Finite Group Databasebeta

← #12009697

Subgroups — #12009697

Order 1280.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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#10614217C211yesmaximal, characteristic
2C4×C5×#101C211yesmaximal, characteristic
3#10602417C211yesmaximal, characteristic
4#10597987C212yesmaximal
5#10597986C212yesmaximal
6C2×C4×C5×Q8C2211yescharacteristic
7C2×#4016C411yescharacteristic
8C2×C5×#101—21no—
9C4×C5×M16—21no—
10#65518—21no—
11#65275C411yescharacteristic
12#65275C2211yescharacteristic
13#65272C411yescharacteristic
14#65272C2211yescharacteristic
15#65271—21no—
16#65226C411yescharacteristic
17#65222—21no—
18#65222—21no—
19#65214—21no—
20C5×#343C2212yes—
21#64748—21no—
22#64748C2212yes—
23#11740—51nomaximal, Sylow
24C22×C5×Q8D411yescharacteristic
25C2×C5×M16—22no—
26C4×C5×Q8—41no—
27C4×C5×Q8—41no—
28C2×C5×C4⋊C4C2×C411yescharacteristic
29C2×C5×C4⋊C4D411yescharacteristic
30C2×C5×C4⋊C4C2311yescharacteristic
31C2×C42×C5C2×C411yescharacteristic
32C2×C42×C5D411yescharacteristic
33C2×C42×C5D411yescharacteristic
34C2×C4⋊Dic5C2×C411yescharacteristic
35C2×C4⋊Dic5C2×C411yescharacteristic
36C2×#683—21no—
37C2×#683—21no—
38C2×#683—21no—
39C2×#683—21no—
40#4016—41no—
41#4016—41no—
42C5×#101—24no—
43C5×#97—41no—
44C4×C5×C8—41no—
45#3963—21no—
46#3963—21no—
47#3963—21no—
48#3963—21no—
49#3963—21no—
50#3963—21no—
51#3963—21no—
52#3963—21no—
53#3963C2×C411yescharacteristic
54#3963C2×C411yescharacteristic
55C22⋊#168—22no—
56C4⋊#168—41no—
57C4×#168—41no—
58#2634—51no—
59C4×#101D511yescharacteristic
60#1461—51no—
61#1353—52no—
62#1346—52no—
63C2×C5×Q8—22no—
64C2×C5×Q8—22no—
65C2×C5×Q8—41no—
66C22×C4×C5C22⋊C411yescharacteristic
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22⋊C411yescharacteristic
69C22×C4×C5C22⋊C411yescharacteristic
70C22×C4×C5C22×C411yescharacteristic
71C22×C4×C5C2×D411yescharacteristic
72C22×C4×C5C2×D411yescharacteristic
73C22×Dic5—21no—
74C22×Dic5—21no—
75C22×Dic5—21no—
76C22×Dic5—21no—
77C5×M16—24no—
78C5×M16—42no—
79C2×C5×C8—42no—
80C5×C4⋊C4—41no—
81C5×C4⋊C4—41no—
82C5×C4⋊C4—41no—
83C42×C5—21no—
84C42×C5—21no—
85C42×C5—21no—
86C42×C5—21no—
87C42×C5—21no—
88C42×C5—21no—
89C4⋊Dic5—41no—
90C4⋊Dic5—41no—
91#683—42no—
92#683—41no—
93#683—41no—
94#683—42no—
95#683—42no—
96C2×#168—42no—
97C2×#125—51no—
98C2×C4×Q8C2×D511yescharacteristic
99#431—101no—
100C2×#101—21no—
101C4×M16—21no—
102#400—51no—
103#400—51no—
104#400—101no—
105#398—51no—
106#398—51no—
107#395—101no—
108#387—101no—
109#387—101no—
110#383—51no—
111#343C2×D512yes—
112#324—52no—
113#324—101no—
114C23×C5C2×C22⋊C411yescharacteristic
115C5×Q8—44no—
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—21no—
126C2×C4×C5—41no—
127C2×C4×C5—41no—
128C2×C4×C5—41no—
129C2×C4×C5—41no—
130C2×C4×C5#9911yescharacteristic
131C2×C4×C5#9911yescharacteristic
132C2×C4×C5#10412yes—
133C2×C4×C5#13512yes—
134C2×Dic5—41no—
135C2×Dic5—41no—
136C2×Dic5—41no—
137C2×Dic5—41no—
138C2×Dic5—42no—
139C2×Dic5—41no—
140C2×Dic5—41no—
141C2×Dic5—41no—
142C2×Dic5—41no—
143C2×Dic5—41no—
144C2×Dic5—41no—
145C5×C8—44no—
146#168—82no—
147C22×Q8C22⋊D511yescharacteristic
148C2×M16—22no—
149#125—201no—
150#125—201no—
151C4×Q8—41no—
152C4×Q8—41no—
153C2×C4⋊C4—51no—
154C2×C4⋊C4—51no—
155C2×C4⋊C4—101no—
156C2×C4⋊C4—101no—
157C2×C4⋊C4—101no—
158C2×C4⋊C4—101no—
159C2×C4⋊C4C4×D511yescharacteristic
160C2×C4⋊C4D2011yescharacteristic
161C2×C4⋊C4C22×D511yescharacteristic
162C2×C42C4×D511yescharacteristic
163C2×C42D2011yescharacteristic
164C2×C42C22⋊D511yescharacteristic
165C4⋊C8—201no—
166#101—24no—
167C22⋊C8—102no—
168#97—41no—
169C4×C8—41no—
170C4×C8—201no—
171#95—51no—
172#95—51no—
173#95—101no—
174#95—101no—
175#95—101no—
176#95—101no—
177#95—101no—
178#95—101no—
179#95—101no—
180#95—101no—
181C22×C5—21no—
182C22×C5—21no—
183C22×C5C2×#9911yescharacteristic
184C22×C5#41611yescharacteristic
185C22×C5C2×#10411yescharacteristic
186C4×C5—21no—
187C4×C5—21no—
188C4×C5—22no—
189C4×C5—22no—
190C4×C5—41no—
191C4×C5—41no—
192C4×C5—41no—
193C4×C5—41no—
194Dic5—81no—
195Dic5—81no—
196Dic5—81no—
197Dic5—81no—
198C2×Q8—22no—
199C2×Q8—22no—
200C2×Q8—41no—
201C22×C4—101no—
202C22×C4—101no—
203C22×C4—101no—
204C22×C4—101no—
205C22×C4#68511yescharacteristic
206C22×C4#68511yescharacteristic
207C22×C4#68511yescharacteristic
208C22×C4#68511yescharacteristic
209C22×C4C2×C4×D511yescharacteristic
210C22×C4C2×D2011yescharacteristic
211C22×C4C2×C22⋊D511yescharacteristic
212M16—24no—
213M16—42no—
214C2×C8—42no—
215C2×C8—202no—
216C4⋊C4—41no—
217C4⋊C4—41no—
218C4⋊C4—41no—
219C4⋊C4—201no—
220C4⋊C4—201no—
221C4⋊C4—202no—
222C4⋊C4—202no—
223C4⋊C4—202no—
224C4⋊C4—201no—
225C4⋊C4—201no—
226C42—21no—
227C42—21no—
228C42—21no—
229C42—21no—
230C42—21no—
231C42—21no—
232C2×C5—21no—
233C2×C5—21no—
234C2×C5#150111yescharacteristic
235C2×C5#212311yescharacteristic
236C2×C5#213311yescharacteristic
237C23C2×#68511yescharacteristic
238Q8—44no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—201no—
254C2×C4—201no—
255C2×C4—201no—
256C2×C4—201no—
257C2×C4—202no—
258C2×C4—201no—
259C2×C4—201no—
260C2×C4—201no—
261C2×C4—201no—
262C2×C4—201no—
263C2×C4—201no—
264C2×C4#393712yes—
265C2×C4#393811yescharacteristic
266C2×C4#393811yescharacteristic
267C2×C4#409612yes—
268C8—44no—
269C8—402no—
270C5#1174011yescharacteristic, complemented, Sylow
271C22—21no—
272C22—21no—
273C22C2×#393711yescharacteristic
274C22C2×#393811yescharacteristic
275C22#6529111yescharacteristic
276C4—22no—
277C4—22no—
278C4—21no—
279C4—21no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—401no—
285C4—401no—
286C4—401no—
287C4—401no—
288C2—21no—
289C2—21no—
290C2#1060023611yescharacteristic
291C2#1060092111yescharacteristic
292C2#1060094011yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC4×C5×#101C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenterC4×#101D5
hypocenterC5#11740
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ C4×#101

Complements

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

NH ≅ G/Ntype
270. C5#11740semidirect

Maximal subgroups

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

subgroupindex
#106142172
C4×C5×#1012
#106024172
#105979872
#105979862
#117405