Finite Group Databasebeta

← #11995963

Subgroups — #11995963

Order 1280.

422 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 109 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#10611044C211yesmaximal, characteristic
2#10610211C211yesmaximal, characteristic
3#10601586C211yesmaximal, characteristic
4#10601573C211yesmaximal, characteristic
5#10600621C211yesmaximal, characteristic
6C5×#1275C211yesmaximal, characteristic
7#10598229C211yesmaximal, characteristic
8#65804C2211yescharacteristic
9C2×#4015C2211yescharacteristic
10C5×#431C2211yescharacteristic
11C5×#431C2211yescharacteristic
12C2×C5×#97C2211yescharacteristic
13#65391—21no—
14#65390—21no—
15#65225C2211yescharacteristic
16#65213C2211yescharacteristic
17#65138—22no—
18#65028—22no—
19#64990—22no—
20#64990—22no—
21#64988C412yescomplemented
22#64970C412yescomplemented
23#64771—21no—
24#64771—21no—
25#64702—22no—
26#64687—22no—
27#9290—51nomaximal, Sylow
28C22×Dic10—21no—
29C22×C5×C8D411yescharacteristic
30C22×C5×C8D411yescharacteristic
31C2×C42×C5C2311yescharacteristic
32#4072—21no—
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5—21no—
36#4070—21no—
37#4070D412yes—
38C2×#681—21no—
39C2×Dic20—24no—
40#4016—21no—
41#4015—21no—
42#4015—21no—
43#4015—21no—
44#4015C2×C412yes—
45#4015C2×C411yescharacteristic
46#4015C2×C411yescharacteristic
47C4×Dic10—21no—
48C4×Dic10D412yes—
49C5×C4⋊C8—21no—
50C5×C4⋊C8—21no—
51C5×C22⋊C8—21no—
52C5×C22⋊C8—21no—
53C5×#97—21no—
54C5×#97—21no—
55C4×C5×C8—21no—
56C4×C5×C8C2×C412yes—
57#3963—21no—
58#3963—21no—
59#3948—24no—
60#3947—22no—
61#3946—24no—
62C8×Dic5—22no—
63C4⋊#168—21no—
64C4⋊#168D412yes—
65#3209—51no—
66#2961—51no—
67#1993—51no—
68#1549—51no—
69#1518—51no—
70#1286—51no—
71#1275D511yescharacteristic
72C22×C4×C5C2×D411yescharacteristic
73C22×C4×C5C2×D411yescharacteristic
74C22×C4×C5#4111yescharacteristic
75C22×Dic5—41no—
76C22×Dic5—41no—
77C2×Dic10—22no—
78C2×Dic10—21no—
79C2×Dic10—41no—
80C2×Dic10—82no—
81C2×Dic10C22⋊C412yes—
82C2×C5×C8—21no—
83C2×C5×C8—21no—
84C2×C5×C8—22no—
85C2×C5×C8—21no—
86C2×C5×C8—21no—
87C2×C5×C8—21no—
88C2×C5×C8—41no—
89C2×C5×C8Q1612yescomplemented
90C42×C5C22×C411yescharacteristic
91C42×C5C2×D411yescharacteristic
92C42×C5C2×D411yescharacteristic
93C42×C5#4111yescharacteristic
94C22⋊Dic5—22no—
95C4⋊Dic5—21no—
96C4⋊Dic5—21no—
97C4⋊Dic5—21no—
98C4⋊Dic5—22no—
99C4⋊Dic5—22no—
100C4⋊Dic5—41no—
101C4⋊Dic5—41no—
102C4⋊Dic5—41no—
103C4⋊Dic5—41no—
104C4⋊Dic5C22⋊C412yes—
105#683—22no—
106#683—22no—
107C4×Dic5—22no—
108#681—41no—
109#681—41no—
110C2×#168—22no—
111Dic20—84no—
112#533—51no—
113C2×C4⋊Q8—51no—
114#494—52no—
115#487—52no—
116#462—102no—
117#451—102no—
118#446—102no—
119#446—102no—
120#431C2×D511yescharacteristic
121#431C2×D511yescharacteristic
122#424—101no—
123#423—51no—
124#405—101no—
125C2×#97C2×D511yescharacteristic
126#382—51no—
127#340—101no—
128#340—101no—
129#332—102no—
130#328—102no—
131C23×C5#12111yescharacteristic
132C2×C4×C5—41no—
133C2×C4×C5—41no—
134C2×C4×C5C2×C22⋊C411yescharacteristic
135C2×C4×C5C4×D411yescharacteristic
136C2×C4×C5C4×D411yescharacteristic
137C2×C4×C5#12011yescharacteristic
138C2×C4×C5#12111yescharacteristic
139C2×C4×C5#12311yescharacteristic
140C2×C4×C5C2×Q1611yescharacteristic
141C2×C4×C5#13511yescharacteristic
142C2×C4×C5#13711yescharacteristic
143C2×C4×C5#13711yescharacteristic
144C2×Dic5—22no—
145C2×Dic5—22no—
146C2×Dic5—42no—
147C2×Dic5—82no—
148C2×Dic5—81no—
149C2×Dic5—81no—
150C2×Dic5—81no—
151Dic10—42no—
152Dic10—44no—
153Dic10—81no—
154Dic10—82no—
155C5×C8—22no—
156C5×C8—42no—
157C5×C8—41no—
158C5×C8—81no—
159#168—42no—
160C22×Q8—101no—
161C2×Q16—104no—
162C2×M16—101no—
163C22×C8D2011yescharacteristic
164C22×C8D2011yescharacteristic
165C4⋊Q8—51no—
166C4⋊Q8—51no—
167C4⋊Q8—52no—
168C4⋊Q8—101no—
169C4⋊Q8—101no—
170C4⋊Q8—101no—
171#125—101no—
172C22⋊Q8—52no—
173C22⋊Q8—101no—
174C4×Q8—52no—
175C4×Q8—101no—
176#117—101no—
177C2×C4⋊C4—101no—
178C2×C4⋊C4—101no—
179C2×C4⋊C4—101no—
180C2×C42C22×D511yescharacteristic
181C4⋊C8—21no—
182C4⋊C8—21no—
183C4⋊C8—52no—
184C4⋊C8—104no—
185C4⋊C8—101no—
186#103—104no—
187C22⋊C8—21no—
188C22⋊C8—21no—
189#97—21no—
190#97—21no—
191#97—102no—
192C4×C8—21no—
193C4×C8—102no—
194C4×C8C4×D512yes—
195#95—101no—
196#95—101no—
197C22×C5—21no—
198C22×C5—21no—
199C22×C5#38611yescharacteristic
200C22×C5#46211yescharacteristic
201C22×C5#46411yescharacteristic
202C4×C5—21no—
203C4×C5—21no—
204C4×C5—21no—
205C4×C5—21no—
206C4×C5C4×Q1611yescharacteristic
207C4×C5#44111yescharacteristic
208C4×C5#45111yescharacteristic
209C4×C5#45211yescharacteristic
210Dic5—42no—
211Dic5—42no—
212Dic5—82no—
213Dic5—161no—
214C2×Q8—52no—
215C2×Q8—101no—
216C2×Q8—102no—
217C2×Q8—201no—
218C2×Q8—402no—
219C22×C4—201no—
220C22×C4—201no—
221C22×C4C2×D2011yescharacteristic
222C22×C4D4×D511yescharacteristic
223C22×C4#71311yescharacteristic
224Q16—404no—
225M16—201no—
226M16—201no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—22no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—21no—
233C2×C8—41no—
234C2×C8—102no—
235C2×C8Dic2012yescomplemented
236C4⋊C4—52no—
237C4⋊C4—101no—
238C4⋊C4—101no—
239C4⋊C4—102no—
240C4⋊C4—101no—
241C4⋊C4—102no—
242C4⋊C4—102no—
243C4⋊C4—102no—
244C4⋊C4—201no—
245C4⋊C4—201no—
246C4⋊C4—201no—
247C4⋊C4—201no—
248C22⋊C4—102no—
249C42—102no—
250C42C2×C4×D511yescharacteristic
251C42#70911yescharacteristic
252C42D4×D511yescharacteristic
253C42D4×D511yescharacteristic
254C2×C5—21no—
255C2×C5—21no—
256C2×C5#187811yescharacteristic
257C2×C5#190211yescharacteristic
258C2×C5#191011yescharacteristic
259C23#404111yescharacteristic
260Q8—202no—
261Q8—204no—
262Q8—401no—
263Q8—402no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—102no—
267C2×C4—102no—
268C2×C4—202no—
269C2×C4—402no—
270C2×C4—401no—
271C2×C4—401no—
272C2×C4—401no—
273C2×C4C4×D2011yescharacteristic
274C2×C4D5×C22⋊C411yescharacteristic
275C2×C4#402811yescharacteristic
276C2×C4#403011yescharacteristic
277C2×C4#403911yescharacteristic
278C2×C4#404011yescharacteristic
279C2×C4#405011yescharacteristic
280C2×C4C2×Dic2011yescharacteristic
281C2×C4#405511yescharacteristic
282C2×C4#405511yescharacteristic
283C8—22no—
284C8—42no—
285C8—41no—
286C8—81no—
287C8—202no—
288C5#929011yescharacteristic, complemented, Sylow
289C22—21no—
290C22—21no—
291C22#6495411yescharacteristic
292C22#6513411yescharacteristic
293C22#6513811yescharacteristic
294C4—21no—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—202no—
299C4—202no—
300C4—402no—
301C4—801no—
302C4C4×Dic2011yescharacteristic
303C4#6500511yescharacteristic
304C4#6502211yescharacteristic
305C4#6502811yescharacteristic
306C2—21no—
307C2—21no—
308C2#1059947811yescharacteristic
309C2#1059950611yescharacteristic
310C2#1059951811yescharacteristic
subgroupG/H
centerC22#64954
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1275C2
socleC22×C5#386
prime radicalC23×C5#121
cosocleC2×C42×C5C23
hypercenter#1275D5
hypocenterC5#9290
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1275

Complements

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

NH ≅ G/Ntype
21. #64988C4semidirect
22. #64970C4semidirect
89. C2×C5×C8Q16semidirect
235. C2×C8Dic20semidirect
288. C5#9290semidirect

Maximal subgroups

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

subgroupindex
#106110442
#106102112
#106015862
#106015732
#106006212
C5×#12752
#105982292
#92905