Finite Group Databasebeta

← C5×#71824 #14281815

Subgroups — C5×#71824 #14281815

Order 1920.

432 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#533C211yesmaximal, characteristic
2C5×#4925C211yesmaximal, characteristic
3C2×C5×C4⋊(C3⋊C8)C211yesmaximal, characteristic
4C5×#4535C214yesmaximal, complemented
5C5×#1481—31nomaximal, Hall
6C3×C5×C4⋊Q8C411yescharacteristic
7C3×C5×C4⋊Q8C411yescharacteristic
8C3×C5×#125—21no—
9C3×C5×C22⋊Q8—21no—
10C3×C5×C22⋊Q8C412yes—
11C3×C4×C5×Q8—21no—
12C3×C4×C5×Q8C2212yes—
13C3×C5×#117—21no—
14C2×C3×C42×C5C2211yescharacteristic
15C22×C5×C3⋊C8—21no—
16C5×#830—21no—
17C5×C4⋊(C3⋊C8)—21no—
18C5×C4⋊(C3⋊C8)—21no—
19C5×C4⋊(C3⋊C8)C2212yes—
20C4×C5×C3⋊C8C2212yes—
21#71824C511yesmaximal, characteristic, direct product factor, Hall
22C5×#533D311yescharacteristic
23C5×#431—31no—
24C2×C5×C4⋊C8—31no—
25C5×Q8⋊C8—34no—
26C2×C3×C5×Q8—21no—
27C2×C3×C5×Q8C2×C412yes—
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×C3×C4×C5D411yescharacteristic
30C22×C3×C4×C5D411yescharacteristic
31C3×C5×C4⋊C4—21no—
32C3×C5×C4⋊C4—21no—
33C3×C5×C4⋊C4—21no—
34C3×C5×C4⋊C4—22no—
35C3×C5×C4⋊C4—22no—
36C3×C5×C4⋊C4C2×C412yes—
37C3×C5×C22⋊C4—22no—
38C3×C42×C5—22no—
39C3×C42×C5C2×C411yescharacteristic
40C3×C42×C5D411yescharacteristic
41C3×C42×C5D411yescharacteristic
42C3×C42×C5C2311yescharacteristic
43C2×C5×C3⋊C8—22no—
44C2×C5×C3⋊C8—22no—
45C2×C5×C3⋊C8—42no—
46C3×#533C2×C511yescharacteristic
47#4925C2×C511yescharacteristic
48C2×C4⋊(C3⋊C8)C2×C511yescharacteristic
49#4535C2×C514yescomplemented
50C22×C5×C8—61no—
51C5×C4⋊Q8Dic311yescharacteristic
52C5×C4⋊Q8Dic311yescharacteristic
53C5×#125—21no—
54C5×C22⋊Q8—21no—
55C5×C22⋊Q8Dic312yes—
56C4×C5×Q8—21no—
57C4×C5×Q8C2×D312yes—
58C5×#117—21no—
59C2×C42×C5C2×D311yescharacteristic
60C5×C4⋊C8—32no—
61C5×C4⋊C8—61no—
62C5×C4⋊C8—61no—
63C5×C22⋊C8—61no—
64C4×C5×C8—32no—
65#1481—31noSylow
66C23×C3×C5C22⋊C411yescharacteristic
67C3×C5×Q8—24no—
68C3×C5×Q8—42no—
69C2×C3×C4×C5—22no—
70C2×C3×C4×C5—22no—
71C2×C3×C4×C5—22no—
72C2×C3×C4×C5—41no—
73C2×C3×C4×C5C22⋊C411yescharacteristic
74C2×C3×C4×C5C22⋊C411yescharacteristic
75C2×C3×C4×C5C22⋊C411yescharacteristic
76C2×C3×C4×C5SD1612yes—
77C2×C3×C4×C5Q1612yes—
78C2×C3×C4×C5C22×C411yescharacteristic
79C2×C3×C4×C5C2×D411yescharacteristic
80C2×C3×C4×C5C2×D411yescharacteristic
81C5×C3⋊C8—42no—
82C5×C3⋊C8—42no—
83C3×C4⋊Q8C4×C511yescharacteristic
84C3×C4⋊Q8C4×C511yescharacteristic
85C3×#125—21no—
86C3×C22⋊Q8—21no—
87C3×C22⋊Q8C4×C512yes—
88C3×C4×Q8—21no—
89C3×C4×Q8C22×C512yes—
90C3×#117—21no—
91C2×C3×C42C22×C511yescharacteristic
92C22×C3⋊C8—21no—
93#830—21no—
94C4⋊(C3⋊C8)—21no—
95C4⋊(C3⋊C8)—21no—
96C4⋊(C3⋊C8)C22×C512yes—
97C4×C3⋊C8C22×C512yes—
98C2×C5×Q8—21no—
99C2×C5×Q8C2×Dic312yes—
100C22×C4×C5C2×Dic311yescharacteristic
101C22×C4×C5#6711yescharacteristic
102C22×C4×C5#6711yescharacteristic
103C2×C5×C8—62no—
104C2×C5×C8—62no—
105C2×C5×C8—122no—
106C5×C4⋊C4—21no—
107C5×C4⋊C4—21no—
108C5×C4⋊C4—21no—
109C5×C4⋊C4—22no—
110C5×C4⋊C4—22no—
111C5×C4⋊C4C2×Dic312yes—
112C5×C22⋊C4—22no—
113C42×C5—22no—
114C42×C5C2×Dic311yescharacteristic
115C42×C5#6711yescharacteristic
116C42×C5#6711yescharacteristic
117C42×C5C22×D311yescharacteristic
118#533C5×D311yescharacteristic
119#431—31no—
120C2×C4⋊C8—31no—
121Q8⋊C8—34no—
122C22×C3×C5—21no—
123C22×C3×C5—21no—
124C22×C3×C5#10312yes—
125C22×C3×C5C2×C22⋊C411yescharacteristic
126C3×C4×C5—21no—
127C3×C4×C5—21no—
128C3×C4×C5—21no—
129C3×C4×C5—42no—
130C3×C4×C5—42no—
131C3×C4×C5#10312yes—
132C3×C4×C5#13112yes—
133C3×C4×C5C2×SD1611yescharacteristic
134C3×C4×C5C2×Q1611yescharacteristic
135C2×C3×Q8—21no—
136C2×C3×Q8C2×C4×C512yes—
137C22×C3×C4C2×C4×C511yescharacteristic
138C22×C3×C4C5×D411yescharacteristic
139C22×C3×C4C5×D411yescharacteristic
140C3×C4⋊C4—21no—
141C3×C4⋊C4—21no—
142C3×C4⋊C4—21no—
143C3×C4⋊C4—22no—
144C3×C4⋊C4—22no—
145C3×C4⋊C4C2×C4×C512yes—
146C3×C22⋊C4—22no—
147C3×C42—22no—
148C3×C42C2×C4×C511yescharacteristic
149C3×C42C5×D411yescharacteristic
150C3×C42C5×D411yescharacteristic
151C3×C42C23×C511yescharacteristic
152C2×C3⋊C8—22no—
153C2×C3⋊C8—22no—
154C2×C3⋊C8—42no—
155C23×C5#21711yescharacteristic
156C5×Q8—24no—
157C5×Q8—42no—
158C2×C4×C5—22no—
159C2×C4×C5—22no—
160C2×C4×C5—22no—
161C2×C4×C5—41no—
162C2×C4×C5#21512yes—
163C2×C4×C5#21612yes—
164C2×C4×C5#21711yescharacteristic
165C2×C4×C5#21711yescharacteristic
166C2×C4×C5#21711yescharacteristic
167C2×C4×C5C22×Dic311yescharacteristic
168C2×C4×C5C2×#6711yescharacteristic
169C2×C4×C5C2×#6711yescharacteristic
170C5×C8—122no—
171C5×C8—122no—
172C22×C8—61no—
173C4⋊Q8C5×Dic311yescharacteristic
174C4⋊Q8C5×Dic311yescharacteristic
175#125—21no—
176C22⋊Q8—21no—
177C22⋊Q8C5×Dic312yes—
178C4×Q8—21no—
179C4×Q8C2×C5×D312yes—
180#117—21no—
181C2×C42C2×C5×D311yescharacteristic
182C4⋊C8—32no—
183C4⋊C8—61no—
184C4⋊C8—61no—
185C22⋊C8—61no—
186C4×C8—32no—
187C2×C3×C5—22no—
188C2×C3×C5#40811yescharacteristic
189C2×C3×C5C2×#10311yescharacteristic
190C2×C3×C5#42111yescharacteristic
191C23×C3C5×C22⋊C411yescharacteristic
192C3×Q8—24no—
193C3×Q8—42no—
194C2×C3×C4—22no—
195C2×C3×C4—22no—
196C2×C3×C4—22no—
197C2×C3×C4—41no—
198C2×C3×C4C5×C22⋊C411yescharacteristic
199C2×C3×C4C5×C22⋊C411yescharacteristic
200C2×C3×C4C5×C22⋊C411yescharacteristic
201C2×C3×C4C5×SD1612yes—
202C2×C3×C4C5×Q1612yes—
203C2×C3×C4C22×C4×C511yescharacteristic
204C2×C3×C4C2×C5×D411yescharacteristic
205C2×C3×C4C2×C5×D411yescharacteristic
206C3⋊C8—42no—
207C3⋊C8—42no—
208C22×C5—21no—
209C22×C5—21no—
210C22×C5#83512yes—
211C22×C5C2×#21711yescharacteristic
212C4×C5—21no—
213C4×C5—21no—
214C4×C5—21no—
215C4×C5—42no—
216C4×C5—42no—
217C4×C5#83512yes—
218C4×C5C2×#21511yescharacteristic
219C4×C5C2×#21611yescharacteristic
220C4×C5#94812yes—
221C2×Q8—21no—
222C2×Q8C2×C5×Dic312yes—
223C22×C4C2×C5×Dic311yescharacteristic
224C22×C4C5×#6711yescharacteristic
225C22×C4C5×#6711yescharacteristic
226C2×C8—62no—
227C2×C8—62no—
228C2×C8—122no—
229C4⋊C4—21no—
230C4⋊C4—21no—
231C4⋊C4—21no—
232C4⋊C4—22no—
233C4⋊C4—22no—
234C4⋊C4C2×C5×Dic312yes—
235C22⋊C4—22no—
236C42—22no—
237C42C2×C5×Dic311yescharacteristic
238C42C5×#6711yescharacteristic
239C42C5×#6711yescharacteristic
240C42C22×C5×D311yescharacteristic
241C3×C5#148111yescharacteristic, complemented, Hall
242C22×C3—21no—
243C22×C3—21no—
244C22×C3C5×#10312yes—
245C22×C3C2×C5×C22⋊C411yescharacteristic
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—42no—
250C3×C4—42no—
251C3×C4C5×#10312yes—
252C3×C4C5×#13112yes—
253C3×C4C2×C5×SD1611yescharacteristic
254C3×C4C2×C5×Q1611yescharacteristic
255C2×C5—22no—
256C2×C5C2×#83511yescharacteristic
257C2×C5#523411yescharacteristic
258C2×C5#523611yescharacteristic
259C23C5×#21711yescharacteristic
260Q8—24no—
261Q8—42no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—22no—
265C2×C4—41no—
266C2×C4C5×#21512yes—
267C2×C4C5×#21612yes—
268C2×C4C5×#21711yescharacteristic
269C2×C4C5×#21711yescharacteristic
270C2×C4C5×#21711yescharacteristic
271C2×C4C22×C5×Dic311yescharacteristic
272C2×C4C2×C5×#6711yescharacteristic
273C2×C4C2×C5×#6711yescharacteristic
274C8—122no—
275C8—122no—
276C2×C3—22no—
277C2×C3C5×#40811yescharacteristic
278C2×C3C2×C5×#10311yescharacteristic
279C2×C3C5×#42111yescharacteristic
280C5#7182411yescharacteristic, direct product factor, Sylow
281C22—21no—
282C22—21no—
283C22C5×#83512yes—
284C22C2×C5×#21711yescharacteristic
285C4—21no—
286C4—21no—
287C4—21no—
288C4—42no—
289C4—42no—
290C4C5×#83512yes—
291C4C2×C5×#21511yescharacteristic
292C4C2×C5×#21611yescharacteristic
293C4C5×#94812yes—
294C3C5×#148111yescharacteristic, complemented, Sylow
295C2—22no—
296C2C2×C5×#83511yescharacteristic
297C2C5×#523411yescharacteristic
298C2C5×#523611yescharacteristic
subgroupG/H
centerC2×C4×C5C2×#67
commutatorC2×C3×C4C22×C4×C5
FrattiniC42C22×C5×D3
FittingC3×C5×#533C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C22⋊C4
cosocleC3×C42C23×C5
hypercenterC5×#533D3
hypocenterC3C5×#1481
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4×C5 ◁ C2×C42×C5 ◁ C5×#533

Complements

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

NH ≅ G/Ntype
4. C5×#4535C2semidirect
21. #71824C5direct (N × H)
49. #4535C2×C5semidirect
241. C3×C5#1481semidirect
280. C5#71824direct (N × H)
294. C3C5×#1481semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5332
C5×#49252
C2×C5×C4⋊(C3⋊C8)2
C5×#45352
C5×#14813
#718245