Finite Group Databasebeta

← #11996845

Subgroups — #11996845

Order 1280.

422 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 95 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#10614962C211yesmaximal, characteristic
2#10614938C211yesmaximal, characteristic
3C5×#1556C211yesmaximal, characteristic
4#10601630C211yesmaximal, characteristic
5#10601630C211yesmaximal, characteristic
6#10598243C211yesmaximal, characteristic
7#10598243C211yesmaximal, characteristic
8C2×C5×C4⋊Q8C2211yescharacteristic
9#65804C2211yescharacteristic
10C5×#432C2211yescharacteristic
11C5×#432C2211yescharacteristic
12#65519—22no—
13#65369—22no—
14#65368C412yescomplemented
15#65367C412yescomplemented
16#65270—22no—
17#65270—22no—
18#65253—22no—
19#65226C2211yescharacteristic
20#65226C2211yescharacteristic
21C4×#681C2211yescharacteristic
22C5×#332—22no—
23#64687—22no—
24#64687—22no—
25#9427—51nomaximal, Sylow
26C22×C5×Q8—21no—
27C5×C4⋊Q8—21no—
28C5×C4⋊Q8—21no—
29C5×C4⋊Q8C2×C412yes—
30C5×C4⋊Q8D412yes—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4D412yes—
33C2×C42×C5C2311yescharacteristic
34#4072—21no—
35C2×C4⋊Dic5—22no—
36#4070—21no—
37#4070—21no—
38C2×C4×Dic5—22no—
39C2×#681—21no—
40#4016—21no—
41#4015C2×C411yescharacteristic
42#4015C2×C411yescharacteristic
43C4×Dic10—21no—
44C4×Dic10—21no—
45C5×C4⋊C8—21no—
46C5×C4⋊C8—21no—
47C5×C22⋊C8—21no—
48C5×C22⋊C8—21no—
49C5×#97—21no—
50C5×#97—21no—
51#3963—24no—
52#3963—21no—
53#3963—21no—
54#3963—21no—
55#3963—21no—
56#3963D412yes—
57#3963D412yes—
58#3940—24no—
59#3939—24no—
60#3935—21no—
61C4×#168C2×C412yes—
62#3165—51no—
63#2381—51no—
64#1556D511yescharacteristic
65#1515—51no—
66#1515—51no—
67#1288—51no—
68#1288—51no—
69C2×C5×Q8—22no—
70C2×C5×Q8—22no—
71C2×C5×Q8—81no—
72C2×C5×Q8—81no—
73C22×C4×C5—22no—
74C22×C4×C5C2×D411yescharacteristic
75C22×C4×C5C2×D411yescharacteristic
76C22×C4×C5C2×D411yescharacteristic
77C22×Dic5—22no—
78C22×Dic5—22no—
79C2×Dic10—21no—
80C2×Dic10—21no—
81C2×C5×C8—41no—
82C2×C5×C8—41no—
83C5×C4⋊C4—22no—
84C5×C4⋊C4—22no—
85C5×C4⋊C4—22no—
86C5×C4⋊C4C22⋊C414yes—
87C42×C5C22×C411yescharacteristic
88C42×C5C2×D411yescharacteristic
89C42×C5#4111yescharacteristic
90C42×C5#4111yescharacteristic
91C22⋊Dic5—41no—
92C4⋊Dic5—21no—
93C4⋊Dic5—21no—
94C4⋊Dic5—21no—
95C4⋊Dic5—21no—
96C4⋊Dic5—82no—
97#683—41no—
98#683—41no—
99C4×Dic5—41no—
100C4×Dic5—82no—
101#681—24no—
102C2×#168—22no—
103#533—51no—
104C2×C4⋊Q8C2×D511yescharacteristic
105#501—102no—
106#500—52no—
107#498—52no—
108#432C2×D511yescharacteristic
109#432C2×D511yescharacteristic
110#428—102no—
111C4×M16—51no—
112#391—102no—
113#387—102no—
114#387—102no—
115#383—51no—
116#383—51no—
117#332—22no—
118#328—102no—
119#328—102no—
120C23×C5#12011yescharacteristic
121C5×Q8—82no—
122C5×Q8—82no—
123C2×C4×C5—22no—
124C2×C4×C5—24no—
125C2×C4×C5—41no—
126C2×C4×C5—41no—
127C2×C4×C5—42no—
128C2×C4×C5—42no—
129C2×C4×C5C2×C22⋊C411yescharacteristic
130C2×C4×C5C4×D411yescharacteristic
131C2×C4×C5C4×D411yescharacteristic
132C2×C4×C5#12111yescharacteristic
133C2×C4×C5#12111yescharacteristic
134C2×C4×C5#12311yescharacteristic
135C2×Dic5—42no—
136C2×Dic5—42no—
137C2×Dic5—42no—
138C2×Dic5—42no—
139C2×Dic5—41no—
140C2×Dic5—41no—
141C2×Dic5—42no—
142C2×Dic5—42no—
143Dic10—81no—
144Dic10—81no—
145C5×C8—81no—
146C5×C8—81no—
147#168—24no—
148C22×Q8—21no—
149C2×M16—101no—
150C4⋊Q8—21no—
151C4⋊Q8—21no—
152C4⋊Q8—51no—
153C4⋊Q8—51no—
154C4⋊Q8C4×D512yes—
155C4⋊Q8C22⋊D512yes—
156#125—101no—
157C22⋊Q8—101no—
158C22⋊Q8—101no—
159C4×Q8—101no—
160C4×Q8—101no—
161#117—101no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—102no—
164C2×C4⋊C4D2012yes—
165C2×C42—102no—
166C2×C42C22×D511yescharacteristic
167#107—104no—
168#106—104no—
169C4⋊C8—21no—
170C4⋊C8—21no—
171C22⋊C8—21no—
172C22⋊C8—21no—
173#97—21no—
174#97—21no—
175#97—101no—
176C4×C8—52no—
177#95—52no—
178#95—52no—
179#95—104no—
180#95—101no—
181#95—101no—
182#95—101no—
183#95—101no—
184C22×C5—21no—
185C22×C5—21no—
186C22×C5#38611yescharacteristic
187C22×C5#45612yes—
188C4×C5—21no—
189C4×C5—21no—
190C4×C5—21no—
191C4×C5—21no—
192C4×C5—21no—
193C4×C5—21no—
194C4×C5—44no—
195Dic5—82no—
196Dic5—82no—
197Dic5—81no—
198Dic5—81no—
199C2×Q8—22no—
200C2×Q8—22no—
201C2×Q8—81no—
202C2×Q8—81no—
203C2×Q8—101no—
204C2×Q8—101no—
205C22×C4—22no—
206C22×C4—102no—
207C22×C4—102no—
208C22×C4C2×D2011yescharacteristic
209C22×C4D4×D511yescharacteristic
210C22×C4D4×D511yescharacteristic
211M16—104no—
212C2×C8—41no—
213C2×C8—41no—
214C2×C8—102no—
215C4⋊C4—22no—
216C4⋊C4—22no—
217C4⋊C4—22no—
218C4⋊C4—101no—
219C4⋊C4—101no—
220C4⋊C4—101no—
221C4⋊C4—101no—
222C4⋊C4—201no—
223C4⋊C4—201no—
224C4⋊C4—402no—
225C4⋊C4#68514yes—
226C22⋊C4—201no—
227C42—201no—
228C42—402no—
229C42C2×C4×D511yescharacteristic
230C42#71111yescharacteristic
231C42#71111yescharacteristic
232C42C2×C22⋊D511yescharacteristic
233C2×C5—22no—
234C2×C5#188611yescharacteristic
235C2×C5#190411yescharacteristic
236C2×C5#190511yescharacteristic
237C23#402811yescharacteristic
238Q8—82no—
239Q8—82no—
240Q8—401no—
241Q8—401no—
242C2×C4—22no—
243C2×C4—24no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4—202no—
249C2×C4—202no—
250C2×C4—202no—
251C2×C4—202no—
252C2×C4—202no—
253C2×C4—202no—
254C2×C4—201no—
255C2×C4—201no—
256C2×C4#402711yescharacteristic
257C2×C4#402711yescharacteristic
258C2×C4#403211yescharacteristic
259C2×C4C2×#68511yescharacteristic
260C2×C4#408511yescharacteristic
261C2×C4#408511yescharacteristic
262C8—81no—
263C8—81no—
264C8—104no—
265C5#942711yescharacteristic, complemented, Sylow
266C22—21no—
267C22—21no—
268C22#6504112yes—
269C22#6524711yescharacteristic
270C4—21no—
271C4—21no—
272C4—21no—
273C4—21no—
274C4—21no—
275C4—21no—
276C4—44no—
277C4—402no—
278C4—402no—
279C4—401no—
280C4—401no—
281C2—22no—
282C2#1060089611yescharacteristic
283C2#1060110711yescharacteristic
284C2#1060112711yescharacteristic
subgroupG/H
centerC22#65247
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1556C2
socleC22×C5#386
prime radicalC23×C5#120
cosocleC2×C42×C5C23
hypercenter#1556D5
hypocenterC5#9427
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1556

Complements

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

NH ≅ G/Ntype
14. #65368C4semidirect
15. #65367C4semidirect
265. C5#9427semidirect

Maximal subgroups

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

subgroupindex
#106149622
#106149382
C5×#15562
#106016302
#105982432
#94275