Finite Group Databasebeta

← #11989423

Subgroups — #11989423

Order 1280.

788 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×#117C211yesmaximal, characteristic
2C4×#4072C211yesmaximal, characteristic
3#10613780C211yesmaximal, characteristic
4#10598109C214yesmaximal
5C2×C5×#117—21no—
6C22×C42×C5C2211yescharacteristic
7C2×#4072—21no—
8C4×C5×C4⋊C4—21no—
9C4×C5×C4⋊C4C412yescomplemented
10C4×C5×C22⋊C4—21no—
11C4×C5×C22⋊C4C2212yes—
12C5×#376C412yescomplemented
13C43×C5—21no—
14C4×C22⋊Dic5—21no—
15C4×C22⋊Dic5C2212yes—
16#65496C2212yes—
17C4×C4⋊Dic5—21no—
18C4×C4⋊Dic5C412yescomplemented
19#65221C412yescomplemented
20C42×Dic5—21no—
21#65215—21no—
22#65215—21no—
23#65214—21no—
24#65214—21no—
25#65213C412yescomplemented
26C4×#681C412yescomplemented
27#8048—51nomaximal, Sylow
28C23×C4×C5D411yescharacteristic
29C23×C4×C5D411yescharacteristic
30C23×C4×C5C2311yescharacteristic
31C5×#117—28no—
32C2×C5×C4⋊C4—22no—
33C2×C5×C22⋊C4—22no—
34C2×C42×C5—22no—
35C2×C42×C5—22no—
36C2×C42×C5—22no—
37C2×C42×C5C2×C411yescharacteristic
38C2×C42×C5C2×C411yescharacteristic
39C2×C42×C5C2×C411yescharacteristic
40C2×C42×C5C2×C411yescharacteristic
41C2×C42×C5C2×C411yescharacteristic
42C2×C42×C5C2×C411yescharacteristic
43C2×C42×C5D411yescharacteristic
44C2×C42×C5D411yescharacteristic
45C2×C42×C5D411yescharacteristic
46C2×C42×C5D411yescharacteristic
47C2×C42×C5Q811yescharacteristic
48C2×C42×C5Q811yescharacteristic
49C2×C22⋊Dic5—22no—
50#4072—28no—
51C2×C4⋊Dic5—22no—
52C2×C4×Dic5—22no—
53C2×C4×Dic5—22no—
54C2×C4×Dic5—22no—
55C2×#681C2×C414yes—
56C5×#95—22no—
57C5×#95C2×C414yes—
58#3963—22no—
59#3963C2×C414yes—
60C22⋊#168—22no—
61C22⋊#168—22no—
62C4⋊#168—22no—
63C4⋊#168—22no—
64#3935—22no—
65C4×#168—22no—
66#2920—51no—
67C4×#117—51no—
68C4×#117D511yescharacteristic
69#1297—54no—
70C24×C5C2×D411yescharacteristic
71C22×C4×C5—24no—
72C22×C4×C5—24no—
73C22×C4×C5—24no—
74C22×C4×C5—42no—
75C22×C4×C5C22⋊C411yescharacteristic
76C22×C4×C5C22⋊C411yescharacteristic
77C22×C4×C5C22⋊C411yescharacteristic
78C22×C4×C5C22⋊C411yescharacteristic
79C22×C4×C5C22⋊C411yescharacteristic
80C22×C4×C5C22⋊C411yescharacteristic
81C22×C4×C5C22⋊C411yescharacteristic
82C22×C4×C5C22⋊C411yescharacteristic
83C22×C4×C5C4⋊C411yescharacteristic
84C22×C4×C5C4⋊C411yescharacteristic
85C22×C4×C5C4⋊C411yescharacteristic
86C22×C4×C5C4⋊C411yescharacteristic
87C22×C4×C5C22×C411yescharacteristic
88C22×C4×C5C22×C411yescharacteristic
89C22×C4×C5C22×C411yescharacteristic
90C22×C4×C5C2×D411yescharacteristic
91C22×C4×C5C2×D411yescharacteristic
92C22×C4×C5C2×Q811yescharacteristic
93C22×Dic5—24no—
94C5×C4⋊C4—28no—
95C5×C22⋊C4—28no—
96C42×C5—28no—
97C42×C5—44no—
98C42×C5—44no—
99C42×C5C4211yescharacteristic
100C42×C5C4211yescharacteristic
101C42×C5C4211yescharacteristic
102C42×C5C4211yescharacteristic
103C42×C5C22⋊C411yescharacteristic
104C42×C5C22⋊C411yescharacteristic
105C42×C5C22⋊C411yescharacteristic
106C42×C5C22⋊C411yescharacteristic
107C42×C5C4⋊C411yescharacteristic
108C42×C5C4⋊C411yescharacteristic
109C42×C5C4⋊C411yescharacteristic
110C42×C5C4⋊C411yescharacteristic
111C42×C5C4⋊C411yescharacteristic
112C42×C5C4⋊C411yescharacteristic
113C42×C5C4⋊C411yescharacteristic
114C42×C5C4⋊C411yescharacteristic
115C22⋊Dic5—28no—
116C4⋊Dic5—28no—
117C4×Dic5—28no—
118C4×Dic5—44no—
119C4×Dic5—44no—
120#681—44no—
121C2×#168—24no—
122C2×#117—21no—
123C2×#117—101no—
124C22×C42C2×D511yescharacteristic
125#432—101no—
126#432—101no—
127#431—101no—
128#431—101no—
129#423—52no—
130#407—52no—
131C4×M16—52no—
132C4×C4⋊C4—21no—
133C4×C4⋊C4—52no—
134C4×C4⋊C4—101no—
135C4×C4⋊C4Dic512yescomplemented
136C4×C22⋊C4—21no—
137C4×C22⋊C4—52no—
138C4×C22⋊C4—101no—
139C4×C22⋊C4C2×D512yes—
140#376—52no—
141#376Dic512yescomplemented
142C43—21no—
143C43—101no—
144C23×C5—22no—
145C23×C5—22no—
146C23×C5—41no—
147C23×C5C2×C22⋊C411yescharacteristic
148C23×C5C2×C22⋊C411yescharacteristic
149C23×C5C2×C4⋊C411yescharacteristic
150C2×C4×C5—22no—
151C2×C4×C5—22no—
152C2×C4×C5—22no—
153C2×C4×C5—22no—
154C2×C4×C5—22no—
155C2×C4×C5—22no—
156C2×C4×C5—22no—
157C2×C4×C5—22no—
158C2×C4×C5—22no—
159C2×C4×C5—22no—
160C2×C4×C5—22no—
161C2×C4×C5—22no—
162C2×C4×C5—22no—
163C2×C4×C5—28no—
164C2×C4×C5—41no—
165C2×C4×C5—41no—
166C2×C4×C5—41no—
167C2×C4×C5—44no—
168C2×C4×C5—44no—
169C2×C4×C5#9511yescharacteristic
170C2×C4×C5#9511yescharacteristic
171C2×C4×C5#9511yescharacteristic
172C2×C4×C5#9511yescharacteristic
173C2×C4×C5#9511yescharacteristic
174C2×C4×C5#9511yescharacteristic
175C2×C4×C5#9511yescharacteristic
176C2×C4×C5#9511yescharacteristic
177C2×C4×C5#10414yes—
178C2×C4×C5#10414yes—
179C2×C4×C5C2×C4211yescharacteristic
180C2×C4×C5C2×C22⋊C411yescharacteristic
181C2×C4×C5C2×C4⋊C411yescharacteristic
182C2×C4×C5C2×C4⋊C411yescharacteristic
183C2×Dic5—28no—
184C2×Dic5—44no—
185C2×Dic5—44no—
186#168—44no—
187C23×C4C22⋊D511yescharacteristic
188C23×C4C22⋊D511yescharacteristic
189C23×C4C22×D511yescharacteristic
190C2×M16—54no—
191#117—28no—
192#117—108no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—102no—
195C2×C22⋊C4—22no—
196C2×C22⋊C4—102no—
197C2×C42—22no—
198C2×C42—22no—
199C2×C42—22no—
200C2×C42—102no—
201C2×C42—102no—
202C2×C42—102no—
203C2×C42Dic1011yescharacteristic
204C2×C42Dic1011yescharacteristic
205C2×C42C4×D511yescharacteristic
206C2×C42C4×D511yescharacteristic
207C2×C42C4×D511yescharacteristic
208C2×C42C4×D511yescharacteristic
209C2×C42D2011yescharacteristic
210C2×C42D2011yescharacteristic
211C2×C42C2×Dic511yescharacteristic
212C2×C42C2×Dic511yescharacteristic
213C2×C42C22⋊D511yescharacteristic
214C2×C42C22⋊D511yescharacteristic
215C4⋊C8—102no—
216C4⋊C8—102no—
217C22⋊C8—102no—
218C22⋊C8—102no—
219#97—102no—
220C4×C8—102no—
221#95—22no—
222#95—54no—
223#95—102no—
224#95C2×Dic514yes—
225C22×C5—21no—
226C22×C5—21no—
227C22×C5—21no—
228C22×C5—21no—
229C22×C5—21no—
230C22×C5—21no—
231C22×C5—21no—
232C22×C5—44no—
233C22×C5C2×#9511yescharacteristic
234C22×C5C2×#10412yes—
235C22×C5C2×#10412yes—
236C4×C5—21no—
237C4×C5—21no—
238C4×C5—21no—
239C4×C5—21no—
240C4×C5—21no—
241C4×C5—21no—
242C4×C5—21no—
243C4×C5—48no—
244C4×C5#33912yes—
245C4×C5#33912yes—
246C4×C5#33912yes—
247C4×C5#33912yes—
248C4×C5#41012yes—
249Dic5—48no—
250C24C2×C22⋊D511yescharacteristic
251C22×C4—24no—
252C22×C4—24no—
253C22×C4—24no—
254C22×C4—42no—
255C22×C4—104no—
256C22×C4#68311yescharacteristic
257C22×C4#68311yescharacteristic
258C22×C4#68311yescharacteristic
259C22×C4#68311yescharacteristic
260C22×C4#68511yescharacteristic
261C22×C4#68511yescharacteristic
262C22×C4#68511yescharacteristic
263C22×C4#68511yescharacteristic
264C22×C4C22⋊Dic511yescharacteristic
265C22×C4C22⋊Dic511yescharacteristic
266C22×C4C22⋊Dic511yescharacteristic
267C22×C4C22⋊Dic511yescharacteristic
268C22×C4C2×Dic1011yescharacteristic
269C22×C4C2×C4×D511yescharacteristic
270C22×C4C2×C4×D511yescharacteristic
271C22×C4C2×D2011yescharacteristic
272C22×C4C22×Dic511yescharacteristic
273C22×C4C2×C22⋊D511yescharacteristic
274M16—204no—
275C2×C8—104no—
276C4⋊C4—28no—
277C4⋊C4—108no—
278C22⋊C4—28no—
279C22⋊C4—108no—
280C42—28no—
281C42—44no—
282C42—44no—
283C42—108no—
284C42—204no—
285C42—204no—
286C42C4×Dic511yescharacteristic
287C42C4×Dic511yescharacteristic
288C42C4×Dic511yescharacteristic
289C42C4×Dic511yescharacteristic
290C42#68311yescharacteristic
291C42#68311yescharacteristic
292C42#68311yescharacteristic
293C42#68311yescharacteristic
294C42C4⋊Dic511yescharacteristic
295C42C4⋊Dic511yescharacteristic
296C42C4⋊Dic511yescharacteristic
297C42C4⋊Dic511yescharacteristic
298C42#68511yescharacteristic
299C42#68511yescharacteristic
300C42#68511yescharacteristic
301C42#68511yescharacteristic
302C2×C5—22no—
303C2×C5—22no—
304C2×C5—41no—
305C2×C5C2×#33911yescharacteristic
306C2×C5C2×#33911yescharacteristic
307C2×C5#174011yescharacteristic
308C23—22no—
309C23—22no—
310C23—41no—
311C23C2×#68311yescharacteristic
312C23C2×#68511yescharacteristic
313C23C2×C22⋊Dic511yescharacteristic
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—22no—
326C2×C4—22no—
327C2×C4—28no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—44no—
332C2×C4—44no—
333C2×C4—108no—
334C2×C4—204no—
335C2×C4—204no—
336C2×C4#393714yes—
337C2×C4#396311yescharacteristic
338C2×C4#396311yescharacteristic
339C2×C4#396311yescharacteristic
340C2×C4#396311yescharacteristic
341C2×C4#396311yescharacteristic
342C2×C4#396311yescharacteristic
343C2×C4#396311yescharacteristic
344C2×C4#396311yescharacteristic
345C2×C4#396914yes—
346C2×C4C2×C4×Dic511yescharacteristic
347C2×C4C2×#68311yescharacteristic
348C2×C4C2×C4⋊Dic511yescharacteristic
349C2×C4C2×#68511yescharacteristic
350C8—204no—
351C5#804811yescharacteristic, complemented, Sylow
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—44no—
360C22C2×#393712yes—
361C22C2×#396311yescharacteristic
362C22C2×#396912yes—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—48no—
371C4—208no—
372C4#6474312yes—
373C4#6474312yes—
374C4#6475212yes—
375C4#6475212yes—
376C4#6529512yes—
377C2—22no—
378C2—22no—
379C2—41no—
380C2C2×#6474311yescharacteristic
381C2C2×#6475211yescharacteristic
382C2#1060238611yescharacteristic
subgroupG/H
centerC42#685
commutatorC2×C4×C5C2×C42
FrattiniC23×C4C22×D5
FittingC4×C5×#117C2
socleC22×C5C2×#95
prime radicalC24×C5C2×D4
cosocleC23×C4×C5C23
hypercenterC4×#117D5
hypocenterC5#8048
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C42 ◁ C22×C42 ◁ C4×#117

Complements

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

NH ≅ G/Ntype
9. C4×C5×C4⋊C4C4semidirect
12. C5×#376C4semidirect
18. C4×C4⋊Dic5C4semidirect
19. #65221C4semidirect
25. #65213C4semidirect
26. C4×#681C4semidirect
135. C4×C4⋊C4Dic5semidirect
141. #376Dic5semidirect
351. C5#8048semidirect

Maximal subgroups

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

subgroupindex
C4×C5×#1172
C4×#40722
#106137802
#105981092
#80485