Finite Group Databasebeta

← #14291165

Subgroups — #14291165

Order 1920.

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

normal subgroups only

This group has 392 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#11746936C211yesmaximal, characteristic, complemented
4#11746893C211yesmaximal, characteristic, complemented
5C5×#4540C211yesmaximal, characteristic, complemented
6#11745849C211yesmaximal, characteristic, complemented
7#11745846C211yesmaximal, characteristic, complemented
8#10599151—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
19#91119—21no—
20#91116—21no—
21#91087C2211yescharacteristic
22C5×#803C2211yescharacteristic
23C5×#803C2211yescharacteristic
24#90974—21no—
25#90974—21no—
26#90971—21no—
27#90965—21no—
28#71954—51nomaximal, Hall
29#66018D311yescharacteristic
30#65344—31no—
31#65003—31no—
32#64992—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—
63C3×#562—51no—
64#5069—51no—
65#5055—51no—
66#5055—51no—
67#4543—51no—
68#4540—51no—
69#4540D511yescharacteristic, complemented
70C5×#124C2×D311yescharacteristic
71#4092—21no—
72#4085—21no—
73#4032—21no—
74#4030—21no—
75#4029—21no—
76#4024—21no—
77#4021C2×D311yescharacteristic
78#4016C2×D311yescharacteristic
79#4015—31no—
80C5×#97—31no—
81C5×#97—31no—
82#3967—61no—
83#3964—61no—
84#3953—61no—
85#3948—61no—
86#3948—61no—
87#3948—61no—
88#3935—31no—
89#1662—151noSylow
90C23×C3×C5—21no—
91C22×C3×D5—21no—
92C3×C5×Q8—41no—
93C3×C5×D4—41no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×Dic15—41no—
99Dic30—42no—
100C3×C22⋊D5—81no—
101C3×C22⋊D5—81no—
102C2×C3×Dic5—21no—
103C2×C3×Dic5—21no—
104C2×C3×Dic5—21no—
105C2×C3×Dic5—81no—
106C3×D20—41no—
107C3×C4×D5—81no—
108C3×Dic10—41no—
109C3⋊#168—41no—
110C5×C3⋊C8—41no—
111C5×C3⋊C8—41no—
112C3×#125—51no—
113C3×#124—51no—
114C3×#124C2×D511yescharacteristic
115C3×#123—101no—
116C3×#123—101no—
117C3×C22⋊Q8—101no—
118C3×C22⋊Q8—101no—
119C3×#121—101no—
120C3×#121—101no—
121#869—51no—
122#835—101no—
123#835—101no—
124#832—101no—
125#832—101no—
126#810—101no—
127#810—101no—
128#803—51no—
129#803C2×D511yescharacteristic
130#803C2×D511yescharacteristic
131C2×C5×Q8#6711yescharacteristic
132C2×C5×D4#6711yescharacteristic
133C2×C22⋊D5—21no—
134C2×C22⋊D5—21no—
135C22×Dic5—21no—
136C2×D20#6711yescharacteristic
137C2×C4×D5—21no—
138C2×Dic10—61no—
139C2×Dic10#6711yescharacteristic
140C2×C5×C8—61no—
141C2×C5×C8—61no—
142C5×C22⋊C4—21no—
143C5×C22⋊C4—21no—
144C42×C5C22×D311yescharacteristic
145C22⋊Dic5—21no—
146#685—21no—
147#685—21no—
148#685—21no—
149C4⋊Dic5—21no—
150C4⋊Dic5—61no—
151C4⋊Dic5—61no—
152C4⋊Dic5#6711yescharacteristic
153C4⋊Dic5#6711yescharacteristic
154#683—21no—
155#683—21no—
156#683—21no—
157C2×#168—61no—
158#562—51no—
159#491—151no—
160#489—151no—
161#489—151no—
162#330—151no—
163#329—31no—
164#329—151no—
165C22×C3×C5—41no—
166C22×C3×C5—41no—
167C22×C3×C5—41no—
168C22×C3×C5#12011yescharacteristic
169C2×C3×D5—41no—
170C2×C3×D5—41no—
171C2×C3×D5—41no—
172C3×C4×C5—21no—
173C3×C4×C5—21no—
174C3×C4×C5—21no—
175C3×C4×C5—41no—
176Dic15—81no—
177C3×Dic5—41no—
178C3×Dic5—41no—
179C3×Dic5—41no—
180C2×C3×Q8—51no—
181C2×C3×Q8D2011yescharacteristic
182C2×C3×D4—51no—
183C2×C3×D4—101no—
184C2×C3×D4—101no—
185C2×C3×D4D2011yescharacteristic
186C22×C3×C4—101no—
187C22×C3×C4—101no—
188C2×Dic6—101no—
189C3×C4⋊C4—51no—
190C3×C4⋊C4—51no—
191C3×C4⋊C4—101no—
192C3×C4⋊C4—101no—
193C3×C4⋊C4—101no—
194C3×C4⋊C4—101no—
195C3×C22⋊C4—21no—
196C3×C22⋊C4—21no—
197C3×C22⋊C4—101no—
198C3×C22⋊C4—101no—
199C3×C22⋊C4—101no—
200C3×C22⋊C4—101no—
201C3×C42C22×D511yescharacteristic
202C4⋊Dic3—101no—
203C4⋊Dic3—101no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—101no—
207C23×C5—21no—
208C22×D5—21no—
209C5×Q8—41no—
210C5×D4—41no—
211C2×C4×C5—21no—
212C2×C4×C5C2×#6711yescharacteristic
213C2×C4×C5C2×#6711yescharacteristic
214C2×C4×C5C2×#6711yescharacteristic
215C22⋊D5—81no—
216C22⋊D5—81no—
217C2×Dic5—21no—
218C2×Dic5—21no—
219C2×Dic5—21no—
220C2×Dic5—81no—
221C2×Dic5—121no—
222D20—41no—
223C4×D5—81no—
224Dic10—41no—
225Dic10—122no—
226C5×C8—121no—
227C5×C8—121no—
228#168—121no—
229C4⋊Q8—151no—
230#125—51no—
231#124—51no—
232#124D3×D511yescharacteristic
233#123—101no—
234#123—101no—
235C22⋊Q8—101no—
236C22⋊Q8—101no—
237#121—101no—
238#121—101no—
239#103—301no—
240#103—301no—
241#103—301no—
242#103—301no—
243#102—301no—
244#102—301no—
245#97—31no—
246#97—31no—
247#97—151no—
248C2×C3×C5—81no—
249C2×C3×C5#45411yescharacteristic
250C2×C3×C5#45511yescharacteristic
251C2×C3×C5#45511yescharacteristic
252C3×D5—81no—
253C23×C3—21no—
254C23×C3—101no—
255C3×Q8—41no—
256C3×Q8—201no—
257C3×D4—41no—
258C3×D4—201no—
259C3×D4—401no—
260C3×D4—401no—
261C2×C3×C4—21no—
262C2×C3×C4—101no—
263C2×C3×C4—101no—
264C2×C3×C4—101no—
265C2×C3×C4—401no—
266C2×C3×C4—401no—
267C2×C3×C4C2×D2011yescharacteristic
268C2×C3×C4D4×D511yescharacteristic
269C2×C3×C4D4×D511yescharacteristic
270C2×Dic3—201no—
271Dic6—202no—
272C3⋊C8—41no—
273C3⋊C8—41no—
274C3⋊C8—201no—
275C22×C5—41no—
276C22×C5—41no—
277C22×C5—41no—
278C22×C5#95311yescharacteristic
279C2×D5—41no—
280C2×D5—41no—
281C2×D5—41no—
282C4×C5—21no—
283C4×C5—21no—
284C4×C5—21no—
285C4×C5—41no—
286Dic5—41no—
287Dic5—41no—
288Dic5—41no—
289Dic5—241no—
290C2×Q8—51no—
291C2×Q8—301no—
292C2×Q8#120211yescharacteristic
293C2×D4—51no—
294C2×D4—101no—
295C2×D4—101no—
296C2×D4#120211yescharacteristic
297C22×C4—101no—
298C22×C4—101no—
299C2×C8—61no—
300C2×C8—61no—
301C2×C8—301no—
302C4⋊C4—51no—
303C4⋊C4—51no—
304C4⋊C4—101no—
305C4⋊C4—101no—
306C4⋊C4—101no—
307C4⋊C4—101no—
308C4⋊C4—301no—
309C4⋊C4—301no—
310C22⋊C4—21no—
311C22⋊C4—21no—
312C22⋊C4—101no—
313C22⋊C4—101no—
314C22⋊C4—101no—
315C22⋊C4—101no—
316C42C2×D3×D511yescharacteristic
317C3×C5#166211yescharacteristic, complemented, Hall
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—41no—
321C22×C3—201no—
322C22×C3—201no—
323C22×C3—201no—
324C22×C3#402811yescharacteristic
325C3×C4—21no—
326C3×C4—21no—
327C3×C4—21no—
328C3×C4—41no—
329C3×C4—201no—
330C3×C4—201no—
331C3×C4—201no—
332Dic3—401no—
333C2×C5—81no—
334C2×C5#524211yescharacteristic
335C2×C5#524211yescharacteristic
336C2×C5#524511yescharacteristic
337D5—81no—
338C23—21no—
339C23—101no—
340Q8—41no—
341Q8—201no—
342Q8—602no—
343D4—41no—
344D4—201no—
345D4—401no—
346D4—401no—
347C2×C4—21no—
348C2×C4—101no—
349C2×C4—101no—
350C2×C4—101no—
351C2×C4—401no—
352C2×C4—401no—
353C2×C4—601no—
354C2×C4C2×#120211yescharacteristic
355C2×C4D5×#6711yescharacteristic
356C2×C4D5×#6711yescharacteristic
357C8—121no—
358C8—121no—
359C8—601no—
360C2×C3—81no—
361C2×C3—401no—
362C2×C3#6503511yescharacteristic
363C2×C3#6511411yescharacteristic
364C2×C3#6511611yescharacteristic
365C5#7195411yescharacteristic, complemented, Sylow
366C22—41no—
367C22—41no—
368C22—41no—
369C22—201no—
370C22—201no—
371C22—201no—
372C22#9156411yescharacteristic
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—201no—
378C4—201no—
379C4—201no—
380C4—1201no—
381C3#1059915111yescharacteristic, complemented, Sylow
382C2—81no—
383C2—401no—
384C2#1174914511yescharacteristic
385C2#1174945711yescharacteristic
386C2#1174946311yescharacteristic
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#1662
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. #11746936C2semidirect
4. #11746893C2semidirect
5. C5×#4540C2semidirect
6. #11745849C2semidirect
7. #11745846C2semidirect
69. #4540D5semidirect
317. C3×C5#1662semidirect
365. C5#71954semidirect
381. C3#10599151semidirect

Maximal subgroups

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

subgroupindex
C3×#660182
#117511562
#117469362
#117468932
C5×#45402
#117458492
#117458462
#105991513
#719545