Finite Group Databasebeta

← #11987461

Subgroups — #11987461

Order 1280.

516 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10613800C211yesmaximal, characteristic
2C5×#1749C211yesmaximal, characteristic
3#10602323C211yesmaximal, characteristic
4#10597969C212yesmaximal, complemented
5#10597968C212yesmaximal, complemented
6C22×C42×C5C2211yescharacteristic
7C2×#4072C411yescharacteristic
8C2×#4072C411yescharacteristic
9C2×C5×C22⋊C8—21no—
10C2×C5×#97—21no—
11#65499—21no—
12#65499—21no—
13C2×C22⋊#168—21no—
14C4×#683—21no—
15C4×#683—21no—
16#65217C411yescharacteristic
17#65217C411yescharacteristic
18#65217C2211yescharacteristic
19#65217C2211yescharacteristic
20C2×C4⋊#168—21no—
21C5×#336C2212yes—
22#64744C2212yes—
23#7613—51nomaximal, Sylow
24C23×C4×C5C2×C411yescharacteristic
25C23×C4×C5D411yescharacteristic
26C23×C4×C5D411yescharacteristic
27C22×C5×C8—22no—
28C2×C42×C5—42no—
29C2×C42×C5C2×C411yescharacteristic
30C2×C42×C5D411yescharacteristic
31C2×C42×C5D411yescharacteristic
32C2×C42×C5C2311yescharacteristic
33C2×C22⋊Dic5—21no—
34C2×C22⋊Dic5—21no—
35#4072—22no—
36#4072—22no—
37#4072—42no—
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—
46C2×C4×Dic5—21no—
47C2×C4×Dic5—21no—
48C22×#168—22no—
49C5×C22⋊C8—24no—
50C5×#97—42no—
51#3963—21no—
52#3963—21no—
53#3963—21no—
54#3963—21no—
55C22⋊#168—42no—
56C4⋊#168—42no—
57#2296—51no—
58#1797—51no—
59#1749D511yescharacteristic
60#1271—52no—
61#1271—52no—
62C24×C5C22⋊C411yescharacteristic
63C22×C4×C5—22no—
64C22×C4×C5—22no—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—22no—
68C22×C4×C5—22no—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—41no—
72C22×C4×C5—41no—
73C22×C4×C5—41no—
74C22×C4×C5C22⋊C411yescharacteristic
75C22×C4×C5C22⋊C411yescharacteristic
76C22×C4×C5C22⋊C411yescharacteristic
77C22×C4×C5C22×C411yescharacteristic
78C22×C4×C5C2×D411yescharacteristic
79C22×C4×C5C2×D411yescharacteristic
80C22×Dic5—21no—
81C22×Dic5—21no—
82C22×Dic5—21no—
83C22×Dic5—21no—
84C2×C5×C8—24no—
85C2×C5×C8—42no—
86C2×C5×C8—42no—
87C42×C5—22no—
88C42×C5—22no—
89C42×C5—41no—
90C42×C5—41no—
91C22⋊Dic5—24no—
92C22⋊Dic5—42no—
93C4⋊Dic5—21no—
94C4⋊Dic5—21no—
95C4⋊Dic5—41no—
96C4⋊Dic5—41no—
97C4⋊Dic5M1612yes—
98C4⋊Dic5M1612yes—
99#683—42no—
100#683—42no—
101#683—42no—
102#683—41no—
103#683—41no—
104C4×Dic5—24no—
105C4×Dic5—42no—
106C2×#168—42no—
107C2×#168—42no—
108C2×#168—42no—
109C2×#117—51no—
110C2×#117—51no—
111C22×C42C2×D511yescharacteristic
112C2×C4⋊C8—101no—
113C2×C22⋊C8—21no—
114C2×C22⋊C8—101no—
115C2×#97—21no—
116#389—51no—
117#389—51no—
118#389—51no—
119#389—51no—
120#385—101no—
121#385—101no—
122C4×C4⋊C4—101no—
123C4×C4⋊C4—101no—
124#336—52no—
125#336C2×D512yes—
126C23×C5—21no—
127C23×C5—21no—
128C23×C5—21no—
129C23×C5—21no—
130C23×C5—21no—
131C23×C5—21no—
132C23×C5#10112yes—
133C23×C5C2×C22⋊C411yescharacteristic
134C2×C4×C5—24no—
135C2×C4×C5—24no—
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—21no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—44no—
150C2×C4×C5—42no—
151C2×C4×C5—42no—
152C2×C4×C5#9912yes—
153C2×C4×C5#10412yes—
154C2×C4×C5C2×M1611yescharacteristic
155C2×C4×C5C2×M1611yescharacteristic
156C2×C4×C5#13512yes—
157C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
158C2×C4×C5#13711yescharacteristic
159C2×Dic5—22no—
160C2×Dic5—22no—
161C2×Dic5—41no—
162C2×Dic5—41no—
163C2×Dic5—41no—
164C2×Dic5—41no—
165C2×Dic5—41no—
166C2×Dic5—41no—
167C2×Dic5—41no—
168C2×Dic5—41no—
169C2×Dic5—41no—
170C2×Dic5—41no—
171C5×C8—44no—
172#168—82no—
173C23×C4C4×D511yescharacteristic
174C23×C4D2011yescharacteristic
175C23×C4C22⋊D511yescharacteristic
176C22×C8—22no—
177C22×C8—102no—
178#117—102no—
179#117—102no—
180#117—202no—
181C2×C4⋊C4—51no—
182C2×C4⋊C4—51no—
183C2×C4⋊C4—51no—
184C2×C4⋊C4—51no—
185C2×C4⋊C4—101no—
186C2×C4⋊C4—101no—
187C2×C4⋊C4—101no—
188C2×C4⋊C4—101no—
189C2×C22⋊C4—101no—
190C2×C22⋊C4—101no—
191C2×C42—42no—
192C2×C42—101no—
193C2×C42—101no—
194C2×C42C4×D511yescharacteristic
195C2×C42D2011yescharacteristic
196C2×C42C22⋊D511yescharacteristic
197C2×C42C22×D511yescharacteristic
198C4⋊C8—202no—
199C22⋊C8—24no—
200C22⋊C8—202no—
201#97—42no—
202#95—101no—
203#95—101no—
204#95—101no—
205#95—101no—
206C22×C5—22no—
207C22×C5—22no—
208C22×C5—22no—
209C22×C5—41no—
210C22×C5—41no—
211C22×C5—41no—
212C22×C5—41no—
213C22×C5#40711yescharacteristic
214C22×C5C2×#9911yescharacteristic
215C22×C5C2×#10111yescharacteristic
216C22×C5#41611yescharacteristic
217C22×C5#41711yescharacteristic
218C22×C5C2×#10411yescharacteristic
219C22×C5#42111yescharacteristic
220C4×C5—22no—
221C4×C5—21no—
222C4×C5—21no—
223C4×C5—22no—
224C4×C5—22no—
225C4×C5—21no—
226C4×C5—21no—
227C4×C5—41no—
228Dic5—42no—
229Dic5—42no—
230Dic5—81no—
231Dic5—81no—
232C24#68511yescharacteristic
233C22×C4—22no—
234C22×C4—22no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—101no—
245C22×C4—101no—
246C22×C4—101no—
247C22×C4—101no—
248C22×C4#68511yescharacteristic
249C22×C4#68511yescharacteristic
250C22×C4#68511yescharacteristic
251C22×C4C2×C4×D511yescharacteristic
252C22×C4C2×D2011yescharacteristic
253C22×C4C2×C22⋊D511yescharacteristic
254C2×C8—24no—
255C2×C8—42no—
256C2×C8—42no—
257C2×C8—202no—
258C2×C8—202no—
259C2×C8—202no—
260C4⋊C4—52no—
261C4⋊C4—52no—
262C4⋊C4—101no—
263C4⋊C4—101no—
264C4⋊C4—201no—
265C4⋊C4—201no—
266C4⋊C4—202no—
267C4⋊C4—202no—
268C4⋊C4—202no—
269C4⋊C4—201no—
270C4⋊C4—201no—
271C22⋊C4—104no—
272C22⋊C4—202no—
273C42—22no—
274C42—22no—
275C42—41no—
276C42—41no—
277C42—104no—
278C42—202no—
279C2×C5—42no—
280C2×C5#146311yescharacteristic
281C2×C5#148811yescharacteristic
282C2×C5#148911yescharacteristic
283C2×C5#150111yescharacteristic
284C2×C5#151311yescharacteristic
285C2×C5#153111yescharacteristic
286C2×C5#155211yescharacteristic
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23#395612yes—
294C23C2×#68511yescharacteristic
295C2×C4—24no—
296C2×C4—24no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
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—44no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—102no—
314C2×C4—102no—
315C2×C4—201no—
316C2×C4—201no—
317C2×C4—201no—
318C2×C4—201no—
319C2×C4—201no—
320C2×C4—201no—
321C2×C4—201no—
322C2×C4—201no—
323C2×C4—201no—
324C2×C4—201no—
325C2×C4#393712yes—
326C2×C4#393812yes—
327C2×C4D5×M1611yescharacteristic
328C2×C4D5×M1611yescharacteristic
329C2×C4#405411yescharacteristic
330C2×C4#405511yescharacteristic
331C2×C4#409612yes—
332C8—44no—
333C8—402no—
334C5#761311yescharacteristic, complemented, Sylow
335C22—22no—
336C22—22no—
337C22—22no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22C2×#393711yescharacteristic
343C22C2×#393811yescharacteristic
344C22#6529111yescharacteristic
345C22#6541511yescharacteristic
346C22#6542211yescharacteristic
347C22C2×#395611yescharacteristic
348C22#6542811yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—21no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—41no—
357C4—202no—
358C4—202no—
359C4—401no—
360C4—401no—
361C2—42no—
362C2#1060023611yescharacteristic
363C2#1060059411yescharacteristic
364C2#1060064711yescharacteristic
365C2#1060076411yescharacteristic
366C2#1060077211yescharacteristic
367C2#1060159111yescharacteristic
368C2#1060161311yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1749C2
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1749D5
hypocenterC5#7613
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
4. #10597969C2semidirect
5. #10597968C2semidirect
334. C5#7613semidirect

Maximal subgroups

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

subgroupindex
#106138002
C5×#17492
#106023232
#105979692
#105979682
#76135