Finite Group Databasebeta

← #11987492

Subgroups — #11987492

Order 1280.

410 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 101 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#10607697C211yesmaximal, characteristic
2#10599398C211yesmaximal, characteristic
3#10599390C211yesmaximal, characteristic
4C5×#1271C211yesmaximal, characteristic
5#10598129C211yesmaximal, characteristic
6#10597969C211yesmaximal, characteristic
7#10597968C211yesmaximal, characteristic
8C2×#4036C411yescharacteristic
9C5×#389C2211yescharacteristic
10C2×#3947—21no—
11C2×#3946—21no—
12#65267—21no—
13#65266C411yescharacteristic
14C4⋊C4×Dic5—21no—
15C4⋊C4×Dic5C411yescharacteristic
16C4⋊C4×Dic5C411yescharacteristic
17C42×Dic5C2211yescharacteristic
18#65217C2211yescharacteristic
19#64942—21no—
20#64938—21no—
21C5×#336C2211yescharacteristic
22C5×#336C2211yescharacteristic
23#64770—21no—
24#64770—21no—
25#64744C2211yescharacteristic
26#64744C2211yescharacteristic
27#7619—51nomaximal, Sylow
28C22×C5×C8—21no—
29C22×C5×C8—21no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4C2×C411yescharacteristic
32C2×C5×C4⋊C4C2×C411yescharacteristic
33C2×C42×C5C2311yescharacteristic
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5C2×C411yescharacteristic
36C2×C4⋊Dic5C2×C411yescharacteristic
37C2×#683—21no—
38C2×#683—21no—
39C2×C4×Dic5—21no—
40C2×C4×Dic5—21no—
41C2×C4×Dic5C2×C411yescharacteristic
42C2×C4×Dic5C2×C411yescharacteristic
43C2×C4×Dic5D411yescharacteristic
44C2×C4×Dic5D411yescharacteristic
45C2×C4×Dic5D411yescharacteristic
46C2×C4×Dic5D411yescharacteristic
47C22×#168—21no—
48C22×#168—21no—
49#4036—22no—
50#4036—22no—
51C5×#95—21no—
52#3963—21no—
53#3963—21no—
54#3963—21no—
55#3963—21no—
56#3963—21no—
57#3947—24no—
58#3946—42no—
59C4×#125—51no—
60#1831—51no—
61#1745—51no—
62#1271—51no—
63#1271—51no—
64#1271—51no—
65#1271D511yescharacteristic
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5C22×C411yescharacteristic
69C22×C4×C5C2×D411yescharacteristic
70C22×C4×C5C2×D411yescharacteristic
71C22×Dic5—21no—
72C22×Dic5—21no—
73C22×Dic5C22⋊C411yescharacteristic
74C22×Dic5C22⋊C411yescharacteristic
75C22×Dic5C22⋊C411yescharacteristic
76C22×Dic5C22⋊C411yescharacteristic
77C2×C5×C8—22no—
78C2×C5×C8—41no—
79C2×C5×C8—41no—
80C2×C5×C8—41no—
81C2×C5×C8—41no—
82C2×C5×C8—41no—
83C5×C4⋊C4—21no—
84C5×C4⋊C4—41no—
85C5×C4⋊C4—41no—
86C5×C4⋊C4—41no—
87C5×C4⋊C4M1612yes—
88C42×C5—41no—
89C4⋊Dic5—24no—
90C4⋊Dic5—21no—
91C4⋊Dic5—41no—
92C4⋊Dic5M1612yes—
93#683—24no—
94#683—41no—
95#683—41no—
96C4×Dic5—21no—
97C4×Dic5—21no—
98C4×Dic5—21no—
99C4×Dic5—21no—
100C4×Dic5—21no—
101C4×Dic5—21no—
102C4×Dic5—22no—
103C4×Dic5—22no—
104C4×Dic5—41no—
105C4×Dic5—42no—
106C4×Dic5—42no—
107C2×#168—22no—
108C2×#168—41no—
109C2×#168—41no—
110C2×#168—41no—
111C2×#168—41no—
112C2×#168—41no—
113C2×#125—51no—
114C2×C4⋊C8—101no—
115C2×#97—101no—
116#389—51no—
117#389C2×D511yescharacteristic
118#387—101no—
119#387—101no—
120#382—51no—
121C4×C4⋊C4—51no—
122C4×C4⋊C4—51no—
123C4×C4⋊C4—101no—
124C4×C4⋊C4—101no—
125C43—51no—
126#336—51no—
127#336—51no—
128#336—101no—
129#336—101no—
130#336C2×D511yescharacteristic
131#336C2×D511yescharacteristic
132C23×C5C2×C22⋊C411yescharacteristic
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—22no—
140C2×C4×C5—41no—
141C2×C4×C5—41no—
142C2×C4×C5—41no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
145C2×C4×C5C2×M1611yescharacteristic
146C2×C4×C5C2×M1611yescharacteristic
147C2×C4×C5#13511yescharacteristic
148C2×C4×C5#13511yescharacteristic
149C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
150C2×C4×C5#13711yescharacteristic
151C2×Dic5—21no—
152C2×Dic5—21no—
153C2×Dic5—21no—
154C2×Dic5—21no—
155C2×Dic5—21no—
156C2×Dic5—21no—
157C2×Dic5—22no—
158C2×Dic5—21no—
159C2×Dic5—21no—
160C2×Dic5—21no—
161C2×Dic5—21no—
162C2×Dic5—41no—
163C2×Dic5—41no—
164C2×Dic5—41no—
165C2×Dic5—41no—
166C2×Dic5—41no—
167C2×Dic5#10112yes—
168C2×Dic5#10412yes—
169C5×C8—42no—
170C5×C8—81no—
171#168—42no—
172#168—81no—
173C22×C8—21no—
174C22×C8—21no—
175C22×C8—101no—
176C22×C8—101no—
177#125—102no—
178#125—102no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—51no—
181C2×C4⋊C4—51no—
182C2×C4⋊C4—101no—
183C2×C4⋊C4—101no—
184C2×C4⋊C4—101no—
185C2×C4⋊C4C4×D511yescharacteristic
186C2×C4⋊C4C4×D511yescharacteristic
187C2×C42—51no—
188C2×C42—51no—
189C2×C42—51no—
190C2×C42—51no—
191C2×C42—51no—
192C2×C42—51no—
193C2×C42—101no—
194C2×C42—101no—
195C2×C42C22×D511yescharacteristic
196C4⋊C8—202no—
197#97—104no—
198#95—21no—
199#95—101no—
200#95—101no—
201#95—101no—
202#95—101no—
203#95—101no—
204C22×C5#40711yescharacteristic
205C22×C5#41011yescharacteristic
206C22×C5C2×#10111yescharacteristic
207C22×C5#41611yescharacteristic
208C22×C5#41711yescharacteristic
209C22×C5C2×#10411yescharacteristic
210C22×C5#42111yescharacteristic
211C4×C5—21no—
212C4×C5—21no—
213C4×C5—21no—
214C4×C5—21no—
215C4×C5—21no—
216C4×C5—21no—
217C4×C5—42no—
218C4×C5—81no—
219Dic5—22no—
220Dic5—22no—
221Dic5—41no—
222Dic5—41no—
223Dic5—42no—
224Dic5—81no—
225C22×C4—21no—
226C22×C4—21no—
227C22×C4—51no—
228C22×C4—51no—
229C22×C4—51no—
230C22×C4—51no—
231C22×C4—101no—
232C22×C4—101no—
233C22×C4C2×C4×D511yescharacteristic
234C22×C4D4×D511yescharacteristic
235C22×C4D4×D511yescharacteristic
236C2×C8—22no—
237C2×C8—41no—
238C2×C8—41no—
239C2×C8—41no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—102no—
243C2×C8—201no—
244C2×C8—201no—
245C2×C8—201no—
246C2×C8—201no—
247C2×C8—201no—
248C4⋊C4—21no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—52no—
253C4⋊C4—104no—
254C4⋊C4—104no—
255C4⋊C4—101no—
256C4⋊C4—201no—
257C4⋊C4—201no—
258C4⋊C4—201no—
259C4⋊C4#67612yes—
260C42—41no—
261C42—102no—
262C42—102no—
263C42—101no—
264C42—101no—
265C42—101no—
266C42—101no—
267C42—101no—
268C42—101no—
269C42—201no—
270C42—202no—
271C42—202no—
272C2×C5#146711yescharacteristic
273C2×C5#148811yescharacteristic
274C2×C5#148911yescharacteristic
275C2×C5#150011yescharacteristic
276C2×C5#151211yescharacteristic
277C2×C5#152811yescharacteristic
278C2×C5#155211yescharacteristic
279C23D5×C22⋊C411yescharacteristic
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—52no—
293C2×C4—52no—
294C2×C4—101no—
295C2×C4—101no—
296C2×C4—101no—
297C2×C4—101no—
298C2×C4—101no—
299C2×C4—101no—
300C2×C4—101no—
301C2×C4—101no—
302C2×C4—101no—
303C2×C4—101no—
304C2×C4—102no—
305C2×C4—201no—
306C2×C4—201no—
307C2×C4—201no—
308C2×C4—201no—
309C2×C4—201no—
310C2×C4C2×#67611yescharacteristic
311C2×C4D5×M1611yescharacteristic
312C2×C4#405811yescharacteristic
313C2×C4#406011yescharacteristic
314C2×C4#406211yescharacteristic
315C2×C4#406411yescharacteristic
316C8—42no—
317C8—81no—
318C8—202no—
319C8—401no—
320C5#761911yescharacteristic, complemented, Sylow
321C22#6501511yescharacteristic
322C22#6502911yescharacteristic
323C22D5×#10111yescharacteristic
324C22#6506111yescharacteristic
325C22#6509211yescharacteristic
326C22D5×#10411yescharacteristic
327C22#6511011yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4—81no—
336C4—102no—
337C4—102no—
338C4—201no—
339C4—201no—
340C4—202no—
341C4—401no—
342C2#1059892011yescharacteristic
343C2#1059896611yescharacteristic
344C2#1059903111yescharacteristic
345C2#1059906911yescharacteristic
346C2#1059910511yescharacteristic
347C2#1059915611yescharacteristic
348C2#1059921711yescharacteristic
subgroupG/H
centerC23D5×C22⋊C4
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1271C2
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1271D5
hypocenterC5#7619
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1271

Complements

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

NH ≅ G/Ntype
320. C5#7619semidirect

Maximal subgroups

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

subgroupindex
#106076972
#105993982
#105993902
C5×#12712
#105981292
#105979692
#105979682
#76195