Finite Group Databasebeta

← #12008987

Subgroups — #12008987

Order 1280.

426 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 91 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
1C5×#2579C211yesmaximal, characteristic
2#10602396C211yesmaximal, characteristic
3#10602393C211yesmaximal, characteristic
4#10598127C212yesmaximal, complemented
5#10598127C212yesmaximal, complemented
6C2×C4×C5×D4C2211yescharacteristic
7C22×C5×C4⋊C4C411yescharacteristic
8C5×#398—21no—
9C5×#396—21no—
10C5×#387—21no—
11C5×#386C411yescharacteristic
12C5×#386C411yescharacteristic
13C5×#385—21no—
14C5×#385C2211yescharacteristic
15C5×#385C2211yescharacteristic
16C5×#380C411yescharacteristic
17C2×C22⋊#168—21no—
18#65215—21no—
19#64748—21no—
20#64745—21no—
21#64745C2212yes—
22#64745C2212yes—
23#11578—51nomaximal, Sylow
24C22×C5×D4C2×C411yescharacteristic
25C23×C4×C5C2×C411yescharacteristic
26C23×C4×C5C2×C411yescharacteristic
27C23×C4×C5C2×C411yescharacteristic
28C23×C4×C5D411yescharacteristic
29C4×C5×D4—41no—
30C4×C5×D4—41no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4—41no—
37C2×C5×C4⋊C4—41no—
38C2×C5×C4⋊C4D411yescharacteristic
39C2×C5×C22⋊C4—21no—
40C2×C5×C22⋊C4—21no—
41C2×C5×C22⋊C4C2×C411yescharacteristic
42C2×C5×C22⋊C4C2×C411yescharacteristic
43C2×C5×C22⋊C4D411yescharacteristic
44C2×C5×C22⋊C4C2311yescharacteristic
45C2×C42×C5D411yescharacteristic
46C22×#168—41no—
47C5×#95—21no—
48C5×#95—21no—
49C5×#95—21no—
50C5×#95—21no—
51C5×#95—21no—
52C22⋊#168—22no—
53C22⋊#168—22no—
54C22⋊#168—41no—
55C4⋊#168—41no—
56#3935—41no—
57#2579D511yescharacteristic
58#1466—51no—
59#1459—51no—
60#1326—52no—
61#1326—52no—
62C24×C5C22⋊C411yescharacteristic
63C24×C5C22×C411yescharacteristic
64C2×C5×D4—22no—
65C2×C5×D4—22no—
66C2×C5×D4—41no—
67C22×C4×C5—21no—
68C22×C4×C5—21no—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—21no—
73C22×C4×C5—21no—
74C22×C4×C5—21no—
75C22×C4×C5—42no—
76C22×C4×C5—41no—
77C22×C4×C5—41no—
78C22×C4×C5—81no—
79C22×C4×C5—81no—
80C22×C4×C5—81no—
81C22×C4×C5C22⋊C411yescharacteristic
82C22×C4×C5C22⋊C411yescharacteristic
83C22×C4×C5C22⋊C411yescharacteristic
84C22×C4×C5C2×D411yescharacteristic
85C22×C4×C5C2×D411yescharacteristic
86C5×C4⋊C4—41no—
87C5×C4⋊C4—42no—
88C5×C4⋊C4—42no—
89C5×C4⋊C4—41no—
90C5×C4⋊C4—41no—
91C5×C4⋊C4—81no—
92C5×C4⋊C4—81no—
93C5×C22⋊C4—22no—
94C5×C22⋊C4—22no—
95C5×C22⋊C4—41no—
96C5×C22⋊C4—41no—
97C5×C22⋊C4—42no—
98C5×C22⋊C4—81no—
99C42×C5—21no—
100C42×C5—21no—
101C2×#168—42no—
102C2×#168—42no—
103C2×#168—82no—
104C2×C4×D4C2×D511yescharacteristic
105C22×C4⋊C4Dic511yescharacteristic
106#432—101no—
107C2×C22⋊C8—101no—
108#398—21no—
109#396—21no—
110#387—21no—
111#386Dic511yescharacteristic
112#386Dic511yescharacteristic
113#385—21no—
114#385C2×D511yescharacteristic
115#385C2×D511yescharacteristic
116#380Dic511yescharacteristic
117#324—101no—
118#323—52no—
119#323—52no—
120#323—101no—
121C23×C5—21no—
122C23×C5—21no—
123C23×C5—21no—
124C23×C5—21no—
125C23×C5—41no—
126C23×C5—41no—
127C23×C5—41no—
128C23×C5—41no—
129C23×C5#10112yes—
130C23×C5C2×C22⋊C411yescharacteristic
131C23×C5#13112yes—
132C5×D4—44no—
133C2×C4×C5—22no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5—41no—
141C2×C4×C5—42no—
142C2×C4×C5—41no—
143C2×C4×C5—42no—
144C2×C4×C5—41no—
145C2×C4×C5—41no—
146C2×C4×C5—41no—
147C2×C4×C5—41no—
148C2×C4×C5—42no—
149C2×C4×C5—41no—
150C2×C4×C5—41no—
151C2×C4×C5—41no—
152C2×C4×C5—41no—
153C2×C4×C5—41no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—81no—
159C2×C4×C5—81no—
160C2×C4×C5—81no—
161C2×C4×C5—82no—
162C2×C4×C5#9911yescharacteristic
163C2×C4×C5#9911yescharacteristic
164#168—82no—
165#168—82no—
166C22×D4C2×Dic511yescharacteristic
167C23×C4C2×Dic511yescharacteristic
168C23×C4C2×Dic511yescharacteristic
169C23×C4C2×Dic511yescharacteristic
170C23×C4C22⋊D511yescharacteristic
171C22×C8—201no—
172C4×D4—41no—
173C4×D4—41no—
174C2×C4⋊C4—21no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—41no—
180C2×C4⋊C4—41no—
181C2×C4⋊C4C22⋊D511yescharacteristic
182C2×C22⋊C4—21no—
183C2×C22⋊C4—21no—
184C2×C22⋊C4C2×Dic511yescharacteristic
185C2×C22⋊C4C2×Dic511yescharacteristic
186C2×C22⋊C4C22⋊D511yescharacteristic
187C2×C22⋊C4C22×D511yescharacteristic
188C2×C42C22⋊D511yescharacteristic
189C4⋊C8—201no—
190C22⋊C8—102no—
191C22⋊C8—102no—
192C22⋊C8—201no—
193#97—201no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95—21no—
199C22×C5—21no—
200C22×C5—21no—
201C22×C5—22no—
202C22×C5—22no—
203C22×C5—42no—
204C22×C5—42no—
205C22×C5—42no—
206C22×C5—41no—
207C22×C5—41no—
208C22×C5—41no—
209C22×C5—41no—
210C22×C5—81no—
211C22×C5#40811yescharacteristic
212C22×C5C2×#9911yescharacteristic
213C22×C5C2×#10111yescharacteristic
214C4×C5—21no—
215C4×C5—21no—
216C4×C5—41no—
217C4×C5—42no—
218C4×C5—41no—
219C4×C5—41no—
220C4×C5—41no—
221C4×C5—81no—
222C4×C5—81no—
223C4×C5—81no—
224C24C22⋊Dic511yescharacteristic
225C24C22×Dic511yescharacteristic
226C2×D4—22no—
227C2×D4—22no—
228C2×D4—41no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—42no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—81no—
241C22×C4—81no—
242C22×C4—81no—
243C22×C4C22⋊Dic511yescharacteristic
244C22×C4C22⋊Dic511yescharacteristic
245C22×C4C22⋊Dic511yescharacteristic
246C22×C4C2×C22⋊D511yescharacteristic
247C22×C4C2×C22⋊D511yescharacteristic
248C2×C8—202no—
249C2×C8—202no—
250C2×C8—402no—
251C4⋊C4—41no—
252C4⋊C4—42no—
253C4⋊C4—42no—
254C4⋊C4—41no—
255C4⋊C4—41no—
256C4⋊C4—81no—
257C4⋊C4—81no—
258C22⋊C4—22no—
259C22⋊C4—22no—
260C22⋊C4—41no—
261C22⋊C4—41no—
262C22⋊C4—42no—
263C22⋊C4—81no—
264C42—21no—
265C42—21no—
266C2×C5—21no—
267C2×C5—21no—
268C2×C5—42no—
269C2×C5—42no—
270C2×C5#147211yescharacteristic
271C2×C5#212011yescharacteristic
272C2×C5#212111yescharacteristic
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—41no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23#396812yes—
282C23#409412yes—
283C23C2×C22⋊Dic511yescharacteristic
284D4—44no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—81no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—82no—
314C2×C4#396611yescharacteristic
315C2×C4#396611yescharacteristic
316C8—402no—
317C8—402no—
318C5#1157811yescharacteristic, complemented, Sylow
319C22—21no—
320C22—21no—
321C22—22no—
322C22—22no—
323C22—42no—
324C22—42no—
325C22—42no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—81no—
331C22C2×#396611yescharacteristic
332C22C2×#396811yescharacteristic
333C22#6552311yescharacteristic
334C4—21no—
335C4—21no—
336C4—41no—
337C4—42no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—81no—
342C4—81no—
343C4—81no—
344C2—21no—
345C2—21no—
346C2—42no—
347C2—42no—
348C2#1060248411yescharacteristic
349C2#1060250911yescharacteristic
350C2#1060264011yescharacteristic
subgroupG/H
centerC22C2×#3966
commutatorC24×C5C22×C4
FrattiniC2×C22⋊C4C22×D5
FittingC5×#2579C2
socleC22×C5C2×#99
prime radicalC22×C5×D4C2×C4
cosocleC2×C5×C22⋊C4C23
hypercenter#2579D5
hypocenterC5#11578
LCSG ▷ C24×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #2579

Complements

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

NH ≅ G/Ntype
4. #10598127C2semidirect
5. #10598127C2semidirect
318. C5#11578semidirect

Maximal subgroups

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

subgroupindex
C5×#25792
#106023962
#106023932
#105981272
#115785