Finite Group Databasebeta

← #14288610

Subgroups — #14288610

Order 1920.

416 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 95 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×C5×#539C211yesmaximal, characteristic
2#11751145C211yesmaximal, characteristic, complemented
3#11751135C211yesmaximal, characteristic
4#11751087C211yesmaximal, characteristic, complemented
5#11746359C211yesmaximal, characteristic, complemented
6#11746358C211yesmaximal, characteristic
7#11746349C211yesmaximal, characteristic, complemented
8#10602680—31nomaximal, Hall
9C3×C5×#126—21no—
10C3×C5×#125—21no—
11C3×C5×#123—21no—
12C3×C5×#123—21no—
13C3×C5×C22⋊Q8—21no—
14C3×C5×C22⋊Q8C2211yescharacteristic
15C3×C5×#121C2211yescharacteristic
16C3×C4×C5×D4—21no—
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C4⋊Dic15C2211yescharacteristic
19#91119—21no—
20#91116—21no—
21#91115—21no—
22#91115—21no—
23#91115C2211yescharacteristic
24#91114C2211yescharacteristic
25#91114C2211yescharacteristic
26#91092—21no—
27#91091—21no—
28#71887—51nomaximal, Hall
29C5×#539D311yescharacteristic
30#65333—31no—
31#65323—31no—
32#65275—31no—
33#64758—31no—
34#64757—31no—
35#64748—31no—
36C2×C3×C5×Q8D411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4D411yescharacteristic
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5D411yescharacteristic
41C22×C3×C4×C5D411yescharacteristic
42C22×C3×C4×C5C2311yescharacteristic
43C22×Dic15—21no—
44C22×Dic15—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4D411yescharacteristic
52C3×C5×C4⋊C4D411yescharacteristic
53C3×C5×C22⋊C4—21no—
54C3×C5×C22⋊C4—21no—
55C3×C5×C22⋊C4—21no—
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4—21no—
58C3×C42×C5—21no—
59C4⋊Dic15—21no—
60C4⋊Dic15—21no—
61C2×C3⋊#168—21no—
62C2×C3⋊#168—21no—
63C3×#539D511yescharacteristic
64#5044—51no—
65#5034—51no—
66#4986—51no—
67#4538—51no—
68#4537—51no—
69#4528—51no—
70C5×#126—21no—
71C5×#125—21no—
72C5×#123—21no—
73C5×#123—21no—
74C5×C22⋊Q8—21no—
75C5×C22⋊Q8C2×D311yescharacteristic
76C5×#121C2×D311yescharacteristic
77C4×C5×D4—21no—
78C2×C5×C4⋊C4C2×D311yescharacteristic
79C2×C4⋊Dic5—31no—
80#3967—61no—
81#3964—61no—
82#3963—31no—
83#3963—61no—
84#3963—61no—
85C22⋊#168—31no—
86C22⋊#168—31no—
87#3940—61no—
88#3939—61no—
89#1615—151noSylow
90C23×C3×C5—21no—
91C23×C3×C5C2×D411yescharacteristic
92C3×C5×Q8—41no—
93C3×C5×D4—41no—
94C3×C5×D4—41no—
95C3×C5×D4—41no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—21no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—81no—
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×Dic15—41no—
109C2×Dic15—41no—
110C2×Dic15—42no—
111C2×Dic15—41no—
112C2×Dic15—41no—
113C3⋊#168—41no—
114C3⋊#168—41no—
115C3×#126—21no—
116C3×#125—21no—
117C3×#123—21no—
118C3×#123—21no—
119C3×C22⋊Q8—21no—
120C3×C22⋊Q8C2×D511yescharacteristic
121C3×#121C2×D511yescharacteristic
122C3×C4×D4—21no—
123C2×C3×C4⋊C4C2×D511yescharacteristic
124C2×C4⋊Dic3—51no—
125#835—101no—
126#832—101no—
127C3⋊#95—51no—
128C3⋊#95—101no—
129C3⋊#95—101no—
130#830—51no—
131#830—51no—
132#808—101no—
133#807—101no—
134C2×C5×Q8#6711yescharacteristic
135C2×C5×D4—21no—
136C2×C5×D4#6711yescharacteristic
137C22×C4×C5—21no—
138C22×C4×C5#6711yescharacteristic
139C22×C4×C5#6711yescharacteristic
140C22×C4×C5C22×D311yescharacteristic
141C22×Dic5—61no—
142C22×Dic5—61no—
143C5×C4⋊C4—21no—
144C5×C4⋊C4—21no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4—21no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4#6711yescharacteristic
150C5×C4⋊C4#6711yescharacteristic
151C5×C22⋊C4—21no—
152C5×C22⋊C4—21no—
153C5×C22⋊C4—21no—
154C5×C22⋊C4—21no—
155C5×C22⋊C4—21no—
156C42×C5—21no—
157C4⋊Dic5—61no—
158C4⋊Dic5—61no—
159C2×#168—61no—
160C2×#168—61no—
161#539D1511yescharacteristic
162#484—151no—
163#481—151no—
164#400—151no—
165#328—151no—
166#327—151no—
167#324—151no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5—41no—
171C22×C3×C5—41no—
172C22×C3×C5—41no—
173C22×C3×C5#12011yescharacteristic
174C22×C3×C5#13511yescharacteristic
175C22×C3×C5#13711yescharacteristic
176C3×C4×C5—21no—
177C3×C4×C5—21no—
178C3×C4×C5—41no—
179C3×C4×C5—41no—
180C3×C4×C5—41no—
181C3×C4×C5—41no—
182C3×C4×C5—41no—
183Dic15—81no—
184Dic15—81no—
185C2×C3×Q8C22⋊D511yescharacteristic
186C2×C3×D4—21no—
187C2×C3×D4C22⋊D511yescharacteristic
188C22×C3×C4—21no—
189C22×C3×C4C22⋊D511yescharacteristic
190C22×C3×C4C22⋊D511yescharacteristic
191C22×C3×C4C22×D511yescharacteristic
192C22×Dic3—101no—
193C22×Dic3—101no—
194C3×C4⋊C4—21no—
195C3×C4⋊C4—21no—
196C3×C4⋊C4—21no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4C22⋊D511yescharacteristic
201C3×C4⋊C4C22⋊D511yescharacteristic
202C3×C22⋊C4—21no—
203C3×C22⋊C4—21no—
204C3×C22⋊C4—21no—
205C3×C22⋊C4—21no—
206C3×C22⋊C4—21no—
207C3×C42—21no—
208C4⋊Dic3—101no—
209C4⋊Dic3—101no—
210C2×C3⋊C8—101no—
211C2×C3⋊C8—101no—
212C23×C5—21no—
213C23×C5C2×#6711yescharacteristic
214C5×Q8—41no—
215C5×D4—41no—
216C5×D4—41no—
217C5×D4—41no—
218C2×C4×C5—21no—
219C2×C4×C5—21no—
220C2×C4×C5—21no—
221C2×C4×C5—21no—
222C2×C4×C5—21no—
223C2×C4×C5—21no—
224C2×C4×C5—21no—
225C2×C4×C5—41no—
226C2×C4×C5—41no—
227C2×C4×C5—81no—
228C2×C4×C5C2×#6711yescharacteristic
229C2×C4×C5C2×#6711yescharacteristic
230C2×Dic5—121no—
231C2×Dic5—121no—
232C2×Dic5—122no—
233C2×Dic5—121no—
234C2×Dic5—121no—
235#168—121no—
236#168—121no—
237#126—21no—
238#125—21no—
239#123—21no—
240#123—21no—
241C22⋊Q8—21no—
242C22⋊Q8C2×D1511yescharacteristic
243#121C2×D1511yescharacteristic
244C4×D4—21no—
245C2×C4⋊C4—151no—
246C2×C4⋊C4C2×D1511yescharacteristic
247#107—301no—
248#106—301no—
249#103—301no—
250#102—301no—
251C22⋊C8—151no—
252C22⋊C8—151no—
253#95—151no—
254#95—301no—
255#95—301no—
256C2×C3×C5—21no—
257C2×C3×C5—21no—
258C2×C3×C5—81no—
259C2×C3×C5#45211yescharacteristic
260C2×C3×C5#45411yescharacteristic
261C2×C3×C5#45811yescharacteristic
262C23×C3—21no—
263C23×C3C2×C22⋊D511yescharacteristic
264C3×Q8—41no—
265C3×D4—41no—
266C3×D4—41no—
267C3×D4—41no—
268C2×C3×C4—21no—
269C2×C3×C4—21no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—41no—
276C2×C3×C4—41no—
277C2×C3×C4—81no—
278C2×C3×C4C2×C22⋊D511yescharacteristic
279C2×C3×C4C2×C22⋊D511yescharacteristic
280C2×Dic3—201no—
281C2×Dic3—201no—
282C2×Dic3—202no—
283C2×Dic3—201no—
284C2×Dic3—201no—
285C3⋊C8—201no—
286C3⋊C8—201no—
287C22×C5—21no—
288C22×C5—21no—
289C22×C5—41no—
290C22×C5—41no—
291C22×C5—41no—
292C22×C5#95011yescharacteristic
293C22×C5#95111yescharacteristic
294C22×C5#95311yescharacteristic
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—41no—
298C4×C5—41no—
299C4×C5—41no—
300C4×C5—41no—
301C4×C5—41no—
302Dic5—241no—
303Dic5—241no—
304C2×Q8#122011yescharacteristic
305C2×D4—21no—
306C2×D4#122011yescharacteristic
307C22×C4—21no—
308C22×C4—301no—
309C22×C4—301no—
310C22×C4#122011yescharacteristic
311C22×C4#122011yescharacteristic
312C22×C4C22×D1511yescharacteristic
313C2×C8—301no—
314C2×C8—301no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—301no—
322C4⋊C4—301no—
323C4⋊C4#122011yescharacteristic
324C4⋊C4#122011yescharacteristic
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—21no—
330C42—21no—
331C3×C5#161511yescharacteristic, complemented, Hall
332C22×C3—21no—
333C22×C3—21no—
334C22×C3—41no—
335C22×C3—41no—
336C22×C3—41no—
337C22×C3#409611yescharacteristic
338C22×C3#409711yescharacteristic
339C22×C3#409911yescharacteristic
340C3×C4—21no—
341C3×C4—21no—
342C3×C4—41no—
343C3×C4—41no—
344C3×C4—41no—
345C3×C4—41no—
346C3×C4—41no—
347Dic3—401no—
348Dic3—401no—
349C2×C5—21no—
350C2×C5—21no—
351C2×C5—81no—
352C2×C5#523911yescharacteristic
353C2×C5#524311yescharacteristic
354C2×C5#524511yescharacteristic
355C23—21no—
356C23C2×#122011yescharacteristic
357Q8—41no—
358D4—41no—
359D4—41no—
360D4—41no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—81no—
371C2×C4—601no—
372C2×C4—601no—
373C2×C4—602no—
374C2×C4—601no—
375C2×C4—601no—
376C2×C4C2×#122011yescharacteristic
377C2×C4C2×#122011yescharacteristic
378C8—601no—
379C8—601no—
380C2×C3—21no—
381C2×C3—21no—
382C2×C3—81no—
383C2×C3#6552811yescharacteristic
384C2×C3#6553211yescharacteristic
385C2×C3#6553411yescharacteristic
386C5#7188711yescharacteristic, complemented, Sylow
387C22—21no—
388C22—21no—
389C22—41no—
390C22—41no—
391C22—41no—
392C22#9183911yescharacteristic
393C22#9184011yescharacteristic
394C22#9184211yescharacteristic
395C4—21no—
396C4—21no—
397C4—41no—
398C4—41no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—1201no—
403C4—1201no—
404C3#1060268011yescharacteristic, complemented, Sylow
405C2—21no—
406C2—21no—
407C2—81no—
408C2#1175134011yescharacteristic
409C2#1175134411yescharacteristic
410C2#1175134611yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#539C2
socleC22×C3×C5#120
prime radicalC3×C5×#121C22
hypercenter#539D15
hypocenterC3×C5#1615
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #539

Complements

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

NH ≅ G/Ntype
2. #11751145C2semidirect
4. #11751087C2semidirect
5. #11746359C2semidirect
7. #11746349C2semidirect
331. C3×C5#1615semidirect
386. C5#71887semidirect
404. C3#10602680semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5392
#117511452
#117511352
#117510872
#117463592
#117463582
#117463492
#106026803
#718875