Finite Group Databasebeta

← #12008841

Subgroups — #12008841

Order 1280.

460 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 87 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×#2482C211yesmaximal, characteristic
2#10602365C211yesmaximal, characteristic, complemented
3#10602364C211yesmaximal, characteristic, complemented
4#10598127C212yesmaximal, complemented
5#10598113C212yesmaximal
6C2×C5×#117C2211yescharacteristic
7C22×C5×C22⋊C4C411yescharacteristic
8C5×#399—21no—
9C5×#397—21no—
10C5×#388—21no—
11C5×#388—21no—
12C5×#385C411yescharacteristic
13C5×#385C2211yescharacteristic
14C5×#381C411yescharacteristic
15C5×#379C411yescharacteristic
16C5×#379C2211yescharacteristic
17#65215—21no—
18#65214—21no—
19#64748—21no—
20#64748—21no—
21#64745C2212yes—
22#64745C2212yes—
23#11546—51nomaximal, Sylow
24C25×C5C2×C411yescharacteristic
25C23×C4×C5C2×C411yescharacteristic
26C23×C4×C5C2×C411yescharacteristic
27C5×#117—41no—
28C5×#117—41no—
29C2×C5×C4⋊C4—21no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4D411yescharacteristic
32C2×C5×C4⋊C4D411yescharacteristic
33C2×C5×C22⋊C4—21no—
34C2×C5×C22⋊C4—21no—
35C2×C5×C22⋊C4—21no—
36C2×C5×C22⋊C4—21no—
37C2×C5×C22⋊C4—21no—
38C2×C5×C22⋊C4—21no—
39C2×C5×C22⋊C4—41no—
40C2×C5×C22⋊C4—41no—
41C2×C5×C22⋊C4C2×C411yescharacteristic
42C2×C5×C22⋊C4C2×C411yescharacteristic
43C2×C5×C22⋊C4C2×C411yescharacteristic
44C2×C5×C22⋊C4C2311yescharacteristic
45C2×C42×C5D411yescharacteristic
46C2×C42×C5D411yescharacteristic
47C5×#95—21no—
48C5×#95—21no—
49C5×#95—21no—
50C5×#95—21no—
51C22⋊#168—22no—
52C22⋊#168—22no—
53C4⋊#168—41no—
54C4⋊#168—41no—
55#3935—41no—
56C4×#168—41no—
57#2482D511yescharacteristic
58#1464—51no—
59#1458—51no—
60#1326—52no—
61#1316—52no—
62C24×C5—21no—
63C24×C5—22no—
64C24×C5—41no—
65C24×C5—42no—
66C24×C5—41no—
67C24×C5—81no—
68C24×C5C22×C411yescharacteristic
69C22×C4×C5—22no—
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—21no—
73C22×C4×C5—21no—
74C22×C4×C5—21no—
75C22×C4×C5—41no—
76C22×C4×C5—41no—
77C22×C4×C5—81no—
78C22×C4×C5C22⋊C411yescharacteristic
79C22×C4×C5C22⋊C411yescharacteristic
80C22×C4×C5C22⋊C411yescharacteristic
81C22×C4×C5C22⋊C411yescharacteristic
82C22×C4×C5C2×D411yescharacteristic
83C22×C4×C5C2×D411yescharacteristic
84C5×C4⋊C4—41no—
85C5×C4⋊C4—41no—
86C5×C4⋊C4—81no—
87C5×C4⋊C4—81no—
88C5×C22⋊C4—22no—
89C5×C22⋊C4—41no—
90C5×C22⋊C4—41no—
91C5×C22⋊C4—42no—
92C5×C22⋊C4—42no—
93C5×C22⋊C4—42no—
94C5×C22⋊C4—41no—
95C5×C22⋊C4—41no—
96C5×C22⋊C4—41no—
97C5×C22⋊C4—81no—
98C5×C22⋊C4—81no—
99C42×C5—21no—
100C42×C5—21no—
101C42×C5—21no—
102C42×C5—21no—
103C2×#168—42no—
104C2×#168—42no—
105C2×#117C2×D511yescharacteristic
106C22×C22⋊C4Dic511yescharacteristic
107#432—101no—
108#431—101no—
109#399—21no—
110#397—21no—
111#388—21no—
112#388—21no—
113#385Dic511yescharacteristic
114#385C2×D511yescharacteristic
115#381Dic511yescharacteristic
116#379Dic511yescharacteristic
117#379C2×D511yescharacteristic
118#324—101no—
119#324—101no—
120#323—52no—
121#323—52no—
122C23×C5—21no—
123C23×C5—21no—
124C23×C5—22no—
125C23×C5—41no—
126C23×C5—41no—
127C23×C5—41no—
128C23×C5—41no—
129C23×C5—41no—
130C23×C5—42no—
131C23×C5—42no—
132C23×C5—41no—
133C23×C5—41no—
134C23×C5—41no—
135C23×C5—82no—
136C23×C5—84no—
137C23×C5—84no—
138C23×C5—82no—
139C23×C5C2×C22⋊C411yescharacteristic
140C23×C5#13112yes—
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—21no—
150C2×C4×C5—42no—
151C2×C4×C5—42no—
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—41no—
159C2×C4×C5—41no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—41no—
163C2×C4×C5—41no—
164C2×C4×C5—41no—
165C2×C4×C5—82no—
166C2×C4×C5#9911yescharacteristic
167C2×C4×C5#9911yescharacteristic
168#168—82no—
169#168—82no—
170C25C2×Dic511yescharacteristic
171C23×C4C2×Dic511yescharacteristic
172C23×C4C2×Dic511yescharacteristic
173#117—41no—
174#117—41no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4C22⋊D511yescharacteristic
178C2×C4⋊C4C22⋊D511yescharacteristic
179C2×C22⋊C4—21no—
180C2×C22⋊C4—21no—
181C2×C22⋊C4—21no—
182C2×C22⋊C4—21no—
183C2×C22⋊C4—21no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4—41no—
186C2×C22⋊C4—41no—
187C2×C22⋊C4C2×Dic511yescharacteristic
188C2×C22⋊C4C2×Dic511yescharacteristic
189C2×C22⋊C4C2×Dic511yescharacteristic
190C2×C22⋊C4C22×D511yescharacteristic
191C2×C42C22⋊D511yescharacteristic
192C2×C42C22⋊D511yescharacteristic
193C4⋊C8—201no—
194C4⋊C8—201no—
195C22⋊C8—102no—
196C22⋊C8—102no—
197#97—201no—
198C4×C8—201no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95—21no—
203C22×C5—21no—
204C22×C5—21no—
205C22×C5—22no—
206C22×C5—42no—
207C22×C5—42no—
208C22×C5—42no—
209C22×C5—42no—
210C22×C5—41no—
211C22×C5—41no—
212C22×C5—42no—
213C22×C5—81no—
214C22×C5—81no—
215C22×C5—84no—
216C22×C5—84no—
217C22×C5—81no—
218C22×C5—81no—
219C22×C5#40811yescharacteristic
220C22×C5C2×#9911yescharacteristic
221C22×C5#41311yescharacteristic
222C4×C5—21no—
223C4×C5—21no—
224C4×C5—41no—
225C4×C5—41no—
226C4×C5—41no—
227C4×C5—41no—
228C4×C5—41no—
229C4×C5—81no—
230C4×C5—81no—
231C4×C5—81no—
232C24—21no—
233C24—22no—
234C24—41no—
235C24—42no—
236C24—41no—
237C24—81no—
238C24C22×Dic511yescharacteristic
239C22×C4—22no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—21no—
244C22×C4—21no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—81no—
248C22×C4C22⋊Dic511yescharacteristic
249C22×C4C22⋊Dic511yescharacteristic
250C22×C4C22⋊Dic511yescharacteristic
251C22×C4C22⋊Dic511yescharacteristic
252C22×C4C2×C22⋊D511yescharacteristic
253C22×C4C2×C22⋊D511yescharacteristic
254C2×C8—202no—
255C2×C8—202no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—81no—
259C4⋊C4—81no—
260C22⋊C4—22no—
261C22⋊C4—41no—
262C22⋊C4—41no—
263C22⋊C4—42no—
264C22⋊C4—42no—
265C22⋊C4—42no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—41no—
269C22⋊C4—81no—
270C22⋊C4—81no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—21no—
275C2×C5—21no—
276C2×C5—21no—
277C2×C5—42no—
278C2×C5—82no—
279C2×C5#146811yescharacteristic
280C2×C5#212011yescharacteristic
281C2×C5#212211yescharacteristic
282C23—21no—
283C23—21no—
284C23—22no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23—42no—
291C23—42no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—82no—
296C23—84no—
297C23—84no—
298C23—82no—
299C23#409412yes—
300C23C2×C22⋊Dic511yescharacteristic
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—82no—
326C2×C4#396611yescharacteristic
327C2×C4#396611yescharacteristic
328C8—402no—
329C8—402no—
330C5#1154611yescharacteristic, complemented, Sylow
331C22—21no—
332C22—21no—
333C22—22no—
334C22—42no—
335C22—42no—
336C22—42no—
337C22—42no—
338C22—41no—
339C22—41no—
340C22—42no—
341C22—81no—
342C22—81no—
343C22—84no—
344C22—84no—
345C22—81no—
346C22—81no—
347C22C2×#396611yescharacteristic
348C22#6552311yescharacteristic
349C22#6552611yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—81no—
360C2—21no—
361C2—21no—
362C2—42no—
363C2—82no—
364C2#1060249511yescharacteristic
365C2#1060250911yescharacteristic
366C2#1060265211yescharacteristic
subgroupG/H
centerC22C2×#3966
commutatorC24×C5C22×C4
FrattiniC2×C22⋊C4C22×D5
FittingC5×#2482C2
socleC22×C5C2×#99
prime radicalC25×C5C2×C4
cosocleC2×C5×C22⋊C4C23
hypercenter#2482D5
hypocenterC5#11546
LCSG ▷ C24×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117 ◁ #2482

Complements

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

NH ≅ G/Ntype
2. #10602365C2semidirect
3. #10602364C2semidirect
4. #10598127C2semidirect
330. C5#11546semidirect

Maximal subgroups

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

subgroupindex
C5×#24822
#106023652
#106023642
#105981272
#105981132
#115465