Finite Group Databasebeta

← #14288625

Subgroups — #14288625

Order 1920.

416 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 78 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#11754482C211yesmaximal, characteristic
2#11751069C211yesmaximal, characteristic
3C5×#4970C211yesmaximal, characteristic, complemented
4C3×#65271C211yesmaximal, characteristic, complemented
5#11745962C211yesmaximal, characteristic, complemented
6#11745958C211yesmaximal, characteristic
7#11745951C211yesmaximal, characteristic, complemented
8#10601971—31nomaximal, Hall
9C2×C3×C5×C4⋊C4C2211yescharacteristic
10#91819C2211yescharacteristic
11C5×#924C2211yescharacteristic
12C2×C3×#683C2211yescharacteristic
13#91552—21no—
14#91546—21no—
15#91433—21no—
16#91424—21no—
17#91343—21no—
18#91337—21no—
19#91114C2211yescharacteristic
20#91093—21no—
21#91092—21no—
22C5×#830C2211yescharacteristic
23C5×#810—21no—
24C5×#807—21no—
25C3×#3963—21no—
26C3×#3963—21no—
27C3×#3963C2211yescharacteristic
28#69717—51nomaximal, Hall
29#65979—31no—
30C5×#484—31no—
31#65271D311yescharacteristic, complemented
32#65257—31no—
33#64758—31no—
34#64690—31no—
35#64689—31no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C2×#1220—21no—
39C2×D60D411yescharacteristic
40C2×C5×Dic6D411yescharacteristic
41C22×C3×Dic5—21no—
42C22×C3×Dic5D411yescharacteristic
43C22×C3×Dic5D411yescharacteristic
44C2×#1200—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47#6714—21no—
48C4⋊Dic15D411yescharacteristic
49C2×C3⋊#168—21no—
50C5×#217—21no—
51C5×C4⋊Dic3D411yescharacteristic
52C5×Dic3⋊C4—21no—
53C2×C5×C3⋊C8—21no—
54C3×#683—21no—
55C3×#683—21no—
56Dic3⋊Dic5—21no—
57Dic3⋊Dic5—21no—
58#6669—21no—
59#6667—21no—
60#6667—21no—
61#6667—21no—
62Dic3×Dic5—21no—
63#5515—51no—
64C3×#400—51no—
65#4970D511yescharacteristic, complemented
66#4968—51no—
67#4528—51no—
68#4452—51no—
69#4451—51no—
70C5×C22⋊Q8—31no—
71C2×C5×C4⋊C4C2×D311yescharacteristic
72#4092—61no—
73#4076—31no—
74C2×#683C2×D311yescharacteristic
75#4044—61no—
76#4040—61no—
77#4036—61no—
78#4032—61no—
79#4027—61no—
80C5×#107—61no—
81C5×#103—61no—
82C5×C22⋊C8—31no—
83#3963—21no—
84#3963—21no—
85#3963C2×D311yescharacteristic
86C22⋊#168—31no—
87#3941—61no—
88#3940—61no—
89#1615—151noSylow
90C23×C3×C5C2×D411yescharacteristic
91C22×D15—21no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5—42no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97#1220—41no—
98#1220—41no—
99C2×Dic15—21no—
100D60—41no—
101C2×C5×Dic3—21no—
102C2×C5×Dic3—21no—
103C5×Dic6—41no—
104C2×C3×Dic5—21no—
105C2×C3×Dic5—21no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—41no—
109C2×C3×Dic5—41no—
110C2×C3×Dic5—41no—
111C2×C3×Dic5—41no—
112#1200—81no—
113C3⋊#168—41no—
114C5×C3⋊C8—41no—
115C2×C3×C4⋊C4—51no—
116C2×C3×C4⋊C4C2×D511yescharacteristic
117#930—51no—
118#929—101no—
119C4×#67—101no—
120#924C2×D511yescharacteristic
121#898—101no—
122#896—101no—
123#894—101no—
124#889—101no—
125C3×#95—51no—
126C3×#95—101no—
127C3×#95—101no—
128#830—51no—
129#830C2×D511yescharacteristic
130#810—21no—
131#809—101no—
132#808—101no—
133#807—21no—
134C2×C5×Q8—31no—
135C22×C4×C5—21no—
136C22×C4×C5C22×D311yescharacteristic
137C2×C22⋊D5—61no—
138C22×Dic5—21no—
139C22×Dic5#6711yescharacteristic
140C22×Dic5#6711yescharacteristic
141C2×D20—31no—
142C2×C4×D5—61no—
143C2×C5×C8—61no—
144C5×C4⋊C4—21no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4—31no—
147C5×C4⋊C4—61no—
148C5×C22⋊C4—61no—
149#685—61no—
150#685—61no—
151#685—61no—
152#685—61no—
153C4⋊Dic5—31no—
154C4⋊Dic5—61no—
155C4⋊Dic5—61no—
156#683—21no—
157#683—21no—
158#683—61no—
159C4×Dic5—61no—
160C2×#168—61no—
161#539—151no—
162#484—31no—
163#481—151no—
164#400—51no—
165#328—151no—
166#327—151no—
167#324—151no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5#12011yescharacteristic
171C22×C3×C5#13511yescharacteristic
172C22×C3×C5#13711yescharacteristic
173C2×D15—41no—
174C2×D15—41no—
175C2×D15—41no—
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—81no—
179Dic15—41no—
180C3×Dic5—41no—
181C3×Dic5—41no—
182C3×Dic5—81no—
183C5×Dic3—41no—
184C5×Dic3—41no—
185C22×C3×C4—21no—
186C22×C3×C4—51no—
187C22×C3×C4—51no—
188C22×C3×C4—101no—
189C22×C3×C4C22×D511yescharacteristic
190C2×#67—101no—
191C2×D12—51no—
192C2×C4×D3—101no—
193C2×Dic6C22⋊D511yescharacteristic
194C3×C4⋊C4—21no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—101no—
197C3×C4⋊C4—101no—
198#217—21no—
199(C2×D3)⋊C4—101no—
200(C2×D3)⋊C4—101no—
201(C2×D3)⋊C4—101no—
202(C2×D3)⋊C4—101no—
203C4⋊Dic3—51no—
204C4⋊Dic3C22⋊D511yescharacteristic
205Dic3⋊C4—21no—
206Dic3⋊C4—101no—
207Dic3⋊C4—101no—
208Dic3⋊C4—101no—
209C4×Dic3—101no—
210C2×C3⋊C8—21no—
211C2×C3⋊C8—101no—
212C23×C5C2×#6711yescharacteristic
213C22×D5—61no—
214C5×Q8—121no—
215C2×C4×C5—41no—
216C2×C4×C5—42no—
217C2×C4×C5—41no—
218C2×C4×C5—61no—
219C2×C4×C5—61no—
220C2×C4×C5D3×D411yescharacteristic
221C2×C4×C5D3×D411yescharacteristic
222C22⋊D5—121no—
223C22⋊D5—121no—
224C2×Dic5—21no—
225C2×Dic5—21no—
226C2×Dic5—21no—
227C2×Dic5—21no—
228C2×Dic5—41no—
229C2×Dic5—41no—
230C2×Dic5—41no—
231C2×Dic5—41no—
232C2×Dic5—61no—
233D20—121no—
234C4×D5—241no—
235C5×C8—121no—
236#168—121no—
237#126—301no—
238#125—301no—
239#123—301no—
240#123—301no—
241C22⋊Q8—31no—
242C22⋊Q8—301no—
243#121—151no—
244C4×D4—301no—
245C2×C4⋊C4—51no—
246C2×C4⋊C4D3×D511yescharacteristic
247#107—61no—
248#106—301no—
249#103—61no—
250#102—301no—
251C22⋊C8—31no—
252C22⋊C8—151no—
253#95—51no—
254#95—101no—
255#95—101no—
256C2×C3×C5—21no—
257C2×C3×C5—21no—
258C2×C3×C5#45211yescharacteristic
259C2×C3×C5#45411yescharacteristic
260C2×C3×C5#45811yescharacteristic
261D15—81no—
262C23×C3D4×D511yescharacteristic
263C22×D3—101no—
264C2×C3×C4—41no—
265C2×C3×C4—42no—
266C2×C3×C4—41no—
267C2×C3×C4—101no—
268C2×C3×C4—101no—
269C2×C3×C4—101no—
270C2×C3×C4—101no—
271C2×C3×C4—201no—
272C2×C3×C4—201no—
273C2×C3×C4—201no—
274C2×C3×C4—201no—
275C2×C3×C4D4×D511yescharacteristic
276C2×C3×C4C2×C22⋊D511yescharacteristic
277#67—201no—
278#67—201no—
279C2×Dic3—21no—
280C2×Dic3—21no—
281C2×Dic3—101no—
282D12—201no—
283C4×D3—401no—
284Dic6—41no—
285C3⋊C8—41no—
286C3⋊C8—201no—
287C22×C5—21no—
288C22×C5—21no—
289C22×C5#93711yescharacteristic
290C22×C5#94211yescharacteristic
291C22×C5#95011yescharacteristic
292C2×D5—121no—
293C2×D5—121no—
294C2×D5—121no—
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—81no—
298C4×C5—121no—
299C4×C5—121no—
300Dic5—41no—
301Dic5—41no—
302Dic5—81no—
303Dic5—121no—
304C2×Q8—31no—
305C2×D4—151no—
306C2×D4—301no—
307C22×C4—21no—
308C22×C4—51no—
309C22×C4—51no—
310C22×C4—101no—
311C22×C4—301no—
312C22×C4C2×D3×D511yescharacteristic
313C2×C8—61no—
314C2×C8—301no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—31no—
318C4⋊C4—61no—
319C4⋊C4—101no—
320C4⋊C4—101no—
321C4⋊C4—151no—
322C4⋊C4—301no—
323C4⋊C4—301no—
324C4⋊C4—301no—
325C22⋊C4—61no—
326C22⋊C4—301no—
327C22⋊C4—301no—
328C22⋊C4—301no—
329C22⋊C4—301no—
330C42—301no—
331C3×C5#161511yescharacteristic, complemented, Hall
332C22×C3—21no—
333C22×C3—21no—
334C22×C3#406411yescharacteristic
335C22×C3#406511yescharacteristic
336C22×C3#408311yescharacteristic
337C2×D3—201no—
338C2×D3—201no—
339C2×D3—201no—
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—81no—
343C3×C4—201no—
344C3×C4—201no—
345C3×C4—401no—
346Dic3—41no—
347Dic3—41no—
348Dic3—201no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5#504711yescharacteristic
352C2×C5#505311yescharacteristic
353C2×C5#506211yescharacteristic
354D5—241no—
355C23—301no—
356C23D5×#6711yescharacteristic
357Q8—121no—
358D4—601no—
359D4—601no—
360D4—601no—
361C2×C4—41no—
362C2×C4—42no—
363C2×C4—41no—
364C2×C4—61no—
365C2×C4—61no—
366C2×C4—101no—
367C2×C4—101no—
368C2×C4—101no—
369C2×C4—101no—
370C2×C4—201no—
371C2×C4—201no—
372C2×C4—201no—
373C2×C4—201no—
374C2×C4—301no—
375C2×C4—1201no—
376C2×C4D3×C22⋊D511yescharacteristic
377C2×C4#679011yescharacteristic
378C8—121no—
379C8—601no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3#6534211yescharacteristic
383C2×C3#6547611yescharacteristic
384C2×C3#6549011yescharacteristic
385D3—401no—
386C5#6971711yescharacteristic, complemented, Sylow
387C22—21no—
388C22—21no—
389C22—601no—
390C22—601no—
391C22—601no—
392C22#9151511yescharacteristic
393C22#9151611yescharacteristic
394C22#9157711yescharacteristic
395C4—21no—
396C4—21no—
397C4—81no—
398C4—121no—
399C4—121no—
400C4—201no—
401C4—201no—
402C4—401no—
403C4—601no—
404C3#1060197111yescharacteristic, complemented, Sylow
405C2—21no—
406C2—21no—
407C2—1201no—
408C2#1174893911yescharacteristic
409C2#1174916811yescharacteristic
410C2#1174940611yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radical#91819C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1615
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C5×#4970C2semidirect
4. C3×#65271C2semidirect
5. #11745962C2semidirect
7. #11745951C2semidirect
31. #65271D3semidirect
65. #4970D5semidirect
331. C3×C5#1615semidirect
386. C5#69717semidirect
404. C3#10601971semidirect

Maximal subgroups

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

subgroupindex
#117544822
#117510692
C5×#49702
C3×#652712
#117459622
#117459582
#117459512
#106019713
#697175