Finite Group Databasebeta

← #14412777

Subgroups — #14412777

Order 1920.

1452 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4150C211yesmaximal, characteristic
2#11756586C211yesmaximal, characteristic, complemented
3C2×C5×#948C211yesmaximal, characteristic, complemented
4#11748400C213yesmaximal, complemented
5C2×#90971C213yesmaximal, complemented
6#11748369C213yesmaximal, complemented
7#11748365C213yesmaximal, complemented
8#10615537—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C3×#4150—24no—
11C3×#4150C418yescomplemented
12C2×C3×Q8×D5—21no—
13C2×C3×#711—23no—
14C2×C3×#709C2213yes—
15C22×C3×Dic10C2213yes—
16Q8×Dic15—21no—
17D4×Dic15—23no—
18#91815C2213yes—
19C2×C4⋊Dic15C2213yes—
20C5×#948—24no—
21C2×C5×#208C2213yes—
22C22×C5×C3⋊C8C2213yes—
23#90971C2213yes—
24#90971C2213yes—
25#90971C2216yes—
26#90965C2211yescharacteristic
27#90965C2213yes—
28#84111—51nomaximal, Hall
29C2×#4150D311yescharacteristic
30C2×C5×#131—31no—
31#66161—31no—
32#65422—33no—
33#65409—33no—
34#65402—33no—
35C2×#3948—33no—
36C3×C5×#41C2×C414yes—
37C3×C5×#41D414yes—
38C2×C3×C5×Q8D411yescharacteristic
39C2×C3×C5×D4D413yes—
40C22×C3×C4×C5C2313yes—
41C22×Dic15—23no—
42C2×C3×C22⋊D5—23no—
43C22×C3×Dic5—23no—
44C3×Q8×D5—28no—
45C3×#711—224no—
46C3×#709—26no—
47C3×#709C2×C4112yescomplemented
48C2×C3×D20C2311yescharacteristic
49C2×C3×C4×D5—23no—
50C2×C3×Dic10—23no—
51C2×C3×Dic10—26no—
52C2×C3×Dic10C2×C4112yescomplemented
53C2×C3×Dic10C2313yes—
54#6719—23no—
55C4⋊Dic15—23no—
56C4⋊Dic15C2313yes—
57C4⋊Dic15C2311yescharacteristic
58C4×Dic15—23no—
59C5×#208—26no—
60C2×C5×C3⋊C8—26no—
61C2×C5×C3⋊C8C2311yescharacteristic
62C2×C5×C3⋊C8C2313yes—
63C2×C3×2−1+4—51no—
64#5827—51no—
65C2×#948D511yescharacteristic, complemented
66#5233—53no—
67#5232—53no—
68#5225—53no—
69C2×#835—53no—
70C2×C5×#41C2×D311yescharacteristic
71#4150—24no—
72#4150Dic318yescomplemented
73C2×Q8×D5—21no—
74C2×#711—23no—
75C2×#709C2×D313yes—
76C22×Dic10C2×D313yes—
77C5×#131—64no—
78C2×C5×M16—33no—
79C22×C5×C8—33no—
80Q8×Dic5—61no—
81D4×Dic5—63no—
82#4072—33no—
83C2×C4⋊Dic5—33no—
84#3953—31no—
85#3953—33no—
86#3948—33no—
87#3948—36no—
88#3948—33no—
89#2898—151noSylow
90C23×C3×C5C2×D413yes—
91C22×C3×D5—21no—
92C3×C5×Q8C22⋊C414yes—
93C3×C5×D4C22⋊C4112yes—
94C2×C3×C4×C5C22×C416yes—
95C2×C3×C4×C5C2×D413yes—
96C2×C3×C4×C5C2×D416yes—
97C2×C3×C4×C5C2411yescharacteristic
98C2×Dic15—21no—
99C2×Dic15—23no—
100C2×Dic15—83no—
101C3×C22⋊D5—212no—
102C2×C3×Dic5—212no—
103C2×C3×Dic5—23no—
104C3×D20—21no—
105C3×D20C22×C412yes—
106C3×C4×D5—212no—
107C3×Dic10—212no—
108C3×Dic10—23no—
109C3×Dic10C22×C416yes—
110C5×C3⋊C8—21no—
111C5×C3⋊C8—23no—
112C3×2−1+4—58no—
113C3×2−1+4—104no—
114C2×C3×#41—53no—
115C2×C3×#41—103no—
116C2×C3×#41C2×D511yescharacteristic
117C22×C3×Q8—53no—
118C22×C3×Q8—101no—
119#948—24no—
120Q8×Dic3—101no—
121D4×Dic3—103no—
122#926—53no—
123C2×C4⋊Dic3—53no—
124C2×#208C2×D513yes—
125C22×C3⋊C8C2×D513yes—
126#835—53no—
127#835—56no—
128#835—53no—
129#832—53no—
130#832—51no—
131C5×#41C2×Dic314yes—
132C5×#41#6714yes—
133C2×C5×Q8#6711yescharacteristic
134C2×C5×D4#6713yes—
135C22×C4×C5C22×D313yes—
136C2×C22⋊D5—23no—
137C22×Dic5—23no—
138C22×Dic5—63no—
139Q8×D5—28no—
140#711—224no—
141#709—26no—
142#709C2×Dic3112yescomplemented
143C2×D20C22×D311yescharacteristic
144C2×C4×D5—23no—
145C2×Dic10—23no—
146C2×Dic10—26no—
147C2×Dic10C2×Dic3112yescomplemented
148C2×Dic10C22×D313yes—
149C5×M16—66no—
150C2×C5×C8—31no—
151C2×C5×C8—33no—
152C2×C5×C8—66no—
153C22⋊Dic5—63no—
154C4⋊Dic5—33no—
155C4⋊Dic5—31no—
156C4⋊Dic5—63no—
157C4×Dic5—63no—
158C2×2−1+4—51no—
159C2×#131—31no—
160#520—151no—
161#419—153no—
162#417—153no—
163#416—153no—
164C2×#103—153no—
165C22×C3×C5—23no—
166C22×C3×C5—23no—
167C22×C3×C5C2×C22⋊C416yes—
168C22×C3×C5C22×D411yescharacteristic
169C2×C3×D5—22no—
170C2×C3×D5—41no—
171C2×C3×D5—41no—
172C3×C4×C5C2×C22⋊C416yes—
173C3×C4×C5C23×C411yescharacteristic
174C3×C4×C5C22×D411yescharacteristic
175Dic15—43no—
176Dic15—41no—
177C3×Dic5—26no—
178C3×#41—512no—
179C3×#41—1024no—
180C3×#41—106no—
181C3×#41C4×D514yes—
182C3×#41C22⋊D514yes—
183C2×C3×Q8—512no—
184C2×C3×Q8—53no—
185C2×C3×Q8—108no—
186C2×C3×Q8—103no—
187C2×C3×Q8—106no—
188C2×C3×Q8D2011yescharacteristic
189C2×C3×D4—51no—
190C2×C3×D4—103no—
191C2×C3×D4D2013yes—
192C22×C3×C4—103no—
193C22×C3×C4—103no—
194C22×C3×C4C22×D513yes—
195C22×Dic3—103no—
196#217—103no—
197C4⋊Dic3—53no—
198C4⋊Dic3—51no—
199C4⋊Dic3—103no—
200C4×Dic3—103no—
201#208—26no—
202C2×C3⋊C8—26no—
203C2×C3⋊C8C22×D511yescharacteristic
204C2×C3⋊C8C22×D513yes—
205C23×C5C2×#6713yes—
206C22×D5—21no—
207C5×Q8#21714yes—
208C5×D4#217112yes—
209C2×C4×C5C22×Dic316yes—
210C2×C4×C5C2×#6716yes—
211C2×C4×C5C2×#6713yes—
212C2×C4×C5C23×D311yescharacteristic
213C22⋊D5—212no—
214C2×Dic5—212no—
215C2×Dic5—23no—
216C2×Dic5—61no—
217C2×Dic5—63no—
218C2×Dic5—243no—
219D20—21no—
220D20C22×Dic312yes—
221C4×D5—212no—
222Dic10—212no—
223Dic10—23no—
224Dic10C22×Dic316yes—
225C5×C8—61no—
226C5×C8—63no—
2272−1+4—58no—
2282−1+4—104no—
229C2×#41—53no—
230C2×#41—103no—
231C2×#41D3×D511yescharacteristic
232C22×Q8—53no—
233C22×Q8—101no—
234#131—64no—
235C2×M16—33no—
236C22×C8—33no—
237C4×Q8—301no—
238C4×D4—303no—
239#117—153no—
240C2×C4⋊C4—153no—
241#103—153no—
242#103—156no—
243#103—153no—
244#102—151no—
245#102—153no—
246C2×C3×C5—26no—
247C2×C3×C5C22×C22⋊C411yescharacteristic
248C2×C3×C5#57711yescharacteristic
249C2×C3×C5#57811yescharacteristic
250C3×D5—42no—
251C23×C3—101no—
252C23×C3C2×D2013yes—
253C3×Q8—56no—
254C3×Q8—103no—
255C3×Q8—1012no—
256C3×Q8#68514yes—
257C3×D4—52no—
258C3×D4—1012no—
259C3×D4—101no—
260C3×D4#685112yes—
261C2×C3×C4—103no—
262C2×C3×C4—1012no—
263C2×C3×C4—1012no—
264C2×C3×C4C2×C4×D516yes—
265C2×C3×C4C2×D2013yes—
266C2×C3×C4C2×C22⋊D516yes—
267C2×C3×C4C23×D511yescharacteristic
268C2×Dic3—101no—
269C2×Dic3—103no—
270C2×Dic3—403no—
271C3⋊C8—21no—
272C3⋊C8—23no—
273C22×C5—23no—
274C22×C5—23no—
275C22×C5C2×#21716yes—
276C22×C5C22×#6711yescharacteristic
277C2×D5—22no—
278C2×D5—41no—
279C2×D5—41no—
280C4×C5C2×#21716yes—
281C4×C5C23×Dic311yescharacteristic
282C4×C5C22×#6711yescharacteristic
283Dic5—26no—
284Dic5—123no—
285Dic5—121no—
286#41—512no—
287#41—1024no—
288#41—106no—
289#41D5×Dic314yes—
290#41#120114yes—
291C2×Q8—512no—
292C2×Q8—53no—
293C2×Q8—108no—
294C2×Q8—106no—
295C2×Q8—103no—
296C2×Q8#120211yescharacteristic
297C2×D4—51no—
298C2×D4—103no—
299C2×D4#120213yes—
300C22×C4—103no—
301C22×C4—103no—
302C22×C4—303no—
303C22×C4C2×D3×D513yes—
304M16—66no—
305C2×C8—31no—
306C2×C8—33no—
307C2×C8—66no—
308C4⋊C4—153no—
309C4⋊C4—151no—
310C4⋊C4—303no—
311C22⋊C4—303no—
312C42—303no—
313C3×C5#289811yescharacteristic, complemented, Hall
314C22×C3—23no—
315C22×C3—23no—
316C22×C3—102no—
317C22×C3—201no—
318C22×C3—201no—
319C22×C3C2×#68516yes—
320C22×C3C22×D2011yescharacteristic
321C3×C4—106no—
322C3×C4C2×#68516yes—
323C3×C4C22×C4×D511yescharacteristic
324C3×C4C22×C22⋊D511yescharacteristic
325Dic3—203no—
326Dic3—201no—
327C2×C5—26no—
328C2×C5#583711yescharacteristic
329C2×C5#583811yescharacteristic
330C2×C5C22×#21711yescharacteristic
331D5—42no—
332C23—101no—
333C23C2×#120213yes—
334Q8—56no—
335Q8—103no—
336Q8—1012no—
337Q8#666514yes—
338D4—52no—
339D4—1012no—
340D4—101no—
341D4#6665112yes—
342C2×C4—103no—
343C2×C4—1012no—
344C2×C4—1012no—
345C2×C4—301no—
346C2×C4—303no—
347C2×C4—1203no—
348C2×C4C2×D5×Dic316yes—
349C2×C4C2×#120116yes—
350C2×C4C2×#120213yes—
351C2×C4C22×D3×D511yescharacteristic
352C8—61no—
353C8—63no—
354C2×C3—26no—
355C2×C3—202no—
356C2×C3#6608511yescharacteristic
357C2×C3#6608711yescharacteristic
358C2×C3C22×#68511yescharacteristic
359C5#8411111yescharacteristic, complemented, Sylow
360C22—23no—
361C22—23no—
362C22—102no—
363C22—201no—
364C22—201no—
365C22C2×#666516yes—
366C22C22×#120211yescharacteristic
367C4—106no—
368C4—603no—
369C4—601no—
370C4C2×#666516yes—
371C4C22×D5×Dic311yescharacteristic
372C4C22×#120111yescharacteristic
373C3#1061553711yescharacteristic, complemented, Sylow
374C2—26no—
375C2—202no—
376C2#1175531011yescharacteristic
377C2#1175531211yescharacteristic
378C2C22×#666511yescharacteristic
subgroupG/H
centerC22C22×#1202
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4150C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5#2898
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11756586C2semidirect
3. C2×C5×#948C2semidirect
4. #11748400C2semidirect
5. C2×#90971C2semidirect
6. #11748369C2semidirect
7. #11748365C2semidirect
11. C3×#4150C4semidirect
47. C3×#709C2×C4semidirect
52. C2×C3×Dic10C2×C4semidirect
65. C2×#948D5semidirect
72. #4150Dic3semidirect
142. #709C2×Dic3semidirect
147. C2×Dic10C2×Dic3semidirect
313. C3×C5#2898semidirect
359. C5#84111semidirect
373. C3#10615537semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41502
#117565862
C2×C5×#9482
#117484002
C2×#909712
#117483692
#117483652
#106155373
#841115