Finite Group Databasebeta

← #12008563

Subgroups — #12008563

Order 1280.

460 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 103 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10614057C211yesmaximal, characteristic
2C5×#1459C211yesmaximal, characteristic
3#10602394C211yesmaximal, characteristic
4#10597937C212yesmaximal, complemented
5#10597936C212yesmaximal, complemented
6C2×C4×C5×D4C2211yescharacteristic
7C2×#4081C411yescharacteristic
8C22×#683C411yescharacteristic
9C2×C5×C22⋊C8—21no—
10#65509C411yescharacteristic
11#65499—21no—
12C4×C22⋊Dic5C411yescharacteristic
13#65261—21no—
14#65235C2211yescharacteristic
15#65234—21no—
16#65232C2211yescharacteristic
17#65222—21no—
18#65214—21no—
19C5×#324—21no—
20C5×#323C2212yes—
21#64745—21no—
22#64745C2212yes—
23#11474—51nomaximal, Sylow
24C22×C5×D4C2×C411yescharacteristic
25C23×C4×C5C2×C411yescharacteristic
26C23×C4×C5D411yescharacteristic
27C23×Dic5C2×C411yescharacteristic
28C23×Dic5C2×C411yescharacteristic
29C22×C5×C8—41no—
30C4×C5×D4—41no—
31C4×C5×D4—41no—
32C2×C5×C4⋊C4D411yescharacteristic
33C2×C5×C22⋊C4D411yescharacteristic
34C2×C5×C22⋊C4C2311yescharacteristic
35C2×C42×C5D411yescharacteristic
36C2×C22⋊Dic5—21no—
37C2×C22⋊Dic5—21no—
38C2×C22⋊Dic5C2×C411yescharacteristic
39C2×C22⋊Dic5C2×C411yescharacteristic
40#4081—22no—
41#4081C814yescomplemented
42C2×#683—21no—
43C2×#683—21no—
44C2×#683—21no—
45C2×#683—21no—
46C2×#683—41no—
47C2×#683—41no—
48C2×C4×Dic5—21no—
49C5×C22⋊C8—22no—
50C5×C22⋊C8—41no—
51#3963—21no—
52#3963—21no—
53#3963—21no—
54#3963—21no—
55#3963—21no—
56C22⋊#168—22no—
57C4⋊#168—41no—
58C4×#168—41no—
59#2322—51no—
60#1460—51no—
61#1459D511yescharacteristic
62#1326—52no—
63#1317—52no—
64C24×C5C22⋊C411yescharacteristic
65C24×C5C22×C411yescharacteristic
66C2×C5×D4—41no—
67C2×C5×D4—41no—
68C2×C5×D4C2×C812yes—
69C2×C5×D4M1612yes—
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—21no—
73C22×C4×C5—21no—
74C22×C4×C5—81no—
75C22×C4×C5—81no—
76C22×C4×C5C22⋊C411yescharacteristic
77C22×C4×C5C22⋊C411yescharacteristic
78C22×C4×C5C22⋊C411yescharacteristic
79C22×C4×C5C2×D411yescharacteristic
80C22×C4×C5C2×D411yescharacteristic
81C22×Dic5—21no—
82C22×Dic5—21no—
83C22×Dic5—21no—
84C22×Dic5—21no—
85C22×Dic5—21no—
86C22×Dic5—41no—
87C22×Dic5—41no—
88C22×Dic5—41no—
89C22×Dic5—81no—
90C22×Dic5C2×C812yescomplemented
91C2×C5×C8—42no—
92C2×C5×C8—82no—
93C5×C4⋊C4—41no—
94C5×C22⋊C4—41no—
95C5×C22⋊C4—41no—
96C42×C5—21no—
97C42×C5—21no—
98C22⋊Dic5—24no—
99C22⋊Dic5—21no—
100C22⋊Dic5—41no—
101C22⋊Dic5—81no—
102C22⋊Dic5C2×C812yescomplemented
103#683—24no—
104#683—42no—
105#683—41no—
106#683—41no—
107#683—81no—
108C4×Dic5—81no—
109C2×#168—42no—
110C2×#123—51no—
111C2×C4×D4C2×D511yescharacteristic
112C22×C4⋊C4—51no—
113#431—101no—
114C2×C22⋊C8—21no—
115#389—101no—
116#388—101no—
117#387—101no—
118#386—51no—
119#385—51no—
120#385—101no—
121#381—51no—
122C4×C22⋊C4—51no—
123#324—21no—
124#323—52no—
125#323—101no—
126#323C2×D512yes—
127C23×C5—21no—
128C23×C5—21no—
129C23×C5—21no—
130C23×C5—21no—
131C23×C5—41no—
132C23×C5—41no—
133C23×C5—41no—
134C23×C5—41no—
135C23×C5C22⋊C812yes—
136C23×C5C2×C22⋊C411yescharacteristic
137C23×C5C22×C811yescharacteristic
138C23×C5C2×M1611yescharacteristic
139C5×D4—42no—
140C5×D4—42no—
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—41no—
147C2×C4×C5—42no—
148C2×C4×C5—41no—
149C2×C4×C5—41no—
150C2×C4×C5—41no—
151C2×C4×C5—81no—
152C2×C4×C5—81no—
153C2×C4×C5—81no—
154C2×C4×C5C22⋊C812yes—
155C2×C4×C5#9911yescharacteristic
156C2×C4×C5#9911yescharacteristic
157C2×Dic5—22no—
158C2×Dic5—22no—
159C2×Dic5—41no—
160C2×Dic5—41no—
161C2×Dic5—42no—
162C2×Dic5—41no—
163C2×Dic5—41no—
164C2×Dic5—42no—
165C2×Dic5—41no—
166C2×Dic5—41no—
167C2×Dic5—41no—
168C2×Dic5—41no—
169C2×Dic5—41no—
170C2×Dic5—41no—
171C2×Dic5—82no—
172C5×C8—82no—
173#168—82no—
174C22×D4C4×D511yescharacteristic
175C23×C4—51no—
176C23×C4—51no—
177C23×C4C4×D511yescharacteristic
178C23×C4C22⋊D511yescharacteristic
179C22×C8—41no—
180#123—54no—
181#123—102no—
182C4×D4—41no—
183C4×D4—41no—
184C2×C4⋊C4—101no—
185C2×C4⋊C4—101no—
186C2×C4⋊C4—101no—
187C2×C4⋊C4—101no—
188C2×C4⋊C4—201no—
189C2×C4⋊C4—201no—
190C2×C4⋊C4C22⋊D511yescharacteristic
191C2×C22⋊C4—51no—
192C2×C22⋊C4—51no—
193C2×C22⋊C4—101no—
194C2×C22⋊C4—101no—
195C2×C22⋊C4D2011yescharacteristic
196C2×C22⋊C4C22×D511yescharacteristic
197C2×C42—101no—
198C2×C42D2011yescharacteristic
199C4⋊C8—201no—
200C22⋊C8—22no—
201C22⋊C8—41no—
202C22⋊C8—102no—
203C4×C8—201no—
204#95—101no—
205#95—101no—
206#95—101no—
207#95—101no—
208#95—101no—
209C22×C5—21no—
210C22×C5—21no—
211C22×C5—21no—
212C22×C5—21no—
213C22×C5—22no—
214C22×C5—42no—
215C22×C5—41no—
216C22×C5—41no—
217C22×C5—42no—
218C22×C5—41no—
219C22×C5—41no—
220C22×C5—41no—
221C22×C5—41no—
222C22×C5—81no—
223C22×C5C2×C22⋊C811yescharacteristic
224C22×C5C2×#9911yescharacteristic
225C22×C5#41311yescharacteristic
226C4×C5—21no—
227C4×C5—21no—
228C4×C5—22no—
229C4×C5—41no—
230C4×C5—41no—
231C4×C5—41no—
232Dic5—42no—
233Dic5—42no—
234Dic5—81no—
235Dic5—81no—
236C24#68511yescharacteristic
237C24C2×C4×D511yescharacteristic
238C2×D4—41no—
239C2×D4—41no—
240C2×D4C8×D512yes—
241C2×D4#67612yes—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—52no—
247C22×C4—81no—
248C22×C4—81no—
249C22×C4—101no—
250C22×C4—101no—
251C22×C4—101no—
252C22×C4—101no—
253C22×C4—101no—
254C22×C4—201no—
255C22×C4—201no—
256C22×C4—201no—
257C22×C4—401no—
258C22×C4#68511yescharacteristic
259C22×C4#68511yescharacteristic
260C22×C4#68511yescharacteristic
261C22×C4C2×D2011yescharacteristic
262C22×C4C2×C22⋊D511yescharacteristic
263C2×C8—42no—
264C2×C8—82no—
265C2×C8—202no—
266C4⋊C4—41no—
267C4⋊C4—104no—
268C4⋊C4—202no—
269C4⋊C4—201no—
270C4⋊C4—201no—
271C4⋊C4—401no—
272C22⋊C4—41no—
273C22⋊C4—41no—
274C22⋊C4—52no—
275C22⋊C4—104no—
276C22⋊C4—101no—
277C22⋊C4—201no—
278C22⋊C4—401no—
279C42—21no—
280C42—21no—
281C42—401no—
282C2×C5—21no—
283C2×C5—21no—
284C2×C5—41no—
285C2×C5—41no—
286C2×C5—42no—
287C2×C5#145911yescharacteristic
288C2×C5#212111yescharacteristic
289C2×C5#212311yescharacteristic
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23#395212yes—
299C23C2×C8×D511yescharacteristic
300C23C2×#67611yescharacteristic
301C23C2×#68511yescharacteristic
302D4—42no—
303D4—42no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—41no—
310C2×C4—42no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—102no—
318C2×C4—102no—
319C2×C4—201no—
320C2×C4—202no—
321C2×C4—201no—
322C2×C4—201no—
323C2×C4—201no—
324C2×C4—202no—
325C2×C4—201no—
326C2×C4—201no—
327C2×C4—201no—
328C2×C4—201no—
329C2×C4—201no—
330C2×C4—201no—
331C2×C4—402no—
332C2×C4#393811yescharacteristic
333C2×C4#393811yescharacteristic
334C2×C4#395212yes—
335C8—82no—
336C8—402no—
337C5#1147411yescharacteristic, complemented, Sylow
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—22no—
343C22—42no—
344C22—41no—
345C22—41no—
346C22—42no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—81no—
352C22C2×#393811yescharacteristic
353C22C2×#395211yescharacteristic
354C22#6542111yescharacteristic
355C4—22no—
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—202no—
362C4—202no—
363C4—401no—
364C4—401no—
365C2—21no—
366C2—21no—
367C2—41no—
368C2—41no—
369C2—42no—
370C2#1060071211yescharacteristic
371C2#1060080811yescharacteristic
372C2#1060094011yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC23×C5C22×C8
FrattiniC2×C22⋊C4C22×D5
FittingC5×#1459C2
socleC22×C5C2×#99
prime radicalC22×C5×D4C2×C4
cosocleC2×C5×C22⋊C4C23
hypercenter#1459D5
hypocenterC5#11474
LCSG ▷ C23×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
4. #10597937C2semidirect
5. #10597936C2semidirect
41. #4081C8semidirect
90. C22×Dic5C2×C8semidirect
102. C22⋊Dic5C2×C8semidirect
337. C5#11474semidirect

Maximal subgroups

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

subgroupindex
#106140572
C5×#14592
#106023942
#105979372
#105979362
#114745