Finite Group Databasebeta

← #14291129

Subgroups — #14291129

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
2#11751156C211yesmaximal, characteristic, complemented
3#11747074C211yesmaximal, characteristic, complemented
4#11746953C211yesmaximal, characteristic, complemented
5C5×#4540C211yesmaximal, characteristic, complemented
6#11745849C211yesmaximal, characteristic, complemented
7#11745846C211yesmaximal, characteristic, complemented
8#10599150—31nomaximal, Hall
9C3×C5×#124C2211yescharacteristic
10#91758C2211yescharacteristic
11C3×#4092—21no—
12C3×#4085—21no—
13C3×#4032—21no—
14C3×#4030—21no—
15C3×#4029—21no—
16C3×#4024—21no—
17C3×#4021C2211yescharacteristic
18C3×#4016C2211yescharacteristic
19C2×#6662—21no—
20C2×#6657—21no—
21#91119—21no—
22#91116—21no—
23#91087C2211yescharacteristic
24C5×#803C2211yescharacteristic
25C5×#803C2211yescharacteristic
26#90990—21no—
27#90987—21no—
28#71953—51nomaximal, Hall
29#66018D311yescharacteristic
30#65344—31no—
31#65004—31no—
32#64991—31no—
33C5×#329—31no—
34#64685—31no—
35#64684—31no—
36C2×C3×C5×Q8D411yescharacteristic
37C2×C3×C5×D4D411yescharacteristic
38C2×Dic30—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
48C4⋊Dic15—21no—
49C4⋊Dic15—21no—
50C2×C3⋊#168—21no—
51C2×C5×C3⋊C8—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#6662—42no—
64#6657—42no—
65C3×#562—51no—
66#5064—51no—
67#5060—51no—
68#5055—51no—
69#4543—51no—
70#4540—51no—
71#4540D511yescharacteristic, complemented
72C5×#124C2×D311yescharacteristic
73#4092—21no—
74#4085—21no—
75C2×Dic20—61no—
76C2×#677—61no—
77#4032—21no—
78#4030—21no—
79#4029—21no—
80#4024—21no—
81#4021C2×D311yescharacteristic
82#4016C2×D311yescharacteristic
83#4015—31no—
84C5×#97—31no—
85C5×#97—31no—
86#3967—61no—
87#3964—61no—
88#3950—61no—
89#3949—61no—
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×Dic15—41no—
101Dic30—41no—
102Dic30—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—41no—
113C5×C3⋊C8—22no—
114C5×C3⋊C8—22no—
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#869—51no—
127#835—101no—
128#832—101no—
129#808—101no—
130#807—101no—
131#803—51no—
132#803C2×D511yescharacteristic
133#803C2×D511yescharacteristic
134C2×C5×Q8#6711yescharacteristic
135C2×C5×D4#6711yescharacteristic
136C2×C22⋊D5—21no—
137C2×C22⋊D5—21no—
138C22×Dic5—21no—
139C2×D20#6711yescharacteristic
140C2×C4×D5—21no—
141C2×Dic10—61no—
142C2×Dic10#6711yescharacteristic
143C2×C5×C8—61no—
144C2×C5×C8—61no—
145C5×C22⋊C4—21no—
146C5×C22⋊C4—21no—
147C42×C5C22×D311yescharacteristic
148C22⋊Dic5—21no—
149#685—21no—
150#685—21no—
151#685—21no—
152C4⋊Dic5—21no—
153C4⋊Dic5—61no—
154C4⋊Dic5—61no—
155C4⋊Dic5#6711yescharacteristic
156C4⋊Dic5#6711yescharacteristic
157#683—21no—
158#683—21no—
159#683—21no—
160C2×#168—61no—
161Dic20—122no—
162#677—122no—
163#562—51no—
164#501—151no—
165#497—151no—
166#489—151no—
167#330—151no—
168#329—31no—
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—
181Dic15—81no—
182C3×Dic5—41no—
183C3×Dic5—41no—
184C3×Dic5—41no—
185C2×C3×Q8—51no—
186C2×C3×Q8D2011yescharacteristic
187C2×C3×D4—51no—
188C2×C3×D4—101no—
189C2×C3×D4—101no—
190C2×C3×D4D2011yescharacteristic
191C22×C3×C4—101no—
192C22×C3×C4—101no—
193C2×Dic6—101no—
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—101no—
210C4⋊Dic3—101no—
211C2×C3⋊C8—21no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—101no—
214C23×C5—21no—
215C22×D5—21no—
216C5×Q8—41no—
217C5×D4—41no—
218C2×C4×C5—21no—
219C2×C4×C5C2×#6711yescharacteristic
220C2×C4×C5C2×#6711yescharacteristic
221C2×C4×C5C2×#6711yescharacteristic
222C22⋊D5—81no—
223C22⋊D5—81no—
224C2×Dic5—21no—
225C2×Dic5—21no—
226C2×Dic5—21no—
227C2×Dic5—81no—
228C2×Dic5—121no—
229D20—41no—
230C4×D5—81no—
231Dic10—41no—
232Dic10—121no—
233Dic10—121no—
234C5×C8—62no—
235C5×C8—62no—
236#168—121no—
237C2×Q16—301no—
238C2×SD16—301no—
239C4⋊Q8—151no—
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—301no—
252#102—301no—
253#97—31no—
254#97—31no—
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×C4C2×D2011yescharacteristic
276C2×C3×C4D4×D511yescharacteristic
277C2×C3×C4D4×D511yescharacteristic
278C2×Dic3—201no—
279Dic6—201no—
280Dic6—201no—
281C3⋊C8—22no—
282C3⋊C8—22no—
283C3⋊C8—201no—
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—
295Dic5—41no—
296Dic5—41no—
297Dic5—41no—
298Dic5—241no—
299C2×Q8—51no—
300C2×Q8—301no—
301C2×Q8#120211yescharacteristic
302C2×D4—51no—
303C2×D4—101no—
304C2×D4—101no—
305C2×D4#120211yescharacteristic
306C22×C4—101no—
307C22×C4—101no—
308Q16—602no—
309SD16—602no—
310C2×C8—61no—
311C2×C8—61no—
312C2×C8—301no—
313C4⋊C4—51no—
314C4⋊C4—51no—
315C4⋊C4—101no—
316C4⋊C4—101no—
317C4⋊C4—101no—
318C4⋊C4—101no—
319C4⋊C4—301no—
320C4⋊C4—301no—
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#402811yescharacteristic
336C3×C4—21no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—41no—
340C3×C4—201no—
341C3×C4—201no—
342C3×C4—201no—
343Dic3—401no—
344C2×C5—81no—
345C2×C5#524111yescharacteristic
346C2×C5#524211yescharacteristic
347C2×C5#524611yescharacteristic
348D5—81no—
349C23—21no—
350C23—101no—
351Q8—41no—
352Q8—201no—
353Q8—601no—
354Q8—601no—
355D4—41no—
356D4—201no—
357D4—401no—
358D4—401no—
359C2×C4—21no—
360C2×C4—101no—
361C2×C4—101no—
362C2×C4—101no—
363C2×C4—401no—
364C2×C4—401no—
365C2×C4—601no—
366C2×C4C2×#120211yescharacteristic
367C2×C4D5×#6711yescharacteristic
368C2×C4D5×#6711yescharacteristic
369C8—62no—
370C8—62no—
371C8—601no—
372C2×C3—81no—
373C2×C3—401no—
374C2×C3#6503511yescharacteristic
375C2×C3#6511111yescharacteristic
376C2×C3#6511511yescharacteristic
377C5#7195311yescharacteristic, complemented, Sylow
378C22—41no—
379C22—41no—
380C22—41no—
381C22—201no—
382C22—201no—
383C22—201no—
384C22#9156411yescharacteristic
385C4—21no—
386C4—21no—
387C4—21no—
388C4—41no—
389C4—201no—
390C4—201no—
391C4—201no—
392C4—1201no—
393C3#1059915011yescharacteristic, complemented, Sylow
394C2—81no—
395C2—401no—
396C2#1174914511yescharacteristic
397C2#1174941811yescharacteristic
398C2#1174946411yescharacteristic
subgroupG/H
centerC22#91564
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. #11751156C2semidirect
3. #11747074C2semidirect
4. #11746953C2semidirect
5. C5×#4540C2semidirect
6. #11745849C2semidirect
7. #11745846C2semidirect
71. #4540D5semidirect
328. C3×C5#1661semidirect
377. C5#71953semidirect
393. C3#10599150semidirect

Maximal subgroups

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

subgroupindex
C3×#660182
#117511562
#117470742
#117469532
C5×#45402
#117458492
#117458462
#105991503
#719535