Finite Group Databasebeta

← #14412688

Subgroups — #14412688

Order 1920.

1556 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#1009C211yesmaximal, characteristic
2#11756586C211yesmaximal, characteristic, complemented
3C2×C3×#4094C211yesmaximal, characteristic, complemented
4#11748390C213yesmaximal, complemented
5#11748389C213yesmaximal, complemented
6#11748388C213yesmaximal, complemented
7C2×#90967C213yesmaximal, complemented
8#10615830—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C5×#1009—24no—
11C5×#1009C418yescomplemented
12C2×C5×#239—21no—
13C2×C5×D3×D4—23no—
14C2×C5×#235C2213yes—
15C22×C5×D12C2213yes—
16Q8×Dic15—21no—
17D4×Dic15—23no—
18#91815C2213yescomplemented
19C2×C4⋊Dic15C2213yescomplemented
20C3×#4094—24no—
21C2×C3×#681C2213yescomplemented
22C22×C3×#168C2213yescomplemented
23#90973C2211yescharacteristic, complemented
24#90973C2213yescomplemented
25#90967C2213yescomplemented
26#90967C2216yescomplemented
27#90967C2213yescomplemented
28#83797—51nomaximal, Hall
29C2×C5×H(5,𝔽2)—31no—
30#66161—31no—
31C2×#4094D311yescharacteristic, complemented
32#65522—33no—
33#65521—33no—
34#65504—33no—
35C2×#3964—33no—
36C23×C5×D3—23no—
37C3×C5×#41C2×C414yes—
38C3×C5×#41D414yes—
39C2×C3×C5×Q8D411yescharacteristic
40C2×C3×C5×D4D413yes—
41C22×C3×C4×C5C2313yes—
42C22×Dic15—23no—
43C2×C5×#67—23no—
44C5×#239—28no—
45C5×D3×D4—224no—
46C5×#235—26no—
47C5×#235C2×C4112yescomplemented
48C2×C5×D12—23no—
49C2×C5×D12—26no—
50C2×C5×D12C2×C4112yescomplemented
51C2×C5×D12C2313yes—
52C2×C4×C5×D3—23no—
53C2×C5×Dic6C2311yescharacteristic
54#6719—23no—
55C4⋊Dic15—23no—
56C4⋊Dic15C2313yes—
57C4⋊Dic15C2311yescharacteristic
58C4×Dic15—23no—
59C3×#681—26no—
60C2×C3×#168—26no—
61C2×C3×#168C2311yescharacteristic
62C2×C3×#168C2313yes—
63C2×#1009D511yescharacteristic
64C2×C3×#131—51no—
65#5827—51no—
66#5133—53no—
67#5131—53no—
68#5113—53no—
69C2×#821—53no—
70C5×H(5,𝔽2)—38no—
71C5×H(5,𝔽2)—64no—
72C2×C5×#41—33no—
73C2×C5×#41—61no—
74C2×C5×#41C2×D311yescharacteristic
75C22×C5×D4—33no—
76C22×C5×D4—63no—
77#4094—24no—
78Q8×Dic5—61no—
79D4×Dic5—63no—
80#4072—33no—
81C2×C4⋊Dic5—33no—
82C2×#681C2×D313yescomplemented
83C22×#168C2×D313yescomplemented
84#3967—33no—
85#3967—31no—
86#3964—33no—
87#3964—36no—
88#3964—33no—
89#2897—151noSylow
90C23×C3×C5C2×D413yes—
91C22×C5×D3—23no—
92C22×C5×D3—212no—
93C22×C5×D3—83no—
94C22×C5×D3—83no—
95C3×C5×Q8C22⋊C414yes—
96C3×C5×D4C22⋊C4112yes—
97C2×C3×C4×C5C22×C416yes—
98C2×C3×C4×C5C2×D413yes—
99C2×C3×C4×C5C2×D416yes—
100C2×C3×C4×C5C2411yescharacteristic
101C2×Dic15—21no—
102C2×Dic15—23no—
103C2×Dic15—83no—
104C5×#67—212no—
105C2×C5×Dic3—21no—
106C5×D12—212no—
107C5×D12—23no—
108C5×D12C22×C416yes—
109C4×C5×D3—212no—
110C5×Dic6—21no—
111C5×Dic6C22×C412yes—
112C3×#168—21no—
113C3×#168—23no—
114C2×C3×#41C2×D511yescharacteristic
115#1009—24no—
116#1009Dic518yescomplemented
117C2×#239—21no—
118C2×D3×D4—23no—
119C2×#235C2×D513yes—
120C22×D12C2×D513yes—
121C3×#131—104no—
122C2×C3×M16—53no—
123C22×C3×C8—53no—
124Q8×Dic3—101no—
125D4×Dic3—103no—
126#926—53no—
127C2×C4⋊Dic3—53no—
128#821—53no—
129#821—56no—
130#821—53no—
131#816—53no—
132#816—51no—
133C24×C5—63no—
134C5×#41—312no—
135C5×#41—68no—
136C5×#41—66no—
137C5×#41C4×D314yes—
138C5×#41#6714yes—
139C2×C5×Q8—31no—
140C2×C5×Q8D1211yescharacteristic
141C2×C5×D4—312no—
142C2×C5×D4—33no—
143C2×C5×D4—63no—
144C2×C5×D4—624no—
145C2×C5×D4—63no—
146C2×C5×D4—66no—
147C2×C5×D4D1213yes—
148C22×C4×C5—63no—
149C22×C4×C5C22×D313yes—
150C22×Dic5—63no—
151C22⋊Dic5—63no—
152C4⋊Dic5—33no—
153C4⋊Dic5—31no—
154C4⋊Dic5—63no—
155C4×Dic5—63no—
156#681—26no—
157C2×#168—26no—
158C2×#168C22×D311yescharacteristic
159C2×#168C22×D313yes—
160C2×H(5,𝔽2)—31no—
161C2×#131—51no—
162#520—151no—
163#418—153no—
164#417—153no—
165#416—153no—
166C2×#102—153no—
167C22×C3×C5—23no—
168C22×C3×C5—23no—
169C22×C3×C5C2×C22⋊C416yes—
170C22×C3×C5C22×D411yescharacteristic
171C2×C5×D3—26no—
172C2×C5×D3—43no—
173C2×C5×D3—43no—
174C2×C5×D3—812no—
175C3×C4×C5C2×C22⋊C416yes—
176C3×C4×C5C23×C411yescharacteristic
177C3×C4×C5C22×D411yescharacteristic
178Dic15—43no—
179Dic15—41no—
180C5×Dic3—22no—
181C23×D3—23no—
182C3×#41C2×Dic514yes—
183C3×#41C22⋊D514yes—
184C2×C3×Q8C22⋊D511yescharacteristic
185C2×C3×D4C22⋊D513yes—
186C22×C3×C4C22×D513yes—
187C2×#67—23no—
188C22×Dic3—103no—
189#239—28no—
190D3×D4—224no—
191#235—26no—
192#235C2×Dic5112yescomplemented
193C2×D12—23no—
194C2×D12—26no—
195C2×D12C2×Dic5112yescomplemented
196C2×D12C22×D513yes—
197C2×C4×D3—23no—
198C2×Dic6C22×D511yescharacteristic
199C3×M16—106no—
200C2×C3×C8—51no—
201C2×C3×C8—53no—
202C2×C3×C8—106no—
203#217—103no—
204C4⋊Dic3—53no—
205C4⋊Dic3—51no—
206C4⋊Dic3—103no—
207C4×Dic3—103no—
208C23×C5—63no—
209C23×C5—612no—
210C23×C5—243no—
211C23×C5—243no—
212C23×C5C2×D1213yes—
213C5×Q8—32no—
214C5×Q8—61no—
215C5×Q8(C2×D3)⋊C414yes—
216C5×D4—36no—
217C5×D4—612no—
218C5×D4—612no—
219C5×D4—63no—
220C5×D4(C2×D3)⋊C4112yes—
221C2×C4×C5—61no—
222C2×C4×C5—612no—
223C2×C4×C5C2×C4×D316yes—
224C2×C4×C5C2×D1213yes—
225C2×C4×C5C2×#6716yes—
226C2×C4×C5C23×D311yescharacteristic
227C2×Dic5—61no—
228C2×Dic5—63no—
229C2×Dic5—243no—
230#168—21no—
231#168—23no—
232H(5,𝔽2)—38no—
233H(5,𝔽2)—64no—
234C2×#41—33no—
235C2×#41—61no—
236C2×#41D3×D511yescharacteristic
237C22×D4—33no—
238C22×D4—63no—
239#131—104no—
240C2×M16—53no—
241C22×C8—53no—
242C4×Q8—301no—
243C4×D4—303no—
244#117—153no—
245C2×C4⋊C4—153no—
246#103—151no—
247#103—153no—
248#102—153no—
249#102—156no—
250#102—153no—
251C2×C3×C5—26no—
252C2×C3×C5C22×C22⋊C411yescharacteristic
253C2×C3×C5#57611yescharacteristic
254C2×C3×C5#57711yescharacteristic
255C5×D3—46no—
256C23×C3C2×C22⋊D513yes—
257C22×D3—23no—
258C22×D3—212no—
259C22×D3—83no—
260C22×D3—83no—
261C3×Q8C22⋊Dic514yes—
262C3×D4C22⋊Dic5112yes—
263C2×C3×C4C22×Dic516yes—
264C2×C3×C4C2×C22⋊D516yes—
265C2×C3×C4C2×C22⋊D513yes—
266C2×C3×C4C23×D511yescharacteristic
267#67—212no—
268C2×Dic3—21no—
269C2×Dic3—101no—
270C2×Dic3—103no—
271C2×Dic3—403no—
272D12—212no—
273D12—23no—
274D12C22×Dic516yes—
275C4×D3—212no—
276Dic6—21no—
277Dic6C22×Dic512yes—
278C3×C8—101no—
279C3×C8—103no—
280C22×C5—23no—
281C22×C5—23no—
282C22×C5—66no—
283C22×C5—123no—
284C22×C5—123no—
285C22×C5—2412no—
286C22×C5C2×(C2×D3)⋊C416yes—
287C22×C5C22×D1211yescharacteristic
288C4×C5—62no—
289C4×C5C2×(C2×D3)⋊C416yes—
290C4×C5C22×C4×D311yescharacteristic
291C4×C5C22×#6711yescharacteristic
292Dic5—121no—
293Dic5—123no—
294C24—63no—
295#41—312no—
296#41—68no—
297#41—66no—
298#41D3×Dic514yes—
299#41#120114yes—
300C2×Q8—31no—
301C2×Q8#120311yescharacteristic
302C2×D4—312no—
303C2×D4—33no—
304C2×D4—63no—
305C2×D4—624no—
306C2×D4—66no—
307C2×D4—63no—
308C2×D4#120313yes—
309C22×C4—63no—
310C22×C4—303no—
311C22×C4C2×D3×D513yes—
312M16—106no—
313C2×C8—51no—
314C2×C8—53no—
315C2×C8—106no—
316C4⋊C4—153no—
317C4⋊C4—151no—
318C4⋊C4—303no—
319C22⋊C4—303no—
320C42—303no—
321C3×C5#289711yescharacteristic, complemented, Hall
322C22×C3—23no—
323C22×C3—23no—
324C22×C3C2×C22⋊Dic516yes—
325C22×C3C22×C22⋊D511yescharacteristic
326C2×D3—26no—
327C2×D3—43no—
328C2×D3—43no—
329C2×D3—812no—
330C3×C4C2×C22⋊Dic516yes—
331C3×C4C23×Dic511yescharacteristic
332C3×C4C22×C22⋊D511yescharacteristic
333Dic3—22no—
334Dic3—203no—
335Dic3—201no—
336C2×C5—26no—
337C2×C5—126no—
338C2×C5#575111yescharacteristic
339C2×C5#575211yescharacteristic
340C2×C5C22×(C2×D3)⋊C411yescharacteristic
341C23—63no—
342C23—612no—
343C23—243no—
344C23—243no—
345C23C2×#120313yes—
346Q8—32no—
347Q8—61no—
348Q8(C2×D3)⋊Dic514yes—
349D4—36no—
350D4—612no—
351D4—63no—
352D4—612no—
353D4(C2×D3)⋊Dic5112yes—
354C2×C4—61no—
355C2×C4—612no—
356C2×C4—301no—
357C2×C4—303no—
358C2×C4—1203no—
359C2×C4C2×D3×Dic516yes—
360C2×C4C2×#120116yes—
361C2×C4C2×#120313yes—
362C2×C4C22×D3×D511yescharacteristic
363C8—101no—
364C8—103no—
365C2×C3—26no—
366C2×C3#6616911yescharacteristic
367C2×C3#6617011yescharacteristic
368C2×C3C22×C22⋊Dic511yescharacteristic
369D3—46no—
370C5#8379711yescharacteristic, complemented, Sylow
371C22—23no—
372C22—23no—
373C22—66no—
374C22—123no—
375C22—123no—
376C22—2412no—
377C22C2×(C2×D3)⋊Dic516yes—
378C22C22×#120311yescharacteristic
379C4—62no—
380C4—603no—
381C4—601no—
382C4C2×(C2×D3)⋊Dic516yes—
383C4C22×D3×Dic511yescharacteristic
384C4C22×#120111yescharacteristic
385C3#1061583011yescharacteristic, complemented, Sylow
386C2—26no—
387C2—126no—
388C2#1175530511yescharacteristic
389C2#1175530711yescharacteristic
390C2C22×(C2×D3)⋊Dic511yescharacteristic
subgroupG/H
centerC22C22×#1203
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#1009C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5#2897
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×C3×#4094C2semidirect
4. #11748390C2semidirect
5. #11748389C2semidirect
6. #11748388C2semidirect
7. C2×#90967C2semidirect
11. C5×#1009C4semidirect
18. #91815C22semidirect
19. C2×C4⋊Dic15C22semidirect
21. C2×C3×#681C22semidirect
22. C22×C3×#168C22semidirect
23. #90973C22semidirect
24. #90973C22semidirect
25. #90967C22semidirect
26. #90967C22semidirect
27. #90967C22semidirect
31. C2×#4094D3semidirect
47. C5×#235C2×C4semidirect
50. C2×C5×D12C2×C4semidirect
82. C2×#681C2×D3semidirect
83. C22×#168C2×D3semidirect
116. #1009Dic5semidirect
192. #235C2×Dic5semidirect
195. C2×D12C2×Dic5semidirect
321. C3×C5#2897semidirect
370. C5#83797semidirect
385. C3#10615830semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10092
#117565862
C2×C3×#40942
#117483902
#117483892
#117483882
C2×#909672
#106158303
#837975