Finite Group Databasebeta

← #12010137

Subgroups — #12010137

Order 1280.

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

normal subgroups only

This group has 340 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#10614217C211yesmaximal, characteristic
2C5×#1467C211yesmaximal, characteristic
3#10602430C211yesmaximal, characteristic
4#10597950C212yesmaximal
5#10597949C212yesmaximal
6C2×C4×C5×Q8C2211yescharacteristic
7C2×#4016C411yescharacteristic
8C5×#432—21no—
9#65518—21no—
10C2×#3968—21no—
11#65275C411yescharacteristic
12#65275C2211yescharacteristic
13#65272C411yescharacteristic
14#65272C2211yescharacteristic
15#65271—21no—
16#65226C411yescharacteristic
17#65222—21no—
18#65222—21no—
19#65213—21no—
20C5×#324—21no—
21C5×#324C2212yes—
22#64750C2212yes—
23#11835—51nomaximal, Sylow
24C22×C5×Q8D411yescharacteristic
25C4×C5×Q8—41no—
26C4×C5×Q8—41no—
27C2×C5×C4⋊C4C2×C411yescharacteristic
28C2×C5×C4⋊C4D411yescharacteristic
29C2×C5×C4⋊C4C2311yescharacteristic
30C2×C42×C5C2×C411yescharacteristic
31C2×C42×C5D411yescharacteristic
32C2×C42×C5D411yescharacteristic
33C2×C4⋊Dic5C2×C411yescharacteristic
34C2×C4⋊Dic5C2×C411yescharacteristic
35C2×#683—21no—
36C2×#683—21no—
37C2×#683—21no—
38C2×#683—21no—
39C2×#681—22no—
40#4016—41no—
41#4016—41no—
42C5×C4⋊C8—41no—
43C5×C22⋊C8—22no—
44C5×#97—41no—
45#3968—42no—
46#3963—21no—
47#3963—21no—
48#3963—21no—
49#3963—21no—
50#3963—21no—
51#3963—21no—
52#3963—21no—
53#3963—21no—
54#3963C2×C411yescharacteristic
55#3963C2×C411yescharacteristic
56C4⋊#168—41no—
57C4⋊#168—41no—
58#2634—51no—
59#1801—51no—
60#1467D511yescharacteristic
61#1353—52no—
62#1346—52no—
63C2×C5×Q8—21no—
64C2×C5×Q8—21no—
65C2×C5×Q8—41no—
66C2×C5×Q8—41no—
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22⋊C411yescharacteristic
69C22×C4×C5C22⋊C411yescharacteristic
70C22×C4×C5C22⋊C411yescharacteristic
71C22×C4×C5C22×C411yescharacteristic
72C22×C4×C5C2×D411yescharacteristic
73C22×C4×C5C2×D411yescharacteristic
74C22×Dic5—21no—
75C22×Dic5—21no—
76C22×Dic5—21no—
77C22×Dic5—21no—
78C2×C5×C8—42no—
79C5×C4⋊C4—41no—
80C5×C4⋊C4—41no—
81C5×C4⋊C4—41no—
82C42×C5—21no—
83C42×C5—21no—
84C42×C5—21no—
85C42×C5—21no—
86C42×C5—21no—
87C42×C5—21no—
88C4⋊Dic5—41no—
89C4⋊Dic5—41no—
90#683—42no—
91#683—42no—
92#683—41no—
93#683—41no—
94#683—41no—
95#683—41no—
96#681—42no—
97#681—42no—
98C2×#168—42no—
99C2×#125—51no—
100C2×C4×Q8C2×D511yescharacteristic
101#432—21no—
102#423—101no—
103C2×#101—101no—
104#400—51no—
105#400—51no—
106#400—101no—
107#398—51no—
108#398—51no—
109#395—101no—
110#387—101no—
111#387—101no—
112#383—51no—
113#343—52no—
114#324—21no—
115#324C2×D512yes—
116C23×C5C2×C22⋊C411yescharacteristic
117C5×Q8—42no—
118C5×Q8—42no—
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—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—41no—
131C2×C4×C5—41no—
132C2×C4×C5—41no—
133C2×C4×C5—41no—
134C2×C4×C5#9911yescharacteristic
135C2×C4×C5#9911yescharacteristic
136C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C5#13711yescharacteristic
138C2×Dic5—41no—
139C2×Dic5—41no—
140C2×Dic5—41no—
141C2×Dic5—41no—
142C2×Dic5—42no—
143C2×Dic5—41no—
144C2×Dic5—41no—
145C2×Dic5—41no—
146C2×Dic5—41no—
147C2×Dic5—41no—
148C2×Dic5—41no—
149C5×C8—82no—
150#168—82no—
151C22×Q8D2011yescharacteristic
152C2×M16—102no—
153#125—201no—
154#125—201no—
155C4×Q8—41no—
156C4×Q8—41no—
157C2×C4⋊C4—51no—
158C2×C4⋊C4—51no—
159C2×C4⋊C4—101no—
160C2×C4⋊C4—101no—
161C2×C4⋊C4—101no—
162C2×C4⋊C4—101no—
163C2×C4⋊C4C4×D511yescharacteristic
164C2×C4⋊C4C22⋊D511yescharacteristic
165C2×C4⋊C4C22×D511yescharacteristic
166C2×C42C4×D511yescharacteristic
167C2×C42D2011yescharacteristic
168C2×C42C22⋊D511yescharacteristic
169C4⋊C8—41no—
170C4⋊C8—201no—
171C4⋊C8—201no—
172#101—202no—
173C22⋊C8—22no—
174#97—41no—
175#95—51no—
176#95—51no—
177#95—101no—
178#95—101no—
179#95—101no—
180#95—101no—
181#95—101no—
182#95—101no—
183#95—101no—
184#95—101no—
185C22×C5—21no—
186C22×C5—21no—
187C22×C5C2×#9911yescharacteristic
188C22×C5#41711yescharacteristic
189C22×C5#42111yescharacteristic
190C4×C5—21no—
191C4×C5—21no—
192C4×C5—21no—
193C4×C5—21no—
194C4×C5—41no—
195C4×C5—41no—
196C4×C5—41no—
197C4×C5—41no—
198C4×C5—41no—
199Dic5—81no—
200Dic5—81no—
201Dic5—81no—
202Dic5—81no—
203C2×Q8—21no—
204C2×Q8—21no—
205C2×Q8—41no—
206C2×Q8—41no—
207C22×C4—101no—
208C22×C4—101no—
209C22×C4—101no—
210C22×C4—101no—
211C22×C4#68511yescharacteristic
212C22×C4#68511yescharacteristic
213C22×C4#68511yescharacteristic
214C22×C4#68511yescharacteristic
215C22×C4C2×C4×D511yescharacteristic
216C22×C4C2×D2011yescharacteristic
217C22×C4C2×C22⋊D511yescharacteristic
218M16—202no—
219M16—202no—
220C2×C8—42no—
221C2×C8—202no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—201no—
226C4⋊C4—201no—
227C4⋊C4—202no—
228C4⋊C4—202no—
229C4⋊C4—201no—
230C4⋊C4—201no—
231C4⋊C4—201no—
232C4⋊C4—201no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—21no—
238C42—21no—
239C2×C5—21no—
240C2×C5—21no—
241C2×C5#151311yescharacteristic
242C2×C5#212311yescharacteristic
243C2×C5#213311yescharacteristic
244C23C2×#68511yescharacteristic
245Q8—42no—
246Q8—42no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—201no—
263C2×C4—201no—
264C2×C4—201no—
265C2×C4—201no—
266C2×C4—202no—
267C2×C4—201no—
268C2×C4—201no—
269C2×C4—201no—
270C2×C4—201no—
271C2×C4—201no—
272C2×C4—201no—
273C2×C4#393811yescharacteristic
274C2×C4#393811yescharacteristic
275C2×C4#405411yescharacteristic
276C2×C4#405511yescharacteristic
277C8—82no—
278C8—402no—
279C5#1183511yescharacteristic, complemented, Sylow
280C22—21no—
281C22—21no—
282C22C2×#393811yescharacteristic
283C22#6542211yescharacteristic
284C22#6542811yescharacteristic
285C4—21no—
286C4—21no—
287C4—21no—
288C4—21no—
289C4—41no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—401no—
295C4—401no—
296C4—401no—
297C4—401no—
298C2—21no—
299C2—21no—
300C2#1060077211yescharacteristic
301C2#1060085111yescharacteristic
302C2#1060092111yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#1467C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#1467D5
hypocenterC5#11835
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
279. C5#11835semidirect

Maximal subgroups

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

subgroupindex
#106142172
C5×#14672
#106024302
#105979502
#105979492
#118355