Finite Group Databasebeta

← C5×#71025 #14292513

Subgroups — C5×#71025 #14292513

Order 1920.

368 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#460C211yesmaximal, characteristic, complemented
2C5×#5073C211yesmaximal, characteristic
3C5×#5027C211yesmaximal, characteristic, complemented
4C5×#5024C211yesmaximal, characteristic, complemented
5C5×#4544C211yesmaximal, characteristic, complemented
6C5×#4485C211yesmaximal, characteristic, complemented
7C5×#4480C211yesmaximal, characteristic, complemented
8C5×#1688—31nomaximal, Hall
9C2×C3×C5×SD16—21no—
10C3×C5×#127C2211yescharacteristic
11C3×C4×C5×Q8C2211yescharacteristic
12C2×C5×#215—21no—
13C2×C5×#213—21no—
14C2×C5×#213—21no—
15C5×#874C2211yescharacteristic
16C3×C5×C4⋊C8C2211yescharacteristic
17C3×C5×#102—21no—
18C5×#809—21no—
19C5×C4⋊(C3⋊C8)—21no—
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C5×C4⋊(C3⋊C8)C2211yescharacteristic
22C5×#803—21no—
23C4×C5×C3⋊C8C2211yescharacteristic
24#71025C511yesmaximal, characteristic, direct product factor, Hall
25C5×#493—31no—
26C5×#460—31no—
27C5×#460D311yescharacteristic, complemented
28C5×#446—31no—
29C5×#334—31no—
30C5×#331—31no—
31C5×#331—31no—
32C2×C3×C5×Q8D411yescharacteristic
33C2×C3×C5×D4—21no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C5×D12—21no—
39C3×C5×SD16—42no—
40C2×C3×C5×C8—21no—
41C3×C5×C4⋊C4—21no—
42C3×C5×C4⋊C4D411yescharacteristic
43C3×C42×C5—21no—
44C3×C42×C5C2311yescharacteristic
45C5×#215—42no—
46C5×#213—42no—
47C5×#213—42no—
48C2×C5×C3⋊C8—21no—
49C2×C5×C3⋊C8—21no—
50C2×C5×C3⋊C8D411yescharacteristic
51C2×C5×C3⋊C8D411yescharacteristic
52C3×#460C2×C511yescharacteristic, complemented
53#5073C2×C511yescharacteristic
54#5027C2×C511yescharacteristic, complemented
55#5024C2×C511yescharacteristic, complemented
56#4544C2×C511yescharacteristic, complemented
57#4485C2×C511yescharacteristic, complemented
58#4480C2×C511yescharacteristic, complemented
59C2×C5×SD16—21no—
60C2×C5×SD16—61no—
61C2×C5×D8—61no—
62C2×C5×D8—61no—
63C5×#127—31no—
64C5×#127C2×D311yescharacteristic
65C4×C5×Q8C2×D311yescharacteristic
66C5×C4⋊C8—31no—
67C5×C4⋊C8—31no—
68C5×C4⋊C8—61no—
69C5×C4⋊C8C2×D311yescharacteristic
70C5×#102—21no—
71C5×#102—61no—
72C5×#97—61no—
73C4×C5×C8—31no—
74#1688—31noSylow
75C23×C3×C5—41no—
76C22×C5×D3—41no—
77C3×C5×Q8—21no—
78C3×C5×Q8—21no—
79C3×C5×D4—41no—
80C3×C5×D4—41no—
81C3×C5×D4—41no—
82C3×C5×D4—41no—
83C3×C5×D4—81no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5#4111yescharacteristic
89C5×D12—41no—
90C5×D12—41no—
91C5×D12—41no—
92C5×D12—41no—
93C5×D12—81no—
94C3×C5×C8—41no—
95C5×C3⋊C8—21no—
96C5×C3⋊C8—41no—
97C5×C3⋊C8—41no—
98C5×C3⋊C8SD1612yescomplemented
99C2×C3×SD16—21no—
100C3×#127C22×C511yescharacteristic
101C3×C4×Q8C22×C511yescharacteristic
102C2×#215—21no—
103C2×#213—21no—
104C2×#213—21no—
105#874C22×C511yescharacteristic
106C3×C4⋊C8C22×C511yescharacteristic
107C3×#102—21no—
108#809—21no—
109C4⋊(C3⋊C8)—21no—
110C4⋊(C3⋊C8)C22×C511yescharacteristic
111C4⋊(C3⋊C8)C22×C511yescharacteristic
112#803—21no—
113C4×C3⋊C8C22×C511yescharacteristic
114C2×C5×Q8#6711yescharacteristic
115C2×C5×D4—21no—
116C2×C5×D4—21no—
117C2×C5×D4—21no—
118C2×C5×D4—61no—
119C2×C5×D4—61no—
120C2×C5×D4—61no—
121C5×SD16—42no—
122C5×SD16—122no—
123C5×D8—122no—
124C5×D8—122no—
125C2×C5×C8—21no—
126C2×C5×C8—31no—
127C2×C5×C8—31no—
128C2×C5×C8—61no—
129C2×C5×C8—61no—
130C5×C4⋊C4—21no—
131C5×C4⋊C4#6711yescharacteristic
132C42×C5—21no—
133C42×C5C22×D311yescharacteristic
134#493—31no—
135#460—31no—
136#460C5×D311yescharacteristic, complemented
137#446—31no—
138#334—31no—
139#331—31no—
140#331—31no—
141C22×C3×C5—81no—
142C22×C3×C5—81no—
143C22×C3×C5—81no—
144C22×C3×C5#12111yescharacteristic
145C2×C5×D3—81no—
146C2×C5×D3—81no—
147C2×C5×D3—81no—
148C3×C4×C5—21no—
149C3×C4×C5—41no—
150C3×C4×C5—41no—
151C3×C4×C5C2×SD1611yescharacteristic
152C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
153C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
154C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
155C2×C3×Q8C5×D411yescharacteristic
156C2×C3×D4—21no—
157C2×C3×D4—21no—
158C2×C3×D4—21no—
159C2×D12—21no—
160C2×D12—21no—
161C2×D12—21no—
162C3×SD16—42no—
163C2×C3×C8—21no—
164C3×C4⋊C4—21no—
165C3×C4⋊C4C5×D411yescharacteristic
166C3×C42—21no—
167C3×C42C23×C511yescharacteristic
168#215—42no—
169#213—42no—
170#213—42no—
171C2×C3⋊C8—21no—
172C2×C3⋊C8—21no—
173C2×C3⋊C8C5×D411yescharacteristic
174C2×C3⋊C8C5×D411yescharacteristic
175C23×C5—41no—
176C23×C5—121no—
177C5×Q8—21no—
178C5×Q8—21no—
179C5×D4—41no—
180C5×D4—41no—
181C5×D4—41no—
182C5×D4—41no—
183C5×D4—81no—
184C5×D4—121no—
185C5×D4—121no—
186C5×D4—121no—
187C5×D4—121no—
188C5×D4—241no—
189C2×C4×C5—21no—
190C2×C4×C5—21no—
191C2×C4×C5D3×D411yescharacteristic
192C2×C4×C5#23711yescharacteristic
193C2×C4×C5C2×#6711yescharacteristic
194C5×C8—32no—
195C5×C8—41no—
196C5×C8—61no—
197C5×C8—121no—
198C5×C8—121no—
199C2×SD16—21no—
200C2×SD16—61no—
201C2×D8—61no—
202C2×D8—61no—
203#127—31no—
204#127C2×C5×D311yescharacteristic
205C4×Q8C2×C5×D311yescharacteristic
206C4⋊C8—31no—
207C4⋊C8—31no—
208C4⋊C8—61no—
209C4⋊C8C2×C5×D311yescharacteristic
210#102—21no—
211#102—61no—
212#97—61no—
213C4×C8—31no—
214C2×C3×C5—161no—
215C2×C3×C5#46011yescharacteristic
216C2×C3×C5#46911yescharacteristic
217C2×C3×C5#47211yescharacteristic
218C5×D3—161no—
219C23×C3—41no—
220C22×D3—41no—
221C3×Q8—21no—
222C3×Q8—21no—
223C3×D4—41no—
224C3×D4—41no—
225C3×D4—41no—
226C3×D4—41no—
227C3×D4—81no—
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4C2×C5×D411yescharacteristic
231C2×C3×C4C2×C5×D411yescharacteristic
232C2×C3×C4C5×#4111yescharacteristic
233D12—41no—
234D12—41no—
235D12—41no—
236D12—41no—
237D12—81no—
238C3×C8—41no—
239C3⋊C8—21no—
240C3⋊C8—41no—
241C3⋊C8—41no—
242C3⋊C8C5×SD1612yescomplemented
243C22×C5—81no—
244C22×C5—81no—
245C22×C5—81no—
246C22×C5—241no—
247C22×C5—241no—
248C22×C5—241no—
249C22×C5#93911yescharacteristic
250C4×C5—21no—
251C4×C5—41no—
252C4×C5—41no—
253C4×C5D3×SD1611yescharacteristic
254C4×C5#91411yescharacteristic
255C4×C5#93211yescharacteristic
256C4×C5#94911yescharacteristic
257C2×Q8C5×#6711yescharacteristic
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—61no—
262C2×D4—61no—
263C2×D4—61no—
264SD16—42no—
265SD16—122no—
266D8—122no—
267D8—122no—
268C2×C8—21no—
269C2×C8—31no—
270C2×C8—31no—
271C2×C8—61no—
272C2×C8—61no—
273C4⋊C4—21no—
274C4⋊C4C5×#6711yescharacteristic
275C42—21no—
276C42C22×C5×D311yescharacteristic
277C3×C5#168811yescharacteristic, complemented, Hall
278C22×C3—81no—
279C22×C3—81no—
280C22×C3—81no—
281C22×C3C5×#12111yescharacteristic
282C2×D3—81no—
283C2×D3—81no—
284C2×D3—81no—
285C3×C4—21no—
286C3×C4—41no—
287C3×C4—41no—
288C3×C4C2×C5×SD1611yescharacteristic
289C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
290C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
291C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
292C2×C5—161no—
293C2×C5—481no—
294C2×C5#503911yescharacteristic
295C2×C5#516311yescharacteristic
296C2×C5#519911yescharacteristic
297C23—41no—
298C23—121no—
299Q8—21no—
300Q8—21no—
301D4—41no—
302D4—41no—
303D4—41no—
304D4—41no—
305D4—81no—
306D4—121no—
307D4—121no—
308D4—121no—
309D4—121no—
310D4—241no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4C5×D3×D411yescharacteristic
314C2×C4C5×#23711yescharacteristic
315C2×C4C2×C5×#6711yescharacteristic
316C8—32no—
317C8—41no—
318C8—61no—
319C8—121no—
320C8—121no—
321C2×C3—161no—
322C2×C3C5×#46011yescharacteristic
323C2×C3C5×#46911yescharacteristic
324C2×C3C5×#47211yescharacteristic
325D3—161no—
326C5#7102511yescharacteristic, direct product factor, Sylow
327C22—81no—
328C22—81no—
329C22—81no—
330C22—241no—
331C22—241no—
332C22—241no—
333C22C5×#93911yescharacteristic
334C4—21no—
335C4—41no—
336C4—41no—
337C4C5×D3×SD1611yescharacteristic
338C4C5×#91411yescharacteristic
339C4C5×#93211yescharacteristic
340C4C5×#94911yescharacteristic
341C3C5×#168811yescharacteristic, complemented, Sylow
342C2—161no—
343C2—481no—
344C2C5×#503911yescharacteristic
345C2C5×#516311yescharacteristic
346C2C5×#519911yescharacteristic
subgroupG/H
centerC22×C5#939
commutator, cosocleC3×C42C23×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#460C2
socleC22×C3×C5#121
prime radicalC5×#5073C2
hypercenterC5×#460D3
hypocenterC3C5×#1688
LCSG ▷ C3×C42 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C42×C5 ◁ C5×#460

Complements

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

NH ≅ G/Ntype
1. C3×C5×#460C2semidirect
3. C5×#5027C2semidirect
4. C5×#5024C2semidirect
5. C5×#4544C2semidirect
6. C5×#4485C2semidirect
7. C5×#4480C2semidirect
24. #71025C5direct (N × H)
27. C5×#460D3semidirect
52. C3×#460C2×C5semidirect
54. #5027C2×C5semidirect
55. #5024C2×C5semidirect
56. #4544C2×C5semidirect
57. #4485C2×C5semidirect
58. #4480C2×C5semidirect
98. C5×C3⋊C8SD16semidirect
136. #460C5×D3semidirect
242. C3⋊C8C5×SD16semidirect
277. C3×C5#1688semidirect
326. C5#71025direct (N × H)
341. C3C5×#1688semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#4602
C5×#50732
C5×#50272
C5×#50242
C5×#45442
C5×#44852
C5×#44802
C5×#16883
#710255