Finite Group Databasebeta

← #14288328

Subgroups — #14288328

Order 1920.

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

normal subgroups only

This group has 432 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#11751144C211yesmaximal, characteristic, complemented
3#11751134C211yesmaximal, characteristic
4#11751082C211yesmaximal, characteristic, complemented
5#11746359C211yesmaximal, characteristic, complemented
6#11746358C211yesmaximal, characteristic
7#11746349C211yesmaximal, characteristic, complemented
8#10602679—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
19C2×#6712—21no—
20#91119—21no—
21#91116—21no—
22#91115—21no—
23#91115C2211yescharacteristic
24#91114C2211yescharacteristic
25#91114C2211yescharacteristic
26#91092—21no—
27#91091—21no—
28#71886—51nomaximal, Hall
29C5×#539D311yescharacteristic
30#65332—31no—
31#65322—31no—
32#65272—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—
61#6712—42no—
62C2×C3⋊#168—21no—
63C2×C3⋊#168—21no—
64C3×#539D511yescharacteristic
65#5043—51no—
66#5033—51no—
67#4981—51no—
68#4538—51no—
69#4537—51no—
70#4528—51no—
71C5×#126—21no—
72C5×#125—21no—
73C5×#123—21no—
74C5×#123—21no—
75C5×C22⋊Q8—21no—
76C5×C22⋊Q8C2×D311yescharacteristic
77C5×#121C2×D311yescharacteristic
78C4×C5×D4—21no—
79C2×C5×C4⋊C4C2×D311yescharacteristic
80C2×C4⋊Dic5—31no—
81C2×#683—61no—
82#3967—61no—
83#3964—61no—
84#3963—31no—
85#3963—61no—
86C22⋊#168—31no—
87C22⋊#168—31no—
88#3940—61no—
89#3939—61no—
90#1609—151noSylow
91C23×C3×C5—21no—
92C23×C3×C5C2×D411yescharacteristic
93C3×C5×Q8—41no—
94C3×C5×D4—41no—
95C3×C5×D4—41no—
96C3×C5×D4—41no—
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—21no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—81no—
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×Dic15—22no—
110C2×Dic15—41no—
111C2×Dic15—41no—
112C2×Dic15—41no—
113C2×Dic15—41no—
114C2×Dic15—41no—
115C3⋊#168—41no—
116C3⋊#168—41no—
117C3×#126—21no—
118C3×#125—21no—
119C3×#123—21no—
120C3×#123—21no—
121C3×C22⋊Q8—21no—
122C3×C22⋊Q8C2×D511yescharacteristic
123C3×#121C2×D511yescharacteristic
124C3×C4×D4—21no—
125C2×C3×C4⋊C4C2×D511yescharacteristic
126C2×C4⋊Dic3—51no—
127C2×Dic3⋊C4—101no—
128#835—101no—
129#832—101no—
130C3⋊#95—51no—
131C3⋊#95—101no—
132#830—51no—
133#830—51no—
134#808—101no—
135#807—101no—
136C2×C5×Q8#6711yescharacteristic
137C2×C5×D4—21no—
138C2×C5×D4#6711yescharacteristic
139C22×C4×C5—21no—
140C22×C4×C5#6711yescharacteristic
141C22×C4×C5#6711yescharacteristic
142C22×C4×C5C22×D311yescharacteristic
143C22×Dic5—61no—
144C22×Dic5—61no—
145C5×C4⋊C4—21no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4—21no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4—21no—
150C5×C4⋊C4—21no—
151C5×C4⋊C4#6711yescharacteristic
152C5×C4⋊C4#6711yescharacteristic
153C5×C22⋊C4—21no—
154C5×C22⋊C4—21no—
155C5×C22⋊C4—21no—
156C5×C22⋊C4—21no—
157C5×C22⋊C4—21no—
158C42×C5—21no—
159C4⋊Dic5—61no—
160C4⋊Dic5—61no—
161#683—122no—
162C2×#168—61no—
163C2×#168—61no—
164#539D1511yescharacteristic
165#483—151no—
166#480—151no—
167#398—151no—
168#328—151no—
169#327—151no—
170#324—151no—
171C22×C3×C5—21no—
172C22×C3×C5—21no—
173C22×C3×C5—41no—
174C22×C3×C5—41no—
175C22×C3×C5—41no—
176C22×C3×C5#12011yescharacteristic
177C22×C3×C5#13511yescharacteristic
178C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
179C3×C4×C5—21no—
180C3×C4×C5—21no—
181C3×C4×C5—41no—
182C3×C4×C5—41no—
183C3×C4×C5—41no—
184C3×C4×C5—41no—
185C3×C4×C5—41no—
186Dic15—42no—
187Dic15—81no—
188C2×C3×Q8C22⋊D511yescharacteristic
189C2×C3×D4—21no—
190C2×C3×D4C22⋊D511yescharacteristic
191C22×C3×C4—21no—
192C22×C3×C4C22⋊D511yescharacteristic
193C22×C3×C4C22⋊D511yescharacteristic
194C22×C3×C4C22×D511yescharacteristic
195C22×Dic3—101no—
196C22×Dic3—101no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4—21no—
202C3×C4⋊C4—21no—
203C3×C4⋊C4C22⋊D511yescharacteristic
204C3×C4⋊C4C22⋊D511yescharacteristic
205C3×C22⋊C4—21no—
206C3×C22⋊C4—21no—
207C3×C22⋊C4—21no—
208C3×C22⋊C4—21no—
209C3×C22⋊C4—21no—
210C3×C42—21no—
211C4⋊Dic3—101no—
212C4⋊Dic3—101no—
213Dic3⋊C4—202no—
214C2×C3⋊C8—101no—
215C2×C3⋊C8—101no—
216C23×C5—21no—
217C23×C5C2×#6711yescharacteristic
218C5×Q8—41no—
219C5×D4—41no—
220C5×D4—41no—
221C5×D4—41no—
222C2×C4×C5—21no—
223C2×C4×C5—21no—
224C2×C4×C5—21no—
225C2×C4×C5—21no—
226C2×C4×C5—21no—
227C2×C4×C5—21no—
228C2×C4×C5—21no—
229C2×C4×C5—41no—
230C2×C4×C5—41no—
231C2×C4×C5—81no—
232C2×C4×C5C2×#6711yescharacteristic
233C2×C4×C5C2×#6711yescharacteristic
234C2×Dic5—62no—
235C2×Dic5—121no—
236C2×Dic5—121no—
237C2×Dic5—121no—
238C2×Dic5—121no—
239C2×Dic5—121no—
240#168—121no—
241#168—121no—
242#126—21no—
243#125—21no—
244#123—21no—
245#123—21no—
246C22⋊Q8—21no—
247C22⋊Q8C2×D1511yescharacteristic
248#121C2×D1511yescharacteristic
249C4×D4—21no—
250C2×C4⋊C4—151no—
251C2×C4⋊C4—301no—
252C2×C4⋊C4C2×D1511yescharacteristic
253#107—301no—
254#106—301no—
255#103—301no—
256#102—301no—
257C22⋊C8—151no—
258C22⋊C8—151no—
259#95—151no—
260#95—301no—
261C2×C3×C5—21no—
262C2×C3×C5—21no—
263C2×C3×C5—81no—
264C2×C3×C5#44911yescharacteristic
265C2×C3×C5#45611yescharacteristic
266C2×C3×C5#45811yescharacteristic
267C23×C3—21no—
268C23×C3C2×C22⋊D511yescharacteristic
269C3×Q8—41no—
270C3×D4—41no—
271C3×D4—41no—
272C3×D4—41no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—41no—
281C2×C3×C4—41no—
282C2×C3×C4—81no—
283C2×C3×C4C2×C22⋊D511yescharacteristic
284C2×C3×C4C2×C22⋊D511yescharacteristic
285C2×Dic3—102no—
286C2×Dic3—201no—
287C2×Dic3—201no—
288C2×Dic3—201no—
289C2×Dic3—201no—
290C2×Dic3—201no—
291C3⋊C8—201no—
292C3⋊C8—201no—
293C22×C5—21no—
294C22×C5—21no—
295C22×C5—41no—
296C22×C5—41no—
297C22×C5—41no—
298C22×C5#94911yescharacteristic
299C22×C5#95011yescharacteristic
300C22×C5#95311yescharacteristic
301C4×C5—21no—
302C4×C5—21no—
303C4×C5—41no—
304C4×C5—41no—
305C4×C5—41no—
306C4×C5—41no—
307C4×C5—41no—
308Dic5—122no—
309Dic5—241no—
310C2×Q8#122011yescharacteristic
311C2×D4—21no—
312C2×D4#122011yescharacteristic
313C22×C4—21no—
314C22×C4—301no—
315C22×C4—301no—
316C22×C4#122011yescharacteristic
317C22×C4#122011yescharacteristic
318C22×C4C22×D1511yescharacteristic
319C2×C8—301no—
320C2×C8—301no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—21no—
325C4⋊C4—21no—
326C4⋊C4—21no—
327C4⋊C4—301no—
328C4⋊C4—301no—
329C4⋊C4—602no—
330C4⋊C4#122011yescharacteristic
331C4⋊C4#122011yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—21no—
337C42—21no—
338C3×C5#160911yescharacteristic, complemented, Hall
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—41no—
342C22×C3—41no—
343C22×C3—41no—
344C22×C3#409511yescharacteristic
345C22×C3#409611yescharacteristic
346C22×C3#409911yescharacteristic
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—41no—
350C3×C4—41no—
351C3×C4—41no—
352C3×C4—41no—
353C3×C4—41no—
354Dic3—202no—
355Dic3—401no—
356C2×C5—21no—
357C2×C5—21no—
358C2×C5—81no—
359C2×C5#523811yescharacteristic
360C2×C5#524311yescharacteristic
361C2×C5#524611yescharacteristic
362C23—21no—
363C23C2×#122011yescharacteristic
364Q8—41no—
365D4—41no—
366D4—41no—
367D4—41no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—81no—
378C2×C4—302no—
379C2×C4—601no—
380C2×C4—601no—
381C2×C4—601no—
382C2×C4—601no—
383C2×C4—601no—
384C2×C4C2×#122011yescharacteristic
385C2×C4C2×#122011yescharacteristic
386C8—601no—
387C8—601no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—81no—
391C2×C3#6552711yescharacteristic
392C2×C3#6553211yescharacteristic
393C2×C3#6553511yescharacteristic
394C5#7188611yescharacteristic, complemented, Sylow
395C22—21no—
396C22—21no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22#9183811yescharacteristic
401C22#9183911yescharacteristic
402C22#9184211yescharacteristic
403C4—21no—
404C4—21no—
405C4—41no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—41no—
410C4—602no—
411C4—1201no—
412C3#1060267911yescharacteristic, complemented, Sylow
413C2—21no—
414C2—21no—
415C2—81no—
416C2#1175133911yescharacteristic
417C2#1175134411yescharacteristic
418C2#1175134711yescharacteristic
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#1609
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. #11751144C2semidirect
4. #11751082C2semidirect
5. #11746359C2semidirect
7. #11746349C2semidirect
338. C3×C5#1609semidirect
394. C5#71886semidirect
412. C3#10602679semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5392
#117511442
#117511342
#117510822
#117463592
#117463582
#117463492
#106026793
#718865