Finite Group Databasebeta

← #12010433

Subgroups — #12010433

Order 1280.

452 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 452 conjugacy classes of subgroups — too many to draw. Only its 99 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#10614115C211yesmaximal, characteristic
2C5×#1459C211yesmaximal, characteristic
3#10602412C211yesmaximal, characteristic
4#10597940C214yesmaximal, complemented
5C2×C4×C5×D4C2211yescharacteristic
6C2×#4015C411yescharacteristic, complemented
7C2×C5×C22⋊C8—21no—
8#65510—21no—
9C2×#3966—21no—
10#65501—21no—
11#65501—21no—
12#65501—21no—
13#65266—21no—
14#65236C412yescomplemented
15#65236C2212yes—
16C4×C4⋊Dic5C411yescharacteristic, complemented
17C5×#324—21no—
18C5×#323C2212yes—
19#64746C2212yes—
20#11900—51nomaximal, Sylow
21C22×C5×D4D411yescharacteristic
22C23×C4×C5D411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C22×Dic10C2×C412yes—
25C22×C5×C8—41no—
26C4×C5×D4—41no—
27C4×C5×D4—41no—
28C2×C5×C4⋊C4D411yescharacteristic
29C2×C5×C22⋊C4C2×C411yescharacteristic
30C2×C5×C22⋊C4C2311yescharacteristic
31C2×C42×C5C2×C411yescharacteristic
32C2×C22⋊Dic5—22no—
33C2×C22⋊Dic5—22no—
34C2×C22⋊Dic5—22no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—21no—
38C2×C4⋊Dic5—41no—
39C2×C4×Dic5—21no—
40#4015—41no—
41#4015—41no—
42C5×C22⋊C8—22no—
43C5×C22⋊C8—41no—
44#3966—42no—
45#3963—22no—
46#3963—22no—
47#3963—41no—
48#3963C2×C412yes—
49#2563—51no—
50#1799—51no—
51#1459D511yescharacteristic
52#1351—54no—
53C24×C5C22⋊C411yescharacteristic
54C24×C5C2×D411yescharacteristic
55C2×C5×D4—41no—
56C2×C5×D4—41no—
57C2×C5×D4SD1612yes—
58C2×C5×D4Q1612yes—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—42no—
64C22×C4×C5—42no—
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22⋊C411yescharacteristic
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22×C411yescharacteristic
69C22×C4×C5C2×D411yescharacteristic
70C22×Dic5—22no—
71C22×Dic5—22no—
72C22×Dic5—42no—
73C2×Dic10—42no—
74C2×Dic10—82no—
75C2×C5×C8—42no—
76C2×C5×C8—82no—
77C5×C4⋊C4—41no—
78C5×C22⋊C4—41no—
79C5×C22⋊C4—41no—
80C42×C5—21no—
81C42×C5—21no—
82C22⋊Dic5—42no—
83C22⋊Dic5—42no—
84C22⋊Dic5—82no—
85C22⋊Dic5—82no—
86C4⋊Dic5—42no—
87C4⋊Dic5—42no—
88C4⋊Dic5—41no—
89C4⋊Dic5—41no—
90C4⋊Dic5—82no—
91C4×Dic5—42no—
92C2×C4⋊Q8—51no—
93C2×C4×D4C2×D511yescharacteristic
94C2×#99—101no—
95C2×C22⋊C8—21no—
96#393—52no—
97#393—52no—
98#390—101no—
99#382—101no—
100#380—101no—
101#380—101no—
102#380—101no—
103C4×C4⋊C4—51no—
104#342—52no—
105#324—21no—
106#323C2×D512yes—
107C23×C5—21no—
108C23×C5—21no—
109C23×C5—21no—
110C23×C5—21no—
111C23×C5—41no—
112C23×C5—41no—
113C23×C5—41no—
114C23×C5—41no—
115C23×C5#10312yes—
116C23×C5C2×C22⋊C411yescharacteristic
117C23×C5C2×SD1611yescharacteristic
118C23×C5C2×Q1611yescharacteristic
119C5×D4—42no—
120C5×D4—42no—
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5—22no—
124C2×C4×C5—21no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—42no—
128C2×C4×C5—42no—
129C2×C4×C5—41no—
130C2×C4×C5—41no—
131C2×C4×C5—41no—
132C2×C4×C5—81no—
133C2×C4×C5—81no—
134C2×C4×C5#9911yescharacteristic
135C2×C4×C5#9911yescharacteristic
136C2×C4×C5#10312yes—
137C2×Dic5—42no—
138C2×Dic5—42no—
139C2×Dic5—42no—
140C2×Dic5—42no—
141C2×Dic5—42no—
142C2×Dic5—42no—
143C2×Dic5—82no—
144C2×Dic5—82no—
145C2×Dic5—82no—
146Dic10—84no—
147C5×C8—82no—
148C22×Q8—52no—
149C22×D4D2011yescharacteristic
150C23×C4D2011yescharacteristic
151C23×C4C22⋊D511yescharacteristic
152C22×C8—41no—
153C4⋊Q8—201no—
154C4⋊Q8—201no—
155C4×D4—41no—
156C4×D4—41no—
157C2×C4⋊C4—101no—
158C2×C4⋊C4—101no—
159C2×C4⋊C4—101no—
160C2×C4⋊C4—201no—
161C2×C4⋊C4C22⋊D511yescharacteristic
162C2×C22⋊C4—102no—
163C2×C22⋊C4—102no—
164C2×C22⋊C4—102no—
165C2×C22⋊C4C4×D511yescharacteristic
166C2×C22⋊C4C22×D511yescharacteristic
167C2×C42—101no—
168C2×C42C4×D511yescharacteristic
169#99—202no—
170C22⋊C8—22no—
171C22⋊C8—41no—
172#95—52no—
173#95—102no—
174#95—102no—
175#95—201no—
176C22×C5—21no—
177C22×C5—21no—
178C22×C5—21no—
179C22×C5—22no—
180C22×C5—21no—
181C22×C5—42no—
182C22×C5—41no—
183C22×C5—41no—
184C22×C5—41no—
185C22×C5—41no—
186C22×C5—41no—
187C22×C5—41no—
188C22×C5—81no—
189C22×C5—81no—
190C22×C5C2×#9911yescharacteristic
191C22×C5C2×#10311yescharacteristic
192C22×C5#42111yescharacteristic
193C4×C5—21no—
194C4×C5—22no—
195C4×C5—41no—
196C4×C5—41no—
197C4×C5—41no—
198C4×C5#35412yes—
199Dic5—82no—
200Dic5—82no—
201Dic5—162no—
202C24#68511yescharacteristic
203C24C2×D2011yescharacteristic
204C2×Q8—202no—
205C2×Q8—402no—
206C2×D4—41no—
207C2×D4—41no—
208C2×D4#67712yes—
209C2×D4Dic2012yes—
210C22×C4—21no—
211C22×C4—21no—
212C22×C4—21no—
213C22×C4—21no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—102no—
217C22×C4—102no—
218C22×C4—202no—
219C22×C4#68511yescharacteristic
220C22×C4#68511yescharacteristic
221C22×C4#68511yescharacteristic
222C22×C4C2×C4×D511yescharacteristic
223C22×C4C2×C22⋊D511yescharacteristic
224C2×C8—42no—
225C2×C8—82no—
226C4⋊C4—41no—
227C4⋊C4—202no—
228C4⋊C4—202no—
229C4⋊C4—201no—
230C4⋊C4—201no—
231C4⋊C4—402no—
232C22⋊C4—41no—
233C22⋊C4—41no—
234C22⋊C4—202no—
235C22⋊C4—202no—
236C22⋊C4—402no—
237C22⋊C4—402no—
238C42—21no—
239C42—21no—
240C42—202no—
241C2×C5—21no—
242C2×C5—21no—
243C2×C5—41no—
244C2×C5—42no—
245C2×C5—41no—
246C2×C5#152011yescharacteristic
247C2×C5#212211yescharacteristic
248C2×C5C2×#35411yescharacteristic
249C23—21no—
250C23—21no—
251C23—21no—
252C23—21no—
253C23—41no—
254C23—41no—
255C23—41no—
256C23—41no—
257C23#394812yes—
258C23C2×#67711yescharacteristic
259C23C2×Dic2011yescharacteristic
260C23C2×#68511yescharacteristic
261Q8—404no—
262D4—42no—
263D4—42no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—202no—
278C2×C4—202no—
279C2×C4—202no—
280C2×C4—202no—
281C2×C4—202no—
282C2×C4—202no—
283C2×C4—402no—
284C2×C4—402no—
285C2×C4—402no—
286C2×C4#393811yescharacteristic
287C2×C4#393811yescharacteristic
288C2×C4#394812yes—
289C8—82no—
290C5#1190011yescharacteristic, complemented, Sylow
291C22—21no—
292C22—21no—
293C22—21no—
294C22—22no—
295C22—21no—
296C22—42no—
297C22—41no—
298C22—41no—
299C22—41no—
300C22—41no—
301C22—41no—
302C22—41no—
303C22—81no—
304C22—81no—
305C22C2×#393811yescharacteristic
306C22C2×#394811yescharacteristic
307C22#6542811yescharacteristic
308C4—22no—
309C4—21no—
310C4—41no—
311C4—41no—
312C4—41no—
313C4—402no—
314C4—402no—
315C4—802no—
316C4#6469312yes—
317C2—21no—
318C2—21no—
319C2—41no—
320C2—42no—
321C2—41no—
322C2#1060073911yescharacteristic
323C2C2×#6469311yescharacteristic
324C2#1060093911yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C22⋊C4C22×D5
FittingC5×#1459C2
socleC22×C5C2×#99
prime radicalC22×C5×D4D4
cosocleC2×C5×C22⋊C4C23
hypercenter#1459D5
hypocenterC5#11900
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1459

Complements

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

NH ≅ G/Ntype
4. #10597940C2semidirect
6. C2×#4015C4semidirect
14. #65236C4semidirect
16. C4×C4⋊Dic5C4semidirect
290. C5#11900semidirect

Maximal subgroups

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

subgroupindex
#106141152
C5×#14592
#106024122
#105979402
#119005