Finite Group Databasebeta

← #14288325

Subgroups — #14288325

Order 1920.

432 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 83 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#11756404C211yesmaximal, characteristic
2C3×C5×#483C211yesmaximal, characteristic, complemented
3#11751084C211yesmaximal, characteristic, complemented
4#11751068C211yesmaximal, characteristic
5#11746359C211yesmaximal, characteristic, complemented
6#11746291C211yesmaximal, characteristic
7#11746290C211yesmaximal, characteristic, complemented
8#10601967—31nomaximal, Hall
9C3×C5×C22⋊Q8C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11#91835—21no—
12#91819C2211yescharacteristic
13C2×#6712—21no—
14C2×#6712C2211yescharacteristic
15#91787—21no—
16#91783—21no—
17#91779—21no—
18#91775—21no—
19#91770—21no—
20C3×C5×#106—21no—
21C3×C5×#103—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23#91115—21no—
24#91115C2211yescharacteristic
25#91114C2211yescharacteristic
26#91093—21no—
27#91091—21no—
28#71174—51nomaximal, Hall
29#65979—31no—
30C5×#483D311yescharacteristic, complemented
31#65269—31no—
32#65256—31no—
33#64758—31no—
34#64690—31no—
35#64689—31no—
36C2×C3×C5×Q8D411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C2×#1220—21no—
40C22×Dic15—21no—
41C22×Dic15D411yescharacteristic
42C22×Dic15D411yescharacteristic
43C2×D60D411yescharacteristic
44C2×C4×D15—21no—
45C2×C3×C5×C8—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4D411yescharacteristic
50C3×C5×C22⋊C4—21no—
51#6714—21no—
52#6714—21no—
53#6714—21no—
54#6714—21no—
55C4⋊Dic15—21no—
56C4⋊Dic15—21no—
57C4⋊Dic15D411yescharacteristic
58#6712—21no—
59#6712—21no—
60#6712—21no—
61#6712—42no—
62C4×Dic15—21no—
63C2×C3⋊#168—21no—
64#5645—51no—
65C3×#483D511yescharacteristic, complemented
66#4983—51no—
67#4967—51no—
68#4538—51no—
69#4470—51no—
70#4469—51no—
71C5×C22⋊Q8C2×D311yescharacteristic
72C2×C5×C4⋊C4C2×D311yescharacteristic
73#4092—61no—
74#4076—31no—
75C2×#683—31no—
76C2×#683—61no—
77#4044—61no—
78#4040—61no—
79#4036—61no—
80#4032—61no—
81#4027—61no—
82C5×#106—21no—
83C5×#103—21no—
84C5×C22⋊C8C2×D311yescharacteristic
85#3963—31no—
86#3963—61no—
87C22⋊#168—31no—
88#3941—61no—
89#3939—61no—
90#1609—151noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×D15—21no—
93C3×C5×Q8—41no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5—41no—
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102#1220—41no—
103#1220—41no—
104C2×Dic15—22no—
105C2×Dic15—21no—
106C2×Dic15—21no—
107C2×Dic15—21no—
108C2×Dic15—21no—
109C2×Dic15—21no—
110C2×Dic15—41no—
111C2×Dic15—41no—
112C2×Dic15—41no—
113D60—41no—
114C4×D15—81no—
115C3×C5×C8—41no—
116C3⋊#168—41no—
117C3×C22⋊Q8C2×D511yescharacteristic
118C2×C3×C4⋊C4C2×D511yescharacteristic
119#946—101no—
120#930—51no—
121C2×Dic3⋊C4—51no—
122C2×Dic3⋊C4—101no—
123#898—101no—
124#894—101no—
125#890—101no—
126#886—101no—
127#67⋊C4—101no—
128C3×#106—21no—
129C3×#103—21no—
130C3×C22⋊C8C2×D511yescharacteristic
131C3⋊#95—51no—
132C3⋊#95—101no—
133#830—51no—
134#809—101no—
135#807—101no—
136C2×C5×Q8#6711yescharacteristic
137C22×C4×C5—21no—
138C22×C4×C5C22×D311yescharacteristic
139C2×C22⋊D5—61no—
140C22×Dic5—31no—
141C22×Dic5—31no—
142C22×Dic5—61no—
143C2×D20—31no—
144C2×C4×D5—61no—
145C2×C5×C8—21no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4—21no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4#6711yescharacteristic
150C5×C22⋊C4—21no—
151#685—61no—
152#685—61no—
153#685—61no—
154#685—61no—
155C4⋊Dic5—31no—
156C4⋊Dic5—61no—
157C4⋊Dic5—61no—
158#683—61no—
159#683—61no—
160#683—61no—
161#683—122no—
162C4×Dic5—61no—
163C2×#168—61no—
164#539—151no—
165#483D1511yescharacteristic, complemented
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#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—41no—
182C3×C4×C5—41no—
183C3×C4×C5—81no—
184Dic15—42no—
185Dic15—41no—
186Dic15—41no—
187Dic15—41no—
188C2×C3×Q8C22⋊D511yescharacteristic
189C22×C3×C4—21no—
190C22×C3×C4C22×D511yescharacteristic
191C2×#67—101no—
192C22×Dic3—51no—
193C22×Dic3—51no—
194C22×Dic3—101no—
195C2×D12—51no—
196C2×C4×D3—101no—
197C2×C3×C8—21no—
198C3×C4⋊C4—21no—
199C3×C4⋊C4—21no—
200C3×C4⋊C4—21no—
201C3×C4⋊C4C22⋊D511yescharacteristic
202C3×C22⋊C4—21no—
203(C2×D3)⋊C4—101no—
204(C2×D3)⋊C4—101no—
205(C2×D3)⋊C4—101no—
206(C2×D3)⋊C4—101no—
207C4⋊Dic3—51no—
208C4⋊Dic3—101no—
209C4⋊Dic3—101no—
210Dic3⋊C4—101no—
211Dic3⋊C4—101no—
212Dic3⋊C4—101no—
213Dic3⋊C4—202no—
214C4×Dic3—101no—
215C2×C3⋊C8—101no—
216C23×C5D3×D411yescharacteristic
217C22×D5—61no—
218C5×Q8—41no—
219C2×C4×C5—21no—
220C2×C4×C5—21no—
221C2×C4×C5—41no—
222C2×C4×C5—41no—
223C2×C4×C5—41no—
224C2×C4×C5—41no—
225C2×C4×C5D3×D411yescharacteristic
226C2×C4×C5C2×#6711yescharacteristic
227C22⋊D5—121no—
228C22⋊D5—121no—
229C2×Dic5—62no—
230C2×Dic5—61no—
231C2×Dic5—61no—
232C2×Dic5—61no—
233C2×Dic5—61no—
234C2×Dic5—61no—
235C2×Dic5—121no—
236C2×Dic5—121no—
237C2×Dic5—121no—
238D20—121no—
239C4×D5—241no—
240C5×C8—41no—
241#168—121no—
242#126—301no—
243#125—301no—
244#123—301no—
245#123—301no—
246C22⋊Q8—301no—
247C22⋊Q8C2×D1511yescharacteristic
248#121—151no—
249C4×D4—301no—
250C2×C4⋊C4—151no—
251C2×C4⋊C4—301no—
252C2×C4⋊C4C2×D1511yescharacteristic
253#107—301no—
254#106—21no—
255#103—21no—
256#102—301no—
257C22⋊C8—151no—
258C22⋊C8C2×D1511yescharacteristic
259#95—151no—
260#95—301no—
261C2×C3×C5—21no—
262C2×C3×C5—21no—
263C2×C3×C5#44911yescharacteristic
264C2×C3×C5#45611yescharacteristic
265C2×C3×C5#45811yescharacteristic
266D15—81no—
267C23×C3D4×D511yescharacteristic
268C22×D3—101no—
269C3×Q8—41no—
270C2×C3×C4—21no—
271C2×C3×C4—21no—
272C2×C3×C4—41no—
273C2×C3×C4—41no—
274C2×C3×C4—41no—
275C2×C3×C4—41no—
276C2×C3×C4D4×D511yescharacteristic
277C2×C3×C4C2×C22⋊D511yescharacteristic
278#67—201no—
279#67—201no—
280C2×Dic3—102no—
281C2×Dic3—101no—
282C2×Dic3—101no—
283C2×Dic3—101no—
284C2×Dic3—101no—
285C2×Dic3—101no—
286C2×Dic3—201no—
287C2×Dic3—201no—
288C2×Dic3—201no—
289D12—201no—
290C4×D3—401no—
291C3×C8—41no—
292C3⋊C8—201no—
293C22×C5—21no—
294C22×C5—21no—
295C22×C5#91411yescharacteristic
296C22×C5#91611yescharacteristic
297C22×C5#93711yescharacteristic
298C2×D5—121no—
299C2×D5—121no—
300C2×D5—121no—
301C4×C5—21no—
302C4×C5—21no—
303C4×C5—41no—
304C4×C5—41no—
305C4×C5—81no—
306Dic5—122no—
307Dic5—121no—
308Dic5—121no—
309Dic5—121no—
310C2×Q8#122011yescharacteristic
311C2×D4—151no—
312C2×D4—301no—
313C22×C4—21no—
314C22×C4—151no—
315C22×C4—151no—
316C22×C4—301no—
317C22×C4—301no—
318C22×C4C22×D1511yescharacteristic
319C2×C8—21no—
320C2×C8—301no—
321C4⋊C4—21no—
322C4⋊C4—21no—
323C4⋊C4—21no—
324C4⋊C4—151no—
325C4⋊C4—301no—
326C4⋊C4—301no—
327C4⋊C4—301no—
328C4⋊C4—301no—
329C4⋊C4—301no—
330C4⋊C4—602no—
331C4⋊C4#122011yescharacteristic
332C22⋊C4—21no—
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#406011yescharacteristic
342C22×C3#406211yescharacteristic
343C22×C3#408311yescharacteristic
344C2×D3—201no—
345C2×D3—201no—
346C2×D3—201no—
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—41no—
350C3×C4—41no—
351C3×C4—81no—
352Dic3—202no—
353Dic3—201no—
354Dic3—201no—
355Dic3—201no—
356C2×C5—21no—
357C2×C5—21no—
358C2×C5#505311yescharacteristic
359C2×C5#517211yescharacteristic
360C2×C5#520511yescharacteristic
361D5—241no—
362C23—301no—
363C23D4×D1511yescharacteristic
364Q8—41no—
365D4—601no—
366D4—601no—
367D4—601no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—41no—
374C2×C4—302no—
375C2×C4—301no—
376C2×C4—301no—
377C2×C4—301no—
378C2×C4—301no—
379C2×C4—301no—
380C2×C4—601no—
381C2×C4—601no—
382C2×C4—601no—
383C2×C4—1201no—
384C2×C4D4×D1511yescharacteristic
385C2×C4C2×#122011yescharacteristic
386C8—41no—
387C8—601no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3#6534211yescharacteristic
391C2×C3#6546111yescharacteristic
392C2×C3#6549411yescharacteristic
393D3—401no—
394C5#7117411yescharacteristic, complemented, Sylow
395C22—21no—
396C22—21no—
397C22—601no—
398C22—601no—
399C22—601no—
400C22#9180311yescharacteristic
401C22#9180511yescharacteristic
402C22#9182611yescharacteristic
403C4—21no—
404C4—21no—
405C4—41no—
406C4—41no—
407C4—81no—
408C4—602no—
409C4—601no—
410C4—601no—
411C4—601no—
412C3#1060196711yescharacteristic, complemented, Sylow
413C2—21no—
414C2—21no—
415C2—1201no—
416C2#1175115411yescharacteristic
417C2#1175127311yescharacteristic
418C2#1175130611yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#483C2
socleC22×C3×C5#120
prime radical#91819C22
hypercenter#483D15
hypocenterC3×C5#1609
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. C3×C5×#483C2semidirect
3. #11751084C2semidirect
5. #11746359C2semidirect
7. #11746290C2semidirect
30. C5×#483D3semidirect
65. C3×#483D5semidirect
165. #483D15semidirect
338. C3×C5#1609semidirect
394. C5#71174semidirect
412. C3#10601967semidirect

Maximal subgroups

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

subgroupindex
#117564042
C3×C5×#4832
#117510842
#117510682
#117463592
#117462912
#117462902
#106019673
#711745