Finite Group Databasebeta

← #14412709

Subgroups — #14412709

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
2C3×C5×#520C211yesmaximal, characteristic, complemented
3C2×#91837C211yesmaximal, characteristic, complemented
4#11751105C213yesmaximal, complemented
5#11751103C213yesmaximal, complemented
6C2×#91094C213yesmaximal, complemented
7#11751067C213yesmaximal, complemented
8#10614301—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10#92101—24no—
11#92101C418yescomplemented
12C2×Q8×D15—21no—
13C2×#6819—23no—
14C2×#6817C2213yes—
15C22×Dic30C2213yes—
16C3×C4×C5×Q8—21no—
17C3×C4×C5×D4—23no—
18C3×C5×#117C2213yes—
19C2×C3×C5×C4⋊C4C2213yes—
20#91837—24no—
21C2×#6710C2213yes—
22C22×C3⋊#168C2213yes—
23#91094C2216yes—
24#91094C2213yes—
25#91094C2213yes—
26#91093C2213yes—
27#91093C2211yescharacteristic
28#82570—51nomaximal, Hall
29C2×#4150—31no—
30C5×#520D311yescharacteristic, complemented
31C2×#4094—31no—
32#65293—33no—
33#65291—33no—
34C2×#3942—33no—
35#65255—33no—
36C3×C5×#41C2×C414yes—
37C3×C5×#41D414yes—
38C2×C3×C5×Q8D411yescharacteristic
39C2×C3×C5×D4D413yes—
40C22×C3×C4×C5—23no—
41C22×C3×C4×C5C2313yes—
42C2×#1220—23no—
43C22×Dic15—23no—
44Q8×D15—28no—
45#6819—224no—
46#6817—26no—
47#6817C2×C4112yescomplemented
48C2×D60C2311yescharacteristic
49C2×C4×D15—23no—
50C2×Dic30—23no—
51C2×Dic30—26no—
52C2×Dic30C2×C4112yescomplemented
53C2×Dic30C2313yes—
54C3×C5×C4⋊C4—23no—
55C3×C5×C4⋊C4C2313yes—
56C3×C5×C4⋊C4C2311yescharacteristic
57C3×C5×C22⋊C4—23no—
58C3×C42×C5—23no—
59#6710—26no—
60C2×C3⋊#168—26no—
61C2×C3⋊#168C2311yescharacteristic
62C2×C3⋊#168C2313yes—
63C2×#1010—51no—
64C3×#520D511yescharacteristic, complemented
65C2×#948—51no—
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—
77C4×C5×Q8—21no—
78C4×C5×D4—23no—
79C5×#117C2×D313yes—
80C2×C5×C4⋊C4C2×D313yes—
81#4094—64no—
82C2×#681—33no—
83C22×#168—33no—
84#3942—33no—
85#3942—33no—
86#3942—36no—
87#3941—31no—
88#3941—33no—
89#2898—151noSylow
90C23×C3×C5C2×D413yes—
91C22×D15—21no—
92C3×C5×Q8C22⋊C414yes—
93C3×C5×D4C22⋊C4112yes—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—23no—
96C2×C3×C4×C5—83no—
97C2×C3×C4×C5C22×C416yes—
98C2×C3×C4×C5C2×D413yes—
99C2×C3×C4×C5C2×D416yes—
100C2×C3×C4×C5C2411yescharacteristic
101#1220—212no—
102C2×Dic15—212no—
103C2×Dic15—23no—
104D60—21no—
105D60C22×C412yes—
106C4×D15—212no—
107Dic30—212no—
108Dic30—23no—
109Dic30C22×C416yes—
110C3⋊#168—21no—
111C3⋊#168—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—21no—
120C3×C4×D4—23no—
121C3×#117C2×D513yes—
122C2×C3×C4⋊C4C2×D513yes—
123#948—104no—
124C2×#208—53no—
125C22×C3⋊C8—53no—
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×C5—23no—
136C22×C4×C5C22×D313yes—
137C2×C22⋊D5—63no—
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×C4⋊C4—23no—
150C5×C4⋊C4C22×D313yes—
151C5×C4⋊C4C22×D311yescharacteristic
152C5×C22⋊C4—23no—
153C42×C5—23no—
154#681—66no—
155C2×#168—31no—
156C2×#168—33no—
157C2×#168—66no—
158C2×2−1+4—151no—
159C2×#131—151no—
160#520D1511yescharacteristic, complemented
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×C5—43no—
173C3×C4×C5—41no—
174C3×C4×C5C2×C22⋊C416yes—
175C3×C4×C5C23×C411yescharacteristic
176C3×C4×C5C22×D411yescharacteristic
177Dic15—26no—
178C3×#41C4×D514yes—
179C3×#41D2014yes—
180C2×C3×Q8C22⋊D511yescharacteristic
181C2×C3×D4C22⋊D513yes—
182C22×C3×C4—23no—
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—106no—
195C2×Dic6—103no—
196C3×C4⋊C4—23no—
197C3×C4⋊C4C22×D513yes—
198C3×C4⋊C4C22×D511yescharacteristic
199C3×C22⋊C4—23no—
200C3×C42—23no—
201#208—106no—
202C2×C3⋊C8—51no—
203C2×C3⋊C8—53no—
204C2×C3⋊C8—106no—
205C23×C5C2×#6713yes—
206C22×D5—61no—
207C5×Q8(C2×D3)⋊C414yes—
208C5×D4(C2×D3)⋊C4112yes—
209C2×C4×C5—21no—
210C2×C4×C5—23no—
211C2×C4×C5—83no—
212C2×C4×C5C2×C4×D316yes—
213C2×C4×C5C2×D1216yes—
214C2×C4×C5C2×#6713yes—
215C2×C4×C5C23×D311yescharacteristic
216C22⋊D5—612no—
217C2×Dic5—612no—
218C2×Dic5—63no—
219D20—32no—
220D20—61no—
221C4×D5—612no—
222Dic10—36no—
223Dic10—612no—
224Dic10—63no—
225#168—61no—
226#168—63no—
2272−1+4—158no—
2282−1+4—304no—
229C2×#41—153no—
230C2×#41—303no—
231C2×#41C2×D1511yescharacteristic
232C22×Q8—153no—
233C22×Q8—301no—
234#131—304no—
235C2×M16—153no—
236C22×C8—153no—
237C4×Q8—21no—
238C4×D4—23no—
239#117C2×D1513yes—
240C2×C4⋊C4C2×D1513yes—
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×C22⋊D513yes—
252C22×D3—101no—
253C3×Q8#68514yes—
254C3×D4#685112yes—
255C2×C3×C4—21no—
256C2×C3×C4—23no—
257C2×C3×C4—83no—
258C2×C3×C4C2×C4×D516yes—
259C2×C3×C4C2×D2016yes—
260C2×C3×C4C2×C22⋊D513yes—
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—101no—
272C3⋊C8—103no—
273C22×C5—23no—
274C22×C5—23no—
275C22×C5C2×(C2×D3)⋊C416yes—
276C22×C5C22×#6711yescharacteristic
277C2×D5—62no—
278C2×D5—121no—
279C2×D5—121no—
280C4×C5—43no—
281C4×C5—41no—
282C4×C5C2×(C2×D3)⋊C416yes—
283C4×C5C22×C4×D311yescharacteristic
284C4×C5C22×D1211yescharacteristic
285Dic5—66no—
286#41—1512no—
287#41—3024no—
288#41—306no—
289#41C4×D1514yes—
290#41D6014yes—
291C2×Q8—1512no—
292C2×Q8—153no—
293C2×Q8—308no—
294C2×Q8—306no—
295C2×Q8—303no—
296C2×Q8#122011yescharacteristic
297C2×D4—151no—
298C2×D4—303no—
299C2×D4#122013yes—
300C22×C4—23no—
301C22×C4—303no—
302C22×C4—303no—
303C22×C4C22×D1513yes—
304M16—306no—
305C2×C8—151no—
306C2×C8—153no—
307C2×C8—306no—
308C4⋊C4—23no—
309C4⋊C4C22×D1513yes—
310C4⋊C4C22×D1511yescharacteristic
311C22⋊C4—23no—
312C42—23no—
313C3×C5#289811yescharacteristic, complemented, Hall
314C22×C3—23no—
315C22×C3—23no—
316C22×C3C2×#68516yes—
317C22×C3C22×C22⋊D511yescharacteristic
318C2×D3—102no—
319C2×D3—201no—
320C2×D3—201no—
321C3×C4—43no—
322C3×C4—41no—
323C3×C4C2×#68516yes—
324C3×C4C22×C4×D511yescharacteristic
325C3×C4C22×D2011yescharacteristic
326Dic3—106no—
327C2×C5—26no—
328C2×C5C22×(C2×D3)⋊C411yescharacteristic
329C2×C5#583611yescharacteristic
330C2×C5#583811yescharacteristic
331D5—122no—
332C23—301no—
333C23C2×#122013yes—
334Q8—156no—
335Q8—3012no—
336Q8—303no—
337Q8#671414yes—
338D4—152no—
339D4—3012no—
340D4—301no—
341D4#6714112yes—
342C2×C4—21no—
343C2×C4—23no—
344C2×C4—83no—
345C2×C4—3012no—
346C2×C4—303no—
347C2×C4—3012no—
348C2×C4C2×C4×D1516yes—
349C2×C4C2×D6016yes—
350C2×C4C2×#122013yes—
351C2×C4C23×D1511yescharacteristic
352C8—301no—
353C8—303no—
354C2×C3—26no—
355C2×C3C22×#68511yescharacteristic
356C2×C3#6617011yescharacteristic
357C2×C3#6617211yescharacteristic
358D3—202no—
359C5#8257011yescharacteristic, complemented, Sylow
360C22—23no—
361C22—23no—
362C22—302no—
363C22—601no—
364C22—601no—
365C22C2×#671416yes—
366C22C22×#122011yescharacteristic
367C4—43no—
368C4—41no—
369C4—306no—
370C4C2×#671416yes—
371C4C22×C4×D1511yescharacteristic
372C4C22×D6011yescharacteristic
373C3#1061430111yescharacteristic, complemented, Sylow
374C2—26no—
375C2—602no—
376C2C22×#671411yescharacteristic
377C2#1175659511yescharacteristic
378C2#1175659711yescharacteristic
subgroupG/H
centerC22C22×#1220
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#520C2
socleC22×C3×C5C22×D4
prime radicalC2×#92101C2
cosocleC2×C3×C4×C5C24
hypercenter#520D15
hypocenterC3×C5#2898
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41 ◁ #520

Complements

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

NH ≅ G/Ntype
2. C3×C5×#520C2semidirect
3. C2×#91837C2semidirect
4. #11751105C2semidirect
5. #11751103C2semidirect
6. C2×#91094C2semidirect
7. #11751067C2semidirect
11. #92101C4semidirect
30. C5×#520D3semidirect
47. #6817C2×C4semidirect
52. C2×Dic30C2×C4semidirect
64. C3×#520D5semidirect
160. #520D15semidirect
313. C3×C5#2898semidirect
359. C5#82570semidirect
373. C3#10614301semidirect

Maximal subgroups

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

subgroupindex
C2×#921012
C3×C5×#5202
C2×#918372
#117511052
#117511032
C2×#910942
#117510672
#106143013
#825705