⋊C4—101no—
311C4⋊C4—101no—
312C4⋊C4—101no—
313C22⋊C4—21no—
314C22⋊C4—21no—
315C22⋊C4—101no—
316C22⋊C4—101no—
317C22⋊C4—101no—
318C42—51no—
319C42—51no—
320C42—51no—
321C42—101no—
322C42C2×D3×D511yescharacteristic
323C3×C5#152911yescharacteristic, complemented, Hall
324C22×C3—41no—
325C22×C3—41no—
326C22×C3—41no—
327C22×C3—101no—
328C22×C3—101no—
329C22×C3—101no—
330C22×C3D5×C22⋊C411yescharacteristic
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—41no—
335C3×C4—52no—
336C3×C4—101no—
337C3×C4—101no—
338C3×C4—201no—
339C3×C4—201no—
340C2×C5—81no—
341C2×C5C2×#83711yescharacteristic
342C2×C5#523611yescharacteristic
343C2×C5#523711yescharacteristic
344D5—41no—
345C23—21no—
346C23—51no—
347Q8—41no—
348D4—41no—
349D4—202no—
350C2×C4—21no—
351C2×C4—51no—
352C2×C4—51no—
353C2×C4—51no—
354C2×C4—102no—
355C2×C4—101no—
356C2×C4—101no—
357C2×C4—201no—
358C2×C4—201no—
359C2×C4—202no—
360C2×C4C2×D5×Dic311yescharacteristic
361C2×C4D5×#6711yescharacteristic
362C2×C4D5×#6711yescharacteristic
363C8—62no—
364C8—121no—
365C8—302no—
366C8—601no—
367C2×C3—81no—
368C2×C3—201no—
369C2×C3#6503411yescharacteristic
370C2×C3D5×#10411yescharacteristic
371C2×C3#6511011yescharacteristic
372C5#7174711yescharacteristic, complemented, Sylow
373C22—41no—
374C22—41no—
375C22—41no—
376C22—101no—
377C22—101no—
378C22—101no—
379C22D5×#21711yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—41no—
384C4—52no—
385C4—101no—
386C4—101no—
387C4—201no—
388C4—201no—
389C3#1059913711yescharacteristic, complemented, Sylow
390C2—81no—
391C2—201no—
392C2#1174912311yescharacteristic
393C2D5×#83711yescharacteristic
394C2#1174942711yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#4084C4
cosocleC3×C42×C5C23
hypercenter#124D3×D5
hypocenterC3×C5#1529
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11747003C2semidirect
3. #11746870C2semidirect
4. #11746361C2semidirect
5. C5×#4540C2semidirect
6. #11745849C2semidirect
7. #11745849C2semidirect
70. #4540D5semidirect
323. C3×C5#1529semidirect
372. C5#71747semidirect
389. C3#10599137semidirect

Maximal subgroups

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

subgroupindex
C3×#660142
#117470032
#117468702
#117463612
C5×#45402
#117458492
#105991373
#717475