Finite Group Databasebeta

← #11987610

Subgroups — #11987610

Order 1280.

500 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×C22⋊Q8C211yesmaximal, characteristic
2#10602324C211yesmaximal, characteristic
3#10602323C211yesmaximal, characteristic
4#10598133C212yesmaximal, complemented
5#10598129C212yesmaximal, complemented
6C2×C5×C22⋊Q8C411yescharacteristic
7C2×C4×C5×Q8C411yescharacteristic
8C22×C42×C5C2211yescharacteristic
9C5×#391C2211yescharacteristic
10C5×#389C2211yescharacteristic
11C5×#387—21no—
12C5×#385—21no—
13C5×#380C411yescharacteristic
14C4×C5×C4⋊C4—21no—
15C4×C5×C4⋊C4C411yescharacteristic
16C4×C5×C22⋊C4—21no—
17C2×C22⋊#168—21no—
18C2×C22⋊#168—21no—
19C2×C4⋊#168—21no—
20#64744—21no—
21#64744C2212yes—
22#64744C2212yes—
23#7648—51nomaximal, Sylow
24C22×C5×Q8C2×C411yescharacteristic
25C23×C4×C5C2×C411yescharacteristic
26C23×C4×C5D411yescharacteristic
27C23×C4×C5D411yescharacteristic
28C5×C22⋊Q8—22no—
29C5×C22⋊Q8—22no—
30C4×C5×Q8—42no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4C2×C411yescharacteristic
35C2×C5×C4⋊C4C2×C411yescharacteristic
36C2×C5×C4⋊C4C2×C411yescharacteristic
37C2×C5×C22⋊C4—21no—
38C2×C5×C22⋊C4—21no—
39C2×C42×C5—21no—
40C2×C42×C5—21no—
41C2×C42×C5—42no—
42C2×C42×C5C2×C411yescharacteristic
43C2×C42×C5D411yescharacteristic
44C2×C42×C5D411yescharacteristic
45C2×C42×C5C2311yescharacteristic
46C22×#168—22no—
47C22×#168—22no—
48C5×#95—21no—
49C5×#95—21no—
50C5×#95—21no—
51C5×#95—21no—
52C5×#95—21no—
53C22⋊#168—42no—
54C22⋊#168—42no—
55C4⋊#168—42no—
56C4×C22⋊Q8D511yescharacteristic
57#1817—51no—
58#1797—51no—
59#1272—52no—
60#1271—52no—
61C24×C5C22⋊C411yescharacteristic
62C2×C5×Q8—21no—
63C2×C5×Q8—41no—
64C2×C5×Q8—41no—
65C2×C5×Q8M1612yes—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5—22no—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—22no—
72C22×C4×C5—21no—
73C22×C4×C5—21no—
74C22×C4×C5—41no—
75C22×C4×C5—41no—
76C22×C4×C5—41no—
77C22×C4×C5—41no—
78C22×C4×C5—41no—
79C22×C4×C5C22⋊C411yescharacteristic
80C22×C4×C5C22⋊C411yescharacteristic
81C22×C4×C5C22⋊C411yescharacteristic
82C22×C4×C5SD1612yes—
83C22×C4×C5Q1612yes—
84C22×C4×C5C22×C411yescharacteristic
85C22×C4×C5C2×D411yescharacteristic
86C22×C4×C5C2×D411yescharacteristic
87C5×C4⋊C4—24no—
88C5×C4⋊C4—21no—
89C5×C4⋊C4—41no—
90C5×C4⋊C4—41no—
91C5×C4⋊C4—42no—
92C5×C4⋊C4—42no—
93C5×C4⋊C4M1612yes—
94C5×C22⋊C4—24no—
95C5×C22⋊C4—42no—
96C42×C5—22no—
97C42×C5—22no—
98C42×C5—41no—
99C42×C5—41no—
100C42×C5—42no—
101C42×C5—42no—
102C2×#168—42no—
103C2×#168—42no—
104C2×#168—42no—
105C2×#168—42no—
106C2×#168—42no—
107C2×#168—42no—
108C2×C22⋊Q8Dic511yescharacteristic
109C2×C4×Q8Dic511yescharacteristic
110C22×C42C2×D511yescharacteristic
111C2×C4⋊C8—101no—
112C2×C22⋊C8—101no—
113C2×C22⋊C8—101no—
114#391C2×D511yescharacteristic
115#389C2×D511yescharacteristic
116#387—21no—
117#385—21no—
118#380Dic511yescharacteristic
119C4×C4⋊C4—21no—
120C4×C4⋊C4Dic511yescharacteristic
121C4×C22⋊C4—21no—
122#336—52no—
123#336—52no—
124#336—101no—
125C23×C5—21no—
126C23×C5—21no—
127C23×C5—21no—
128C23×C5—21no—
129C23×C5—21no—
130C23×C5—21no—
131C23×C5#10312yes—
132C23×C5C2×C22⋊C411yescharacteristic
133C5×Q8—42no—
134C5×Q8—42no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—22no—
146C2×C4×C5—22no—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—21no—
150C2×C4×C5—42no—
151C2×C4×C5—42no—
152C2×C4×C5—44no—
153C2×C4×C5—42no—
154C2×C4×C5—42no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—41no—
163C2×C4×C5—41no—
164C2×C4×C5—41no—
165C2×C4×C5#9912yes—
166C2×C4×C5#10312yes—
167C2×C4×C5C2×M1611yescharacteristic
168C2×C4×C5C2×M1611yescharacteristic
169C2×C4×C5C2×SD1611yescharacteristic
170C2×C4×C5C2×Q1611yescharacteristic
171C2×C4×C5#13512yes—
172#168—82no—
173#168—82no—
174C22×Q8C2×Dic511yescharacteristic
175C23×C4C2×Dic511yescharacteristic
176C23×C4C22⋊D511yescharacteristic
177C23×C4C22⋊D511yescharacteristic
178C22×C8—102no—
179C22×C8—102no—
180C22⋊Q8—22no—
181C22⋊Q8—22no—
182C4×Q8—42no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4C2×Dic511yescharacteristic
187C2×C4⋊C4C2×Dic511yescharacteristic
188C2×C4⋊C4C2×Dic511yescharacteristic
189C2×C22⋊C4—21no—
190C2×C22⋊C4—21no—
191C2×C42—21no—
192C2×C42—21no—
193C2×C42—42no—
194C2×C42C2×Dic511yescharacteristic
195C2×C42C22⋊D511yescharacteristic
196C2×C42C22⋊D511yescharacteristic
197C2×C42C22×D511yescharacteristic
198C4⋊C8—202no—
199C22⋊C8—202no—
200C22⋊C8—202no—
201#95—21no—
202#95—21no—
203#95—21no—
204#95—21no—
205#95—21no—
206C22×C5—22no—
207C22×C5—22no—
208C22×C5—22no—
209C22×C5—41no—
210C22×C5—41no—
211C22×C5—41no—
212C22×C5—41no—
213C22×C5#40711yescharacteristic
214C22×C5C2×#9911yescharacteristic
215C22×C5#41311yescharacteristic
216C22×C5C2×#10311yescharacteristic
217C22×C5#41611yescharacteristic
218C22×C5#42111yescharacteristic
219C22×C5#42111yescharacteristic
220C4×C5—21no—
221C4×C5—21no—
222C4×C5—22no—
223C4×C5—22no—
224C4×C5—21no—
225C4×C5—22no—
226C4×C5—21no—
227C4×C5—41no—
228C4×C5—42no—
229C4×C5—42no—
230C4×C5—81no—
231C4×C5—81no—
232C24C22⋊Dic511yescharacteristic
233C2×Q8—21no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8#68112yes—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—22no—
240C22×C4—22no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4#68812yes—
251C22×C4#68912yes—
252C22×C4C22⋊Dic511yescharacteristic
253C22×C4C22⋊Dic511yescharacteristic
254C22×C4C22⋊Dic511yescharacteristic
255C22×C4C22×Dic511yescharacteristic
256C22×C4C2×C22⋊D511yescharacteristic
257C22×C4C2×C22⋊D511yescharacteristic
258C2×C8—202no—
259C2×C8—202no—
260C2×C8—202no—
261C2×C8—202no—
262C2×C8—202no—
263C2×C8—202no—
264C4⋊C4—24no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4#68112yes—
271C22⋊C4—24no—
272C22⋊C4—42no—
273C42—22no—
274C42—22no—
275C42—41no—
276C42—41no—
277C42—42no—
278C42—42no—
279C2×C5—42no—
280C2×C5#146511yescharacteristic
281C2×C5#148711yescharacteristic
282C2×C5#148811yescharacteristic
283C2×C5#151611yescharacteristic
284C2×C5#152011yescharacteristic
285C2×C5#153511yescharacteristic
286C2×C5#154211yescharacteristic
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23#396712yes—
294C23C2×C22⋊Dic511yescharacteristic
295Q8—42no—
296Q8—42no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—44no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4#396612yes—
328C2×C4#396712yes—
329C2×C4C2×#68111yescharacteristic
330C2×C4C2×#68111yescharacteristic
331C2×C4C2×#68811yescharacteristic
332C2×C4C2×#68911yescharacteristic
333C2×C4#409612yes—
334C8—402no—
335C8—402no—
336C5#764811yescharacteristic, complemented, Sylow
337C22—22no—
338C22—22no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22#6549611yescharacteristic
345C22C2×#396611yescharacteristic
346C22C2×#396711yescharacteristic
347C22#6552211yescharacteristic
348C22#6552511yescharacteristic
349C22#6552511yescharacteristic
350C22#6552611yescharacteristic
351C4—22no—
352C4—22no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—22no—
357C4—21no—
358C4—41no—
359C4—42no—
360C4—42no—
361C4—81no—
362C4—81no—
363C2—42no—
364C2#1060239511yescharacteristic
365C2#1060241511yescharacteristic
366C2#1060243311yescharacteristic
367C2#1060248311yescharacteristic
368C2#1060250311yescharacteristic
369C2#1060254211yescharacteristic
370C2#1060262111yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic5
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC4×C5×C22⋊Q8C2
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C22⋊C4
cosocleC2×C42×C5C23
hypercenterC4×C22⋊Q8D5
hypocenterC5#7648
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ C4×C22⋊Q8

Complements

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

NH ≅ G/Ntype
4. #10598133C2semidirect
5. #10598129C2semidirect
336. C5#7648semidirect

Maximal subgroups

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

subgroupindex
C4×C5×C22⋊Q82
#106023242
#106023232
#105981332
#105981292
#76485