Finite Group Databasebeta

← C5×#83806 #14412719

Subgroups — C5×#83806 #14412719

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×C5×#1010C211yesmaximal, characteristic
2C2×C3×C5×#131C211yesmaximal, characteristic, complemented
3C5×#5827C211yesmaximal, characteristic, complemented
4C5×#5133C213yesmaximal, complemented
5C5×#5120C213yesmaximal, complemented
6C5×#5113C213yesmaximal, complemented
7C2×C5×#816C213yesmaximal, complemented
8C5×#2898—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C5×#1010—24no—
11C5×#1010C418yescomplemented
12C2×C5×D3×Q8—21no—
13C2×C5×#237—23no—
14C2×C5×#235C2213yes—
15C22×C5×Dic6C2213yes—
16C3×C5×#131—24no—
17C2×C3×C5×M16C2213yes—
18C22×C3×C5×C8C2213yes—
19C5×Q8×Dic3—21no—
20C5×D4×Dic3—23no—
21C5×#926C2213yes—
22C2×C5×C4⋊Dic3C2213yes—
23C5×#821C2211yescharacteristic
24C5×#821C2213yes—
25C5×#816C2213yes—
26C5×#816C2216yes—
27C5×#816C2213yes—
28#83806C511yesmaximal, characteristic, direct product factor, Hall
29C2×C5×2−1+4—31no—
30C2×C5×#131D311yescharacteristic, complemented
31C5×#520—31no—
32C5×#419—33no—
33C5×#417—33no—
34C5×#416—33no—
35C2×C5×#103—33no—
36C3×C5×#41C2×C414yes—
37C3×C5×#41D414yes—
38C2×C3×C5×Q8D411yescharacteristic
39C2×C3×C5×D4D413yes—
40C22×C3×C4×C5C2313yes—
41C2×C5×#67—23no—
42C22×C5×Dic3—23no—
43C22×C5×Dic3—23no—
44C5×D3×Q8—28no—
45C5×#237—224no—
46C5×#235—26no—
47C5×#235C2×C4112yescomplemented
48C2×C5×D12C2311yescharacteristic
49C2×C4×C5×D3—23no—
50C2×C5×Dic6—23no—
51C2×C5×Dic6—26no—
52C2×C5×Dic6C2×C4112yescomplemented
53C2×C5×Dic6C2313yes—
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×#1010C2×C511yescharacteristic
64C2×C3×#131C2×C511yescharacteristic, complemented
65#5827C2×C511yescharacteristic, complemented
66#5133C2×C513yescomplemented
67#5120C2×C513yescomplemented
68#5113C2×C513yescomplemented
69C2×#816C2×C513yescomplemented
70C5×2−1+4—38no—
71C5×2−1+4—64no—
72C2×C5×#41—33no—
73C2×C5×#41—63no—
74C2×C5×#41C2×D311yescharacteristic
75C22×C5×Q8—33no—
76C22×C5×Q8—61no—
77C5×#131—24no—
78C2×C5×M16C2×D313yes—
79C22×C5×C8C2×D313yes—
80C4×C5×Q8—61no—
81C4×C5×D4—63no—
82C5×#117—33no—
83C2×C5×C4⋊C4—33no—
84C5×#103—33no—
85C5×#103—36no—
86C5×#103—33no—
87C5×#102—31no—
88C5×#102—33no—
89#2898—31noSylow
90C23×C3×C5C2×D413yes—
91C22×C5×D3—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
98C5×#67—212no—
99C2×C5×Dic3—212no—
100C2×C5×Dic3—23no—
101C2×C5×Dic3—21no—
102C2×C5×Dic3—23no—
103C2×C5×Dic3—83no—
104C5×D12—21no—
105C5×D12C22×C412yes—
106C4×C5×D3—212no—
107C5×Dic6—212no—
108C5×Dic6—23no—
109C5×Dic6C22×C416yes—
110C3×C5×C8—21no—
111C3×C5×C8—23no—
112C2×C3×#41C22×C511yescharacteristic
113#1010—24no—
114#1010C4×C518yescomplemented
115C2×D3×Q8—21no—
116C2×#237—23no—
117C2×#235C22×C513yes—
118C22×Dic6C22×C513yes—
119C3×#131—24no—
120C2×C3×M16C22×C513yes—
121C22×C3×C8C22×C513yes—
122Q8×Dic3—21no—
123D4×Dic3—23no—
124#926C22×C513yes—
125C2×C4⋊Dic3C22×C513yes—
126#821C22×C513yes—
127#821C22×C511yescharacteristic
128#816C22×C513yes—
129#816C22×C516yes—
130#816C22×C513yes—
131C5×#41—312no—
132C5×#41—624no—
133C5×#41—66no—
134C5×#41C4×D314yes—
135C5×#41#6714yes—
136C2×C5×Q8—312no—
137C2×C5×Q8—33no—
138C2×C5×Q8—68no—
139C2×C5×Q8—63no—
140C2×C5×Q8—66no—
141C2×C5×Q8D1211yescharacteristic
142C2×C5×D4—31no—
143C2×C5×D4—63no—
144C2×C5×D4D1213yes—
145C22×C4×C5—63no—
146C22×C4×C5—63no—
147C22×C4×C5—63no—
148C22×C4×C5C22×D313yes—
149C5×M16—26no—
150C2×C5×C8—26no—
151C2×C5×C8C22×D311yescharacteristic
152C2×C5×C8C22×D313yes—
153C5×C4⋊C4—33no—
154C5×C4⋊C4—31no—
155C5×C4⋊C4—63no—
156C5×C22⋊C4—63no—
157C42×C5—63no—
158C2×2−1+4—31no—
159C2×#131C5×D311yescharacteristic, complemented
160#520—31no—
161#419—33no—
162#417—33no—
163#416—33no—
164C2×#103—33no—
165C22×C3×C5—23no—
166C22×C3×C5—23no—
167C22×C3×C5C2×C22⋊C416yes—
168C22×C3×C5C22×D411yescharacteristic
169C2×C5×D3—22no—
170C2×C5×D3—41no—
171C2×C5×D3—41no—
172C3×C4×C5C2×C22⋊C416yes—
173C3×C4×C5C23×C411yescharacteristic
174C3×C4×C5C22×D411yescharacteristic
175C5×Dic3—26no—
176C5×Dic3—43no—
177C5×Dic3—41no—
178C3×#41C2×C4×C514yes—
179C3×#41C5×D414yes—
180C2×C3×Q8C5×D411yescharacteristic
181C2×C3×D4C5×D413yes—
182C22×C3×C4C23×C513yes—
183C2×#67—23no—
184C22×Dic3—23no—
185C22×Dic3—23no—
186D3×Q8—28no—
187#237—224no—
188#235—26no—
189#235C2×C4×C5112yescomplemented
190C2×D12C23×C511yescharacteristic
191C2×C4×D3—23no—
192C2×Dic6—23no—
193C2×Dic6—26no—
194C2×Dic6C2×C4×C5112yescomplemented
195C2×Dic6C23×C513yes—
196C3×M16—26no—
197C2×C3×C8—26no—
198C2×C3×C8C23×C511yescharacteristic
199C2×C3×C8C23×C513yes—
200#217—23no—
201C4⋊Dic3—23no—
202C4⋊Dic3C23×C513yes—
203C4⋊Dic3C23×C511yescharacteristic
204C4×Dic3—23no—
205C23×C5—61no—
206C23×C5C2×D1213yes—
207C5×Q8—36no—
208C5×Q8—612no—
209C5×Q8—63no—
210C5×Q8(C2×D3)⋊C414yes—
211C5×D4—32no—
212C5×D4—612no—
213C5×D4—61no—
214C5×D4(C2×D3)⋊C4112yes—
215C2×C4×C5—612no—
216C2×C4×C5—63no—
217C2×C4×C5—612no—
218C2×C4×C5—61no—
219C2×C4×C5—63no—
220C2×C4×C5—243no—
221C2×C4×C5C2×C4×D316yes—
222C2×C4×C5C2×D1213yes—
223C2×C4×C5C2×#6716yes—
224C2×C4×C5C23×D311yescharacteristic
225C5×C8—21no—
226C5×C8—23no—
2272−1+4—38no—
2282−1+4—64no—
229C2×#41—33no—
230C2×#41—63no—
231C2×#41C2×C5×D311yescharacteristic
232C22×Q8—33no—
233C22×Q8—61no—
234#131—24no—
235C2×M16C2×C5×D313yes—
236C22×C8C2×C5×D313yes—
237C4×Q8—61no—
238C4×D4—63no—
239#117—33no—
240C2×C4⋊C4—33no—
241#103—33no—
242#103—36no—
243#103—33no—
244#102—31no—
245#102—33no—
246C2×C3×C5—26no—
247C2×C3×C5C22×C22⋊C411yescharacteristic
248C2×C3×C5#57711yescharacteristic
249C2×C3×C5#57811yescharacteristic
250C5×D3—42no—
251C23×C3C2×C5×D413yes—
252C22×D3—21no—
253C3×Q8C5×C22⋊C414yes—
254C3×D4C5×C22⋊C4112yes—
255C2×C3×C4C22×C4×C516yes—
256C2×C3×C4C2×C5×D413yes—
257C2×C3×C4C2×C5×D416yes—
258C2×C3×C4C24×C511yescharacteristic
259#67—212no—
260C2×Dic3—212no—
261C2×Dic3—23no—
262C2×Dic3—21no—
263C2×Dic3—23no—
264C2×Dic3—83no—
265D12—21no—
266D12C22×C4×C512yes—
267C4×D3—212no—
268Dic6—212no—
269Dic6—23no—
270Dic6C22×C4×C516yes—
271C3×C8—21no—
272C3×C8—23no—
273C22×C5—23no—
274C22×C5—23no—
275C22×C5—62no—
276C22×C5—121no—
277C22×C5—121no—
278C22×C5C2×(C2×D3)⋊C416yes—
279C22×C5C22×D1211yescharacteristic
280C4×C5—66no—
281C4×C5—123no—
282C4×C5—121no—
283C4×C5C2×(C2×D3)⋊C416yes—
284C4×C5C22×C4×D311yescharacteristic
285C4×C5C22×#6711yescharacteristic
286#41—312no—
287#41—624no—
288#41—66no—
289#41C4×C5×D314yes—
290#41C5×#6714yes—
291C2×Q8—312no—
292C2×Q8—33no—
293C2×Q8—68no—
294C2×Q8—63no—
295C2×Q8—66no—
296C2×Q8C5×D1211yescharacteristic
297C2×D4—31no—
298C2×D4—63no—
299C2×D4C5×D1213yes—
300C22×C4—63no—
301C22×C4—63no—
302C22×C4—63no—
303C22×C4C22×C5×D313yes—
304M16—26no—
305C2×C8—26no—
306C2×C8C22×C5×D311yescharacteristic
307C2×C8C22×C5×D313yes—
308C4⋊C4—33no—
309C4⋊C4—31no—
310C4⋊C4—63no—
311C22⋊C4—63no—
312C42—63no—
313C3×C5#289811yescharacteristic, complemented, Hall
314C22×C3—23no—
315C22×C3—23no—
316C22×C3C2×C5×C22⋊C416yes—
317C22×C3C22×C5×D411yescharacteristic
318C2×D3—22no—
319C2×D3—41no—
320C2×D3—41no—
321C3×C4C2×C5×C22⋊C416yes—
322C3×C4C23×C4×C511yescharacteristic
323C3×C4C22×C5×D411yescharacteristic
324Dic3—26no—
325Dic3—43no—
326Dic3—41no—
327C2×C5—26no—
328C2×C5—122no—
329C2×C5#575111yescharacteristic
330C2×C5#575311yescharacteristic
331C2×C5C22×(C2×D3)⋊C411yescharacteristic
332C23—61no—
333C23C2×C5×D1213yes—
334Q8—36no—
335Q8—612no—
336Q8—63no—
337Q8C5×(C2×D3)⋊C414yes—
338D4—32no—
339D4—612no—
340D4—61no—
341D4C5×(C2×D3)⋊C4112yes—
342C2×C4—612no—
343C2×C4—63no—
344C2×C4—612no—
345C2×C4—61no—
346C2×C4—63no—
347C2×C4—243no—
348C2×C4C2×C4×C5×D316yes—
349C2×C4C2×C5×D1213yes—
350C2×C4C2×C5×#6716yes—
351C2×C4C23×C5×D311yescharacteristic
352C8—21no—
353C8—23no—
354C2×C3—26no—
355C2×C3C22×C5×C22⋊C411yescharacteristic
356C2×C3C5×#57711yescharacteristic
357C2×C3C5×#57811yescharacteristic
358D3—42no—
359C5#8380611yescharacteristic, direct product factor, Sylow
360C22—23no—
361C22—23no—
362C22—62no—
363C22—121no—
364C22—121no—
365C22C2×C5×(C2×D3)⋊C416yes—
366C22C22×C5×D1211yescharacteristic
367C4—66no—
368C4—123no—
369C4—121no—
370C4C2×C5×(C2×D3)⋊C416yes—
371C4C22×C4×C5×D311yescharacteristic
372C4C22×C5×#6711yescharacteristic
373C3C5×#289811yescharacteristic, complemented, Sylow
374C2—26no—
375C2—122no—
376C2C5×#575111yescharacteristic
377C2C5×#575311yescharacteristic
378C2C22×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×#1010C2
cosocleC2×C3×C4C24×C5
hypercenterC2×C5×#131D3
hypocenterC3C5×#2898
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×#5120C2semidirect
6. C5×#5113C2semidirect
7. C2×C5×#816C2semidirect
11. C5×#1010C4semidirect
28. #83806C5direct (N × H)
30. C2×C5×#131D3semidirect
47. C5×#235C2×C4semidirect
52. C2×C5×Dic6C2×C4semidirect
64. C2×C3×#131C2×C5semidirect
65. #5827C2×C5semidirect
66. #5133C2×C5semidirect
67. #5120C2×C5semidirect
68. #5113C2×C5semidirect
69. C2×#816C2×C5semidirect
114. #1010C4×C5semidirect
159. C2×#131C5×D3semidirect
189. #235C2×C4×C5semidirect
194. C2×Dic6C2×C4×C5semidirect
313. C3×C5#2898semidirect
359. C5#83806direct (N × H)
373. C3C5×#2898semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#10102
C2×C3×C5×#1312
C5×#58272
C5×#51332
C5×#51202
C5×#51132
C2×C5×#8162
C5×#28983
#838065