Finite Group Databasebeta

← C5×#71138 #14292924

Subgroups — C5×#71138 #14292924

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×#476C211yesmaximal, characteristic, complemented
2C5×#5088C211yesmaximal, characteristic, complemented
3C5×#5015C211yesmaximal, characteristic
4C5×#5012C211yesmaximal, characteristic, complemented
5C5×#4546C211yesmaximal, characteristic, complemented
6C5×#4485C211yesmaximal, characteristic, complemented
7C5×#4479C211yesmaximal, characteristic, complemented
8C5×#1697—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10C3×C4×C5×D4C2211yescharacteristic
11C2×C5×#213—21no—
12C2×C5×#208—21no—
13C5×#874C2211yescharacteristic
14C3×C5×#106—21no—
15C3×C5×C4⋊C8C2211yescharacteristic
16C3×C5×#102—21no—
17C5×#830—21no—
18C5×#809—21no—
19C5×#809—21no—
20C5×#809—21no—
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C4×C5×C3⋊C8C2211yescharacteristic
24#71138C511yesmaximal, characteristic, direct product factor, Hall
25C5×#486—31no—
26C5×#476D311yescharacteristic, complemented
27C5×#459—31no—
28C5×#436—31no—
29C5×#335—31no—
30C5×#333—31no—
31C5×#331—31no—
32C2×C3×C5×Q8—21no—
33C2×C3×C5×D4D411yescharacteristic
34C22×C3×C4×C5—21no—
35C2×C5×D12—21no—
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C3×C5×C8—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4—21no—
41C3×C5×C4⋊C4D411yescharacteristic
42C3×C5×C22⋊C4—21no—
43C3×C42×C5C2311yescharacteristic
44C5×#213—42no—
45C5×#208—42no—
46C2×C5×C3⋊C8—21no—
47C2×C5×C3⋊C8—21no—
48C2×C5×C3⋊C8D411yescharacteristic
49C2×C5×C3⋊C8D411yescharacteristic
50C3×#476C2×C511yescharacteristic, complemented
51#5088C2×C511yescharacteristic, complemented
52#5015C2×C511yescharacteristic
53#5012C2×C511yescharacteristic, complemented
54#4546C2×C511yescharacteristic, complemented
55#4485C2×C511yescharacteristic, complemented
56#4479C2×C511yescharacteristic, complemented
57C2×C5×D8—61no—
58C2×C5×M16—61no—
59C5×C4⋊Q8C2×D311yescharacteristic
60C5×#127—31no—
61C4×C5×D4C2×D311yescharacteristic
62C5×#106—21no—
63C5×C4⋊C8—31no—
64C5×C4⋊C8—31no—
65C5×C4⋊C8C2×D311yescharacteristic
66C5×#102—21no—
67C5×#102—61no—
68C5×#102—61no—
69C5×#102—61no—
70C5×C22⋊C8—61no—
71C4×C5×C8—31no—
72#1697—31noSylow
73C23×C3×C5—21no—
74C22×C5×D3—41no—
75C3×C5×Q8—81no—
76C3×C5×D4—21no—
77C3×C5×D4—21no—
78C2×C3×C4×C5—21no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5C2×D411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5#4111yescharacteristic
85C5×D12—41no—
86C5×D12—41no—
87C5×D12—41no—
88C5×D12—41no—
89C5×D12—81no—
90C3×C5×C8—41no—
91C5×C3⋊C8—21no—
92C5×C3⋊C8—21no—
93C5×C3⋊C8—41no—
94C5×C3⋊C8—41no—
95C3×C4⋊Q8C22×C511yescharacteristic
96C3×C4×D4C22×C511yescharacteristic
97C2×#213—21no—
98C2×#208—21no—
99#874C22×C511yescharacteristic
100C3×#106—21no—
101C3×C4⋊C8C22×C511yescharacteristic
102C3×#102—21no—
103#830—21no—
104#809—21no—
105#809—21no—
106#809—21no—
107C4⋊(C3⋊C8)C22×C511yescharacteristic
108C4⋊(C3⋊C8)C22×C511yescharacteristic
109C4×C3⋊C8C22×C511yescharacteristic
110C2×C5×Q8—21no—
111C2×C5×D4—61no—
112C2×C5×D4—61no—
113C2×C5×D4—61no—
114C2×C5×D4#6711yescharacteristic
115C22×C4×C5—21no—
116C5×D8—122no—
117C5×M16—122no—
118C2×C5×C8—21no—
119C2×C5×C8—31no—
120C2×C5×C8—31no—
121C2×C5×C8—61no—
122C2×C5×C8—61no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4#6711yescharacteristic
126C5×C22⋊C4—21no—
127C42×C5C22×D311yescharacteristic
128#486—31no—
129#476C5×D311yescharacteristic, complemented
130#459—31no—
131#436—31no—
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—81no—
145C3×C4×C5#13511yescharacteristic
146C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
147C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
148C3×C4×C5#13711yescharacteristic
149C2×C3×Q8—21no—
150C2×C3×D4C5×D411yescharacteristic
151C22×C3×C4—21no—
152C2×D12—21no—
153C2×D12—21no—
154C2×D12—21no—
155C2×C3×C8—21no—
156C3×C4⋊C4—21no—
157C3×C4⋊C4—21no—
158C3×C4⋊C4C5×D411yescharacteristic
159C3×C22⋊C4—21no—
160C3×C42C23×C511yescharacteristic
161#213—42no—
162#208—42no—
163C2×C3⋊C8—21no—
164C2×C3⋊C8—21no—
165C2×C3⋊C8C5×D411yescharacteristic
166C2×C3⋊C8C5×D411yescharacteristic
167C23×C5—21no—
168C23×C5—121no—
169C5×Q8—81no—
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—41no—
181C2×C4×C5D3×D411yescharacteristic
182C2×C4×C5#23711yescharacteristic
183C2×C4×C5C2×#6711yescharacteristic
184C5×C8—41no—
185C5×C8—61no—
186C5×C8—61no—
187C5×C8—121no—
188C5×C8—121no—
189C2×D8—61no—
190C2×M16—61no—
191C4⋊Q8C2×C5×D311yescharacteristic
192#127—31no—
193C4×D4C2×C5×D311yescharacteristic
194#106—21no—
195C4⋊C8—31no—
196C4⋊C8—31no—
197C4⋊C8C2×C5×D311yescharacteristic
198#102—21no—
199#102—61no—
200#102—61no—
201#102—61no—
202C22⋊C8—61no—
203C4×C8—31no—
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×Q8—81no—
212C3×D4—21no—
213C3×D4—21no—
214C2×C3×C4—21no—
215C2×C3×C4—41no—
216C2×C3×C4—41no—
217C2×C3×C4—41no—
218C2×C3×C4C2×C5×D411yescharacteristic
219C2×C3×C4C2×C5×D411yescharacteristic
220C2×C3×C4C5×#4111yescharacteristic
221D12—41no—
222D12—41no—
223D12—41no—
224D12—41no—
225D12—81no—
226C3×C8—41no—
227C3⋊C8—21no—
228C3⋊C8—21no—
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#93911yescharacteristic
238C4×C5—21no—
239C4×C5—41no—
240C4×C5—81no—
241C4×C5#91411yescharacteristic
242C4×C5#91611yescharacteristic
243C4×C5#94211yescharacteristic
244C4×C5#94911yescharacteristic
245C2×Q8—21no—
246C2×D4—61no—
247C2×D4—61no—
248C2×D4—61no—
249C2×D4C5×#6711yescharacteristic
250C22×C4—21no—
251D8—122no—
252M16—122no—
253C2×C8—21no—
254C2×C8—31no—
255C2×C8—31no—
256C2×C8—61no—
257C2×C8—61no—
258C4⋊C4—21no—
259C4⋊C4—21no—
260C4⋊C4C5×#6711yescharacteristic
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×C4—81no—
274C3×C4C5×#13511yescharacteristic
275C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
276C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
277C3×C4C5×#13711yescharacteristic
278C2×C5—81no—
279C2×C5—481no—
280C2×C5#504911yescharacteristic
281C2×C5#516511yescharacteristic
282C2×C5#519911yescharacteristic
283C23—21no—
284C23—121no—
285Q8—81no—
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—41no—
297C2×C4C5×D3×D411yescharacteristic
298C2×C4C5×#23711yescharacteristic
299C2×C4C2×C5×#6711yescharacteristic
300C8—41no—
301C8—61no—
302C8—61no—
303C8—121no—
304C8—121no—
305C2×C3—81no—
306C2×C3C5×#46311yescharacteristic
307C2×C3C5×#46811yescharacteristic
308C2×C3C5×#47211yescharacteristic
309D3—161no—
310C5#7113811yescharacteristic, direct product factor, Sylow
311C22—41no—
312C22—41no—
313C22—41no—
314C22—241no—
315C22—241no—
316C22—241no—
317C22C5×#93911yescharacteristic
318C4—21no—
319C4—41no—
320C4—81no—
321C4C5×#91411yescharacteristic
322C4C5×#91611yescharacteristic
323C4C5×#94211yescharacteristic
324C4C5×#94911yescharacteristic
325C3C5×#169711yescharacteristic, complemented, Sylow
326C2—81no—
327C2—481no—
328C2C5×#504911yescharacteristic
329C2C5×#516511yescharacteristic
330C2C5×#519911yescharacteristic
subgroupG/H
centerC22×C5#939
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#476C2
socleC22×C3×C5#121
prime radicalC5×#5015C2
hypercenterC5×#476D3
hypocenterC3C5×#1697
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#476

Complements

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

NH ≅ G/Ntype
1. C3×C5×#476C2semidirect
2. C5×#5088C2semidirect
4. C5×#5012C2semidirect
5. C5×#4546C2semidirect
6. C5×#4485C2semidirect
7. C5×#4479C2semidirect
24. #71138C5direct (N × H)
26. C5×#476D3semidirect
50. C3×#476C2×C5semidirect
51. #5088C2×C5semidirect
53. #5012C2×C5semidirect
54. #4546C2×C5semidirect
55. #4485C2×C5semidirect
56. #4479C2×C5semidirect
129. #476C5×D3semidirect
263. C3×C5#1697semidirect
310. C5#71138direct (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×#4762
C5×#50882
C5×#50152
C5×#50122
C5×#45462
C5×#44852
C5×#44792
C5×#16973
#711385