Finite Group Databasebeta

← C5×#70869 #14292918

Subgroups — C5×#70869 #14292918

Order 1920.

340 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#436C211yesmaximal, characteristic, complemented
2C5×#5015C211yesmaximal, characteristic
3C5×#5008C211yesmaximal, characteristic, complemented
4C5×#4694C211yesmaximal, characteristic, complemented
5C5×#4485C211yesmaximal, characteristic, complemented
6C5×#4481C211yesmaximal, characteristic, complemented
7C5×#4458C211yesmaximal, characteristic, complemented
8C5×#1697—31nomaximal, Hall
9C2×C3×C5×M16—21no—
10C3×C4×C5×D4C2211yescharacteristic
11C2×C5×#213—21no—
12C5×#874C2211yescharacteristic
13C5×#869C2211yescharacteristic
14C3×C5×C4⋊C8C2211yescharacteristic
15C3×C5×C22⋊C8—21no—
16C3×C4×C5×C8C2211yescharacteristic
17C5×#832—21no—
18C5×#821—21no—
19C5×#821—21no—
20C5×#809—21no—
21C5×#808—21no—
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24#70869C511yesmaximal, characteristic, direct product factor, Hall
25C5×#486—31no—
26C5×#476—31no—
27C5×#459—31no—
28C5×#436D311yescharacteristic, complemented
29C5×#335—31no—
30C5×#333—31no—
31C5×#331—31no—
32C2×C3×C5×D4D411yescharacteristic
33C22×C3×C4×C5—21no—
34C2×C5×D12—21no—
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×Dic6—21no—
38C3×C5×M16—42no—
39C2×C3×C5×C8—21no—
40C2×C3×C5×C8D411yescharacteristic
41C2×C3×C5×C8D411yescharacteristic
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C5×C22⋊C4—21no—
44C3×C42×C5C2311yescharacteristic
45C5×#213—42no—
46C5×C4⋊Dic3—21no—
47C5×C4⋊Dic3—21no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C3×#436C2×C511yescharacteristic, complemented
51#5015C2×C511yescharacteristic
52#5008C2×C511yescharacteristic, complemented
53#4694C2×C511yescharacteristic, complemented
54#4485C2×C511yescharacteristic, complemented
55#4481C2×C511yescharacteristic, complemented
56#4458C2×C511yescharacteristic, complemented
57C2×C5×D8—61no—
58C2×C5×M16—21no—
59C5×C4⋊Q8—31no—
60C5×#127—31no—
61C4×C5×D4C2×D311yescharacteristic
62C5×#106—61no—
63C5×C4⋊C8—31no—
64C5×C4⋊C8—31no—
65C5×C4⋊C8C2×D311yescharacteristic
66C5×#102—61no—
67C5×#102—61no—
68C5×#102—61no—
69C5×#102—61no—
70C5×C22⋊C8—21no—
71C4×C5×C8C2×D311yescharacteristic
72#1697—31noSylow
73C23×C3×C5—21no—
74C22×C5×D3—41no—
75C3×C5×D4—21no—
76C3×C5×D4—21no—
77C2×C3×C4×C5—21no—
78C2×C3×C4×C5—41no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5C2×D411yescharacteristic
81C2×C3×C4×C5C2×D411yescharacteristic
82C2×C3×C4×C5#4111yescharacteristic
83C2×C5×Dic3—41no—
84C5×D12—41no—
85C5×D12—41no—
86C5×D12—41no—
87C5×D12—41no—
88C5×D12—81no—
89C5×Dic6—81no—
90C3×C5×C8—21no—
91C3×C5×C8—21no—
92C3×C5×C8—41no—
93C5×C3⋊C8—41no—
94C5×C3⋊C8—41no—
95C2×C3×M16—21no—
96C3×C4×D4C22×C511yescharacteristic
97C2×#213—21no—
98#874C22×C511yescharacteristic
99#869C22×C511yescharacteristic
100C3×C4⋊C8C22×C511yescharacteristic
101C3×C22⋊C8—21no—
102C3×C4×C8C22×C511yescharacteristic
103#832—21no—
104#821—21no—
105#821—21no—
106#809—21no—
107#808—21no—
108C4⋊(C3⋊C8)C22×C511yescharacteristic
109C4⋊(C3⋊C8)C22×C511yescharacteristic
110C2×C5×Q8—61no—
111C2×C5×D4—61no—
112C2×C5×D4—61no—
113C2×C5×D4—61no—
114C2×C5×D4D1211yescharacteristic
115C22×C4×C5—21no—
116C5×D8—122no—
117C5×M16—42no—
118C2×C5×C8—21no—
119C2×C5×C8—61no—
120C2×C5×C8—61no—
121C2×C5×C8#6711yescharacteristic
122C2×C5×C8#6711yescharacteristic
123C5×C4⋊C4—61no—
124C5×C4⋊C4—61no—
125C5×C4⋊C4D1211yescharacteristic
126C5×C22⋊C4—21no—
127C42×C5C22×D311yescharacteristic
128#486—31no—
129#476—31no—
130#459—31no—
131#436C5×D311yescharacteristic, complemented
132#335—31no—
133#333—31no—
134#331—31no—
135C22×C3×C5—41no—
136C22×C3×C5—41no—
137C22×C3×C5—41no—
138C22×C3×C5#12111yescharacteristic
139C2×C5×D3—81no—
140C2×C5×D3—81no—
141C2×C5×D3—81no—
142C3×C4×C5—21no—
143C3×C4×C5—41no—
144C3×C4×C5#13511yescharacteristic
145C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
146C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
147C3×C4×C5#13711yescharacteristic
148C5×Dic3—81no—
149C2×C3×D4C5×D411yescharacteristic
150C22×C3×C4—21no—
151C2×D12—21no—
152C2×D12—21no—
153C2×D12—21no—
154C2×Dic6—21no—
155C3×M16—42no—
156C2×C3×C8—21no—
157C2×C3×C8C5×D411yescharacteristic
158C2×C3×C8C5×D411yescharacteristic
159C3×C4⋊C4C5×D411yescharacteristic
160C3×C22⋊C4—21no—
161C3×C42C23×C511yescharacteristic
162#213—42no—
163C4⋊Dic3—21no—
164C4⋊Dic3—21no—
165C2×C3⋊C8—21no—
166C2×C3⋊C8—21no—
167C23×C5—21no—
168C23×C5—121no—
169C5×Q8—241no—
170C5×D4—21no—
171C5×D4—21no—
172C5×D4—121no—
173C5×D4—121no—
174C5×D4—121no—
175C5×D4—121no—
176C5×D4—241no—
177C2×C4×C5—21no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5—121no—
181C2×C4×C5C2×D1211yescharacteristic
182C2×C4×C5#23511yescharacteristic
183C2×C4×C5C2×#6711yescharacteristic
184C5×C8—21no—
185C5×C8—21no—
186C5×C8—41no—
187C5×C8—121no—
188C5×C8—121no—
189C2×D8—61no—
190C2×M16—21no—
191C4⋊Q8—31no—
192#127—31no—
193C4×D4C2×C5×D311yescharacteristic
194#106—61no—
195C4⋊C8—31no—
196C4⋊C8—31no—
197C4⋊C8C2×C5×D311yescharacteristic
198#102—61no—
199#102—61no—
200#102—61no—
201#102—61no—
202C22⋊C8—21no—
203C4×C8C2×C5×D311yescharacteristic
204C2×C3×C5—81no—
205C2×C3×C5#46311yescharacteristic
206C2×C3×C5#46811yescharacteristic
207C2×C3×C5#47211yescharacteristic
208C5×D3—161no—
209C23×C3—21no—
210C22×D3—41no—
211C3×D4—21no—
212C3×D4—21no—
213C2×C3×C4—21no—
214C2×C3×C4—41no—
215C2×C3×C4—41no—
216C2×C3×C4C2×C5×D411yescharacteristic
217C2×C3×C4C2×C5×D411yescharacteristic
218C2×C3×C4C5×#4111yescharacteristic
219C2×Dic3—41no—
220D12—41no—
221D12—41no—
222D12—41no—
223D12—41no—
224D12—81no—
225Dic6—81no—
226C3×C8—21no—
227C3×C8—21no—
228C3×C8—41no—
229C3⋊C8—41no—
230C3⋊C8—41no—
231C22×C5—41no—
232C22×C5—41no—
233C22×C5—41no—
234C22×C5—241no—
235C22×C5—241no—
236C22×C5—241no—
237C22×C5#93011yescharacteristic
238C4×C5—21no—
239C4×C5—41no—
240C4×C5—241no—
241C4×C5#90811yescharacteristic
242C4×C5#90911yescharacteristic
243C4×C5#93211yescharacteristic
244C4×C5#95011yescharacteristic
245C2×Q8—61no—
246C2×D4—61no—
247C2×D4—61no—
248C2×D4—61no—
249C2×D4C5×D1211yescharacteristic
250C22×C4—21no—
251D8—122no—
252M16—42no—
253C2×C8—21no—
254C2×C8—61no—
255C2×C8—61no—
256C2×C8C5×#6711yescharacteristic
257C2×C8C5×#6711yescharacteristic
258C4⋊C4—61no—
259C4⋊C4—61no—
260C4⋊C4C5×D1211yescharacteristic
261C22⋊C4—21no—
262C42C22×C5×D311yescharacteristic
263C3×C5#169711yescharacteristic, complemented, Hall
264C22×C3—41no—
265C22×C3—41no—
266C22×C3—41no—
267C22×C3C5×#12111yescharacteristic
268C2×D3—81no—
269C2×D3—81no—
270C2×D3—81no—
271C3×C4—21no—
272C3×C4—41no—
273C3×C4C5×#13511yescharacteristic
274C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
275C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
276C3×C4C5×#13711yescharacteristic
277Dic3—81no—
278C2×C5—81no—
279C2×C5—481no—
280C2×C5#501611yescharacteristic
281C2×C5#513411yescharacteristic
282C2×C5#514211yescharacteristic
283C23—21no—
284C23—121no—
285Q8—241no—
286D4—21no—
287D4—21no—
288D4—121no—
289D4—121no—
290D4—121no—
291D4—121no—
292D4—241no—
293C2×C4—21no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—121no—
297C2×C4C2×C5×D1211yescharacteristic
298C2×C4C5×#23511yescharacteristic
299C2×C4C2×C5×#6711yescharacteristic
300C8—21no—
301C8—21no—
302C8—41no—
303C8—121no—
304C8—121no—
305C2×C3—81no—
306C2×C3C5×#46311yescharacteristic
307C2×C3C5×#46811yescharacteristic
308C2×C3C5×#47211yescharacteristic
309D3—161no—
310C5#7086911yescharacteristic, direct product factor, Sylow
311C22—41no—
312C22—41no—
313C22—41no—
314C22—241no—
315C22—241no—
316C22—241no—
317C22C5×#93011yescharacteristic
318C4—21no—
319C4—41no—
320C4—241no—
321C4C5×#90811yescharacteristic
322C4C5×#90911yescharacteristic
323C4C5×#93211yescharacteristic
324C4C5×#95011yescharacteristic
325C3C5×#169711yescharacteristic, complemented, Sylow
326C2—81no—
327C2—481no—
328C2C5×#501611yescharacteristic
329C2C5×#513411yescharacteristic
330C2C5×#514211yescharacteristic
subgroupG/H
centerC22×C5#930
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#436C2
socleC22×C3×C5#121
prime radicalC5×#5015C2
hypercenterC5×#436D3
hypocenterC3C5×#1697
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#436

Complements

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

NH ≅ G/Ntype
1. C3×C5×#436C2semidirect
3. C5×#5008C2semidirect
4. C5×#4694C2semidirect
5. C5×#4485C2semidirect
6. C5×#4481C2semidirect
7. C5×#4458C2semidirect
24. #70869C5direct (N × H)
28. C5×#436D3semidirect
50. C3×#436C2×C5semidirect
52. #5008C2×C5semidirect
53. #4694C2×C5semidirect
54. #4485C2×C5semidirect
55. #4481C2×C5semidirect
56. #4458C2×C5semidirect
131. #436C5×D3semidirect
263. C3×C5#1697semidirect
310. C5#70869direct (N × H)
325. C3C5×#1697semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4362
C5×#50152
C5×#50082
C5×#46942
C5×#44852
C5×#44812
C5×#44582
C5×#16973
#708695