Finite Group Databasebeta

← C5×#83797 #14412632

Subgroups — C5×#83797 #14412632

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
2C2×C3×C5×#131C211yesmaximal, characteristic, complemented
3C5×#5827C211yesmaximal, characteristic, complemented
4C5×#5133C213yesmaximal, complemented
5C5×#5131C213yesmaximal, complemented
6C5×#5113C213yesmaximal, complemented
7C2×C5×#821C213yesmaximal, 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×C5×#131—24no—
17C2×C3×C5×M16C2213yescomplemented
18C22×C3×C5×C8C2213yescomplemented
19C5×Q8×Dic3—21no—
20C5×D4×Dic3—23no—
21C5×#926C2213yescomplemented
22C2×C5×C4⋊Dic3C2213yescomplemented
23C5×#821C2213yescomplemented
24C5×#821C2216yescomplemented
25C5×#821C2213yescomplemented
26C5×#816C2211yescharacteristic, complemented
27C5×#816C2213yescomplemented
28#83797C511yesmaximal, characteristic, direct product factor, Hall
29C2×C5×H(5,𝔽2)—31no—
30C2×C5×#131D311yescharacteristic, complemented
31C5×#520—31no—
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×C5C2313yes—
42C2×C5×#67—23no—
43C22×C5×Dic3—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×M16—26no—
55C2×C3×C5×C8—26no—
56C2×C3×C5×C8C2311yescharacteristic
57C2×C3×C5×C8C2313yes—
58C5×#217—23no—
59C5×C4⋊Dic3—23no—
60C5×C4⋊Dic3C2313yes—
61C5×C4⋊Dic3C2311yescharacteristic
62C4×C5×Dic3—23no—
63C2×#1009C2×C511yescharacteristic
64C2×C3×#131C2×C511yescharacteristic, complemented
65#5827C2×C511yescharacteristic, complemented
66#5133C2×C513yescomplemented
67#5131C2×C513yescomplemented
68#5113C2×C513yescomplemented
69C2×#821C2×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—24no—
78C2×C5×M16C2×D313yescomplemented
79C22×C5×C8C2×D313yescomplemented
80C4×C5×Q8—61no—
81C4×C5×D4—63no—
82C5×#117—33no—
83C2×C5×C4⋊C4—33no—
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×C5C22×C416yes—
98C2×C3×C4×C5C2×D413yes—
99C2×C3×C4×C5C2×D416yes—
100C2×C3×C4×C5C2411yescharacteristic
101C5×#67—212no—
102C2×C5×Dic3—21no—
103C2×C5×Dic3—21no—
104C2×C5×Dic3—23no—
105C2×C5×Dic3—83no—
106C5×D12—212no—
107C5×D12—23no—
108C5×D12C22×C416yes—
109C4×C5×D3—212no—
110C5×Dic6—21no—
111C5×Dic6C22×C412yes—
112C3×C5×C8—21no—
113C3×C5×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×#131—24no—
122C2×C3×M16C22×C513yescomplemented
123C22×C3×C8C22×C513yescomplemented
124Q8×Dic3—21no—
125D4×Dic3—23no—
126#926C22×C513yescomplemented
127C2×C4⋊Dic3C22×C513yescomplemented
128#821C22×C513yescomplemented
129#821C22×C516yescomplemented
130#821C22×C513yescomplemented
131#816C22×C513yescomplemented
132#816C22×C511yescharacteristic, complemented
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×C5—63no—
150C22×C4×C5C22×D313yes—
151C5×M16—26no—
152C2×C5×C8—26no—
153C2×C5×C8C22×D311yescharacteristic
154C2×C5×C8C22×D313yes—
155C5×C4⋊C4—33no—
156C5×C4⋊C4—31no—
157C5×C4⋊C4—63no—
158C5×C22⋊C4—63no—
159C42×C5—63no—
160C2×H(5,𝔽2)—31no—
161C2×#131C5×D311yescharacteristic, complemented
162#520—31no—
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×C5C2×C22⋊C416yes—
176C3×C4×C5C23×C411yescharacteristic
177C3×C4×C5C22×D411yescharacteristic
178C5×Dic3—22no—
179C5×Dic3—43no—
180C5×Dic3—41no—
181C23×D3—23no—
182C3×#41C2×C4×C514yes—
183C3×#41C5×D414yes—
184C2×C3×Q8C5×D411yescharacteristic
185C2×C3×D4C5×D413yes—
186C22×C3×C4C23×C513yes—
187C2×#67—23no—
188C22×Dic3—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×M16—26no—
200C2×C3×C8—26no—
201C2×C3×C8C23×C511yescharacteristic
202C2×C3×C8C23×C513yes—
203#217—23no—
204C4⋊Dic3—23no—
205C4⋊Dic3C23×C513yes—
206C4⋊Dic3C23×C511yescharacteristic
207C4×Dic3—23no—
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×C5—61no—
224C2×C4×C5—63no—
225C2×C4×C5—243no—
226C2×C4×C5C2×C4×D316yes—
227C2×C4×C5C2×D1213yes—
228C2×C4×C5C2×#6716yes—
229C2×C4×C5C23×D311yescharacteristic
230C5×C8—21no—
231C5×C8—23no—
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—24no—
240C2×M16C2×C5×D313yescomplemented
241C22×C8C2×C5×D313yescomplemented
242C4×Q8—61no—
243C4×D4—63no—
244#117—33no—
245C2×C4⋊C4—33no—
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×C4C22×C4×C516yes—
264C2×C3×C4C2×C5×D413yes—
265C2×C3×C4C2×C5×D416yes—
266C2×C3×C4C24×C511yescharacteristic
267#67—212no—
268C2×Dic3—21no—
269C2×Dic3—21no—
270C2×Dic3—23no—
271C2×Dic3—83no—
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×D1211yescharacteristic
288C4×C5—62no—
289C4×C5—121no—
290C4×C5—123no—
291C4×C5C2×(C2×D3)⋊C416yes—
292C4×C5C22×C4×D311yescharacteristic
293C4×C5C22×#6711yescharacteristic
294C24—63no—
295#41—312no—
296#41—68no—
297#41—66no—
298#41C4×C5×D314yes—
299#41C5×#6714yes—
300C2×Q8—31no—
301C2×Q8C5×D1211yescharacteristic
302C2×D4—312no—
303C2×D4—33no—
304C2×D4—63no—
305C2×D4—624no—
306C2×D4—63no—
307C2×D4—66no—
308C2×D4C5×D1213yes—
309C22×C4—63no—
310C22×C4—63no—
311C22×C4C22×C5×D313yes—
312M16—26no—
313C2×C8—26no—
314C2×C8C22×C5×D311yescharacteristic
315C2×C8C22×C5×D313yes—
316C4⋊C4—33no—
317C4⋊C4—31no—
318C4⋊C4—63no—
319C22⋊C4—63no—
320C42—63no—
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×C4C2×C5×C22⋊C416yes—
331C3×C4C23×C4×C511yescharacteristic
332C3×C4C22×C5×D411yescharacteristic
333Dic3—22no—
334Dic3—43no—
335Dic3—41no—
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×C5×D1213yes—
346Q8—32no—
347Q8—61no—
348Q8C5×(C2×D3)⋊C414yes—
349D4—36no—
350D4—612no—
351D4—612no—
352D4—63no—
353D4C5×(C2×D3)⋊C4112yes—
354C2×C4—61no—
355C2×C4—612no—
356C2×C4—61no—
357C2×C4—63no—
358C2×C4—243no—
359C2×C4C2×C4×C5×D316yes—
360C2×C4C2×C5×D1213yes—
361C2×C4C2×C5×#6716yes—
362C2×C4C23×C5×D311yescharacteristic
363C8—21no—
364C8—23no—
365C2×C3—26no—
366C2×C3C22×C5×C22⋊C411yescharacteristic
367C2×C3C5×#57611yescharacteristic
368C2×C3C5×#57711yescharacteristic
369D3—46no—
370C5#8379711yescharacteristic, direct product factor, Sylow
371C22—23no—
372C22—23no—
373C22—66no—
374C22—123no—
375C22—123no—
376C22—2412no—
377C22C2×C5×(C2×D3)⋊C416yes—
378C22C22×C5×D1211yescharacteristic
379C4—62no—
380C4—121no—
381C4—123no—
382C4C2×C5×(C2×D3)⋊C416yes—
383C4C22×C4×C5×D311yescharacteristic
384C4C22×C5×#6711yescharacteristic
385C3C5×#289711yescharacteristic, complemented, Sylow
386C2—26no—
387C2—126no—
388C2C5×#575111yescharacteristic
389C2C5×#575211yescharacteristic
390C2C22×C5×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC22×C5C22×D12
commutatorC3×C4C23×C4×C5
FrattiniC2×C4C23×C5×D3
FittingC2×C3×C5×#131C2
socleC22×C3×C5C22×D4
prime radicalC2×C5×#1009C2
cosocleC2×C3×C4C24×C5
hypercenterC2×C5×#131D3
hypocenterC3C5×#2897
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C5×#41 ◁ C2×C5×#131

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#131C2semidirect
3. C5×#5827C2semidirect
4. C5×#5133C2semidirect
5. C5×#5131C2semidirect
6. C5×#5113C2semidirect
7. C2×C5×#821C2semidirect
11. C5×#1009C4semidirect
17. C2×C3×C5×M16C22semidirect
18. C22×C3×C5×C8C22semidirect
21. C5×#926C22semidirect
22. C2×C5×C4⋊Dic3C22semidirect
23. C5×#821C22semidirect
24. C5×#821C22semidirect
25. C5×#821C22semidirect
26. C5×#816C22semidirect
27. C5×#816C22semidirect
28. #83797C5direct (N × H)
30. C2×C5×#131D3semidirect
47. C5×#235C2×C4semidirect
50. C2×C5×D12C2×C4semidirect
64. C2×C3×#131C2×C5semidirect
65. #5827C2×C5semidirect
66. #5133C2×C5semidirect
67. #5131C2×C5semidirect
68. #5113C2×C5semidirect
69. C2×#821C2×C5semidirect
78. C2×C5×M16C2×D3semidirect
79. C22×C5×C8C2×D3semidirect
116. #1009C4×C5semidirect
122. C2×C3×M16C22×C5semidirect
123. C22×C3×C8C22×C5semidirect
126. #926C22×C5semidirect
127. C2×C4⋊Dic3C22×C5semidirect
128. #821C22×C5semidirect
129. #821C22×C5semidirect
130. #821C22×C5semidirect
131. #816C22×C5semidirect
132. #816C22×C5semidirect
161. C2×#131C5×D3semidirect
192. #235C2×C4×C5semidirect
195. C2×D12C2×C4×C5semidirect
240. C2×M16C2×C5×D3semidirect
241. C22×C8C2×C5×D3semidirect
321. C3×C5#2897semidirect
370. C5#83797direct (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
C2×C3×C5×#1312
C5×#58272
C5×#51332
C5×#51312
C5×#51132
C2×C5×#8212
C5×#28973
#837975