Finite Group Databasebeta

← #12010191

Subgroups — #12010191

Order 1280.

382 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 79 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#10613992C211yesmaximal, characteristic
2C5×#1820C211yesmaximal, characteristic
3#10602364C211yesmaximal, characteristic
4#10597983C212yesmaximal
5#10597982C212yesmaximal
6C2×C5×#117C2211yescharacteristic
7C2×#4016C411yescharacteristic, complemented
8C5×#381—21no—
9#65499—21no—
10#65275C411yescharacteristic, complemented
11#65272C411yescharacteristic, complemented
12#65261—21no—
13#65242C2211yescharacteristic
14#65238C2211yescharacteristic
15#65234—21no—
16#65222—21no—
17#65221C411yescharacteristic, complemented
18#65214—21no—
19C5×#342—21no—
20C5×#342C2212yes—
21#64748—21no—
22#64745C2212yes—
23#11846—51nomaximal, Sylow
24C23×C4×C5D411yescharacteristic
25C5×#117—41no—
26C5×#117—41no—
27C2×C5×C4⋊C4C2×C411yescharacteristic
28C2×C5×C4⋊C4D411yescharacteristic
29C2×C5×C22⋊C4—22no—
30C2×C5×C22⋊C4D411yescharacteristic
31C2×C5×C22⋊C4C2311yescharacteristic
32C2×C42×C5C2×C411yescharacteristic
33C2×C42×C5D411yescharacteristic
34C2×C22⋊Dic5—21no—
35C2×C22⋊Dic5—21no—
36C2×C4⋊Dic5C2×C411yescharacteristic
37C2×C4⋊Dic5C2×C411yescharacteristic
38C2×#683—21no—
39C2×#683—21no—
40C2×#683—21no—
41C2×#683—21no—
42C2×C4×Dic5—21no—
43#4016—41no—
44#4016—41no—
45C5×#95—41no—
46C5×#95—41no—
47#3963—21no—
48#3963—21no—
49#3963—21no—
50#3963—21no—
51#3963—21no—
52#3963C2×C411yescharacteristic
53#3963C2×C411yescharacteristic
54C22⋊#168—22no—
55C4⋊#168—41no—
56C4×#168—41no—
57#2611—51no—
58#1820D511yescharacteristic
59#1458—51no—
60#1352—52no—
61#1344—52no—
62C24×C5C2×D411yescharacteristic
63C22×C4×C5—22no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5—41no—
67C22×C4×C5—42no—
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×Dic5—21no—
75C22×Dic5—21no—
76C22×Dic5—21no—
77C22×Dic5—21no—
78C5×C4⋊C4—41no—
79C5×C4⋊C4—41no—
80C5×C22⋊C4—41no—
81C5×C22⋊C4—41no—
82C5×C22⋊C4—42no—
83C5×C22⋊C4—42no—
84C42×C5—21no—
85C42×C5—21no—
86C42×C5—21no—
87C42×C5—21no—
88C22⋊Dic5—42no—
89C22⋊Dic5—42no—
90C4⋊Dic5—41no—
91C4⋊Dic5—41no—
92#683—42no—
93#683—42no—
94#683—42no—
95#683—41no—
96#683—41no—
97C4×Dic5—42no—
98C2×#168—42no—
99C2×#125—51no—
100C2×#117C2×D511yescharacteristic
101#431—101no—
102#400—51no—
103#399—51no—
104#398—51no—
105#397—51no—
106#389—101no—
107#388—101no—
108#387—101no—
109#385—101no—
110#381—21no—
111#376—51no—
112#342—21no—
113#342C2×D512yes—
114#324—101no—
115#323—52no—
116C23×C5—21no—
117C23×C5—21no—
118C23×C5—41no—
119C23×C5—41no—
120C23×C5C2×C22⋊C411yescharacteristic
121C23×C5#13512yes—
122C2×C4×C5—21no—
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—42no—
132C2×C4×C5—42no—
133C2×C4×C5—41no—
134C2×C4×C5—41no—
135C2×C4×C5—41no—
136C2×C4×C5—41no—
137C2×C4×C5—82no—
138C2×C4×C5—82no—
139C2×C4×C5—82no—
140C2×C4×C5#9911yescharacteristic
141C2×C4×C5#9911yescharacteristic
142C2×Dic5—22no—
143C2×Dic5—41no—
144C2×Dic5—41no—
145C2×Dic5—41no—
146C2×Dic5—41no—
147C2×Dic5—41no—
148C2×Dic5—41no—
149C2×Dic5—41no—
150C2×Dic5—41no—
151C2×Dic5—41no—
152C2×Dic5—41no—
153C2×Dic5—41no—
154#168—82no—
155C23×C4C22⋊D511yescharacteristic
156#125—201no—
157#125—201no—
158#117—41no—
159#117—41no—
160C2×C4⋊C4—51no—
161C2×C4⋊C4—51no—
162C2×C4⋊C4—101no—
163C2×C4⋊C4—101no—
164C2×C4⋊C4—101no—
165C2×C4⋊C4—101no—
166C2×C4⋊C4C4×D511yescharacteristic
167C2×C4⋊C4D2011yescharacteristic
168C2×C22⋊C4—22no—
169C2×C22⋊C4—101no—
170C2×C22⋊C4—101no—
171C2×C22⋊C4C22⋊D511yescharacteristic
172C2×C22⋊C4C22×D511yescharacteristic
173C2×C42—101no—
174C2×C42C4×D511yescharacteristic
175C2×C42D2011yescharacteristic
176C4⋊C8—201no—
177C22⋊C8—102no—
178C4×C8—201no—
179#95—41no—
180#95—41no—
181#95—51no—
182#95—51no—
183#95—101no—
184#95—101no—
185#95—101no—
186#95—101no—
187#95—101no—
188C22×C5—21no—
189C22×C5—21no—
190C22×C5—22no—
191C22×C5—42no—
192C22×C5—41no—
193C22×C5—41no—
194C22×C5—81no—
195C22×C5C2×#9911yescharacteristic
196C22×C5#41611yescharacteristic
197C22×C5#42111yescharacteristic
198C4×C5—21no—
199C4×C5—21no—
200C4×C5—41no—
201C4×C5—41no—
202C4×C5—41no—
203C4×C5—41no—
204C4×C5—41no—
205C4×C5—162no—
206Dic5—42no—
207Dic5—81no—
208Dic5—81no—
209Dic5—81no—
210C24C2×C22⋊D511yescharacteristic
211C22×C4—22no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—41no—
215C22×C4—42no—
216C22×C4—101no—
217C22×C4—101no—
218C22×C4—101no—
219C22×C4—101no—
220C22×C4#68511yescharacteristic
221C22×C4#68511yescharacteristic
222C22×C4#68511yescharacteristic
223C22×C4#68511yescharacteristic
224C22×C4C2×C4×D511yescharacteristic
225C22×C4C2×D2011yescharacteristic
226C2×C8—202no—
227C4⋊C4—41no—
228C4⋊C4—41no—
229C4⋊C4—201no—
230C4⋊C4—201no—
231C4⋊C4—202no—
232C4⋊C4—202no—
233C4⋊C4—202no—
234C4⋊C4—201no—
235C4⋊C4—201no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—42no—
239C22⋊C4—42no—
240C22⋊C4—202no—
241C22⋊C4—202no—
242C42—21no—
243C42—21no—
244C42—21no—
245C42—21no—
246C42—202no—
247C2×C5—21no—
248C2×C5—21no—
249C2×C5—42no—
250C2×C5#151611yescharacteristic
251C2×C5#212311yescharacteristic
252C2×C5#212611yescharacteristic
253C23—21no—
254C23—21no—
255C23—41no—
256C23—41no—
257C23C2×#68511yescharacteristic
258C23#409612yes—
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—42no—
269C2×C4—42no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4—82no—
277C2×C4—102no—
278C2×C4—201no—
279C2×C4—201no—
280C2×C4—201no—
281C2×C4—201no—
282C2×C4—201no—
283C2×C4—201no—
284C2×C4—201no—
285C2×C4—201no—
286C2×C4—201no—
287C2×C4—201no—
288C2×C4—201no—
289C2×C4#393811yescharacteristic
290C2×C4#393811yescharacteristic
291C8—402no—
292C5#1184611yescharacteristic, complemented, Sylow
293C22—21no—
294C22—21no—
295C22—22no—
296C22—42no—
297C22—41no—
298C22—41no—
299C22—81no—
300C22C2×#393811yescharacteristic
301C22#6529111yescharacteristic
302C22#6529411yescharacteristic
303C4—21no—
304C4—21no—
305C4—41no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—162no—
311C4—202no—
312C4—401no—
313C4—401no—
314C4—401no—
315C2—21no—
316C2—21no—
317C2—42no—
318C2#1060032511yescharacteristic
319C2#1060085111yescharacteristic
320C2#1060085311yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C22⋊C4C22×D5
FittingC5×#1820C2
socleC22×C5C2×#99
prime radicalC24×C5C2×D4
cosocleC2×C5×C22⋊C4C23
hypercenter#1820D5
hypocenterC5#11846
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1820

Complements

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

NH ≅ G/Ntype
7. C2×#4016C4semidirect
10. #65275C4semidirect
11. #65272C4semidirect
17. #65221C4semidirect
292. C5#11846semidirect

Maximal subgroups

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

subgroupindex
#106139922
C5×#18202
#106023642
#105979832
#105979822
#118465