Finite Group Databasebeta

← #11987799

Subgroups — #11987799

Order 1280.

530 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10613805C211yesmaximal, characteristic
2C2×C5×#336C211yesmaximal, characteristic
3#10602322C211yesmaximal, characteristic
4#10597969C212yesmaximal, complemented
5#10597968C212yesmaximal, complemented
6C23×C5×C8—21no—
7C22×C42×C5C2211yescharacteristic
8C2×#4016C411yescharacteristic
9#65501C411yescharacteristic
10#65501C411yescharacteristic
11#65499—21no—
12#65499—21no—
13C2×C22⋊#168—21no—
14#65225C411yescharacteristic
15#65222—21no—
16#65222—21no—
17#65217C2211yescharacteristic
18#65217C2211yescharacteristic
19C2×#3935—21no—
20C5×#336—21no—
21C5×#336C2212yes—
22#64744C2212yes—
23#7691—51nomaximal, Sylow
24C23×C4×C5C2×C411yescharacteristic
25C23×C4×C5D411yescharacteristic
26C23×C4×C5D411yescharacteristic
27C22×C5×C8—24no—
28C22×C5×C8—22no—
29C22×C5×C8—42no—
30C22×C5×C8—42no—
31C2×C42×C5—42no—
32C2×C42×C5C2×C411yescharacteristic
33C2×C42×C5D411yescharacteristic
34C2×C42×C5D411yescharacteristic
35C2×C42×C5C2311yescharacteristic
36C2×C22⋊Dic5—21no—
37C2×C22⋊Dic5—21no—
38C2×C4⋊Dic5C2×C411yescharacteristic
39C2×C4⋊Dic5C2×C411yescharacteristic
40C2×C4⋊Dic5C2×C411yescharacteristic
41C2×C4⋊Dic5C2×C411yescharacteristic
42C2×#683—21no—
43C2×#683—21no—
44C2×#683—21no—
45C2×#683—21no—
46C22×#168—22no—
47#4016—42no—
48#3963—21no—
49#3963—21no—
50#3963—21no—
51#3963—21no—
52#3963—21no—
53#3963—21no—
54C22⋊#168—24no—
55#3935—42no—
56#2851—51no—
57#1749—51no—
58C2×#336D511yescharacteristic
59#1271—52no—
60#1271—52no—
61C24×C5C22⋊C411yescharacteristic
62C22×C4×C5—22no—
63C22×C4×C5—22no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5—22no—
67C22×C4×C5—22no—
68C22×C4×C5—22no—
69C22×C4×C5—22no—
70C22×C4×C5—41no—
71C22×C4×C5—41no—
72C22×C4×C5C22⋊C411yescharacteristic
73C22×C4×C5C22⋊C411yescharacteristic
74C22×C4×C5C22⋊C411yescharacteristic
75C22×C4×C5C22×C411yescharacteristic
76C22×C4×C5C2×D411yescharacteristic
77C22×C4×C5C2×D411yescharacteristic
78C22×Dic5—21no—
79C22×Dic5—21no—
80C22×Dic5—21no—
81C22×Dic5—21no—
82C2×C5×C8—24no—
83C2×C5×C8—48no—
84C2×C5×C8—42no—
85C2×C5×C8—42no—
86C42×C5—22no—
87C42×C5—22no—
88C42×C5—41no—
89C42×C5—41no—
90C22⋊Dic5—42no—
91C22⋊Dic5—42no—
92C4⋊Dic5—22no—
93C4⋊Dic5—22no—
94C4⋊Dic5—41no—
95C4⋊Dic5—41no—
96#683—42no—
97#683—42no—
98#683—42no—
99#683—41no—
100#683—41no—
101C2×#168—24no—
102C2×#168—42no—
103C2×#168—42no—
104C23×C8—21no—
105C2×#125—51no—
106C22×C42C2×D511yescharacteristic
107C2×C22⋊C8—101no—
108C2×#97—101no—
109#389—51no—
110#389—51no—
111#387—101no—
112#387—101no—
113#385—101no—
114#385—101no—
115#382—51no—
116#380—51no—
117#380—51no—
118#336—21no—
119#336—52no—
120#336C2×D512yes—
121C23×C5—21no—
122C23×C5—21no—
123C23×C5—21no—
124C23×C5—21no—
125C23×C5#10112yes—
126C23×C5#10412yes—
127C23×C5#10412yes—
128C23×C5C2×C22⋊C411yescharacteristic
129C2×C4×C5—24no—
130C2×C4×C5—24no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—21no—
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—21no—
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—44no—
146C2×C4×C5—44no—
147C2×C4×C5#9912yes—
148C2×C4×C5#13112yes—
149C2×C4×C5#13512yes—
150C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
151C2×C4×C5#13711yescharacteristic
152C2×Dic5—41no—
153C2×Dic5—41no—
154C2×Dic5—41no—
155C2×Dic5—41no—
156C2×Dic5—41no—
157C2×Dic5—41no—
158C2×Dic5—41no—
159C2×Dic5—41no—
160C2×Dic5—41no—
161C2×Dic5—41no—
162C2×Dic5—41no—
163C2×Dic5—41no—
164C5×C8—44no—
165#168—44no—
166C23×C4C4×D511yescharacteristic
167C23×C4D2011yescharacteristic
168C23×C4C22⋊D511yescharacteristic
169C22×C8—24no—
170C22×C8—22no—
171C22×C8—42no—
172C22×C8—42no—
173C22×C8—102no—
174#125—202no—
175C2×C4⋊C4—51no—
176C2×C4⋊C4—51no—
177C2×C4⋊C4—51no—
178C2×C4⋊C4—51no—
179C2×C4⋊C4—101no—
180C2×C4⋊C4—101no—
181C2×C4⋊C4—101no—
182C2×C4⋊C4—101no—
183C2×C22⋊C4—101no—
184C2×C22⋊C4—101no—
185C2×C42—42no—
186C2×C42C4×D511yescharacteristic
187C2×C42D2011yescharacteristic
188C2×C42C22⋊D511yescharacteristic
189C2×C42C22×D511yescharacteristic
190C22⋊C8—104no—
191#97—202no—
192#95—101no—
193#95—101no—
194#95—101no—
195#95—101no—
196#95—101no—
197#95—101no—
198C22×C5—22no—
199C22×C5—22no—
200C22×C5—22no—
201C22×C5—22no—
202C22×C5—22no—
203C22×C5—22no—
204C22×C5#33014yes—
205C22×C5#40811yescharacteristic
206C22×C5C2×#9911yescharacteristic
207C22×C5C2×#10111yescharacteristic
208C22×C5#41611yescharacteristic
209C22×C5#41711yescharacteristic
210C22×C5C2×#10411yescharacteristic
211C22×C5C2×#10411yescharacteristic
212C4×C5—22no—
213C4×C5—22no—
214C4×C5—21no—
215C4×C5—22no—
216C4×C5—21no—
217C4×C5—41no—
218C4×C5—41no—
219Dic5—81no—
220Dic5—81no—
221Dic5—81no—
222Dic5—81no—
223C24#68511yescharacteristic
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—21no—
227C22×C4—21no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—101no—
235C22×C4—101no—
236C22×C4—101no—
237C22×C4—101no—
238C22×C4#68511yescharacteristic
239C22×C4#68511yescharacteristic
240C22×C4#68511yescharacteristic
241C22×C4C2×C4×D511yescharacteristic
242C22×C4C2×D2011yescharacteristic
243C22×C4C2×C22⋊D511yescharacteristic
244C2×C8—24no—
245C2×C8—48no—
246C2×C8—42no—
247C2×C8—42no—
248C2×C8—104no—
249C2×C8—202no—
250C2×C8—202no—
251C4⋊C4—102no—
252C4⋊C4—102no—
253C4⋊C4—201no—
254C4⋊C4—201no—
255C4⋊C4—202no—
256C4⋊C4—202no—
257C4⋊C4—202no—
258C4⋊C4—201no—
259C4⋊C4—201no—
260C22⋊C4—202no—
261C22⋊C4—202no—
262C42—22no—
263C42—22no—
264C42—41no—
265C42—41no—
266C2×C5—24no—
267C2×C5#147211yescharacteristic
268C2×C5#148311yescharacteristic
269C2×C5#149411yescharacteristic
270C2×C5#150111yescharacteristic
271C2×C5#150411yescharacteristic
272C2×C5C2×#33011yescharacteristic
273C2×C5#155211yescharacteristic
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23#393712yes—
279C23#395612yes—
280C23#395712yes—
281C23C2×#68511yescharacteristic
282C2×C4—24no—
283C2×C4—24no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—44no—
299C2×C4—44no—
300C2×C4—201no—
301C2×C4—201no—
302C2×C4—201no—
303C2×C4—201no—
304C2×C4—201no—
305C2×C4—201no—
306C2×C4—201no—
307C2×C4—201no—
308C2×C4—201no—
309C2×C4—201no—
310C2×C4—201no—
311C2×C4—201no—
312C2×C4#393812yes—
313C2×C4#404712yes—
314C2×C4#405012yes—
315C2×C4#407811yescharacteristic
316C2×C4#408811yescharacteristic
317C8—44no—
318C8—204no—
319C5#769111yescharacteristic, complemented, Sylow
320C22—22no—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—22no—
325C22—22no—
326C22#6468514yes—
327C22C2×#393711yescharacteristic
328C22C2×#393811yescharacteristic
329C22#6525511yescharacteristic
330C22#6539911yescharacteristic
331C22#6540211yescharacteristic
332C22C2×#395611yescharacteristic
333C22C2×#395711yescharacteristic
334C4—22no—
335C4—22no—
336C4—21no—
337C4—22no—
338C4—21no—
339C4—41no—
340C4—41no—
341C4—401no—
342C4—401no—
343C4—401no—
344C4—401no—
345C2—24no—
346C2#1060019111yescharacteristic
347C2#1060052911yescharacteristic
348C2C2×#6468511yescharacteristic
349C2#1060071611yescharacteristic
350C2#1060073511yescharacteristic
351C2#1060122011yescharacteristic
352C2#1060123211yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC2×C5×#336C2
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C22⋊C4
cosocleC2×C42×C5C23
hypercenterC2×#336D5
hypocenterC5#7691
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
4. #10597969C2semidirect
5. #10597968C2semidirect
319. C5#7691semidirect

Maximal subgroups

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

subgroupindex
#106138052
C2×C5×#3362
#106023222
#105979692
#105979682
#76915