Finite Group Databasebeta

← C5×#70820 #14285078

Subgroups — C5×#70820 #14285078

Order 1920.

416 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5470C211yesmaximal, characteristic
2C3×C5×#432C211yesmaximal, characteristic
3C2×C5×C4⋊(C3⋊C8)C211yesmaximal, characteristic
4C5×#4486C212yesmaximal, complemented
5C5×#4482C212yesmaximal, complemented
6C5×#1552—31nomaximal, Hall
7C2×C3×C42×C5C2211yescharacteristic
8C5×#926C412yes—
9C5×#924—21no—
10C5×#924—21no—
11C22×C5×C3⋊C8—21no—
12C5×#870C412yes—
13C5×#869C2211yescharacteristic
14C5×#869C2211yescharacteristic
15C4×C5×Dic6—21no—
16C4×C5×Dic6—21no—
17C3×C5×C4⋊C8C2212yes—
18C3×C5×C22⋊C8—21no—
19C3×C5×#97—21no—
20C5×C4⋊(C3⋊C8)—21no—
21C5×C4⋊(C3⋊C8)C2212yes—
22#70820C511yesmaximal, characteristic, direct product factor, Hall
23C5×#533—31no—
24C5×#432D311yescharacteristic
25C2×C5×C4⋊C8—31no—
26C5×#332—32no—
27C5×#332—32no—
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×C3×C4×C5D411yescharacteristic
30C22×C3×C4×C5D411yescharacteristic
31C2×C5×Dic6—21no—
32C2×C5×Dic6—21no—
33C2×C3×C5×C8—22no—
34C3×C42×C5C2×C411yescharacteristic
35C3×C42×C5D411yescharacteristic
36C3×C42×C5D411yescharacteristic
37C3×C42×C5C2311yescharacteristic
38C5×#217—22no—
39C5×C4⋊Dic3—21no—
40C5×C4⋊Dic3—21no—
41C5×C4⋊Dic3C2×C412yes—
42C5×C4⋊Dic3C2×C412yes—
43C5×Dic3⋊C4—22no—
44C5×Dic3⋊C4—22no—
45C4×C5×Dic3—22no—
46C2×C5×C3⋊C8—22no—
47C2×C5×C3⋊C8—42no—
48#5470C2×C511yescharacteristic
49C3×#432C2×C511yescharacteristic
50C2×C4⋊(C3⋊C8)C2×C511yescharacteristic
51#4486C2×C512yescomplemented
52#4482C2×C512yescomplemented
53C22×C5×C8—61no—
54C5×C4⋊Q8—31no—
55C5×C4⋊Q8—31no—
56C5×#125—32no—
57C5×C22⋊Q8—61no—
58C5×C22⋊Q8—61no—
59C4×C5×Q8—61no—
60C4×C5×Q8—61no—
61C5×#117—32no—
62C2×C42×C5C2×D311yescharacteristic
63C5×C4⋊C8—32no—
64C5×C4⋊C8—61no—
65C5×C4⋊C8C2×D312yes—
66C5×C22⋊C8—21no—
67C5×#97—21no—
68#1552—31noSylow
69C23×C3×C5C22⋊C411yescharacteristic
70C2×C3×C4×C5—22no—
71C2×C3×C4×C5—22no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5—21no—
74C2×C3×C4×C5C22⋊C411yescharacteristic
75C2×C3×C4×C5C22⋊C411yescharacteristic
76C2×C3×C4×C5C22⋊C411yescharacteristic
77C2×C3×C4×C5C22×C411yescharacteristic
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×C3×C4×C5C2×D411yescharacteristic
80C2×C5×Dic3—22no—
81C2×C5×Dic3—22no—
82C5×Dic6—42no—
83C5×Dic6—41no—
84C5×Dic6—41no—
85C3×C5×C8—42no—
86C5×C3⋊C8—42no—
87C2×C3×C42C22×C511yescharacteristic
88#926C4×C512yes—
89#924—21no—
90#924—21no—
91C22×C3⋊C8—21no—
92#870C4×C512yes—
93#869C22×C511yescharacteristic
94#869C22×C511yescharacteristic
95C4×Dic6—21no—
96C4×Dic6—21no—
97C3×C4⋊C8C22×C512yes—
98C3×C22⋊C8—21no—
99C3×#97—21no—
100C4⋊(C3⋊C8)—21no—
101C4⋊(C3⋊C8)C22×C512yes—
102C2×C5×Q8—61no—
103C2×C5×Q8—61no—
104C22×C4×C5C4×D311yescharacteristic
105C22×C4×C5D1211yescharacteristic
106C22×C4×C5#6711yescharacteristic
107C2×C5×C8—22no—
108C2×C5×C8—62no—
109C2×C5×C8—122no—
110C5×C4⋊C4—32no—
111C5×C4⋊C4—32no—
112C5×C4⋊C4—62no—
113C5×C4⋊C4—62no—
114C5×C4⋊C4—61no—
115C5×C4⋊C4—61no—
116C5×C22⋊C4—62no—
117C42×C5—62no—
118C42×C5C4×D311yescharacteristic
119C42×C5D1211yescharacteristic
120C42×C5#6711yescharacteristic
121C42×C5C22×D311yescharacteristic
122#533—31no—
123#432C5×D311yescharacteristic
124C2×C4⋊C8—31no—
125#332—32no—
126#332—32no—
127C22×C3×C5—21no—
128C22×C3×C5—21no—
129C22×C3×C5#10112yes—
130C22×C3×C5C2×C22⋊C411yescharacteristic
131C3×C4×C5—21no—
132C3×C4×C5—21no—
133C3×C4×C5—21no—
134C3×C4×C5—21no—
135C3×C4×C5#13512yes—
136C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
137C3×C4×C5#13711yescharacteristic
138C5×Dic3—42no—
139C5×Dic3—42no—
140C22×C3×C4C2×C4×C511yescharacteristic
141C22×C3×C4C5×D411yescharacteristic
142C22×C3×C4C5×D411yescharacteristic
143C2×Dic6—21no—
144C2×Dic6—21no—
145C2×C3×C8—22no—
146C3×C42C2×C4×C511yescharacteristic
147C3×C42C5×D411yescharacteristic
148C3×C42C5×D411yescharacteristic
149C3×C42C23×C511yescharacteristic
150#217—22no—
151C4⋊Dic3—21no—
152C4⋊Dic3—21no—
153C4⋊Dic3C2×C4×C512yes—
154C4⋊Dic3C2×C4×C512yes—
155Dic3⋊C4—22no—
156Dic3⋊C4—22no—
157C4×Dic3—22no—
158C2×C3⋊C8—22no—
159C2×C3⋊C8—42no—
160C23×C5(C2×D3)⋊C411yescharacteristic
161C5×Q8—121no—
162C5×Q8—121no—
163C5×Q8—122no—
164C2×C4×C5—22no—
165C2×C4×C5—21no—
166C2×C4×C5—21no—
167C2×C4×C5—22no—
168C2×C4×C5—62no—
169C2×C4×C5—62no—
170C2×C4×C5(C2×D3)⋊C411yescharacteristic
171C2×C4×C5(C2×D3)⋊C411yescharacteristic
172C2×C4×C5(C2×D3)⋊C411yescharacteristic
173C2×C4×C5C2×C4×D311yescharacteristic
174C2×C4×C5C2×D1211yescharacteristic
175C2×C4×C5C2×#6711yescharacteristic
176C5×C8—42no—
177C5×C8—122no—
178C22×C8—61no—
179C4⋊Q8—31no—
180C4⋊Q8—31no—
181#125—32no—
182C22⋊Q8—61no—
183C22⋊Q8—61no—
184C4×Q8—61no—
185C4×Q8—61no—
186#117—32no—
187C2×C42C2×C5×D311yescharacteristic
188C4⋊C8—32no—
189C4⋊C8—61no—
190C4⋊C8C2×C5×D312yes—
191C22⋊C8—21no—
192#97—21no—
193C2×C3×C5—22no—
194C2×C3×C5C2×#10111yescharacteristic
195C2×C3×C5#41611yescharacteristic
196C2×C3×C5#41711yescharacteristic
197C23×C3C5×C22⋊C411yescharacteristic
198C2×C3×C4—22no—
199C2×C3×C4—22no—
200C2×C3×C4—21no—
201C2×C3×C4—21no—
202C2×C3×C4C5×C22⋊C411yescharacteristic
203C2×C3×C4C5×C22⋊C411yescharacteristic
204C2×C3×C4C5×C22⋊C411yescharacteristic
205C2×C3×C4C22×C4×C511yescharacteristic
206C2×C3×C4C2×C5×D411yescharacteristic
207C2×C3×C4C2×C5×D411yescharacteristic
208C2×Dic3—22no—
209C2×Dic3—22no—
210Dic6—42no—
211Dic6—41no—
212Dic6—41no—
213C3×C8—42no—
214C3⋊C8—42no—
215C22×C5—21no—
216C22×C5—21no—
217C22×C5#82412yes—
218C22×C5C2×(C2×D3)⋊C411yescharacteristic
219C4×C5—21no—
220C4×C5—21no—
221C4×C5—21no—
222C4×C5—21no—
223C4×C5—122no—
224C4×C5—122no—
225C4×C5#90811yescharacteristic
226C4×C5#90911yescharacteristic
227C4×C5#95012yes—
228C2×Q8—61no—
229C2×Q8—61no—
230C22×C4C4×C5×D311yescharacteristic
231C22×C4C5×D1211yescharacteristic
232C22×C4C5×#6711yescharacteristic
233C2×C8—22no—
234C2×C8—62no—
235C2×C8—122no—
236C4⋊C4—32no—
237C4⋊C4—32no—
238C4⋊C4—62no—
239C4⋊C4—62no—
240C4⋊C4—61no—
241C4⋊C4—61no—
242C22⋊C4—62no—
243C42—62no—
244C42C4×C5×D311yescharacteristic
245C42C5×D1211yescharacteristic
246C42C5×#6711yescharacteristic
247C42C22×C5×D311yescharacteristic
248C3×C5#155211yescharacteristic, complemented, Hall
249C22×C3—21no—
250C22×C3—21no—
251C22×C3C5×#10112yes—
252C22×C3C2×C5×C22⋊C411yescharacteristic
253C3×C4—21no—
254C3×C4—21no—
255C3×C4—21no—
256C3×C4—21no—
257C3×C4C5×#13512yes—
258C3×C4C5×AGL(1,ℤ/8)11yescharacteristic
259C3×C4C5×#13711yescharacteristic
260Dic3—42no—
261Dic3—42no—
262C2×C5—22no—
263C2×C5#500211yescharacteristic
264C2×C5#513311yescharacteristic
265C2×C5C2×#82411yescharacteristic
266C23C5×(C2×D3)⋊C411yescharacteristic
267Q8—121no—
268Q8—121no—
269Q8—122no—
270C2×C4—22no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—22no—
274C2×C4—62no—
275C2×C4—62no—
276C2×C4C5×(C2×D3)⋊C411yescharacteristic
277C2×C4C5×(C2×D3)⋊C411yescharacteristic
278C2×C4C5×(C2×D3)⋊C411yescharacteristic
279C2×C4C2×C4×C5×D311yescharacteristic
280C2×C4C2×C5×D1211yescharacteristic
281C2×C4C2×C5×#6711yescharacteristic
282C8—42no—
283C8—122no—
284C2×C3—22no—
285C2×C3C2×C5×#10111yescharacteristic
286C2×C3C5×#41611yescharacteristic
287C2×C3C5×#41711yescharacteristic
288C5#7082011yescharacteristic, direct product factor, Sylow
289C22—21no—
290C22—21no—
291C22C5×#82412yes—
292C22C2×C5×(C2×D3)⋊C411yescharacteristic
293C4—21no—
294C4—21no—
295C4—21no—
296C4—21no—
297C4—122no—
298C4—122no—
299C4C5×#90811yescharacteristic
300C4C5×#90911yescharacteristic
301C4C5×#95012yes—
302C3C5×#155211yescharacteristic, complemented, Sylow
303C2—22no—
304C2C5×#500211yescharacteristic
305C2C5×#513311yescharacteristic
306C2C2×C5×#82411yescharacteristic
subgroupG/H
centerC22×C5C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#432C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
cosocleC3×C42C23×C5
hypercenterC5×#432D3
hypocenterC3C5×#1552
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ C5×#432

Complements

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

NH ≅ G/Ntype
4. C5×#4486C2semidirect
5. C5×#4482C2semidirect
22. #70820C5direct (N × H)
51. #4486C2×C5semidirect
52. #4482C2×C5semidirect
248. C3×C5#1552semidirect
288. C5#70820direct (N × H)
302. C3C5×#1552semidirect

Maximal subgroups

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

subgroupindex
C5×#54702
C3×C5×#4322
C2×C5×C4⋊(C3⋊C8)2
C5×#44862
C5×#44822
C5×#15523
#708205