Finite Group Databasebeta

← #14291124

Subgroups — #14291124

Order 1920.

416 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 76 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×#66018C211yesmaximal, characteristic
2C5×#5055C211yesmaximal, characteristic, complemented
3#11747080C211yesmaximal, characteristic, complemented
4#11746970C211yesmaximal, characteristic, complemented
5#11746361C211yesmaximal, characteristic, complemented
6#11745849C211yesmaximal, characteristic, complemented
7#11745846C211yesmaximal, characteristic, complemented
8#10602038—31nomaximal, Hall
9C3×C5×#124C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×#4092—21no—
12C3×#4085—21no—
13C3×#4032—21no—
14C3×#4030—21no—
15C3×#4029—21no—
16C3×#4024—21no—
17C3×#4021C2211yescharacteristic
18C3×#4016C2211yescharacteristic
19C2×#6661—21no—
20C2×#6655—21no—
21#91087C2211yescharacteristic
22#91087C2211yescharacteristic
23C5×#835—21no—
24C5×#832—21no—
25C5×#803C2211yescharacteristic
26#90989—21no—
27#90986—21no—
28#71953—51nomaximal, Hall
29#66018D311yescharacteristic
30C5×#489—31no—
31#65375—31no—
32#65369—31no—
33#64760—31no—
34#64685—31no—
35#64684—31no—
36C2×C3×C5×Q8D411yescharacteristic
37C2×C3×C5×D4D411yescharacteristic
38C2×C5×Dic6—21no—
39C2×C3×C22⋊D5—21no—
40C2×C3×C22⋊D5—21no—
41C22×C3×Dic5—21no—
42C2×C3×D20D411yescharacteristic
43C2×C3×C4×D5—21no—
44C2×C3×Dic10D411yescharacteristic
45C3×C5×C22⋊C4—21no—
46C3×C5×C22⋊C4—21no—
47C3×C42×C5C2311yescharacteristic
48C2×C3⋊#168—21no—
49C2×C3⋊#168—21no—
50C5×C4⋊Dic3—21no—
51C5×C4⋊Dic3—21no—
52C2×C5×C3⋊C8—21no—
53C3×C22⋊Dic5—21no—
54C3×#685—21no—
55C3×#685—21no—
56C3×#685—21no—
57C3×C4⋊Dic5—21no—
58C3×C4⋊Dic5D411yescharacteristic
59C3×C4⋊Dic5D411yescharacteristic
60C3×#683—21no—
61C3×#683—21no—
62C3×#683—21no—
63#6661—42no—
64#6655—42no—
65C3×#562—51no—
66#5064—51no—
67#5060—51no—
68#5055D511yescharacteristic, complemented
69#4543—51no—
70#4540—51no—
71#4540—51no—
72C5×C4⋊Q8—31no—
73C5×#124C2×D311yescharacteristic
74#4092—21no—
75C2×#689—61no—
76C2×#688—61no—
77#4085—21no—
78#4032—21no—
79#4030—21no—
80#4029—21no—
81#4024—21no—
82#4021C2×D311yescharacteristic
83#4016C2×D311yescharacteristic
84C5×#103—61no—
85C5×#102—61no—
86C5×#97—31no—
87#3940—61no—
88#3939—61no—
89#3935—31no—
90#3935—31no—
91#1661—151noSylow
92C23×C3×C5—21no—
93C22×C3×D5—21no—
94C3×C5×Q8—41no—
95C3×C5×D4—41no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C5×Dic3—41no—
101C5×Dic6—41no—
102C5×Dic6—41no—
103C3×C22⋊D5—81no—
104C3×C22⋊D5—81no—
105C2×C3×Dic5—21no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—81no—
109C3×D20—41no—
110C3×C4×D5—81no—
111C3×Dic10—41no—
112C3⋊#168—22no—
113C3⋊#168—22no—
114C5×C3⋊C8—41no—
115C3×#125—51no—
116C3×#124—51no—
117C3×#124C2×D511yescharacteristic
118C3×#123—101no—
119C3×#123—101no—
120C3×C22⋊Q8—101no—
121C3×C22⋊Q8—101no—
122C3×#121—101no—
123C3×#121—101no—
124C2×#216—101no—
125C2×#214—101no—
126#869C2×D511yescharacteristic
127#835—21no—
128#832—21no—
129#808—101no—
130#807—101no—
131#803—51no—
132#803—51no—
133#803C2×D511yescharacteristic
134C2×C5×Q8—61no—
135C2×C5×Q8#6711yescharacteristic
136C2×C5×D4#6711yescharacteristic
137C2×C22⋊D5—21no—
138C2×C22⋊D5—21no—
139C22×Dic5—21no—
140C2×D20#6711yescharacteristic
141C2×C4×D5—21no—
142C2×Dic10#6711yescharacteristic
143C2×C5×C8—61no—
144C5×C4⋊C4—61no—
145C5×C4⋊C4—61no—
146C5×C22⋊C4—21no—
147C5×C22⋊C4—21no—
148C42×C5C22×D311yescharacteristic
149C22⋊Dic5—21no—
150#689—122no—
151#688—122no—
152#685—21no—
153#685—21no—
154#685—21no—
155C4⋊Dic5—21no—
156C4⋊Dic5#6711yescharacteristic
157C4⋊Dic5#6711yescharacteristic
158#683—21no—
159#683—21no—
160#683—21no—
161C2×#168—61no—
162C2×#168—61no—
163#562—51no—
164#501—151no—
165#497—151no—
166#489—31no—
167#330—151no—
168#329—151no—
169#329—151no—
170C22×C3×C5—41no—
171C22×C3×C5—41no—
172C22×C3×C5—41no—
173C22×C3×C5#12011yescharacteristic
174C2×C3×D5—41no—
175C2×C3×D5—41no—
176C2×C3×D5—41no—
177C3×C4×C5—21no—
178C3×C4×C5—21no—
179C3×C4×C5—21no—
180C3×C4×C5—41no—
181C3×Dic5—41no—
182C3×Dic5—41no—
183C3×Dic5—41no—
184C5×Dic3—81no—
185C2×C3×Q8—51no—
186C2×C3×Q8C22⋊D511yescharacteristic
187C2×C3×D4—51no—
188C2×C3×D4—101no—
189C2×C3×D4—101no—
190C2×C3×D4C22⋊D511yescharacteristic
191C22×C3×C4—101no—
192C22×C3×C4—101no—
193C2×Dic6—21no—
194C3×C4⋊C4—51no—
195C3×C4⋊C4—51no—
196C3×C4⋊C4—101no—
197C3×C4⋊C4—101no—
198C3×C4⋊C4—101no—
199C3×C4⋊C4—101no—
200C3×C22⋊C4—21no—
201C3×C22⋊C4—21no—
202C3×C22⋊C4—101no—
203C3×C22⋊C4—101no—
204C3×C22⋊C4—101no—
205C3×C22⋊C4—101no—
206C3×C42C22×D511yescharacteristic
207#216—202no—
208#214—202no—
209C4⋊Dic3—21no—
210C4⋊Dic3—21no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—101no—
213C2×C3⋊C8—101no—
214C23×C5—21no—
215C22×D5—21no—
216C5×Q8—41no—
217C5×Q8—121no—
218C5×Q8—121no—
219C5×D4—41no—
220C2×C4×C5—21no—
221C2×C4×C5—121no—
222C2×C4×C5C2×#6711yescharacteristic
223C2×C4×C5C2×#6711yescharacteristic
224C2×C4×C5C2×#6711yescharacteristic
225C22⋊D5—81no—
226C22⋊D5—81no—
227C2×Dic5—21no—
228C2×Dic5—21no—
229C2×Dic5—21no—
230C2×Dic5—81no—
231D20—41no—
232C4×D5—81no—
233Dic10—41no—
234C5×C8—121no—
235#168—62no—
236#168—62no—
237C2×Q16—301no—
238C2×SD16—301no—
239C4⋊Q8—31no—
240#125—51no—
241#124—51no—
242#124D3×D511yescharacteristic
243#123—101no—
244#123—101no—
245C22⋊Q8—101no—
246C22⋊Q8—101no—
247#121—101no—
248#121—101no—
249#107—301no—
250#106—301no—
251#103—61no—
252#102—61no—
253#97—31no—
254#97—151no—
255#97—151no—
256C2×C3×C5—81no—
257C2×C3×C5#45311yescharacteristic
258C2×C3×C5#45511yescharacteristic
259C2×C3×C5#45611yescharacteristic
260C3×D5—81no—
261C23×C3—21no—
262C23×C3—101no—
263C3×Q8—41no—
264C3×Q8—201no—
265C3×D4—41no—
266C3×D4—201no—
267C3×D4—401no—
268C3×D4—401no—
269C2×C3×C4—21no—
270C2×C3×C4—101no—
271C2×C3×C4—101no—
272C2×C3×C4—101no—
273C2×C3×C4—401no—
274C2×C3×C4—401no—
275C2×C3×C4D4×D511yescharacteristic
276C2×C3×C4D4×D511yescharacteristic
277C2×C3×C4C2×C22⋊D511yescharacteristic
278C2×Dic3—41no—
279Dic6—41no—
280Dic6—41no—
281C3⋊C8—41no—
282C3⋊C8—102no—
283C3⋊C8—102no—
284C22×C5—41no—
285C22×C5—41no—
286C22×C5—41no—
287C22×C5#95311yescharacteristic
288C2×D5—41no—
289C2×D5—41no—
290C2×D5—41no—
291C4×C5—21no—
292C4×C5—21no—
293C4×C5—21no—
294C4×C5—41no—
295C4×C5—241no—
296Dic5—41no—
297Dic5—41no—
298Dic5—41no—
299C2×Q8—51no—
300C2×Q8—61no—
301C2×Q8#120111yescharacteristic
302C2×D4—51no—
303C2×D4—101no—
304C2×D4—101no—
305C2×D4#120111yescharacteristic
306C22×C4—101no—
307C22×C4—101no—
308Q16—602no—
309SD16—602no—
310C2×C8—61no—
311C2×C8—301no—
312C2×C8—301no—
313C4⋊C4—51no—
314C4⋊C4—51no—
315C4⋊C4—61no—
316C4⋊C4—61no—
317C4⋊C4—101no—
318C4⋊C4—101no—
319C4⋊C4—101no—
320C4⋊C4—101no—
321C22⋊C4—21no—
322C22⋊C4—21no—
323C22⋊C4—101no—
324C22⋊C4—101no—
325C22⋊C4—101no—
326C22⋊C4—101no—
327C42C2×D3×D511yescharacteristic
328C3×C5#166111yescharacteristic, complemented, Hall
329C22×C3—41no—
330C22×C3—41no—
331C22×C3—41no—
332C22×C3—201no—
333C22×C3—201no—
334C22×C3—201no—
335C22×C3#408311yescharacteristic
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—41no—
340C3×C4—201no—
341C3×C4—201no—
342C3×C4—201no—
343Dic3—81no—
344C2×C5—81no—
345C2×C5#524111yescharacteristic
346C2×C5#524211yescharacteristic
347C2×C5#524611yescharacteristic
348D5—81no—
349C23—21no—
350C23—101no—
351Q8—41no—
352Q8—121no—
353Q8—121no—
354Q8—201no—
355D4—41no—
356D4—201no—
357D4—401no—
358D4—401no—
359C2×C4—21no—
360C2×C4—101no—
361C2×C4—101no—
362C2×C4—101no—
363C2×C4—121no—
364C2×C4—401no—
365C2×C4—401no—
366C2×C4C2×#120111yescharacteristic
367C2×C4D5×#6711yescharacteristic
368C2×C4D5×#6711yescharacteristic
369C8—121no—
370C8—302no—
371C8—302no—
372C2×C3—81no—
373C2×C3—401no—
374C2×C3#6535011yescharacteristic
375C2×C3#6548711yescharacteristic
376C2×C3#6549411yescharacteristic
377C5#7195311yescharacteristic, complemented, Sylow
378C22—41no—
379C22—41no—
380C22—41no—
381C22—201no—
382C22—201no—
383C22—201no—
384C22#9156311yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—201no—
390C4—201no—
391C4—201no—
392C4—241no—
393C3#1060203811yescharacteristic, complemented, Sylow
394C2—81no—
395C2—401no—
396C2#1174914411yescharacteristic
397C2#1174941711yescharacteristic
398C2#1174946211yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5#120
prime radicalC3×#66018C2
hypercenter#124D3×D5
hypocenterC3×C5#1661
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. C5×#5055C2semidirect
3. #11747080C2semidirect
4. #11746970C2semidirect
5. #11746361C2semidirect
6. #11745849C2semidirect
7. #11745846C2semidirect
68. #5055D5semidirect
328. C3×C5#1661semidirect
377. C5#71953semidirect
393. C3#10602038semidirect

Maximal subgroups

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

subgroupindex
C3×#660182
C5×#50552
#117470802
#117469702
#117463612
#117458492
#117458462
#106020383
#719535