Finite Group Databasebeta

← #14412776

Subgroups — #14412776

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×#92101C211yesmaximal, characteristic
2C2×C5×#948C211yesmaximal, characteristic, complemented
3C3×#66161C211yesmaximal, characteristic, complemented
4#11748415C213yesmaximal, complemented
5#11748413C213yesmaximal, complemented
6#11748411C213yesmaximal, complemented
7C2×#90974C213yesmaximal, complemented
8#10615537—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10#92101—24no—
11#92101C418yescomplemented
12C2×Q8×D15—21no—
13C2×#6819—23no—
14C2×#6817C2213yes—
15C22×Dic30C2213yes—
16C5×#948—24no—
17C2×C5×#208C2213yes—
18C22×C5×C3⋊C8C2213yes—
19C3×Q8×Dic5—21no—
20C3×D4×Dic5—23no—
21C3×#4072C2213yes—
22C2×C3×C4⋊Dic5C2213yes—
23#90974C2213yes—
24#90974C2216yes—
25#90974C2213yes—
26#90968C2211yescharacteristic
27#90968C2213yes—
28#82570—51nomaximal, Hall
29C2×#4150—31no—
30C2×C5×#131—31no—
31#66161D311yescharacteristic, complemented
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—
41C2×#1220—23no—
42C22×Dic15—23no—
43Q8×D15—28no—
44#6819—224no—
45#6817—26no—
46#6817C2×C4112yescomplemented
47C2×D60C2311yescharacteristic
48C2×C4×D15—23no—
49C2×Dic30—23no—
50C2×Dic30—26no—
51C2×Dic30C2×C4112yescomplemented
52C2×Dic30C2313yes—
53C22×C3×Dic5—23no—
54C5×#208—26no—
55C2×C5×C3⋊C8—26no—
56C2×C5×C3⋊C8C2311yescharacteristic
57C2×C5×C3⋊C8C2313yes—
58C3×C22⋊Dic5—23no—
59C3×C4⋊Dic5—23no—
60C3×C4⋊Dic5C2313yes—
61C3×C4⋊Dic5C2311yescharacteristic
62C3×C4×Dic5—23no—
63C2×#1010—51no—
64C3×#520—51no—
65C2×#948D511yescharacteristic, complemented
66#5004—53no—
67#5002—53no—
68C2×#810—53no—
69#4966—53no—
70C2×C5×#41C2×D311yescharacteristic
71#4150—38no—
72#4150—64no—
73C2×Q8×D5—61no—
74C2×#711—63no—
75C2×#709—33no—
76C22×Dic10—33no—
77C5×#131—64no—
78C2×C5×M16—33no—
79C22×C5×C8—33no—
80Q8×Dic5—21no—
81D4×Dic5—23no—
82#4072C2×D313yes—
83C2×C4⋊Dic5C2×D313yes—
84#3953—31no—
85#3953—33no—
86#3948—33no—
87#3948—36no—
88#3948—33no—
89#2898—151noSylow
90C23×C3×C5C2×D413yes—
91C22×D15—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
98#1220—212no—
99C2×Dic15—212no—
100C2×Dic15—23no—
101D60—21no—
102D60C22×C412yes—
103C4×D15—212no—
104Dic30—212no—
105Dic30—23no—
106Dic30C22×C416yes—
107C2×C3×Dic5—21no—
108C2×C3×Dic5—23no—
109C2×C3×Dic5—83no—
110C5×C3⋊C8—21no—
111C5×C3⋊C8—23no—
112C2×C3×#41C2×D511yescharacteristic
113#1010—58no—
114#1010—104no—
115C2×D3×Q8—101no—
116C2×#237—103no—
117C2×#235—53no—
118C22×Dic6—53no—
119C3×C4×Q8—101no—
120C3×C4×D4—103no—
121C3×#117—53no—
122C2×C3×C4⋊C4—53no—
123#948—24no—
124C2×#208C2×D513yes—
125C22×C3⋊C8C2×D513yes—
126#810—56no—
127#810—53no—
128#810—53no—
129#809—53no—
130#809—51no—
131C5×#41C4×D314yes—
132C5×#41D1214yes—
133C2×C5×Q8#6711yescharacteristic
134C2×C5×D4#6713yes—
135C22×C4×C5C22×D313yes—
136C2×C22⋊D5—63no—
137C22×Dic5—23no—
138C22×Dic5—63no—
139Q8×D5—68no—
140#711—624no—
141#709—312no—
142#709—66no—
143C2×D20—31no—
144C2×C4×D5—63no—
145C2×Dic10—312no—
146C2×Dic10—33no—
147C2×Dic10—66no—
148C2×Dic10—63no—
149C5×M16—66no—
150C2×C5×C8—31no—
151C2×C5×C8—33no—
152C2×C5×C8—66no—
153C22⋊Dic5—23no—
154C4⋊Dic5—23no—
155C4⋊Dic5C22×D313yes—
156C4⋊Dic5C22×D311yescharacteristic
157C4×Dic5—23no—
158C2×2−1+4—151no—
159C2×#131—31no—
160#520—51no—
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×D15—22no—
170C2×D15—41no—
171C2×D15—41no—
172C3×C4×C5C2×C22⋊C416yes—
173C3×C4×C5C23×C411yescharacteristic
174C3×C4×C5C22×D411yescharacteristic
175Dic15—26no—
176C3×Dic5—43no—
177C3×Dic5—41no—
178C3×#41C4×D514yes—
179C3×#41C22⋊D514yes—
180C2×C3×Q8D2011yescharacteristic
181C2×C3×D4D2013yes—
182C22×C3×C4—103no—
183C22×C3×C4C22×D513yes—
184C2×#67—103no—
185C22×Dic3—103no—
186D3×Q8—108no—
187#237—1024no—
188#235—512no—
189#235—106no—
190C2×D12—51no—
191C2×C4×D3—103no—
192C2×Dic6—512no—
193C2×Dic6—53no—
194C2×Dic6—103no—
195C2×Dic6—106no—
196C3×C4⋊C4—53no—
197C3×C4⋊C4—51no—
198C3×C4⋊C4—103no—
199C3×C22⋊C4—103no—
200C3×C42—103no—
201#208—26no—
202C2×C3⋊C8—26no—
203C2×C3⋊C8C22×D511yescharacteristic
204C2×C3⋊C8C22×D513yes—
205C23×C5C2×#6713yes—
206C22×D5—61no—
207C5×Q8(C2×D3)⋊C414yes—
208C5×D4(C2×D3)⋊C4112yes—
209C2×C4×C5C2×C4×D316yes—
210C2×C4×C5C2×D1216yes—
211C2×C4×C5C2×#6713yes—
212C2×C4×C5C23×D311yescharacteristic
213C22⋊D5—612no—
214C2×Dic5—21no—
215C2×Dic5—23no—
216C2×Dic5—612no—
217C2×Dic5—63no—
218C2×Dic5—83no—
219D20—32no—
220D20—61no—
221C4×D5—612no—
222Dic10—36no—
223Dic10—612no—
224Dic10—63no—
225C5×C8—61no—
226C5×C8—63no—
2272−1+4—158no—
2282−1+4—304no—
229C2×#41—153no—
230C2×#41—303no—
231C2×#41D3×D511yescharacteristic
232C22×Q8—153no—
233C22×Q8—301no—
234#131—64no—
235C2×M16—33no—
236C22×C8—33no—
237C4×Q8—101no—
238C4×D4—103no—
239#117—53no—
240C2×C4⋊C4—53no—
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
250D15—42no—
251C23×C3C2×D2013yes—
252C22×D3—101no—
253C3×Q8#68514yes—
254C3×D4#685112yes—
255C2×C3×C4—101no—
256C2×C3×C4—103no—
257C2×C3×C4—403no—
258C2×C3×C4C2×C4×D516yes—
259C2×C3×C4C2×D2013yes—
260C2×C3×C4C2×C22⋊D516yes—
261C2×C3×C4C23×D511yescharacteristic
262#67—1012no—
263C2×Dic3—103no—
264C2×Dic3—1012no—
265D12—52no—
266D12—101no—
267C4×D3—1012no—
268Dic6—56no—
269Dic6—103no—
270Dic6—1012no—
271C3⋊C8—21no—
272C3⋊C8—23no—
273C22×C5—23no—
274C22×C5—23no—
275C22×C5C2×(C2×D3)⋊C416yes—
276C22×C5C22×#6711yescharacteristic
277C2×D5—62no—
278C2×D5—121no—
279C2×D5—121no—
280C4×C5C2×(C2×D3)⋊C416yes—
281C4×C5C22×C4×D311yescharacteristic
282C4×C5C22×D1211yescharacteristic
283Dic5—43no—
284Dic5—41no—
285Dic5—66no—
286#41—1512no—
287#41—3024no—
288#41—306no—
289#41#120014yes—
290#41#120314yes—
291C2×Q8—1512no—
292C2×Q8—153no—
293C2×Q8—308no—
294C2×Q8—303no—
295C2×Q8—306no—
296C2×Q8#120211yescharacteristic
297C2×D4—151no—
298C2×D4—303no—
299C2×D4#120213yes—
300C22×C4—103no—
301C22×C4—303no—
302C22×C4—303no—
303C22×C4C2×D3×D513yes—
304M16—66no—
305C2×C8—31no—
306C2×C8—33no—
307C2×C8—66no—
308C4⋊C4—53no—
309C4⋊C4—51no—
310C4⋊C4—103no—
311C22⋊C4—103no—
312C42—103no—
313C3×C5#289811yescharacteristic, complemented, Hall
314C22×C3—23no—
315C22×C3—23no—
316C22×C3C2×#68516yes—
317C22×C3C22×D2011yescharacteristic
318C2×D3—102no—
319C2×D3—201no—
320C2×D3—201no—
321C3×C4—203no—
322C3×C4—201no—
323C3×C4C2×#68516yes—
324C3×C4C22×C4×D511yescharacteristic
325C3×C4C22×C22⋊D511yescharacteristic
326Dic3—106no—
327C2×C5—26no—
328C2×C5C22×(C2×D3)⋊C411yescharacteristic
329C2×C5#583611yescharacteristic
330C2×C5#583811yescharacteristic
331D5—122no—
332C23—301no—
333C23C2×#120213yes—
334Q8—156no—
335Q8—303no—
336Q8—3012no—
337Q8#666714yes—
338D4—152no—
339D4—3012no—
340D4—301no—
341D4#6667112yes—
342C2×C4—101no—
343C2×C4—103no—
344C2×C4—303no—
345C2×C4—3012no—
346C2×C4—3012no—
347C2×C4—403no—
348C2×C4C2×#120016yes—
349C2×C4C2×#120213yes—
350C2×C4C2×#120316yes—
351C2×C4C22×D3×D511yescharacteristic
352C8—61no—
353C8—63no—
354C2×C3—26no—
355C2×C3#6608511yescharacteristic
356C2×C3#6608711yescharacteristic
357C2×C3C22×#68511yescharacteristic
358D3—202no—
359C5#8257011yescharacteristic, complemented, Sylow
360C22—23no—
361C22—23no—
362C22—302no—
363C22—601no—
364C22—601no—
365C22C2×#666716yes—
366C22C22×#120211yescharacteristic
367C4—203no—
368C4—201no—
369C4—306no—
370C4C2×#666716yes—
371C4C22×#120011yescharacteristic
372C4C22×#120311yescharacteristic
373C3#1061553711yescharacteristic, complemented, Sylow
374C2—26no—
375C2—602no—
376C2#1175530911yescharacteristic
377C2#1175531211yescharacteristic
378C2C22×#666711yescharacteristic
subgroupG/H
centerC22C22×#1202
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×#92101C2
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. C2×C5×#948C2semidirect
3. C3×#66161C2semidirect
4. #11748415C2semidirect
5. #11748413C2semidirect
6. #11748411C2semidirect
7. C2×#90974C2semidirect
11. #92101C4semidirect
31. #66161D3semidirect
46. #6817C2×C4semidirect
51. C2×Dic30C2×C4semidirect
65. C2×#948D5semidirect
313. C3×C5#2898semidirect
359. C5#82570semidirect
373. C3#10615537semidirect

Maximal subgroups

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

subgroupindex
C2×#921012
C2×C5×#9482
C3×#661612
#117484152
#117484132
#117484112
C2×#909742
#106155373
#825705