Finite Group Databasebeta

← #11989612

Subgroups — #11989612

Order 1280.

700 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2920C211yesmaximal, characteristic
2C4×#4072C211yesmaximal, characteristic
3C2×#65213C211yesmaximal, characteristic
4#10598237C214yesmaximal, complemented
5C22×C42×C5C2211yescharacteristic
6C2×#4072—21no—
7C22×#681—21no—
8C5×#432—21no—
9C5×#432C412yescomplemented
10C5×#431—21no—
11C5×#431C2212yes—
12C5×#423C412yescomplemented
13C5×#407—21no—
14C4×C5×M16—21no—
15C4×C22⋊Dic5—21no—
16C4×C22⋊Dic5C412yes—
17C4×C4⋊Dic5—21no—
18C4×C4⋊Dic5C2212yes—
19#65221C412yes—
20C42×Dic5—21no—
21#65213—21no—
22#65213—21no—
23#65213C412yescomplemented
24#65213C2212yes—
25C2×C4⋊#168—21no—
26C2×C4⋊#168C412yescomplemented
27#8097—51nomaximal, Sylow
28C23×C4×C5C2×C411yescharacteristic
29C23×C4×C5D411yescharacteristic
30C23×C4×C5D411yescharacteristic
31C2×C5×M16—22no—
32C2×C42×C5C2×C411yescharacteristic
33C2×C42×C5C2×C411yescharacteristic
34C2×C42×C5C2×C411yescharacteristic
35C2×C42×C5C2×C411yescharacteristic
36C2×C42×C5C2×C411yescharacteristic
37C2×C42×C5D411yescharacteristic
38C2×C42×C5D411yescharacteristic
39C2×C42×C5D411yescharacteristic
40C2×C42×C5D411yescharacteristic
41C2×C42×C5Q811yescharacteristic
42C2×C42×C5Q811yescharacteristic
43C2×C42×C5C2311yescharacteristic
44C2×C22⋊Dic5—22no—
45#4072—28no—
46C2×C4⋊Dic5—22no—
47C2×C4×Dic5—22no—
48C2×C4×Dic5—22no—
49C2×C4×Dic5—22no—
50C2×#681—22no—
51C2×#681—22no—
52C2×#681—44no—
53C22×#168—22no—
54C5×C4⋊C8—22no—
55C5×C4⋊C8C2×C414yes—
56C5×C22⋊C8—22no—
57C5×C22⋊C8—22no—
58C5×#97—22no—
59C4×C5×C8—22no—
60#3963—22no—
61#3963C2×C414yes—
62C4⋊#168—22no—
63C4⋊#168—22no—
64C4⋊#168—22no—
65C4⋊#168C2×C414yes—
66#2920D511yescharacteristic
67C2×#423—51no—
68C4×#117—51no—
69#1303—54no—
70C24×C5C22⋊C411yescharacteristic
71C22×C4×C5—24no—
72C22×C4×C5—22no—
73C22×C4×C5—22no—
74C22×C4×C5—42no—
75C22×C4×C5C4211yescharacteristic
76C22×C4×C5C4211yescharacteristic
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×C5C22⋊C411yescharacteristic
84C22×C4×C5C4⋊C411yescharacteristic
85C22×C4×C5C4⋊C411yescharacteristic
86C22×C4×C5C4⋊C411yescharacteristic
87C22×C4×C5C4⋊C411yescharacteristic
88C22×C4×C5C4⋊C411yescharacteristic
89C22×C4×C5C4⋊C411yescharacteristic
90C22×C4×C5C22×C411yescharacteristic
91C22×C4×C5C2×D411yescharacteristic
92C22×C4×C5C2×D411yescharacteristic
93C22×Dic5—24no—
94C5×M16—44no—
95C2×C5×C8—24no—
96C42×C5C4211yescharacteristic
97C42×C5C4211yescharacteristic
98C42×C5C22⋊C411yescharacteristic
99C42×C5C22⋊C411yescharacteristic
100C42×C5C22⋊C411yescharacteristic
101C42×C5C22⋊C411yescharacteristic
102C42×C5C4⋊C411yescharacteristic
103C42×C5C4⋊C411yescharacteristic
104C42×C5C4⋊C411yescharacteristic
105C42×C5C4⋊C411yescharacteristic
106C42×C5C4⋊C411yescharacteristic
107C42×C5C4⋊C411yescharacteristic
108C42×C5C22×C411yescharacteristic
109C42×C5C22×C411yescharacteristic
110C42×C5C2×D411yescharacteristic
111C42×C5C2×Q811yescharacteristic
112C22⋊Dic5—28no—
113C4⋊Dic5—28no—
114C4×Dic5—28no—
115C4×Dic5—44no—
116C4×Dic5—42no—
117C4×Dic5—42no—
118#681—44no—
119#681—44no—
120C2×#168—24no—
121C2×#168—44no—
122C22×M16—101no—
123C2×#117—101no—
124C22×C42C2×D511yescharacteristic
125#432—21no—
126#432Dic512yescomplemented
127#431—21no—
128#431C2×D512yes—
129#423—52no—
130#423—52no—
131#423—101no—
132#423—101no—
133#423Dic512yescomplemented
134C2×C4⋊C8—52no—
135C2×C4⋊C8—101no—
136#407—21no—
137C4×M16—21no—
138C4×C4⋊C4—52no—
139C4×C4⋊C4—101no—
140C4×C22⋊C4—52no—
141C4×C22⋊C4—101no—
142#376—52no—
143C43—101no—
144C23×C5—22no—
145C23×C5—22no—
146C23×C5—41no—
147C23×C5#9511yescharacteristic
148C23×C5#9511yescharacteristic
149C23×C5C2×C22⋊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—21no—
158C2×C4×C5—21no—
159C2×C4×C5—21no—
160C2×C4×C5—21no—
161C2×C4×C5—22no—
162C2×C4×C5—22no—
163C2×C4×C5—22no—
164C2×C4×C5—22no—
165C2×C4×C5—41no—
166C2×C4×C5—41no—
167C2×C4×C5—41no—
168C2×C4×C5#9511yescharacteristic
169C2×C4×C5#9511yescharacteristic
170C2×C4×C5#9511yescharacteristic
171C2×C4×C5#9511yescharacteristic
172C2×C4×C5#9511yescharacteristic
173C2×C4×C5#9511yescharacteristic
174C2×C4×C5#10414yes—
175C2×C4×C5C2×C4211yescharacteristic
176C2×C4×C5C2×C22⋊C411yescharacteristic
177C2×C4×C5C2×C22⋊C411yescharacteristic
178C2×C4×C5C2×C4⋊C411yescharacteristic
179C2×C4×C5C2×C4⋊C411yescharacteristic
180C2×C4×C5C2×C4⋊C411yescharacteristic
181C2×C4×C5AGL(1,ℤ/8)12yes—
182C2×C4×C5#13712yes—
183C2×Dic5—28no—
184C2×Dic5—44no—
185C2×Dic5—44no—
186C5×C8—44no—
187#168—44no—
188C23×C4C4×D511yescharacteristic
189C23×C4D2011yescharacteristic
190C23×C4C22⋊D511yescharacteristic
191C2×M16—22no—
192C2×M16—102no—
193C2×M16—102no—
194C2×M16—204no—
195C22×C8—102no—
196#117—108no—
197C2×C4⋊C4—102no—
198C2×C22⋊C4—102no—
199C2×C42—102no—
200C2×C42—102no—
201C2×C42—102no—
202C2×C42Dic1011yescharacteristic
203C2×C42Dic1011yescharacteristic
204C2×C42C4×D511yescharacteristic
205C2×C42C4×D511yescharacteristic
206C2×C42C4×D511yescharacteristic
207C2×C42D2011yescharacteristic
208C2×C42C2×Dic511yescharacteristic
209C2×C42C2×Dic511yescharacteristic
210C2×C42C22⋊D511yescharacteristic
211C2×C42C22⋊D511yescharacteristic
212C2×C42C22⋊D511yescharacteristic
213C2×C42C22×D511yescharacteristic
214C4⋊C8—22no—
215C4⋊C8—54no—
216C4⋊C8—102no—
217C4⋊C8—102no—
218C4⋊C8—102no—
219C4⋊C8C2×Dic514yes—
220C22⋊C8—22no—
221C22⋊C8—22no—
222#97—22no—
223C4×C8—22no—
224#95—54no—
225#95—102no—
226C22×C5—21no—
227C22×C5—21no—
228C22×C5—21no—
229C22×C5—21no—
230C22×C5—21no—
231C22×C5—21no—
232C22×C5—21no—
233C22×C5—44no—
234C22×C5#33912yes—
235C22×C5C2×#9511yescharacteristic
236C22×C5#41712yes—
237C4×C5—21no—
238C4×C5—21no—
239C4×C5—21no—
240C4×C5—21no—
241C4×C5—21no—
242C4×C5—21no—
243C4×C5—21no—
244C4×C5#33912yes—
245C4×C5#34412yes—
246C4×C5#41811yescharacteristic
247C4×C5#41911yescharacteristic
248C4×C5C2×#10412yes—
249C4×C5#42812yes—
250Dic5—48no—
251C24#68511yescharacteristic
252C22×C4—24no—
253C22×C4—22no—
254C22×C4—22no—
255C22×C4—42no—
256C22×C4—104no—
257C22×C4C4×Dic511yescharacteristic
258C22×C4C4×Dic511yescharacteristic
259C22×C4#68311yescharacteristic
260C22×C4#68311yescharacteristic
261C22×C4#68311yescharacteristic
262C22×C4#68311yescharacteristic
263C22×C4C4⋊Dic511yescharacteristic
264C22×C4C4⋊Dic511yescharacteristic
265C22×C4#68511yescharacteristic
266C22×C4#68511yescharacteristic
267C22×C4#68511yescharacteristic
268C22×C4#68511yescharacteristic
269C22×C4#68511yescharacteristic
270C22×C4C22⋊Dic511yescharacteristic
271C22×C4C22⋊Dic511yescharacteristic
272C22×C4C2×C4×D511yescharacteristic
273C22×C4C2×D2011yescharacteristic
274C22×C4C2×C22⋊D511yescharacteristic
275M16—44no—
276M16—204no—
277M16—204no—
278C2×C8—24no—
279C2×C8—104no—
280C2×C8—204no—
281C4⋊C4—108no—
282C22⋊C4—108no—
283C42—108no—
284C42—204no—
285C42—202no—
286C42—202no—
287C42C4×Dic511yescharacteristic
288C42C4×Dic511yescharacteristic
289C42#68311yescharacteristic
290C42#68311yescharacteristic
291C42#68311yescharacteristic
292C42#68311yescharacteristic
293C42C4⋊Dic511yescharacteristic
294C42C4⋊Dic511yescharacteristic
295C42#68511yescharacteristic
296C42#68511yescharacteristic
297C42C22⋊Dic511yescharacteristic
298C42C22⋊Dic511yescharacteristic
299C42C2×Dic1011yescharacteristic
300C42C2×C4×D511yescharacteristic
301C42C22×Dic511yescharacteristic
302C42C2×C22⋊D511yescharacteristic
303C2×C5—22no—
304C2×C5—22no—
305C2×C5—41no—
306C2×C5C2×#33911yescharacteristic
307C2×C5#173611yescharacteristic
308C2×C5C2×#34411yescharacteristic
309C23—22no—
310C23—22no—
311C23—41no—
312C23#396311yescharacteristic
313C23#396311yescharacteristic
314C23C2×#68511yescharacteristic
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—22no—
327C2×C4—22no—
328C2×C4—22no—
329C2×C4—22no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—108no—
334C2×C4—204no—
335C2×C4—204no—
336C2×C4#396311yescharacteristic
337C2×C4#396311yescharacteristic
338C2×C4#396311yescharacteristic
339C2×C4#396311yescharacteristic
340C2×C4#396311yescharacteristic
341C2×C4#396311yescharacteristic
342C2×C4#396914yes—
343C2×C4#405412yes—
344C2×C4#405512yes—
345C2×C4C2×C4×Dic511yescharacteristic
346C2×C4C2×#68311yescharacteristic
347C2×C4C2×#68311yescharacteristic
348C2×C4C2×C4⋊Dic511yescharacteristic
349C2×C4C2×#68511yescharacteristic
350C2×C4C2×C22⋊Dic511yescharacteristic
351C8—44no—
352C8—204no—
353C5#809711yescharacteristic, complemented, Sylow
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—44no—
362C22#6475212yes—
363C22#6542212yes—
364C22C2×#396311yescharacteristic
365C4—21no—
366C4—21no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—21no—
371C4—21no—
372C4—208no—
373C4#6475212yes—
374C4#6477912yes—
375C4#6540911yescharacteristic
376C4#6541012yes—
377C4#6542011yescharacteristic
378C4C2×#396912yes—
379C2—22no—
380C2—22no—
381C2—41no—
382C2C2×#6475211yescharacteristic
383C2#1060277811yescharacteristic
384C2C2×#6477911yescharacteristic
subgroupG/H
centerC2×C4C2×#685
commutatorC2×C4×C5C2×C42
FrattiniC2×C42C22×D5
FittingC5×#2920C2
socleC22×C5C2×#95
prime radicalC24×C5C22⋊C4
cosocleC2×C42×C5C23
hypercenter#2920D5
hypocenterC5#8097
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C42 ◁ #2920

Complements

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

NH ≅ G/Ntype
4. #10598237C2semidirect
9. C5×#432C4semidirect
12. C5×#423C4semidirect
23. #65213C4semidirect
26. C2×C4⋊#168C4semidirect
126. #432Dic5semidirect
133. #423Dic5semidirect
353. C5#8097semidirect

Maximal subgroups

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

subgroupindex
C5×#29202
C4×#40722
C2×#652132
#105982372
#80975