Finite Group Databasebeta

← C5×#69533 #14283302

Subgroups — C5×#69533 #14283302

Order 1920.

548 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#924C211yesmaximal, characteristic
2C3×C5×#381C211yesmaximal, characteristic
3C5×#5207C211yesmaximal, characteristic
4C5×#4452C214yesmaximal, complemented
5C5×#1511—31nomaximal, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C22×C5×Dic6C411yescharacteristic, complemented
8C2×C3×C5×C22⋊C4—21no—
9C2×C5×#217—21no—
10C2×C5×C4⋊Dic3C411yescharacteristic, complemented
11C5×#924—21no—
12C5×#924—21no—
13C5×#924C412yescomplemented
14C5×#924C2212yes—
15C2×C5×Dic3⋊C4—21no—
16C2×C5×#208—21no—
17C3×C5×#95—21no—
18C3×C5×#95C2212yes—
19C5×#830—21no—
20C5×#830C2212yes—
21#69533C511yesmaximal, characteristic, direct product factor, Hall
22C2×C5×C22⋊Q8—31no—
23C5×#407—31no—
24C5×#381D311yescharacteristic
25C5×#328—34no—
26C24×C3×C5D411yescharacteristic
27C22×C3×C4×C5—22no—
28C22×C3×C4×C5—42no—
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5C2311yescharacteristic
35C22×C5×Dic3—21no—
36C22×C5×Dic3—21no—
37C2×C5×Dic6—21no—
38C2×C5×Dic6—42no—
39C2×C5×Dic6C2×C412yes—
40C3×C5×C22⋊C4—42no—
41C5×#217—22no—
42C5×#217—22no—
43C5×C4⋊Dic3—21no—
44C5×C4⋊Dic3C2×C412yes—
45C5×Dic3⋊C4—22no—
46C5×Dic3⋊C4—22no—
47C5×#208—42no—
48C2×C5×C3⋊C8—22no—
49C2×#924C2×C511yescharacteristic
50C3×#381C2×C511yescharacteristic
51#5207C2×C511yescharacteristic
52#4452C2×C514yescomplemented
53C22×C5×Q8—31no—
54C23×C4×C5C2×D311yescharacteristic
55C2×C5×M16—61no—
56C5×C22⋊Q8—32no—
57C5×C22⋊Q8—32no—
58C5×C22⋊Q8—61no—
59C5×C22⋊Q8—61no—
60C2×C5×C4⋊C4—31no—
61C2×C5×C4⋊C4—61no—
62C2×C5×C22⋊C4—21no—
63C2×C5×C22⋊C4—61no—
64C5×C22⋊C8—32no—
65C5×C22⋊C8—61no—
66C5×#95—21no—
67C5×#95C2×D312yes—
68#1511—31noSylow
69C23×C3×C5—22no—
70C23×C3×C5—22no—
71C23×C3×C5—41no—
72C23×C3×C5C22⋊C411yescharacteristic
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C2×D411yescharacteristic
75C2×C3×C4×C5—22no—
76C2×C3×C4×C5—22no—
77C2×C3×C4×C5—41no—
78C2×C3×C4×C5—41no—
79C2×C3×C4×C5—41no—
80C2×C3×C4×C5—41no—
81C2×C3×C4×C5—42no—
82C2×C3×C4×C5—42no—
83C2×C3×C4×C5—42no—
84C2×C3×C4×C5C22⋊C411yescharacteristic
85C2×C3×C4×C5C22⋊C411yescharacteristic
86C2×C3×C4×C5C22×C411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C5×Dic3—22no—
89C2×C5×Dic3—22no—
90C2×C5×Dic3—42no—
91C2×C5×Dic3—42no—
92C5×Dic6—42no—
93C5×Dic6—42no—
94C5×C3⋊C8—42no—
95C23×C3×C4C22×C511yescharacteristic
96C22×Dic6C4×C511yescharacteristic, complemented
97C2×C3×C22⋊C4—21no—
98C2×#217—21no—
99C2×C4⋊Dic3C4×C511yescharacteristic, complemented
100#924—21no—
101#924—21no—
102#924C4×C512yescomplemented
103#924C22×C512yes—
104C2×Dic3⋊C4—21no—
105C2×#208—21no—
106C3×#95—21no—
107C3×#95C22×C512yes—
108#830—21no—
109#830C22×C512yes—
110C24×C5#6711yescharacteristic
111C2×C5×Q8—32no—
112C2×C5×Q8—61no—
113C2×C5×Q8—122no—
114C22×C4×C5—22no—
115C22×C4×C5—42no—
116C22×C4×C5—61no—
117C22×C4×C5—61no—
118C22×C4×C5C4×D311yescharacteristic
119C22×C4×C5C4×D311yescharacteristic
120C22×C4×C5D1211yescharacteristic
121C22×C4×C5D1211yescharacteristic
122C22×C4×C5#6711yescharacteristic
123C22×C4×C5C22×D311yescharacteristic
124C5×M16—122no—
125C2×C5×C8—62no—
126C5×C4⋊C4—32no—
127C5×C4⋊C4—61no—
128C5×C4⋊C4—62no—
129C5×C4⋊C4—62no—
130C5×C22⋊C4—42no—
131C5×C22⋊C4—62no—
132C5×C22⋊C4—62no—
133C2×C22⋊Q8—31no—
134#407—31no—
135#381C5×D311yescharacteristic
136#328—34no—
137C22×C3×C5—21no—
138C22×C3×C5—21no—
139C22×C3×C5—21no—
140C22×C3×C5—21no—
141C22×C3×C5—21no—
142C22×C3×C5—21no—
143C22×C3×C5—21no—
144C22×C3×C5—44no—
145C22×C3×C5#9912yes—
146C22×C3×C5C2×C22⋊C411yescharacteristic
147C22×C3×C5#13712yes—
148C3×C4×C5—21no—
149C3×C4×C5—21no—
150C3×C4×C5—21no—
151C3×C4×C5—21no—
152C3×C4×C5—82no—
153C5×Dic3—42no—
154C5×Dic3—42no—
155C24×C3C5×D411yescharacteristic
156C22×C3×C4—22no—
157C22×C3×C4—42no—
158C22×C3×C4C2×C4×C511yescharacteristic
159C22×C3×C4C2×C4×C511yescharacteristic
160C22×C3×C4C5×D411yescharacteristic
161C22×C3×C4C5×D411yescharacteristic
162C22×C3×C4C5×D411yescharacteristic
163C22×C3×C4C23×C511yescharacteristic
164C22×Dic3—21no—
165C22×Dic3—21no—
166C2×Dic6—21no—
167C2×Dic6—42no—
168C2×Dic6C2×C4×C512yes—
169C3×C22⋊C4—42no—
170#217—22no—
171#217—22no—
172C4⋊Dic3—21no—
173C4⋊Dic3C2×C4×C512yes—
174Dic3⋊C4—22no—
175Dic3⋊C4—22no—
176#208—42no—
177C2×C3⋊C8—22no—
178C23×C5—22no—
179C23×C5—22no—
180C23×C5—41no—
181C23×C5(C2×D3)⋊C411yescharacteristic
182C23×C5(C2×D3)⋊C411yescharacteristic
183C23×C5C2×#6711yescharacteristic
184C5×Q8—122no—
185C5×Q8—122no—
186C2×C4×C5—22no—
187C2×C4×C5—22no—
188C2×C4×C5—41no—
189C2×C4×C5—41no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5—42no—
193C2×C4×C5—42no—
194C2×C4×C5—42no—
195C2×C4×C5—62no—
196C2×C4×C5—62no—
197C2×C4×C5—122no—
198C2×C4×C5—122no—
199C2×C4×C5(C2×D3)⋊C411yescharacteristic
200C2×C4×C5(C2×D3)⋊C411yescharacteristic
201C2×C4×C5C2×C4×D311yescharacteristic
202C2×C4×C5C2×D1211yescharacteristic
203C5×C8—122no—
204C22×Q8—31no—
205C23×C4C2×C5×D311yescharacteristic
206C2×M16—61no—
207C22⋊Q8—32no—
208C22⋊Q8—32no—
209C22⋊Q8—61no—
210C22⋊Q8—61no—
211C2×C4⋊C4—31no—
212C2×C4⋊C4—61no—
213C2×C22⋊C4—21no—
214C2×C22⋊C4—61no—
215C22⋊C8—32no—
216C22⋊C8—61no—
217#95—21no—
218#95C2×C5×D312yes—
219C2×C3×C5—22no—
220C2×C3×C5—22no—
221C2×C3×C5—41no—
222C2×C3×C5C2×#9911yescharacteristic
223C2×C3×C5#41911yescharacteristic
224C2×C3×C5#42111yescharacteristic
225C23×C3—22no—
226C23×C3—22no—
227C23×C3—41no—
228C23×C3C5×C22⋊C411yescharacteristic
229C23×C3C5×C22⋊C411yescharacteristic
230C23×C3C2×C5×D411yescharacteristic
231C2×C3×C4—22no—
232C2×C3×C4—22no—
233C2×C3×C4—41no—
234C2×C3×C4—41no—
235C2×C3×C4—41no—
236C2×C3×C4—41no—
237C2×C3×C4—42no—
238C2×C3×C4—42no—
239C2×C3×C4—42no—
240C2×C3×C4C5×C22⋊C411yescharacteristic
241C2×C3×C4C5×C22⋊C411yescharacteristic
242C2×C3×C4C22×C4×C511yescharacteristic
243C2×C3×C4C2×C5×D411yescharacteristic
244C2×Dic3—22no—
245C2×Dic3—22no—
246C2×Dic3—42no—
247C2×Dic3—42no—
248Dic6—42no—
249Dic6—42no—
250C3⋊C8—42no—
251C22×C5—21no—
252C22×C5—21no—
253C22×C5—21no—
254C22×C5—21no—
255C22×C5—21no—
256C22×C5—21no—
257C22×C5—21no—
258C22×C5—44no—
259C22×C5#80612yes—
260C22×C5C2×(C2×D3)⋊C411yescharacteristic
261C22×C5#95112yes—
262C4×C5—21no—
263C4×C5—21no—
264C4×C5—21no—
265C4×C5—21no—
266C4×C5—82no—
267C4×C5—122no—
268C4×C5—122no—
269C24C5×#6711yescharacteristic
270C2×Q8—32no—
271C2×Q8—61no—
272C2×Q8—122no—
273C22×C4—22no—
274C22×C4—42no—
275C22×C4—61no—
276C22×C4—61no—
277C22×C4C4×C5×D311yescharacteristic
278C22×C4C4×C5×D311yescharacteristic
279C22×C4C5×D1211yescharacteristic
280C22×C4C5×D1211yescharacteristic
281C22×C4C5×#6711yescharacteristic
282C22×C4C22×C5×D311yescharacteristic
283M16—122no—
284C2×C8—62no—
285C4⋊C4—32no—
286C4⋊C4—61no—
287C4⋊C4—62no—
288C4⋊C4—62no—
289C22⋊C4—42no—
290C22⋊C4—62no—
291C22⋊C4—62no—
292C3×C5#151111yescharacteristic, complemented, Hall
293C22×C3—21no—
294C22×C3—21no—
295C22×C3—21no—
296C22×C3—21no—
297C22×C3—21no—
298C22×C3—21no—
299C22×C3—21no—
300C22×C3—44no—
301C22×C3C5×#9912yes—
302C22×C3C2×C5×C22⋊C411yescharacteristic
303C22×C3C5×#13712yes—
304C3×C4—21no—
305C3×C4—21no—
306C3×C4—21no—
307C3×C4—21no—
308C3×C4—82no—
309Dic3—42no—
310Dic3—42no—
311C2×C5—22no—
312C2×C5—22no—
313C2×C5—41no—
314C2×C5C2×#80611yescharacteristic
315C2×C5#500411yescharacteristic
316C2×C5#500511yescharacteristic
317C23—22no—
318C23—22no—
319C23—41no—
320C23C5×(C2×D3)⋊C411yescharacteristic
321C23C5×(C2×D3)⋊C411yescharacteristic
322C23C2×C5×#6711yescharacteristic
323Q8—122no—
324Q8—122no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—62no—
335C2×C4—62no—
336C2×C4—122no—
337C2×C4—122no—
338C2×C4C5×(C2×D3)⋊C411yescharacteristic
339C2×C4C5×(C2×D3)⋊C411yescharacteristic
340C2×C4C2×C4×C5×D311yescharacteristic
341C2×C4C2×C5×D1211yescharacteristic
342C8—122no—
343C2×C3—22no—
344C2×C3—22no—
345C2×C3—41no—
346C2×C3C2×C5×#9911yescharacteristic
347C2×C3C5×#41911yescharacteristic
348C2×C3C5×#42111yescharacteristic
349C5#6953311yescharacteristic, direct product factor, Sylow
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—44no—
358C22C5×#80612yes—
359C22C2×C5×(C2×D3)⋊C411yescharacteristic
360C22C5×#95112yes—
361C4—21no—
362C4—21no—
363C4—21no—
364C4—21no—
365C4—82no—
366C4—122no—
367C4—122no—
368C3C5×#151111yescharacteristic, complemented, Sylow
369C2—22no—
370C2—22no—
371C2—41no—
372C2C2×C5×#80611yescharacteristic
373C2C5×#500411yescharacteristic
374C2C5×#500511yescharacteristic
subgroupG/H
centerC22×C5C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#381C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5D4
cosocleC22×C3×C4C23×C5
hypercenterC5×#381D3
hypocenterC3C5×#1511
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ C5×#381

Complements

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

NH ≅ G/Ntype
4. C5×#4452C2semidirect
7. C22×C5×Dic6C4semidirect
10. C2×C5×C4⋊Dic3C4semidirect
13. C5×#924C4semidirect
21. #69533C5direct (N × H)
52. #4452C2×C5semidirect
96. C22×Dic6C4×C5semidirect
99. C2×C4⋊Dic3C4×C5semidirect
102. #924C4×C5semidirect
292. C3×C5#1511semidirect
349. C5#69533direct (N × H)
368. C3C5×#1511semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9242
C3×C5×#3812
C5×#52072
C5×#44522
C5×#15113
#695335