Finite Group Databasebeta

← C5×#71009 #14292474

Subgroups — C5×#71009 #14292474

Order 1920.

396 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#459C211yesmaximal, characteristic, complemented
2C5×#5073C211yesmaximal, characteristic, complemented
3C5×#5015C211yesmaximal, characteristic, complemented
4C5×#5012C211yesmaximal, characteristic, complemented
5C5×#4544C211yesmaximal, characteristic, complemented
6C5×#4485C211yesmaximal, characteristic, complemented
7C5×#4480C211yesmaximal, characteristic, complemented
8C5×#1687—31nomaximal, Hall
9C2×C3×C5×D8—21no—
10C3×C5×#127C2211yescharacteristic
11C3×C4×C5×D4C2211yescharacteristic
12C2×C5×#213—21no—
13C2×C5×#213—21no—
14C2×C5×#213—21no—
15C2×C5×#208—21no—
16C5×#874C2211yescharacteristic
17C3×C5×C4⋊C8C2211yescharacteristic
18C3×C5×#102—21no—
19C5×#830—21no—
20C5×#809—21no—
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C5×C4⋊(C3⋊C8)C2211yescharacteristic
23C4×C5×C3⋊C8C2211yescharacteristic
24#71009C511yesmaximal, characteristic, direct product factor, Hall
25C5×#493—31no—
26C5×#459—31no—
27C5×#459D311yescharacteristic, complemented
28C5×#436—31no—
29C5×#334—31no—
30C5×#331—31no—
31C5×#331—31no—
32C2×C3×C5×D4—21no—
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5—21no—
37C2×C5×D12—21no—
38C2×C5×D12—21no—
39C2×C5×D12—21no—
40C3×C5×D8—42no—
41C2×C3×C5×C8—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C5×C22⋊C4—21no—
44C3×C42×C5C2311yescharacteristic
45C5×#213—42no—
46C5×#213—42no—
47C5×#213—42no—
48C5×#208—42no—
49C2×C5×C3⋊C8—21no—
50C2×C5×C3⋊C8—21no—
51C2×C5×C3⋊C8D411yescharacteristic
52C2×C5×C3⋊C8D411yescharacteristic
53C3×#459C2×C511yescharacteristic, complemented
54#5073C2×C511yescharacteristic, complemented
55#5015C2×C511yescharacteristic, complemented
56#5012C2×C511yescharacteristic, complemented
57#4544C2×C511yescharacteristic, complemented
58#4485C2×C511yescharacteristic, complemented
59#4480C2×C511yescharacteristic, complemented
60C2×C5×D8—21no—
61C2×C5×D8—61no—
62C2×C5×D8—61no—
63C2×C5×D8—61no—
64C2×C5×M16—61no—
65C5×#127—31no—
66C5×#127C2×D311yescharacteristic
67C4×C5×D4C2×D311yescharacteristic
68C5×C4⋊C8—31no—
69C5×C4⋊C8—31no—
70C5×C4⋊C8C2×D311yescharacteristic
71C5×#102—21no—
72C5×#102—61no—
73C5×C22⋊C8—61no—
74C4×C5×C8—31no—
75#1687—31noSylow
76C23×C3×C5—21no—
77C23×C3×C5—41no—
78C22×C5×D3—41no—
79C3×C5×D4—21no—
80C3×C5×D4—21no—
81C3×C5×D4—41no—
82C3×C5×D4—41no—
83C3×C5×D4—41no—
84C3×C5×D4—41no—
85C3×C5×D4—81no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—41no—
88C2×C3×C4×C5—41no—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5#4111yescharacteristic
92C5×D12—41no—
93C5×D12—41no—
94C5×D12—41no—
95C5×D12—41no—
96C5×D12—81no—
97C3×C5×C8—41no—
98C5×C3⋊C8—21no—
99C5×C3⋊C8—41no—
100C5×C3⋊C8—41no—
101C5×C3⋊C8D812yescomplemented
102C2×C3×D8—21no—
103C3×#127C22×C511yescharacteristic
104C3×C4×D4C22×C511yescharacteristic
105C2×#213—21no—
106C2×#213—21no—
107C2×#213—21no—
108C2×#208—21no—
109#874C22×C511yescharacteristic
110C3×C4⋊C8C22×C511yescharacteristic
111C3×#102—21no—
112#830—21no—
113#809—21no—
114C4⋊(C3⋊C8)C22×C511yescharacteristic
115C4⋊(C3⋊C8)C22×C511yescharacteristic
116C4×C3⋊C8C22×C511yescharacteristic
117C2×C5×D4—21no—
118C2×C5×D4—21no—
119C2×C5×D4—21no—
120C2×C5×D4—61no—
121C2×C5×D4—61no—
122C2×C5×D4—61no—
123C2×C5×D4#6711yescharacteristic
124C22×C4×C5—21no—
125C5×D8—42no—
126C5×D8—122no—
127C5×D8—122no—
128C5×D8—122no—
129C5×M16—122no—
130C2×C5×C8—21no—
131C2×C5×C8—31no—
132C2×C5×C8—31no—
133C2×C5×C8—61no—
134C2×C5×C8—61no—
135C5×C4⋊C4#6711yescharacteristic
136C5×C22⋊C4—21no—
137C42×C5C22×D311yescharacteristic
138#493—31no—
139#459—31no—
140#459C5×D311yescharacteristic, complemented
141#436—31no—
142#334—31no—
143#331—31no—
144#331—31no—
145C22×C3×C5—41no—
146C22×C3×C5—41no—
147C22×C3×C5—41no—
148C22×C3×C5—81no—
149C22×C3×C5—81no—
150C22×C3×C5—81no—
151C22×C3×C5#12111yescharacteristic
152C2×C5×D3—81no—
153C2×C5×D3—81no—
154C2×C5×D3—81no—
155C3×C4×C5—21no—
156C3×C4×C5—41no—
157C3×C4×C5C2×D811yescharacteristic
158C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C2×C3×D4—21no—
162C2×C3×D4—21no—
163C2×C3×D4—21no—
164C2×C3×D4C5×D411yescharacteristic
165C22×C3×C4—21no—
166C2×D12—21no—
167C2×D12—21no—
168C2×D12—21no—
169C3×D8—42no—
170C2×C3×C8—21no—
171C3×C4⋊C4C5×D411yescharacteristic
172C3×C22⋊C4—21no—
173C3×C42C23×C511yescharacteristic
174#213—42no—
175#213—42no—
176#213—42no—
177#208—42no—
178C2×C3⋊C8—21no—
179C2×C3⋊C8—21no—
180C2×C3⋊C8C5×D411yescharacteristic
181C2×C3⋊C8C5×D411yescharacteristic
182C23×C5—21no—
183C23×C5—41no—
184C23×C5—121no—
185C5×D4—21no—
186C5×D4—21no—
187C5×D4—41no—
188C5×D4—41no—
189C5×D4—41no—
190C5×D4—41no—
191C5×D4—81no—
192C5×D4—121no—
193C5×D4—121no—
194C5×D4—121no—
195C5×D4—121no—
196C5×D4—241no—
197C2×C4×C5—21no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5D3×D411yescharacteristic
201C2×C4×C5#23711yescharacteristic
202C2×C4×C5C2×#6711yescharacteristic
203C5×C8—32no—
204C5×C8—41no—
205C5×C8—61no—
206C5×C8—121no—
207C5×C8—121no—
208C2×D8—21no—
209C2×D8—61no—
210C2×D8—61no—
211C2×D8—61no—
212C2×M16—61no—
213#127—31no—
214#127C2×C5×D311yescharacteristic
215C4×D4C2×C5×D311yescharacteristic
216C4⋊C8—31no—
217C4⋊C8—31no—
218C4⋊C8C2×C5×D311yescharacteristic
219#102—21no—
220#102—61no—
221C22⋊C8—61no—
222C4×C8—31no—
223C2×C3×C5—81no—
224C2×C3×C5—161no—
225C2×C3×C5#45911yescharacteristic
226C2×C3×C5#46911yescharacteristic
227C2×C3×C5#47211yescharacteristic
228C5×D3—161no—
229C23×C3—21no—
230C23×C3—41no—
231C22×D3—41no—
232C3×D4—21no—
233C3×D4—21no—
234C3×D4—41no—
235C3×D4—41no—
236C3×D4—41no—
237C3×D4—41no—
238C3×D4—81no—
239C2×C3×C4—21no—
240C2×C3×C4—41no—
241C2×C3×C4—41no—
242C2×C3×C4C2×C5×D411yescharacteristic
243C2×C3×C4C2×C5×D411yescharacteristic
244C2×C3×C4C5×#4111yescharacteristic
245D12—41no—
246D12—41no—
247D12—41no—
248D12—41no—
249D12—81no—
250C3×C8—41no—
251C3⋊C8—21no—
252C3⋊C8—41no—
253C3⋊C8—41no—
254C3⋊C8C5×D812yescomplemented
255C22×C5—41no—
256C22×C5—41no—
257C22×C5—41no—
258C22×C5—81no—
259C22×C5—81no—
260C22×C5—81no—
261C22×C5—241no—
262C22×C5—241no—
263C22×C5—241no—
264C22×C5#93911yescharacteristic
265C4×C5—21no—
266C4×C5—41no—
267C4×C5D3×D811yescharacteristic
268C4×C5#91111yescharacteristic
269C4×C5#93211yescharacteristic
270C4×C5#94911yescharacteristic
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—61no—
275C2×D4—61no—
276C2×D4—61no—
277C2×D4C5×#6711yescharacteristic
278C22×C4—21no—
279D8—42no—
280D8—122no—
281D8—122no—
282D8—122no—
283M16—122no—
284C2×C8—21no—
285C2×C8—31no—
286C2×C8—31no—
287C2×C8—61no—
288C2×C8—61no—
289C4⋊C4C5×#6711yescharacteristic
290C22⋊C4—21no—
291C42C22×C5×D311yescharacteristic
292C3×C5#168711yescharacteristic, complemented, Hall
293C22×C3—41no—
294C22×C3—41no—
295C22×C3—41no—
296C22×C3—81no—
297C22×C3—81no—
298C22×C3—81no—
299C22×C3C5×#12111yescharacteristic
300C2×D3—81no—
301C2×D3—81no—
302C2×D3—81no—
303C3×C4—21no—
304C3×C4—41no—
305C3×C4C2×C5×D811yescharacteristic
306C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
307C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
308C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
309C2×C5—81no—
310C2×C5—161no—
311C2×C5—481no—
312C2×C5#503911yescharacteristic
313C2×C5#515011yescharacteristic
314C2×C5#519911yescharacteristic
315C23—21no—
316C23—41no—
317C23—121no—
318D4—21no—
319D4—21no—
320D4—41no—
321D4—41no—
322D4—41no—
323D4—41no—
324D4—81no—
325D4—121no—
326D4—121no—
327D4—121no—
328D4—121no—
329D4—241no—
330C2×C4—21no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4C5×D3×D411yescharacteristic
334C2×C4C5×#23711yescharacteristic
335C2×C4C2×C5×#6711yescharacteristic
336C8—32no—
337C8—41no—
338C8—61no—
339C8—121no—
340C8—121no—
341C2×C3—81no—
342C2×C3—161no—
343C2×C3C5×#45911yescharacteristic
344C2×C3C5×#46911yescharacteristic
345C2×C3C5×#47211yescharacteristic
346D3—161no—
347C5#7100911yescharacteristic, direct product factor, Sylow
348C22—41no—
349C22—41no—
350C22—41no—
351C22—81no—
352C22—81no—
353C22—81no—
354C22—241no—
355C22—241no—
356C22—241no—
357C22C5×#93911yescharacteristic
358C4—21no—
359C4—41no—
360C4C5×D3×D811yescharacteristic
361C4C5×#91111yescharacteristic
362C4C5×#93211yescharacteristic
363C4C5×#94911yescharacteristic
364C3C5×#168711yescharacteristic, complemented, Sylow
365C2—81no—
366C2—161no—
367C2—481no—
368C2C5×#503911yescharacteristic
369C2C5×#515011yescharacteristic
370C2C5×#519911yescharacteristic
subgroupG/H
centerC22×C5#939
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#459C2
socleC22×C3×C5#121
hypercenterC5×#459D3
hypocenterC3C5×#1687
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#459

Complements

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

NH ≅ G/Ntype
1. C3×C5×#459C2semidirect
2. C5×#5073C2semidirect
3. C5×#5015C2semidirect
4. C5×#5012C2semidirect
5. C5×#4544C2semidirect
6. C5×#4485C2semidirect
7. C5×#4480C2semidirect
24. #71009C5direct (N × H)
27. C5×#459D3semidirect
53. C3×#459C2×C5semidirect
54. #5073C2×C5semidirect
55. #5015C2×C5semidirect
56. #5012C2×C5semidirect
57. #4544C2×C5semidirect
58. #4485C2×C5semidirect
59. #4480C2×C5semidirect
101. C5×C3⋊C8D8semidirect
140. #459C5×D3semidirect
254. C3⋊C8C5×D8semidirect
292. C3×C5#1687semidirect
347. C5#71009direct (N × H)
364. C3C5×#1687semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4592
C5×#50732
C5×#50152
C5×#50122
C5×#45442
C5×#44852
C5×#44802
C5×#16873
#710095