Finite Group Databasebeta

← #14291058

Subgroups — #14291058

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×#66033C211yesmaximal, characteristic
2C5×#5064C211yesmaximal, characteristic, complemented
3#11747080C211yesmaximal, characteristic
4#11746970C211yesmaximal, characteristic, complemented
5#11746364C211yesmaximal, characteristic, complemented
6#11745849C211yesmaximal, characteristic, complemented
7#11745846C211yesmaximal, characteristic
8#10602184—31nomaximal, Hall
9C3×C5×#125C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×#4044—21no—
12C3×#4044—21no—
13C3×#4043—21no—
14C3×#4042—21no—
15C3×#4040—21no—
16C3×#4034—21no—
17C3×#4021C2211yescharacteristic
18C3×#4016C2211yescharacteristic
19C2×#6661—21no—
20C2×#6655—21no—
21#91087C2211yescharacteristic
22#91087C2211yescharacteristic
23C5×#808—21no—
24C5×#807—21no—
25C5×#803C2211yescharacteristic
26#90989—21no—
27#90986—21no—
28#71956—51nomaximal, Hall
29#66033D311yescharacteristic
30C5×#501—31no—
31#65375—31no—
32#65369—31no—
33#64763—31no—
34#64685—31no—
35#64684—31no—
36C2×C5×Dic6—21no—
37C2×C3×D20D411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×Dic10—21no—
40C2×C3×Dic10D411yescharacteristic
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4—21no—
43C3×C5×C4⋊C4D411yescharacteristic
44C3×C5×C4⋊C4D411yescharacteristic
45C3×C42×C5C2311yescharacteristic
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C5×C4⋊Dic3—21no—
49C5×C4⋊Dic3—21no—
50C2×C5×C3⋊C8—21no—
51C3×#685—21no—
52C3×#685—21no—
53C3×#685—21no—
54C3×#685—21no—
55C3×#685—21no—
56C3×C4⋊Dic5—21no—
57C3×C4⋊Dic5D411yescharacteristic
58C3×C4⋊Dic5D411yescharacteristic
59C3×#683—21no—
60C3×#683—21no—
61C3×#683—21no—
62C3×C4×Dic5—21no—
63#6661—42no—
64#6655—42no—
65C3×#563—51no—
66#5064—51no—
67#5064D511yescharacteristic, complemented
68#5060—51no—
69#4543—51no—
70#4543—51no—
71#4540—51no—
72C5×C4⋊Q8—31no—
73C5×#125C2×D311yescharacteristic
74C2×#689—61no—
75C2×#688—61no—
76#4044—21no—
77#4044—21no—
78#4043—21no—
79#4042—21no—
80#4040—21no—
81#4034—21no—
82#4021C2×D311yescharacteristic
83#4016C2×D311yescharacteristic
84C5×#107—61no—
85C5×#106—61no—
86C5×#97—31no—
87#3940—61no—
88#3939—61no—
89#3935—31no—
90#3935—31no—
91#1660—151noSylow
92C22×C3×D5—21no—
93C2×C3×C4×C5—21no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5C2×D411yescharacteristic
96C2×C3×C4×C5C2×D411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C5×Dic3—41no—
99C5×Dic6—41no—
100C5×Dic6—41no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—21no—
103C2×C3×Dic5—21no—
104C3×D20—41no—
105C3×C4×D5—81no—
106C3×Dic10—41no—
107C3×Dic10—81no—
108C3⋊#168—22no—
109C3⋊#168—22no—
110C5×C3⋊C8—22no—
111C3×C4⋊Q8—101no—
112C3×#126—101no—
113C3×#126—101no—
114C3×#125—51no—
115C3×#125C2×D511yescharacteristic
116C3×#124—51no—
117C3×#123—101no—
118C3×C22⋊Q8—101no—
119C3×C22⋊Q8—101no—
120C2×#216—101no—
121C2×#214—101no—
122#869C2×D511yescharacteristic
123#808—21no—
124#808—101no—
125#807—21no—
126#807—101no—
127#803—51no—
128#803—51no—
129#803C2×D511yescharacteristic
130C2×C5×Q8—61no—
131C2×D20#6711yescharacteristic
132C2×C4×D5—21no—
133C2×Dic10—21no—
134C2×Dic10#6711yescharacteristic
135C2×C5×C8—61no—
136C5×C4⋊C4—21no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—61no—
139C5×C4⋊C4—61no—
140C5×C4⋊C4#6711yescharacteristic
141C5×C4⋊C4#6711yescharacteristic
142C42×C5C22×D311yescharacteristic
143#689—122no—
144#688—122no—
145#685—21no—
146#685—21no—
147#685—21no—
148#685—21no—
149#685—21no—
150C4⋊Dic5—21no—
151C4⋊Dic5#6711yescharacteristic
152C4⋊Dic5#6711yescharacteristic
153#683—21no—
154#683—21no—
155#683—21no—
156C4×Dic5—21no—
157C2×#168—61no—
158C2×#168—61no—
159#563—51no—
160#501—31no—
161#501—151no—
162#497—151no—
163#330—151no—
164#330—151no—
165#329—151no—
166C22×C3×C5#12011yescharacteristic
167C2×C3×D5—41no—
168C2×C3×D5—41no—
169C2×C3×D5—41no—
170C3×C4×C5—21no—
171C3×C4×C5—21no—
172C3×C4×C5—21no—
173C3×C4×C5—41no—
174C3×C4×C5—41no—
175C3×Dic5—41no—
176C3×Dic5—41no—
177C3×Dic5—41no—
178C5×Dic3—81no—
179C2×C3×Q8—51no—
180C2×C3×Q8—101no—
181C2×C3×D4—51no—
182C22×C3×C4—101no—
183C2×Dic6—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—51no—
187C3×C4⋊C4—51no—
188C3×C4⋊C4—101no—
189C3×C4⋊C4—101no—
190C3×C4⋊C4—101no—
191C3×C4⋊C4—101no—
192C3×C4⋊C4C22⋊D511yescharacteristic
193C3×C4⋊C4C22⋊D511yescharacteristic
194C3×C22⋊C4—101no—
195C3×C22⋊C4—101no—
196C3×C22⋊C4—101no—
197C3×C22⋊C4—101no—
198C3×C22⋊C4—101no—
199C3×C42—101no—
200C3×C42C22×D511yescharacteristic
201#216—202no—
202#214—202no—
203C4⋊Dic3—21no—
204C4⋊Dic3—21no—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—101no—
207C2×C3⋊C8—101no—
208C22×D5—21no—
209C5×Q8—121no—
210C5×Q8—121no—
211C2×C4×C5—21no—
212C2×C4×C5—21no—
213C2×C4×C5—121no—
214C2×C4×C5C2×#6711yescharacteristic
215C2×C4×C5C2×#6711yescharacteristic
216C2×C4×C5C2×#6711yescharacteristic
217C2×Dic5—21no—
218C2×Dic5—21no—
219C2×Dic5—21no—
220D20—41no—
221C4×D5—81no—
222Dic10—41no—
223Dic10—81no—
224C5×C8—62no—
225#168—62no—
226#168—62no—
227C2×Q16—301no—
228C2×SD16—301no—
229C4⋊Q8—31no—
230C4⋊Q8—101no—
231#126—101no—
232#126—101no—
233#125—51no—
234#125D3×D511yescharacteristic
235#124—51no—
236#123—101no—
237C22⋊Q8—101no—
238C22⋊Q8—101no—
239#107—61no—
240#107—301no—
241#106—61no—
242#106—301no—
243#97—31no—
244#97—151no—
245#97—151no—
246C2×C3×C5#45311yescharacteristic
247C2×C3×C5#45611yescharacteristic
248C2×C3×C5#45611yescharacteristic
249C3×D5—81no—
250C23×C3—101no—
251C3×Q8—201no—
252C3×Q8—401no—
253C3×D4—201no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—101no—
257C2×C3×C4—101no—
258C2×C3×C4—101no—
259C2×C3×C4—401no—
260C2×C3×C4D4×D511yescharacteristic
261C2×C3×C4D4×D511yescharacteristic
262C2×C3×C4C2×C22⋊D511yescharacteristic
263C2×Dic3—41no—
264Dic6—41no—
265Dic6—41no—
266C3⋊C8—22no—
267C3⋊C8—102no—
268C3⋊C8—102no—
269C22×C5#95311yescharacteristic
270C2×D5—41no—
271C2×D5—41no—
272C2×D5—41no—
273C4×C5—21no—
274C4×C5—21no—
275C4×C5—21no—
276C4×C5—41no—
277C4×C5—41no—
278C4×C5—241no—
279Dic5—41no—
280Dic5—41no—
281Dic5—41no—
282C2×Q8—51no—
283C2×Q8—61no—
284C2×Q8—101no—
285C2×D4—51no—
286C22×C4—101no—
287Q16—602no—
288SD16—602no—
289C2×C8—61no—
290C2×C8—301no—
291C2×C8—301no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—51no—
295C4⋊C4—51no—
296C4⋊C4—61no—
297C4⋊C4—61no—
298C4⋊C4—101no—
299C4⋊C4—101no—
300C4⋊C4—101no—
301C4⋊C4—101no—
302C4⋊C4#120111yescharacteristic
303C4⋊C4#120111yescharacteristic
304C22⋊C4—101no—
305C22⋊C4—101no—
306C22⋊C4—101no—
307C22⋊C4—101no—
308C22⋊C4—101no—
309C42—101no—
310C42C2×D3×D511yescharacteristic
311C3×C5#166011yescharacteristic, complemented, Hall
312C22×C3—201no—
313C22×C3—201no—
314C22×C3—201no—
315C22×C3#408311yescharacteristic
316C3×C4—21no—
317C3×C4—21no—
318C3×C4—21no—
319C3×C4—41no—
320C3×C4—41no—
321C3×C4—201no—
322C3×C4—201no—
323C3×C4—201no—
324Dic3—81no—
325C2×C5#524111yescharacteristic
326C2×C5#524611yescharacteristic
327C2×C5#524611yescharacteristic
328D5—81no—
329C23—101no—
330Q8—121no—
331Q8—121no—
332Q8—201no—
333Q8—401no—
334D4—201no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—101no—
338C2×C4—101no—
339C2×C4—101no—
340C2×C4—121no—
341C2×C4—401no—
342C2×C4C2×#120111yescharacteristic
343C2×C4D5×#6711yescharacteristic
344C2×C4D5×#6711yescharacteristic
345C8—62no—
346C8—302no—
347C8—302no—
348C2×C3—401no—
349C2×C3#6538411yescharacteristic
350C2×C3#6548711yescharacteristic
351C2×C3#6549411yescharacteristic
352C5#7195611yescharacteristic, complemented, Sylow
353C22—201no—
354C22—201no—
355C22—201no—
356C22#9156311yescharacteristic
357C4—21no—
358C4—21no—
359C4—21no—
360C4—41no—
361C4—41no—
362C4—201no—
363C4—201no—
364C4—201no—
365C4—241no—
366C3#1060218411yescharacteristic, complemented, Sylow
367C2—401no—
368C2#1174939011yescharacteristic
369C2#1174941711yescharacteristic
370C2#1174946211yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5#120
prime radicalC2×C3×D20D4
hypercenter#125D3×D5
hypocenterC3×C5#1660
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. C5×#5064C2semidirect
4. #11746970C2semidirect
5. #11746364C2semidirect
6. #11745849C2semidirect
67. #5064D5semidirect
311. C3×C5#1660semidirect
352. C5#71956semidirect
366. C3#10602184semidirect

Maximal subgroups

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

subgroupindex
C3×#660332
C5×#50642
#117470802
#117469702
#117463642
#117458492
#117458462
#106021843
#719565