Finite Group Databasebeta

← #14291050

Subgroups — #14291050

Order 1920.

392 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 70 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
1#11752637C211yesmaximal, characteristic
2#11751182C211yesmaximal, characteristic, complemented
3C5×#5081C211yesmaximal, characteristic, complemented
4C3×#65375C211yesmaximal, characteristic
5#11745851C211yesmaximal, characteristic, complemented
6#11745850C211yesmaximal, characteristic, complemented
7#11745846C211yesmaximal, characteristic
8#10602184—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91759C2211yescharacteristic
11C5×#870C2211yescharacteristic
12C2×C3×#689—21no—
13C2×C3×#688—21no—
14C3×#4021C2211yescharacteristic
15#91430—21no—
16#91422—21no—
17#91407—21no—
18#91362—21no—
19#91361—21no—
20#91327—21no—
21#91092—21no—
22#91091—21no—
23#91087C2211yescharacteristic
24C5×#808—21no—
25C5×#807—21no—
26C5×#803C2211yescharacteristic
27C3×#3935C2211yescharacteristic
28#71330—51nomaximal, Hall
29#66033—31no—
30C5×#501—31no—
31#65375D311yescharacteristic
32#65369—31no—
33#64763—31no—
34#64685—31no—
35#64684—31no—
36C2×C3×C5×Q8—21no—
37C2×C3×D20D411yescharacteristic
38C2×C3×Dic10D411yescharacteristic
39C2×#1204—21no—
40C2×D5×Dic3—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44C4⋊Dic15D411yescharacteristic
45C4⋊Dic15D411yescharacteristic
46#6712—21no—
47#6712—21no—
48C2×C3⋊#168—21no—
49C5×C4⋊Dic3D411yescharacteristic
50C5×C4⋊Dic3D411yescharacteristic
51C5×Dic3⋊C4—21no—
52C5×Dic3⋊C4—21no—
53C2×C5×C3⋊C8—21no—
54C3×#689—42no—
55C3×#688—42no—
56C3×#685—21no—
57C3×#685—21no—
58C2×C3×#168—21no—
59Dic3⋊Dic5—21no—
60#6669—21no—
61#6665—21no—
62#6665—21no—
63#6665—21no—
64Dic3×Dic5—21no—
65#5672—51no—
66C3×#497—51no—
67#5081—51no—
68#5081D511yescharacteristic, complemented
69#4540—51no—
70#4465—51no—
71#4465—51no—
72C5×C4⋊Q8C2×D311yescharacteristic
73C5×#125—31no—
74C2×#689—21no—
75C2×#688—21no—
76#4044—61no—
77#4044—61no—
78#4043—61no—
79#4042—61no—
80#4040—61no—
81#4034—61no—
82#4021C2×D311yescharacteristic
83#4016—31no—
84C5×#107—61no—
85C5×#106—61no—
86C5×#97—31no—
87#3940—61no—
88#3939—61no—
89#3935—31no—
90#3935C2×D311yescharacteristic
91#1660—151noSylow
92C22×C3×D5—21no—
93C3×C5×Q8—41no—
94C3×C5×Q8—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×Dic15—21no—
100C2×Dic15—21no—
101C2×C5×Dic3—21no—
102C2×C5×Dic3—21no—
103C2×C3×Dic5—21no—
104C3×D20—41no—
105C3×Dic10—41no—
106#1204—81no—
107D5×Dic3—81no—
108C3⋊#168—22no—
109C3×#168—22no—
110C5×C3⋊C8—22no—
111C2×C3×Q16—101no—
112C2×C3×SD16—101no—
113C3×C4⋊Q8C2×D511yescharacteristic
114C3×#124—51no—
115#944—101no—
116#935—101no—
117#879—101no—
118#879—101no—
119#878—101no—
120#878—101no—
121#870—51no—
122#870C2×D511yescharacteristic
123C3×#97—51no—
124#808—21no—
125#808—101no—
126#807—21no—
127#807—101no—
128#803—51no—
129#803C2×D511yescharacteristic
130C2×C5×Q8—21no—
131C2×D20#6711yescharacteristic
132C2×C4×D5—61no—
133C2×Dic10—61no—
134C2×Dic10#6711yescharacteristic
135C2×C5×C8—61no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—31no—
139C5×C4⋊C4—31no—
140C5×C4⋊C4—61no—
141C5×C4⋊C4—61no—
142C42×C5C22×D311yescharacteristic
143#689—42no—
144#688—42no—
145#685—21no—
146#685—21no—
147#685—61no—
148#685—61no—
149#685—61no—
150C4⋊Dic5—31no—
151C4⋊Dic5—31no—
152C4⋊Dic5—61no—
153#683—61no—
154#683—61no—
155#683—61no—
156C4×Dic5—61no—
157C2×#168—21no—
158C2×#168—61no—
159#563—151no—
160#501—31no—
161#501—151no—
162#497—51no—
163#330—151no—
164#330—151no—
165#329—151no—
166C22×C3×C5#12011yescharacteristic
167C2×C3×D5—41no—
168C2×C3×D5—41no—
169C2×C3×D5—41no—
170C3×C4×C5—21no—
171C3×C4×C5—21no—
172C3×C4×C5—21no—
173C3×C4×C5—81no—
174Dic15—41no—
175Dic15—41no—
176C3×Dic5—41no—
177C5×Dic3—41no—
178C5×Dic3—41no—
179C2×C3×Q8—21no—
180C2×C3×Q8—51no—
181C2×C3×D4—51no—
182C22×Dic3—101no—
183C2×Dic6—101no—
184C3×Q16—202no—
185C3×SD16—202no—
186C2×C3×C8—101no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4—21no—
189C3×C22⋊C4—101no—
190C3×C22⋊C4—101no—
191C3×C42C22×D511yescharacteristic
192#217—101no—
193#217—101no—
194#217—101no—
195C4⋊Dic3—51no—
196C4⋊Dic3—51no—
197C4⋊Dic3C22⋊D511yescharacteristic
198C4⋊Dic3C22⋊D511yescharacteristic
199Dic3⋊C4—21no—
200Dic3⋊C4—21no—
201Dic3⋊C4—101no—
202Dic3⋊C4—101no—
203Dic3⋊C4—101no—
204Dic3⋊C4—101no—
205C4×Dic3—101no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—101no—
208C22×D5—21no—
209C5×Q8—41no—
210C5×Q8—41no—
211C2×C4×C5—41no—
212C2×C4×C5—61no—
213C2×C4×C5—61no—
214C2×C4×C5D3×D411yescharacteristic
215C2×C4×C5D3×D411yescharacteristic
216C2×C4×C5C2×#6711yescharacteristic
217C2×Dic5—21no—
218C2×Dic5—61no—
219C2×Dic5—61no—
220D20—41no—
221C4×D5—241no—
222Dic10—41no—
223Dic10—241no—
224C5×C8—62no—
225#168—22no—
226#168—62no—
227C2×Q16—101no—
228C2×SD16—101no—
229C4⋊Q8—301no—
230C4⋊Q8D3×D511yescharacteristic
231#126—301no—
232#126—301no—
233#125—31no—
234#125—151no—
235#124—51no—
236#123—301no—
237C22⋊Q8—301no—
238C22⋊Q8—301no—
239#107—61no—
240#107—301no—
241#106—61no—
242#106—301no—
243#97—31no—
244#97—51no—
245#97—151no—
246C2×C3×C5#45311yescharacteristic
247C2×C3×C5#45611yescharacteristic
248C2×C3×C5#45611yescharacteristic
249C3×D5—81no—
250C23×C3—101no—
251C3×Q8—41no—
252C3×Q8—41no—
253C3×Q8—201no—
254C3×D4—201no—
255C2×C3×C4—41no—
256C2×C3×C4—101no—
257C2×C3×C4D4×D511yescharacteristic
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4C2×C22⋊D511yescharacteristic
260C2×Dic3—21no—
261C2×Dic3—21no—
262C2×Dic3—101no—
263C2×Dic3—101no—
264C2×Dic3—401no—
265Dic6—401no—
266C3×C8—102no—
267C3⋊C8—22no—
268C3⋊C8—102no—
269C22×C5#93711yescharacteristic
270C2×D5—41no—
271C2×D5—41no—
272C2×D5—41no—
273C4×C5—21no—
274C4×C5—21no—
275C4×C5—21no—
276C4×C5—81no—
277C4×C5—121no—
278C4×C5—121no—
279Dic5—41no—
280Dic5—121no—
281Dic5—121no—
282C2×Q8—21no—
283C2×Q8—51no—
284C2×Q8—301no—
285C2×D4—51no—
286C22×C4—301no—
287Q16—202no—
288SD16—202no—
289C2×C8—61no—
290C2×C8—101no—
291C2×C8—301no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—31no—
295C4⋊C4—31no—
296C4⋊C4—61no—
297C4⋊C4—61no—
298C4⋊C4—151no—
299C4⋊C4—151no—
300C4⋊C4—301no—
301C4⋊C4—301no—
302C4⋊C4—301no—
303C4⋊C4—301no—
304C22⋊C4—101no—
305C22⋊C4—101no—
306C22⋊C4—301no—
307C22⋊C4—301no—
308C22⋊C4—301no—
309C42—301no—
310C42C2×D3×D511yescharacteristic
311C3×C5#166011yescharacteristic, complemented, Hall
312C22×C3—201no—
313C22×C3—201no—
314C22×C3—201no—
315C22×C3#408311yescharacteristic
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—81no—
320C3×C4—201no—
321Dic3—41no—
322Dic3—41no—
323Dic3—201no—
324Dic3—201no—
325C2×C5#507711yescharacteristic
326C2×C5#520511yescharacteristic
327C2×C5#520511yescharacteristic
328D5—81no—
329C23—101no—
330Q8—41no—
331Q8—41no—
332Q8—201no—
333Q8—1201no—
334D4—201no—
335C2×C4—41no—
336C2×C4—61no—
337C2×C4—61no—
338C2×C4—101no—
339C2×C4—301no—
340C2×C4—301no—
341C2×C4—1201no—
342C2×C4D5×#6711yescharacteristic
343C2×C4D3×C22⋊D511yescharacteristic
344C2×C4#679011yescharacteristic
345C8—62no—
346C8—102no—
347C8—302no—
348C2×C3—401no—
349C2×C3#6538411yescharacteristic
350C2×C3#6548711yescharacteristic
351C2×C3#6549411yescharacteristic
352C5#7133011yescharacteristic, complemented, Sylow
353C22—201no—
354C22—201no—
355C22—201no—
356C22#9157711yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—81no—
361C4—121no—
362C4—121no—
363C4—201no—
364C4—601no—
365C4—601no—
366C3#1060218411yescharacteristic, complemented, Sylow
367C2—401no—
368C2#1174916311yescharacteristic
369C2#1174941211yescharacteristic
370C2#1174941311yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1660
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11751182C2semidirect
3. C5×#5081C2semidirect
5. #11745851C2semidirect
6. #11745850C2semidirect
68. #5081D5semidirect
311. C3×C5#1660semidirect
352. C5#71330semidirect
366. C3#10602184semidirect

Maximal subgroups

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

subgroupindex
#117526372
#117511822
C5×#50812
C3×#653752
#117458512
#117458502
#117458462
#106021843
#713305