Finite Group Databasebeta

← #12008596

Subgroups — #12008596

Order 1280.

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

normal subgroups only

This group has 392 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#10614187C211yesmaximal, characteristic
2C5×#1461C211yesmaximal, characteristic
3#10602417C211yesmaximal, characteristic
4#10597946C212yesmaximal
5#10597943C212yesmaximal
6C2×C4×C5×Q8C2211yescharacteristic
7C2×#4090C411yescharacteristic
8C2×C4×Dic10C411yescharacteristic
9C5×#431—21no—
10#65519C411yescharacteristic
11#65267—21no—
12#65267—21no—
13#65266C2211yescharacteristic
14#65263C2211yescharacteristic
15#65222—21no—
16#65222—21no—
17#65221C411yescharacteristic
18#65214—21no—
19C5×#324—21no—
20C5×#324C2212yes—
21#64748—21no—
22#64748C2212yes—
23#11482—51nomaximal, Sylow
24C22×C5×Q8C2×C411yescharacteristic
25C22×Dic10C2×C411yescharacteristic
26C4×C5×Q8—41no—
27C4×C5×Q8—41no—
28C2×C5×C4⋊C4D411yescharacteristic
29C2×C5×C4⋊C4D411yescharacteristic
30C2×C5×C4⋊C4C2311yescharacteristic
31C2×C42×C5C2×C411yescharacteristic
32C2×C42×C5D411yescharacteristic
33C2×C42×C5D411yescharacteristic
34#4090—22no—
35#4090C814yescomplemented
36C2×C4⋊Dic5C2×C411yescharacteristic
37C2×#683—21no—
38C2×#683—21no—
39C2×#683—21no—
40C2×C4×Dic5—21no—
41C2×C4×Dic5C2×C411yescharacteristic
42C2×C4×Dic5C2×C411yescharacteristic
43C4×Dic10—41no—
44C4×Dic10—41no—
45C5×C4⋊C8—41no—
46C5×C22⋊C8—22no—
47C4×C5×C8—41no—
48#3963—21no—
49#3963—21no—
50#3963—21no—
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#2327—51no—
60#1461—51no—
61#1461D511yescharacteristic
62#1324—52no—
63#1319—52no—
64C2×C5×Q8—41no—
65C2×C5×Q8—41no—
66C2×C5×Q8C2×C812yes—
67C2×C5×Q8M1612yes—
68C22×C4×C5C22⋊C411yescharacteristic
69C22×C4×C5C22⋊C411yescharacteristic
70C22×C4×C5C22⋊C411yescharacteristic
71C22×C4×C5C22⋊C411yescharacteristic
72C22×C4×C5C22×C411yescharacteristic
73C22×C4×C5C2×D411yescharacteristic
74C22×C4×C5C2×D411yescharacteristic
75C22×Dic5—21no—
76C22×Dic5—21no—
77C22×Dic5—21no—
78C22×Dic5—21no—
79C2×Dic10—21no—
80C2×Dic10—41no—
81C2×Dic10—41no—
82C2×Dic10C2×C812yes—
83C2×C5×C8—42no—
84C5×C4⋊C4—41no—
85C5×C4⋊C4—41no—
86C5×C4⋊C4—41no—
87C42×C5—21no—
88C42×C5—21no—
89C42×C5—21no—
90C42×C5—21no—
91C42×C5—21no—
92C42×C5—21no—
93C4⋊Dic5—41no—
94#683—24no—
95#683—24no—
96#683—41no—
97#683—41no—
98C4×Dic5—21no—
99C4×Dic5—42no—
100C4×Dic5—41no—
101C4×Dic5C2×C812yes—
102C2×#168—42no—
103C2×C4⋊Q8—51no—
104C2×C4×Q8—51no—
105C2×C4×Q8C2×D511yescharacteristic
106#431—21no—
107#431—101no—
108#391—51no—
109#391—51no—
110#387—101no—
111#387—101no—
112#387—101no—
113#387—101no—
114#382—51no—
115#376—51no—
116#324—21no—
117#324—52no—
118#324—101no—
119#324C2×D512yes—
120C23×C5C2×C22⋊C411yescharacteristic
121C5×Q8—42no—
122C5×Q8—42no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—41no—
133C2×C4×C5—41no—
134C2×C4×C5—41no—
135C2×C4×C5—41no—
136C2×C4×C5C22⋊C812yes—
137C2×C4×C5C22⋊C812yes—
138C2×C4×C5#9911yescharacteristic
139C2×C4×C5#9911yescharacteristic
140C2×C4×C5C22×C811yescharacteristic
141C2×C4×C5C2×M1611yescharacteristic
142C2×Dic5—22no—
143C2×Dic5—22no—
144C2×Dic5—41no—
145C2×Dic5—41no—
146C2×Dic5—41no—
147C2×Dic5—41no—
148C2×Dic5—41no—
149C2×Dic5—41no—
150C2×Dic5—42no—
151C2×Dic5—41no—
152C2×Dic5—41no—
153Dic10—42no—
154Dic10—42no—
155C5×C8—82no—
156#168—82no—
157C22×Q8—51no—
158C22×Q8C4×D511yescharacteristic
159C4⋊Q8—54no—
160C4⋊Q8—102no—
161C4×Q8—41no—
162C4×Q8—41no—
163C4×Q8—201no—
164C4×Q8—201no—
165C2×C4⋊C4—51no—
166C2×C4⋊C4—101no—
167C2×C4⋊C4—101no—
168C2×C4⋊C4—101no—
169C2×C4⋊C4D2011yescharacteristic
170C2×C4⋊C4C22⋊D511yescharacteristic
171C2×C4⋊C4C22×D511yescharacteristic
172C2×C42—51no—
173C2×C42—51no—
174C2×C42—101no—
175C2×C42C4×D511yescharacteristic
176C2×C42D2011yescharacteristic
177C2×C42C22⋊D511yescharacteristic
178C4⋊C8—41no—
179C4⋊C8—201no—
180C22⋊C8—22no—
181C22⋊C8—102no—
182C4×C8—41no—
183C4×C8—201no—
184#95—101no—
185#95—101no—
186#95—101no—
187#95—101no—
188#95—101no—
189#95—101no—
190#95—101no—
191#95—101no—
192C22×C5—21no—
193C22×C5—21no—
194C22×C5C2×C22⋊C811yescharacteristic
195C22×C5C2×#9911yescharacteristic
196C22×C5#41311yescharacteristic
197C4×C5—21no—
198C4×C5—21no—
199C4×C5—21no—
200C4×C5—21no—
201C4×C5—22no—
202C4×C5—22no—
203C4×C5—41no—
204C4×C5—41no—
205C4×C5—41no—
206Dic5—42no—
207Dic5—42no—
208Dic5—81no—
209Dic5—81no—
210C2×Q8—41no—
211C2×Q8—41no—
212C2×Q8—52no—
213C2×Q8—101no—
214C2×Q8—201no—
215C2×Q8—201no—
216C2×Q8C8×D512yes—
217C2×Q8#67612yes—
218C22×C4—101no—
219C22×C4—101no—
220C22×C4—101no—
221C22×C4—101no—
222C22×C4#68511yescharacteristic
223C22×C4#68511yescharacteristic
224C22×C4#68511yescharacteristic
225C22×C4#68511yescharacteristic
226C22×C4C2×C4×D511yescharacteristic
227C22×C4C2×D2011yescharacteristic
228C22×C4C2×C22⋊D511yescharacteristic
229C2×C8—42no—
230C2×C8—202no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—104no—
235C4⋊C4—104no—
236C4⋊C4—201no—
237C4⋊C4—201no—
238C4⋊C4—201no—
239C42—21no—
240C42—21no—
241C42—21no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—52no—
246C42—101no—
247C42—201no—
248C42—202no—
249C2×C5—21no—
250C2×C5—21no—
251C2×C5#145911yescharacteristic
252C2×C5#212911yescharacteristic
253C2×C5#213311yescharacteristic
254C23C2×#68511yescharacteristic
255Q8—42no—
256Q8—42no—
257Q8—202no—
258Q8—202no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—102no—
273C2×C4—102no—
274C2×C4—201no—
275C2×C4—201no—
276C2×C4—201no—
277C2×C4—201no—
278C2×C4—201no—
279C2×C4—201no—
280C2×C4—202no—
281C2×C4—201no—
282C2×C4—201no—
283C2×C4#393811yescharacteristic
284C2×C4#393811yescharacteristic
285C2×C4#395212yes—
286C2×C4#395212yes—
287C2×C4C2×C8×D511yescharacteristic
288C2×C4C2×#67611yescharacteristic
289C8—82no—
290C8—402no—
291C5#1148211yescharacteristic, complemented, Sylow
292C22—21no—
293C22—21no—
294C22C2×#393811yescharacteristic
295C22C2×#395211yescharacteristic
296C22#6542111yescharacteristic
297C4—22no—
298C4—22no—
299C4—21no—
300C4—21no—
301C4—21no—
302C4—21no—
303C4—41no—
304C4—41no—
305C4—41no—
306C4—202no—
307C4—202no—
308C4—401no—
309C4—401no—
310C2—21no—
311C2—21no—
312C2#1060071211yescharacteristic
313C2#1060085211yescharacteristic
314C2#1060092111yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC2×C4×C5C22×C8
FrattiniC2×C4⋊C4C22×D5
FittingC5×#1461C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#1461D5
hypocenterC5#11482
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
35. #4090C8semidirect
291. C5#11482semidirect

Maximal subgroups

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

subgroupindex
#106141872
C5×#14612
#106024172
#105979462
#105979432
#114825