Finite Group Databasebeta

← #14288368

Subgroups — #14288368

Order 1920.

432 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 84 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×#65979C211yesmaximal, characteristic
2C5×#5043C211yesmaximal, characteristic, complemented
3#11748588C211yesmaximal, characteristic, complemented
4#11748370C211yesmaximal, characteristic
5#11746359C211yesmaximal, characteristic, complemented
6#11745955C211yesmaximal, characteristic
7#11745951C211yesmaximal, characteristic, complemented
8#10601967—31nomaximal, Hall
9C3×C5×C22⋊Q8C2211yescharacteristic
10C2×C5×C4⋊Dic3C2211yescharacteristic
11C3×#4092—21no—
12C3×#4076C2211yescharacteristic
13C2×C3×#683C2211yescharacteristic
14C3×#4044—21no—
15C3×#4040—21no—
16C3×#4036—21no—
17C3×#4032—21no—
18C3×#4027—21no—
19C2×#6669—21no—
20#91115C2211yescharacteristic
21#91114C2211yescharacteristic
22C5×#835—21no—
23C5×#830C2211yescharacteristic
24C5×#808—21no—
25#90994—21no—
26#90989—21no—
27#90964—21no—
28#71886—51nomaximal, Hall
29#65979D311yescharacteristic
30C5×#483—31no—
31#65269—31no—
32#65256—31no—
33#64758—31no—
34#64690—31no—
35#64689—31no—
36C2×C3×C5×Q8D411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C22×C5×Dic3—21no—
40C2×C3×C22⋊D5—21no—
41C22×C3×Dic5D411yescharacteristic
42C22×C3×Dic5D411yescharacteristic
43C2×C3×D20D411yescharacteristic
44C2×C3×C4×D5—21no—
45C3×C5×C4⋊C4—21no—
46C3×C5×C4⋊C4D411yescharacteristic
47C3×C5×C22⋊C4—21no—
48C2×C3⋊#168—21no—
49C5×C4⋊Dic3—21no—
50C5×C4⋊Dic3—21no—
51C2×C5×C3⋊C8—21no—
52C3×#685—21no—
53C3×#685—21no—
54C3×#685—21no—
55C3×#685—21no—
56C3×C4⋊Dic5—21no—
57C3×C4⋊Dic5—21no—
58C3×C4⋊Dic5D411yescharacteristic
59C3×#683—21no—
60C3×#683—21no—
61C3×#683—21no—
62C3×C4×Dic5—21no—
63#6669—42no—
64C3×#539—51no—
65#5043D511yescharacteristic, complemented
66#5033—51no—
67#4981—51no—
68#4538—51no—
69#4537—51no—
70#4528—51no—
71C5×C22⋊Q8C2×D311yescharacteristic
72C2×C5×C4⋊C4—31no—
73#4092—21no—
74#4076C2×D311yescharacteristic
75C2×#683—61no—
76C2×#683C2×D311yescharacteristic
77#4044—21no—
78#4040—21no—
79#4036—21no—
80#4032—21no—
81#4027—21no—
82C5×#106—61no—
83C5×#103—61no—
84C5×C22⋊C8—31no—
85#3963—31no—
86#3963—61no—
87C22⋊#168—31no—
88#3941—61no—
89#3939—61no—
90#1609—151noSylow
91C23×C3×C5C2×D411yescharacteristic
92C22×C3×D5—21no—
93C3×C5×Q8—41no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×Dic15—22no—
100C2×Dic15—41no—
101C2×Dic15—41no—
102C2×C5×Dic3—41no—
103C2×C5×Dic3—41no—
104C2×C5×Dic3—41no—
105C3×C22⋊D5—41no—
106C3×C22⋊D5—41no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—21no—
109C2×C3×Dic5—21no—
110C2×C3×Dic5—21no—
111C2×C3×Dic5—21no—
112C2×C3×Dic5—41no—
113C3×D20—41no—
114C3×C4×D5—81no—
115C3⋊#168—41no—
116C5×C3⋊C8—41no—
117C3×#126—101no—
118C3×#125—101no—
119C3×#123—101no—
120C3×#123—101no—
121C3×C22⋊Q8—101no—
122C3×C22⋊Q8C2×D511yescharacteristic
123C3×#121—51no—
124C3×C4×D4—101no—
125C2×C3×C4⋊C4—51no—
126C2×C4⋊Dic3C2×D511yescharacteristic
127C2×Dic3⋊C4—101no—
128#835—21no—
129#832—101no—
130C3⋊#95—51no—
131C3⋊#95—101no—
132#830—51no—
133#830C2×D511yescharacteristic
134#808—21no—
135#807—101no—
136C2×C5×Q8#6711yescharacteristic
137C22×C4×C5—61no—
138C22×C4×C5C22×D311yescharacteristic
139C2×C22⋊D5—21no—
140C22×Dic5—61no—
141C22×Dic5#6711yescharacteristic
142C22×Dic5#6711yescharacteristic
143C2×D20#6711yescharacteristic
144C2×C4×D5—21no—
145C2×C5×C8—61no—
146C5×C4⋊C4—21no—
147C5×C4⋊C4—61no—
148C5×C4⋊C4—61no—
149C5×C4⋊C4#6711yescharacteristic
150C5×C22⋊C4—21no—
151#685—21no—
152#685—21no—
153#685—21no—
154#685—21no—
155C4⋊Dic5—21no—
156C4⋊Dic5—21no—
157C4⋊Dic5#6711yescharacteristic
158#683—21no—
159#683—21no—
160#683—21no—
161#683—122no—
162C4×Dic5—21no—
163C2×#168—61no—
164#539—51no—
165#483—31no—
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×C3×D5—41no—
177C2×C3×D5—41no—
178C2×C3×D5—41no—
179C3×C4×C5—21no—
180C3×C4×C5—21no—
181C3×C4×C5—41no—
182C3×C4×C5—41no—
183Dic15—42no—
184C3×Dic5—41no—
185C3×Dic5—41no—
186C3×Dic5—41no—
187C5×Dic3—81no—
188C2×C3×Q8C22⋊D511yescharacteristic
189C2×C3×D4—51no—
190C2×C3×D4—101no—
191C22×C3×C4—51no—
192C22×C3×C4—51no—
193C22×C3×C4—101no—
194C22×C3×C4C22×D511yescharacteristic
195C22×Dic3—21no—
196C22×Dic3—101no—
197C3×C4⋊C4—21no—
198C3×C4⋊C4—51no—
199C3×C4⋊C4—101no—
200C3×C4⋊C4—101no—
201C3×C4⋊C4—101no—
202C3×C4⋊C4—101no—
203C3×C4⋊C4—101no—
204C3×C4⋊C4C22⋊D511yescharacteristic
205C3×C22⋊C4—21no—
206C3×C22⋊C4—101no—
207C3×C22⋊C4—101no—
208C3×C22⋊C4—101no—
209C3×C22⋊C4—101no—
210C3×C42—101no—
211C4⋊Dic3—21no—
212C4⋊Dic3—21no—
213Dic3⋊C4—202no—
214C2×C3⋊C8—21no—
215C2×C3⋊C8—101no—
216C23×C5C2×#6711yescharacteristic
217C22×D5—21no—
218C5×Q8—41no—
219C2×C4×C5—21no—
220C2×C4×C5—21no—
221C2×C4×C5—41no—
222C2×C4×C5—121no—
223C2×C4×C5—121no—
224C2×C4×C5—121no—
225C2×C4×C5C2×#6711yescharacteristic
226C2×C4×C5C2×#6711yescharacteristic
227C22⋊D5—41no—
228C22⋊D5—41no—
229C2×Dic5—21no—
230C2×Dic5—21no—
231C2×Dic5—21no—
232C2×Dic5—21no—
233C2×Dic5—21no—
234C2×Dic5—41no—
235C2×Dic5—62no—
236C2×Dic5—121no—
237C2×Dic5—121no—
238D20—41no—
239C4×D5—81no—
240C5×C8—121no—
241#168—121no—
242#126—101no—
243#125—101no—
244#123—101no—
245#123—101no—
246C22⋊Q8—101no—
247C22⋊Q8D3×D511yescharacteristic
248#121—51no—
249C4×D4—101no—
250C2×C4⋊C4—31no—
251C2×C4⋊C4—51no—
252C2×C4⋊C4—301no—
253#107—301no—
254#106—61no—
255#103—61no—
256#102—301no—
257C22⋊C8—31no—
258C22⋊C8—151no—
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
266C3×D5—81no—
267C23×C3—101no—
268C23×C3D4×D511yescharacteristic
269C3×Q8—41no—
270C3×D4—201no—
271C3×D4—201no—
272C3×D4—201no—
273C2×C3×C4—21no—
274C2×C3×C4—21no—
275C2×C3×C4—41no—
276C2×C3×C4—101no—
277C2×C3×C4—101no—
278C2×C3×C4—101no—
279C2×C3×C4—101no—
280C2×C3×C4—101no—
281C2×C3×C4—201no—
282C2×C3×C4—401no—
283C2×C3×C4D4×D511yescharacteristic
284C2×C3×C4C2×C22⋊D511yescharacteristic
285C2×Dic3—41no—
286C2×Dic3—41no—
287C2×Dic3—41no—
288C2×Dic3—102no—
289C2×Dic3—201no—
290C2×Dic3—201no—
291C3⋊C8—41no—
292C3⋊C8—201no—
293C22×C5—21no—
294C22×C5—21no—
295C22×C5#94911yescharacteristic
296C22×C5#95011yescharacteristic
297C22×C5#95311yescharacteristic
298C2×D5—41no—
299C2×D5—41no—
300C2×D5—41no—
301C4×C5—21no—
302C4×C5—21no—
303C4×C5—41no—
304C4×C5—41no—
305C4×C5—241no—
306Dic5—41no—
307Dic5—41no—
308Dic5—41no—
309Dic5—122no—
310C2×Q8#120111yescharacteristic
311C2×D4—51no—
312C2×D4—101no—
313C22×C4—51no—
314C22×C4—51no—
315C22×C4—61no—
316C22×C4—101no—
317C22×C4—301no—
318C22×C4C2×D3×D511yescharacteristic
319C2×C8—61no—
320C2×C8—301no—
321C4⋊C4—21no—
322C4⋊C4—51no—
323C4⋊C4—61no—
324C4⋊C4—61no—
325C4⋊C4—101no—
326C4⋊C4—101no—
327C4⋊C4—101no—
328C4⋊C4—101no—
329C4⋊C4—101no—
330C4⋊C4—602no—
331C4⋊C4#120111yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—101no—
334C22⋊C4—101no—
335C22⋊C4—101no—
336C22⋊C4—101no—
337C42—101no—
338C3×C5#160911yescharacteristic, complemented, Hall
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—201no—
342C22×C3—201no—
343C22×C3—201no—
344C22×C3#406011yescharacteristic
345C22×C3#406211yescharacteristic
346C22×C3#408311yescharacteristic
347C3×C4—21no—
348C3×C4—21no—
349C3×C4—41no—
350C3×C4—41no—
351C3×C4—201no—
352C3×C4—201no—
353C3×C4—201no—
354Dic3—81no—
355Dic3—202no—
356C2×C5—21no—
357C2×C5—21no—
358C2×C5#523811yescharacteristic
359C2×C5#524311yescharacteristic
360C2×C5#524611yescharacteristic
361D5—81no—
362C23—101no—
363C23D5×#6711yescharacteristic
364Q8—41no—
365D4—201no—
366D4—201no—
367D4—201no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—41no—
371C2×C4—101no—
372C2×C4—101no—
373C2×C4—101no—
374C2×C4—101no—
375C2×C4—101no—
376C2×C4—121no—
377C2×C4—121no—
378C2×C4—121no—
379C2×C4—201no—
380C2×C4—302no—
381C2×C4—401no—
382C2×C4—601no—
383C2×C4—601no—
384C2×C4C2×#120111yescharacteristic
385C2×C4D5×#6711yescharacteristic
386C8—121no—
387C8—601no—
388C2×C3—21no—
389C2×C3—21no—
390C2×C3—401no—
391C2×C3#6534211yescharacteristic
392C2×C3#6546111yescharacteristic
393C2×C3#6549411yescharacteristic
394C5#7188611yescharacteristic, complemented, Sylow
395C22—21no—
396C22—21no—
397C22—201no—
398C22—201no—
399C22—201no—
400C22#9150211yescharacteristic
401C22#9151411yescharacteristic
402C22#9156311yescharacteristic
403C4—21no—
404C4—21no—
405C4—41no—
406C4—41no—
407C4—201no—
408C4—201no—
409C4—201no—
410C4—241no—
411C4—602no—
412C3#1060196711yescharacteristic, complemented, Sylow
413C2—21no—
414C2—21no—
415C2—401no—
416C2#1174918111yescharacteristic
417C2#1174927011yescharacteristic
418C2#1174946211yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊Q8C22
socleC22×C3×C5#120
prime radicalC3×#4076C22
hypercenterC22⋊Q8D3×D5
hypocenterC3×C5#1609
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C5×#5043C2semidirect
3. #11748588C2semidirect
5. #11746359C2semidirect
7. #11745951C2semidirect
65. #5043D5semidirect
338. C3×C5#1609semidirect
394. C5#71886semidirect
412. C3#10601967semidirect

Maximal subgroups

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

subgroupindex
C3×#659792
C5×#50432
#117485882
#117483702
#117463592
#117459552
#117459512
#106019673
#718865