Finite Group Databasebeta

← #12009490

Subgroups — #12009490

Order 1280.

468 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 107 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#10613993C211yesmaximal, characteristic
2C5×#1458C211yesmaximal, characteristic
3#10602385C211yesmaximal, characteristic
4#10597941C214yesmaximal
5C2×C5×#117C2211yescharacteristic
6C2×#4072—21no—
7C2×#4070—21no—
8C2×#4015C411yescharacteristic, complemented
9C5×#431—21no—
10#65272—21no—
11#65272C412yescomplemented
12#65242—21no—
13#65242C2212yes—
14#65225C411yescharacteristic, complemented
15#65218—21no—
16C5×#324—21no—
17C5×#323C2212yes—
18#64746—21no—
19#64746C2212yes—
20#11694—51nomaximal, Sylow
21C23×C4×C5D411yescharacteristic
22C22×Dic10—21no—
23C5×#117—41no—
24C5×#117—41no—
25C2×C5×C4⋊C4C2×C411yescharacteristic
26C2×C5×C4⋊C4D411yescharacteristic
27C2×C5×C22⋊C4D411yescharacteristic
28C2×C5×C22⋊C4C2311yescharacteristic
29C2×C42×C5C2×C411yescharacteristic
30C2×C42×C5D411yescharacteristic
31C2×C22⋊Dic5—22no—
32C2×C22⋊Dic5—22no—
33#4072—24no—
34#4072—42no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—41no—
38C2×C4⋊Dic5C2×C412yes—
39#4070—42no—
40#4070—42no—
41C2×#683—22no—
42C2×C4×Dic5—41no—
43#4015—41no—
44#4015—41no—
45C5×C4⋊C8—41no—
46C5×C22⋊C8—22no—
47C4×C5×C8—41no—
48#3963—22no—
49#3963—21no—
50#3963—22no—
51#3963C2×C412yes—
52#2621—51no—
53#1740—51no—
54#1458D511yescharacteristic
55#1344—54no—
56C24×C5C2×D411yescharacteristic
57C22×C4×C5—21no—
58C22×C4×C5—21no—
59C22×C4×C5—22no—
60C22×C4×C5C22⋊C411yescharacteristic
61C22×C4×C5C22⋊C411yescharacteristic
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22⋊C411yescharacteristic
64C22×C4×C5D812yes—
65C22×C4×C5SD1612yes—
66C22×C4×C5C22×C411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C22×Dic5—22no—
69C22×Dic5—22no—
70C22×Dic5—42no—
71C2×Dic10—41no—
72C2×Dic10—41no—
73C2×Dic10—42no—
74C2×Dic10—42no—
75C2×C5×C8—42no—
76C5×C4⋊C4—41no—
77C5×C4⋊C4—41no—
78C5×C22⋊C4—41no—
79C5×C22⋊C4—41no—
80C42×C5—21no—
81C42×C5—21no—
82C42×C5—21no—
83C42×C5—21no—
84C22⋊Dic5—24no—
85C22⋊Dic5—42no—
86C22⋊Dic5—42no—
87C22⋊Dic5—42no—
88C4⋊Dic5—42no—
89C4⋊Dic5—44no—
90C4⋊Dic5—42no—
91C4⋊Dic5—42no—
92#683—44no—
93C4×Dic5—44no—
94C2×C4⋊Q8—51no—
95C2×C22⋊Q8—101no—
96C2×#117—101no—
97C2×#117C2×D511yescharacteristic
98#431—21no—
99#398—52no—
100#398—101no—
101#397—52no—
102#397—101no—
103#391—101no—
104#382—51no—
105#342—52no—
106#342—101no—
107#324—21no—
108#323C2×D512yes—
109C23×C5—21no—
110C23×C5—21no—
111C23×C5—41no—
112C23×C5—41no—
113C23×C5C2×C22⋊C411yescharacteristic
114C23×C5C2×D811yescharacteristic
115C23×C5C2×SD1611yescharacteristic
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—22no—
119C2×C4×C5—22no—
120C2×C4×C5—22no—
121C2×C4×C5—22no—
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#10212yes—
133C2×C4×C5#10212yes—
134C2×C4×C5#10412yes—
135C2×Dic5—44no—
136C2×Dic5—42no—
137C2×Dic5—42no—
138C2×Dic5—42no—
139C2×Dic5—42no—
140C2×Dic5—42no—
141C2×Dic5—42no—
142C2×Dic5—82no—
143C2×Dic5—82no—
144Dic10—82no—
145Dic10—82no—
146C5×C8—82no—
147C22×Q8—101no—
148C23×C4D2011yescharacteristic
149C4⋊Q8—201no—
150C4⋊Q8—201no—
151C22⋊Q8—202no—
152C22⋊Q8—202no—
153#117—41no—
154#117—41no—
155#117—104no—
156#117—202no—
157C2×C4⋊C4—52no—
158C2×C4⋊C4—102no—
159C2×C4⋊C4—101no—
160C2×C4⋊C4—101no—
161C2×C4⋊C4—201no—
162C2×C4⋊C4C4×D511yescharacteristic
163C2×C4⋊C4C22⋊D511yescharacteristic
164C2×C22⋊C4—102no—
165C2×C22⋊C4—102no—
166C2×C22⋊C4D2011yescharacteristic
167C2×C22⋊C4C22×D511yescharacteristic
168C2×C42—201no—
169C2×C42C4×D511yescharacteristic
170C2×C42C22⋊D511yescharacteristic
171C4⋊C8—41no—
172C22⋊C8—22no—
173C4×C8—41no—
174#95—52no—
175#95—101no—
176#95—102no—
177#95—102no—
178C22×C5—21no—
179C22×C5—21no—
180C22×C5—21no—
181C22×C5—21no—
182C22×C5—41no—
183C22×C5—41no—
184C22×C5—41no—
185C22×C5—41no—
186C22×C5—81no—
187C22×C5C2×#9911yescharacteristic
188C22×C5C2×#10211yescharacteristic
189C22×C5C2×#10411yescharacteristic
190C4×C5—22no—
191C4×C5—41no—
192C4×C5—41no—
193C4×C5—41no—
194C4×C5—41no—
195C4×C5#32712yes—
196C4×C5#32712yes—
197Dic5—82no—
198Dic5—84no—
199Dic5—82no—
200C24C2×D2011yescharacteristic
201C2×Q8—201no—
202C2×Q8—201no—
203C2×Q8—202no—
204C2×Q8—202no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—22no—
208C22×C4—102no—
209C22×C4—102no—
210C22×C4—202no—
211C22×C4#67712yes—
212C22×C4D4012yes—
213C22×C4#68511yescharacteristic
214C22×C4#68511yescharacteristic
215C22×C4#68511yescharacteristic
216C22×C4#68511yescharacteristic
217C22×C4C2×C4×D511yescharacteristic
218C22×C4C2×C22⋊D511yescharacteristic
219C2×C8—42no—
220C4⋊C4—41no—
221C4⋊C4—41no—
222C4⋊C4—202no—
223C4⋊C4—202no—
224C4⋊C4—204no—
225C4⋊C4—204no—
226C4⋊C4—202no—
227C22⋊C4—41no—
228C22⋊C4—41no—
229C22⋊C4—104no—
230C22⋊C4—202no—
231C22⋊C4—202no—
232C22⋊C4—202no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—204no—
238C2×C5—21no—
239C2×C5—21no—
240C2×C5—41no—
241C2×C5—41no—
242C2×C5C2×#32711yescharacteristic
243C2×C5#212311yescharacteristic
244C2×C5#212911yescharacteristic
245C23—21no—
246C23—21no—
247C23—41no—
248C23—41no—
249C23C2×#67711yescharacteristic
250C23C2×D4011yescharacteristic
251C23C2×#68511yescharacteristic
252Q8—402no—
253Q8—402no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—204no—
269C2×C4—202no—
270C2×C4—202no—
271C2×C4—202no—
272C2×C4—202no—
273C2×C4—202no—
274C2×C4—202no—
275C2×C4—402no—
276C2×C4—402no—
277C2×C4#393811yescharacteristic
278C2×C4#393811yescharacteristic
279C2×C4#395312yes—
280C2×C4#395312yes—
281C2×C4#395712yes—
282C8—82no—
283C5#1169411yescharacteristic, complemented, Sylow
284C22—21no—
285C22—21no—
286C22—21no—
287C22—21no—
288C22—41no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—81no—
293C22C2×#393811yescharacteristic
294C22C2×#395311yescharacteristic
295C22C2×#395711yescharacteristic
296C4—22no—
297C4—41no—
298C4—41no—
299C4—41no—
300C4—41no—
301C4—402no—
302C4—404no—
303C4—402no—
304C4#6469012yes—
305C4#6469012yes—
306C2—21no—
307C2—21no—
308C2—41no—
309C2—41no—
310C2C2×#6469011yescharacteristic
311C2#1060085211yescharacteristic
312C2#1060094011yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C22⋊C4C22×D5
FittingC5×#1458C2
socleC22×C5C2×#99
prime radicalC24×C5C2×D4
cosocleC2×C5×C22⋊C4C23
hypercenter#1458D5
hypocenterC5#11694
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #1458

Complements

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

NH ≅ G/Ntype
8. C2×#4015C4semidirect
11. #65272C4semidirect
14. #65225C4semidirect
283. C5#11694semidirect

Maximal subgroups

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

subgroupindex
#106139932
C5×#14582
#106023852
#105979412
#116945