Finite Group Databasebeta

← C5×#82563 #14412620

Subgroups — C5×#82563 #14412620

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
2C3×C5×#520C211yesmaximal, characteristic, complemented
3C2×C5×#948C211yesmaximal, characteristic, complemented
4C5×#5002C213yesmaximal, complemented
5C5×#5001C213yesmaximal, complemented
6C5×#4966C213yesmaximal, complemented
7C2×C5×#809C213yesmaximal, complemented
8C5×#2897—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—
16C3×C4×C5×Q8—21no—
17C3×C4×C5×D4—23no—
18C3×C5×#117C2213yescomplemented
19C2×C3×C5×C4⋊C4C2213yescomplemented
20C5×#948—24no—
21C2×C5×#208C2213yescomplemented
22C22×C5×C3⋊C8C2213yescomplemented
23C5×#810C2213yescomplemented
24C5×#810C2211yescharacteristic, complemented
25C5×#809C2213yescomplemented
26C5×#809C2216yescomplemented
27C5×#809C2213yescomplemented
28#82563C511yesmaximal, characteristic, direct product factor, Hall
29C2×C5×H(5,𝔽2)—31no—
30C2×C5×#131—31no—
31C5×#520D311yescharacteristic, complemented
32C5×#418—33no—
33C5×#417—33no—
34C5×#416—33no—
35C2×C5×#102—33no—
36C23×C5×D3—23no—
37C3×C5×#41C2×C414yes—
38C3×C5×#41D414yes—
39C2×C3×C5×Q8D411yescharacteristic
40C2×C3×C5×D4D413yes—
41C22×C3×C4×C5—23no—
42C22×C3×C4×C5C2313yes—
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
54C3×C5×C4⋊C4—23no—
55C3×C5×C4⋊C4C2313yes—
56C3×C5×C4⋊C4C2311yescharacteristic
57C3×C5×C22⋊C4—23no—
58C3×C42×C5—23no—
59C5×#208—26no—
60C2×C5×C3⋊C8—26no—
61C2×C5×C3⋊C8C2311yescharacteristic
62C2×C5×C3⋊C8C2313yes—
63C2×#1009C2×C511yescharacteristic
64C3×#520C2×C511yescharacteristic, complemented
65C2×#948C2×C511yescharacteristic, complemented
66#5002C2×C513yescomplemented
67#5001C2×C513yescomplemented
68#4966C2×C513yescomplemented
69C2×#809C2×C513yescomplemented
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—
77C5×#131—64no—
78C2×C5×M16—33no—
79C22×C5×C8—33no—
80C4×C5×Q8—21no—
81C4×C5×D4—23no—
82C5×#117C2×D313yescomplemented
83C2×C5×C4⋊C4C2×D313yescomplemented
84C5×#103—31no—
85C5×#103—33no—
86C5×#102—33no—
87C5×#102—36no—
88C5×#102—33no—
89#2897—31noSylow
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×C5—21no—
98C2×C3×C4×C5—23no—
99C2×C3×C4×C5—83no—
100C2×C3×C4×C5C22×C416yes—
101C2×C3×C4×C5C2×D413yes—
102C2×C3×C4×C5C2×D416yes—
103C2×C3×C4×C5C2411yescharacteristic
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—
112C5×C3⋊C8—21no—
113C5×C3⋊C8—23no—
114C2×C3×#41C22×C511yescharacteristic
115#1009—24no—
116#1009C4×C518yescomplemented
117C2×#239—21no—
118C2×D3×D4—23no—
119C2×#235C22×C513yes—
120C22×D12C22×C513yes—
121C3×C4×Q8—21no—
122C3×C4×D4—23no—
123C3×#117C22×C513yescomplemented
124C2×C3×C4⋊C4C22×C513yescomplemented
125#948—24no—
126C2×#208C22×C513yescomplemented
127C22×C3⋊C8C22×C513yescomplemented
128#810C22×C513yescomplemented
129#810C22×C511yescharacteristic, complemented
130#809C22×C513yescomplemented
131#809C22×C516yescomplemented
132#809C22×C513yescomplemented
133C24×C5—63no—
134C5×#41—312no—
135C5×#41—68no—
136C5×#41—66no—
137C5×#41C4×D314yes—
138C5×#41D1214yes—
139C2×C5×Q8—31no—
140C2×C5×Q8#6711yescharacteristic
141C2×C5×D4—312no—
142C2×C5×D4—33no—
143C2×C5×D4—63no—
144C2×C5×D4—624no—
145C2×C5×D4—66no—
146C2×C5×D4—63no—
147C2×C5×D4#6713yes—
148C22×C4×C5—23no—
149C22×C4×C5—63no—
150C22×C4×C5C22×D313yes—
151C5×M16—66no—
152C2×C5×C8—31no—
153C2×C5×C8—33no—
154C2×C5×C8—66no—
155C5×C4⋊C4—23no—
156C5×C4⋊C4C22×D313yes—
157C5×C4⋊C4C22×D311yescharacteristic
158C5×C22⋊C4—23no—
159C42×C5—23no—
160C2×H(5,𝔽2)—31no—
161C2×#131—31no—
162#520C5×D311yescharacteristic, complemented
163#418—33no—
164#417—33no—
165#416—33no—
166C2×#102—33no—
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×C5—43no—
176C3×C4×C5—41no—
177C3×C4×C5C2×C22⋊C416yes—
178C3×C4×C5C23×C411yescharacteristic
179C3×C4×C5C22×D411yescharacteristic
180C5×Dic3—22no—
181C23×D3—23no—
182C3×#41C2×C4×C514yes—
183C3×#41C5×D414yes—
184C2×C3×Q8C5×D411yescharacteristic
185C2×C3×D4C5×D413yes—
186C22×C3×C4—23no—
187C22×C3×C4C23×C513yes—
188C2×#67—23no—
189#239—28no—
190D3×D4—224no—
191#235—26no—
192#235C2×C4×C5112yescomplemented
193C2×D12—23no—
194C2×D12—26no—
195C2×D12C2×C4×C5112yescomplemented
196C2×D12C23×C513yes—
197C2×C4×D3—23no—
198C2×Dic6C23×C511yescharacteristic
199C3×C4⋊C4—23no—
200C3×C4⋊C4C23×C513yes—
201C3×C4⋊C4C23×C511yescharacteristic
202C3×C22⋊C4—23no—
203C3×C42—23no—
204#208—26no—
205C2×C3⋊C8—26no—
206C2×C3⋊C8C23×C511yescharacteristic
207C2×C3⋊C8C23×C513yes—
208C23×C5—63no—
209C23×C5—612no—
210C23×C5—243no—
211C23×C5—243no—
212C23×C5C2×#6713yes—
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—21no—
222C2×C4×C5—23no—
223C2×C4×C5—61no—
224C2×C4×C5—612no—
225C2×C4×C5—83no—
226C2×C4×C5C2×C4×D316yes—
227C2×C4×C5C2×D1216yes—
228C2×C4×C5C2×#6713yes—
229C2×C4×C5C23×D311yescharacteristic
230C5×C8—61no—
231C5×C8—63no—
232H(5,𝔽2)—38no—
233H(5,𝔽2)—64no—
234C2×#41—33no—
235C2×#41—61no—
236C2×#41C2×C5×D311yescharacteristic
237C22×D4—33no—
238C22×D4—63no—
239#131—64no—
240C2×M16—33no—
241C22×C8—33no—
242C4×Q8—21no—
243C4×D4—23no—
244#117C2×C5×D313yescomplemented
245C2×C4⋊C4C2×C5×D313yescomplemented
246#103—31no—
247#103—33no—
248#102—33no—
249#102—36no—
250#102—33no—
251C2×C3×C5—26no—
252C2×C3×C5C22×C22⋊C411yescharacteristic
253C2×C3×C5#57611yescharacteristic
254C2×C3×C5#57711yescharacteristic
255C5×D3—46no—
256C23×C3C2×C5×D413yes—
257C22×D3—23no—
258C22×D3—212no—
259C22×D3—83no—
260C22×D3—83no—
261C3×Q8C5×C22⋊C414yes—
262C3×D4C5×C22⋊C4112yes—
263C2×C3×C4—21no—
264C2×C3×C4—23no—
265C2×C3×C4—83no—
266C2×C3×C4C22×C4×C516yes—
267C2×C3×C4C2×C5×D416yes—
268C2×C3×C4C2×C5×D413yes—
269C2×C3×C4C24×C511yescharacteristic
270#67—212no—
271C2×Dic3—21no—
272D12—212no—
273D12—23no—
274D12C22×C4×C516yes—
275C4×D3—212no—
276Dic6—21no—
277Dic6C22×C4×C512yes—
278C3⋊C8—21no—
279C3⋊C8—23no—
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×#6711yescharacteristic
288C4×C5—43no—
289C4×C5—41no—
290C4×C5—62no—
291C4×C5C2×(C2×D3)⋊C416yes—
292C4×C5C22×C4×D311yescharacteristic
293C4×C5C22×D1211yescharacteristic
294C24—63no—
295#41—312no—
296#41—68no—
297#41—66no—
298#41C4×C5×D314yes—
299#41C5×D1214yes—
300C2×Q8—31no—
301C2×Q8C5×#6711yescharacteristic
302C2×D4—312no—
303C2×D4—33no—
304C2×D4—63no—
305C2×D4—624no—
306C2×D4—66no—
307C2×D4—63no—
308C2×D4C5×#6713yes—
309C22×C4—23no—
310C22×C4—63no—
311C22×C4C22×C5×D313yes—
312M16—66no—
313C2×C8—31no—
314C2×C8—33no—
315C2×C8—66no—
316C4⋊C4—23no—
317C4⋊C4C22×C5×D313yes—
318C4⋊C4C22×C5×D311yescharacteristic
319C22⋊C4—23no—
320C42—23no—
321C3×C5#289711yescharacteristic, complemented, Hall
322C22×C3—23no—
323C22×C3—23no—
324C22×C3C2×C5×C22⋊C416yes—
325C22×C3C22×C5×D411yescharacteristic
326C2×D3—26no—
327C2×D3—43no—
328C2×D3—43no—
329C2×D3—812no—
330C3×C4—43no—
331C3×C4—41no—
332C3×C4C2×C5×C22⋊C416yes—
333C3×C4C23×C4×C511yescharacteristic
334C3×C4C22×C5×D411yescharacteristic
335Dic3—22no—
336C2×C5—26no—
337C2×C5—126no—
338C2×C5C22×(C2×D3)⋊C411yescharacteristic
339C2×C5#583511yescharacteristic
340C2×C5#583711yescharacteristic
341C23—63no—
342C23—612no—
343C23—243no—
344C23—243no—
345C23C2×C5×#6713yes—
346Q8—32no—
347Q8—61no—
348Q8C5×(C2×D3)⋊C414yes—
349D4—36no—
350D4—612no—
351D4—612no—
352D4—63no—
353D4C5×(C2×D3)⋊C4112yes—
354C2×C4—21no—
355C2×C4—23no—
356C2×C4—61no—
357C2×C4—612no—
358C2×C4—83no—
359C2×C4C2×C4×C5×D316yes—
360C2×C4C2×C5×D1216yes—
361C2×C4C2×C5×#6713yes—
362C2×C4C23×C5×D311yescharacteristic
363C8—61no—
364C8—63no—
365C2×C3—26no—
366C2×C3C22×C5×C22⋊C411yescharacteristic
367C2×C3C5×#57611yescharacteristic
368C2×C3C5×#57711yescharacteristic
369D3—46no—
370C5#8256311yescharacteristic, direct product factor, Sylow
371C22—23no—
372C22—23no—
373C22—66no—
374C22—123no—
375C22—123no—
376C22—2412no—
377C22C2×C5×(C2×D3)⋊C416yes—
378C22C22×C5×#6711yescharacteristic
379C4—43no—
380C4—41no—
381C4—62no—
382C4C2×C5×(C2×D3)⋊C416yes—
383C4C22×C4×C5×D311yescharacteristic
384C4C22×C5×D1211yescharacteristic
385C3C5×#289711yescharacteristic, complemented, Sylow
386C2—26no—
387C2—126no—
388C2C22×C5×(C2×D3)⋊C411yescharacteristic
389C2C5×#583511yescharacteristic
390C2C5×#583711yescharacteristic
subgroupG/H
centerC22×C5C22×#67
commutatorC3×C4C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#520C2
socleC22×C3×C5C22×D4
prime radicalC2×C5×#1009C2
cosocleC2×C3×C4C24×C5
hypercenterC5×#520D3
hypocenterC3C5×#2897
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C5×#41 ◁ C5×#520

Complements

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

NH ≅ G/Ntype
2. C3×C5×#520C2semidirect
3. C2×C5×#948C2semidirect
4. C5×#5002C2semidirect
5. C5×#5001C2semidirect
6. C5×#4966C2semidirect
7. C2×C5×#809C2semidirect
11. C5×#1009C4semidirect
18. C3×C5×#117C22semidirect
19. C2×C3×C5×C4⋊C4C22semidirect
21. C2×C5×#208C22semidirect
22. C22×C5×C3⋊C8C22semidirect
23. C5×#810C22semidirect
24. C5×#810C22semidirect
25. C5×#809C22semidirect
26. C5×#809C22semidirect
27. C5×#809C22semidirect
28. #82563C5direct (N × H)
31. C5×#520D3semidirect
47. C5×#235C2×C4semidirect
50. C2×C5×D12C2×C4semidirect
64. C3×#520C2×C5semidirect
65. C2×#948C2×C5semidirect
66. #5002C2×C5semidirect
67. #5001C2×C5semidirect
68. #4966C2×C5semidirect
69. C2×#809C2×C5semidirect
82. C5×#117C2×D3semidirect
83. C2×C5×C4⋊C4C2×D3semidirect
116. #1009C4×C5semidirect
123. C3×#117C22×C5semidirect
124. C2×C3×C4⋊C4C22×C5semidirect
126. C2×#208C22×C5semidirect
127. C22×C3⋊C8C22×C5semidirect
128. #810C22×C5semidirect
129. #810C22×C5semidirect
130. #809C22×C5semidirect
131. #809C22×C5semidirect
132. #809C22×C5semidirect
162. #520C5×D3semidirect
192. #235C2×C4×C5semidirect
195. C2×D12C2×C4×C5semidirect
244. #117C2×C5×D3semidirect
245. C2×C4⋊C4C2×C5×D3semidirect
321. C3×C5#2897semidirect
370. C5#82563direct (N × H)
385. C3C5×#2897semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10092
C3×C5×#5202
C2×C5×#9482
C5×#50022
C5×#50012
C5×#49662
C2×C5×#8092
C5×#28973
#825635