Finite Group Databasebeta

← #14288365

Subgroups — #14288365

Order 1920.

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

normal subgroups only

This group has 432 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#11754483C211yesmaximal, characteristic
2C5×#4661C211yesmaximal, characteristic, complemented
3#11748462C211yesmaximal, characteristic
4#11748401C211yesmaximal, characteristic, complemented
5#11746272C211yesmaximal, characteristic
6C3×#64672C211yesmaximal, characteristic, complemented
7#11745952C211yesmaximal, characteristic, complemented
8#10600504—31nomaximal, Hall
9#91819C2211yescharacteristic
10C2×C5×C4⋊Dic3—21no—
11C2×C5×C4⋊Dic3C2211yescharacteristic
12C2×C5×Dic3⋊C4C2211yescharacteristic
13C3×#4070C2211yescharacteristic
14#91556—21no—
15#91542—21no—
16#91433—21no—
17#91411—21no—
18#91345—21no—
19#91334—21no—
20C3×C5×#95C2211yescharacteristic
21#91114C2211yescharacteristic
22C5×C3⋊#95—21no—
23C3×C22⋊#168C2211yescharacteristic
24#90988—21no—
25#90986—21no—
26#90970—21no—
27#90969—21no—
28#68328—51nomaximal, Hall
29#65849—31no—
30C5×#398—31no—
31#65260—31no—
32#65256—31no—
33#64748—31no—
34#64672D311yescharacteristic, complemented
35#64671—31no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C2×#1220—21no—
39C2×D60D411yescharacteristic
40C22×C5×Dic3—21no—
41C22×C5×Dic3D411yescharacteristic
42C22×C5×Dic3D411yescharacteristic
43C2×C3×Dic10D411yescharacteristic
44C2×#1200—21no—
45#6714—21no—
46C4⋊Dic15D411yescharacteristic
47C2×C3⋊#168—21no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3—42no—
51C5×Dic3⋊C4—21no—
52C5×Dic3⋊C4—21no—
53C3×C22⋊Dic5—21no—
54C3×C4⋊Dic5D411yescharacteristic
55C3×#683—21no—
56C2×C3×#168—21no—
57#6669—21no—
58#6668—21no—
59#6668—21no—
60#6667—21no—
61#6667—21no—
62#6667—21no—
63Dic3×Dic5—21no—
64#5645—51no—
65#5043—51no—
66#4736—51no—
67#4661D511yescharacteristic, complemented
68C3×#328—51no—
69#4469—51no—
70#4451—51no—
71C2×C5×C4⋊C4—31no—
72C2×C5×C4⋊C4—31no—
73C2×C5×C4⋊C4—61no—
74#4076—31no—
75#4075—61no—
76C4×C22⋊D5—61no—
77#4070C2×D311yescharacteristic
78#4044—61no—
79#4042—61no—
80#4040—61no—
81#4035—61no—
82C5×#95—61no—
83C5×#95C2×D311yescharacteristic
84C22⋊#168—31no—
85C22⋊#168C2×D311yescharacteristic
86#3942—61no—
87#3941—61no—
88#3940—61no—
89#3939—61no—
90#1609—151noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×D15—21no—
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99#1220—41no—
100#1220—41no—
101C2×Dic15—21no—
102D60—41no—
103C2×C5×Dic3—21no—
104C2×C5×Dic3—21no—
105C2×C5×Dic3—21no—
106C2×C5×Dic3—21no—
107C2×C5×Dic3—41no—
108C2×C5×Dic3—41no—
109C2×C5×Dic3—41no—
110C2×C5×Dic3—41no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—21no—
113C3×Dic10—41no—
114#1200—81no—
115C3⋊#168—41no—
116C3×#168—41no—
117C3×C22⋊Q8—51no—
118#946—101no—
119#930—51no—
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3C2×D511yescharacteristic
122C2×Dic3⋊C4C2×D511yescharacteristic
123#898—101no—
124#894—101no—
125#890—101no—
126#886—101no—
127#67⋊C4—101no—
128C3×C22⋊C8—51no—
129C3×#95C2×D511yescharacteristic
130#835—101no—
131C3⋊#95—21no—
132#830—51no—
133#821—101no—
134#818—101no—
135#808—101no—
136C22×C4×C5—21no—
137C22×C4×C5—31no—
138C22×C4×C5—31no—
139C22×C4×C5—61no—
140C22×C4×C5C22×D311yescharacteristic
141C2×C22⋊D5—61no—
142C2×D20—31no—
143C2×C4×D5—61no—
144C2×Dic10D1211yescharacteristic
145C5×C4⋊C4—61no—
146C5×C4⋊C4—61no—
147C5×C4⋊C4—61no—
148C5×C4⋊C4—61no—
149C5×C4⋊C4—122no—
150C22⋊Dic5—21no—
151#685—61no—
152#685—61no—
153#685—61no—
154#685—61no—
155C4⋊Dic5—31no—
156C4⋊Dic5D1211yescharacteristic
157#683—21no—
158#683—61no—
159#683—61no—
160#683—61no—
161C4×Dic5—61no—
162C2×#168—21no—
163C2×#168—61no—
164#539—151no—
165#483—151no—
166#480—151no—
167#398—31no—
168#328—51no—
169#327—151no—
170#324—151no—
171C22×C3×C5—21no—
172C22×C3×C5—21no—
173C22×C3×C5#12011yescharacteristic
174C22×C3×C5#13511yescharacteristic
175C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
176C2×D15—41no—
177C2×D15—41no—
178C2×D15—41no—
179C3×C4×C5—21no—
180C3×C4×C5—21no—
181C3×C4×C5—42no—
182Dic15—41no—
183C3×Dic5—41no—
184C3×Dic5—41no—
185C5×Dic3—41no—
186C5×Dic3—41no—
187C5×Dic3—81no—
188C2×C3×Q8—51no—
189C22×C3×C4—21no—
190C22×C3×C4C22×D511yescharacteristic
191C2×#67—101no—
192C22×Dic3—21no—
193C22×Dic3C22⋊D511yescharacteristic
194C22×Dic3C22⋊D511yescharacteristic
195C2×D12—51no—
196C2×C4×D3—101no—
197C2×C3×C8—101no—
198C3×C4⋊C4—51no—
199C3×C4⋊C4—101no—
200C3×C22⋊C4—101no—
201(C2×D3)⋊C4—101no—
202(C2×D3)⋊C4—101no—
203(C2×D3)⋊C4—101no—
204(C2×D3)⋊C4—101no—
205C4⋊Dic3—21no—
206C4⋊Dic3—21no—
207C4⋊Dic3—42no—
208C4⋊Dic3—51no—
209C4⋊Dic3—101no—
210C4⋊Dic3—101no—
211Dic3⋊C4—21no—
212Dic3⋊C4—21no—
213Dic3⋊C4—101no—
214C4×Dic3—101no—
215C2×C3⋊C8—101no—
216C23×C5D3×D411yescharacteristic
217C22×D5—61no—
218C2×C4×C5—22no—
219C2×C4×C5—41no—
220C2×C4×C5—41no—
221C2×C4×C5—41no—
222C2×C4×C5—61no—
223C2×C4×C5—61no—
224C2×C4×C5—61no—
225C2×C4×C5—61no—
226C2×C4×C5—121no—
227C2×C4×C5—121no—
228C2×C4×C5—121no—
229C2×C4×C5—121no—
230C2×C4×C5C2×D1211yescharacteristic
231C2×C4×C5D3×D411yescharacteristic
232C22⋊D5—121no—
233C22⋊D5—121no—
234C2×Dic5—21no—
235C2×Dic5—21no—
236C2×Dic5—61no—
237D20—121no—
238C4×D5—241no—
239Dic10—41no—
240#168—41no—
241#168—121no—
242#126—301no—
243#125—301no—
244#123—301no—
245#123—301no—
246C22⋊Q8—51no—
247C22⋊Q8—301no—
248#121—151no—
249C4×D4—301no—
250C2×C4⋊C4—31no—
251C2×C4⋊C4—31no—
252C2×C4⋊C4—61no—
253#107—301no—
254#106—301no—
255#103—301no—
256#102—301no—
257C22⋊C8—51no—
258C22⋊C8—151no—
259#95—61no—
260#95D3×D511yescharacteristic
261C2×C3×C5—21no—
262C2×C3×C5—21no—
263C2×C3×C5#44911yescharacteristic
264C2×C3×C5#45611yescharacteristic
265C2×C3×C5#45811yescharacteristic
266D15—81no—
267C23×C3C2×C22⋊D511yescharacteristic
268C22×D3—101no—
269C3×Q8—201no—
270C2×C3×C4—22no—
271C2×C3×C4—41no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—101no—
275C2×C3×C4—101no—
276C2×C3×C4D4×D511yescharacteristic
277C2×C3×C4D4×D511yescharacteristic
278#67—201no—
279#67—201no—
280C2×Dic3—21no—
281C2×Dic3—21no—
282C2×Dic3—21no—
283C2×Dic3—21no—
284C2×Dic3—41no—
285C2×Dic3—41no—
286C2×Dic3—41no—
287C2×Dic3—41no—
288C2×Dic3—101no—
289D12—201no—
290C4×D3—401no—
291C3×C8—201no—
292C3⋊C8—201no—
293C22×C5—21no—
294C22×C5—21no—
295C22×C5#88211yescharacteristic
296C22×C5#91411yescharacteristic
297C22×C5#91911yescharacteristic
298C2×D5—121no—
299C2×D5—121no—
300C2×D5—121no—
301C4×C5—21no—
302C4×C5—21no—
303C4×C5—42no—
304C4×C5—121no—
305C4×C5—121no—
306C4×C5—241no—
307Dic5—41no—
308Dic5—41no—
309Dic5—121no—
310C2×Q8—51no—
311C2×D4—151no—
312C2×D4—301no—
313C22×C4—21no—
314C22×C4—31no—
315C22×C4—31no—
316C22×C4—61no—
317C22×C4—301no—
318C22×C4C2×D3×D511yescharacteristic
319C2×C8—101no—
320C2×C8—301no—
321C4⋊C4—51no—
322C4⋊C4—61no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—61no—
326C4⋊C4—101no—
327C4⋊C4—122no—
328C4⋊C4—151no—
329C4⋊C4—301no—
330C4⋊C4—301no—
331C4⋊C4—301no—
332C22⋊C4—101no—
333C22⋊C4—301no—
334C22⋊C4—301no—
335C22⋊C4—301no—
336C22⋊C4—301no—
337C42—301no—
338C3×C5#160911yescharacteristic, complemented, Hall
339C22×C3—21no—
340C22×C3—21no—
341C22×C3#407811yescharacteristic
342C22×C3#408311yescharacteristic
343C22×C3#409611yescharacteristic
344C2×D3—201no—
345C2×D3—201no—
346C2×D3—201no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—42no—
350C3×C4—201no—
351C3×C4—201no—
352Dic3—41no—
353Dic3—41no—
354Dic3—81no—
355Dic3—201no—
356C2×C5—21no—
357C2×C5—21no—
358C2×C5#474211yescharacteristic
359C2×C5#481011yescharacteristic
360C2×C5#482611yescharacteristic
361D5—241no—
362C23—301no—
363C23D3×C22⋊D511yescharacteristic
364Q8—201no—
365D4—601no—
366D4—601no—
367D4—601no—
368C2×C4—22no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—61no—
373C2×C4—61no—
374C2×C4—61no—
375C2×C4—61no—
376C2×C4—101no—
377C2×C4—101no—
378C2×C4—121no—
379C2×C4—121no—
380C2×C4—121no—
381C2×C4—121no—
382C2×C4—301no—
383C2×C4—1201no—
384C2×C4D5×D1211yescharacteristic
385C2×C4#677711yescharacteristic
386C8—201no—
387C8—601no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3#6532611yescharacteristic
391C2×C3#6534211yescharacteristic
392C2×C3#6538411yescharacteristic
393D3—401no—
394C5#6832811yescharacteristic, complemented, Sylow
395C22—21no—
396C22—21no—
397C22—601no—
398C22—601no—
399C22—601no—
400C22#9147511yescharacteristic
401C22#9149611yescharacteristic
402C22#9151911yescharacteristic
403C4—21no—
404C4—21no—
405C4—42no—
406C4—121no—
407C4—121no—
408C4—201no—
409C4—201no—
410C4—241no—
411C4—601no—
412C3#1060050411yescharacteristic, complemented, Sylow
413C2—21no—
414C2—21no—
415C2—1201no—
416C2#1174712211yescharacteristic
417C2#1174713511yescharacteristic
418C2#1174751711yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#95C22
socleC22×C3×C5#120
prime radical#91819C22
hypercenter#95D3×D5
hypocenterC3×C5#1609
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C5×#4661C2semidirect
4. #11748401C2semidirect
6. C3×#64672C2semidirect
7. #11745952C2semidirect
34. #64672D3semidirect
67. #4661D5semidirect
338. C3×C5#1609semidirect
394. C5#68328semidirect
412. C3#10600504semidirect

Maximal subgroups

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

subgroupindex
#117544832
C5×#46612
#117484622
#117484012
#117462722
C3×#646722
#117459522
#106005043
#683285