Finite Group Databasebeta

← #11995953

Subgroups — #11995953

Order 1280.

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

normal subgroups only

This group has 410 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#10614955C211yesmaximal, characteristic
2#10610211C211yesmaximal, characteristic
3C5×#1993C211yesmaximal, characteristic
4#10602567C211yesmaximal, characteristic
5#10600339C211yesmaximal, characteristic
6#10598151C211yesmaximal, characteristic
7#10598122C211yesmaximal, characteristic
8C2×C5×C4⋊Q8C2211yescharacteristic
9#65804C2211yescharacteristic
10C2×C5×#97C2211yescharacteristic
11C5×#382C2211yescharacteristic
12#65391—21no—
13#65390—21no—
14#65382C412yescomplemented
15#65380—22no—
16#65367C412yescomplemented
17#65259—22no—
18#65214C2211yescharacteristic
19#65214C2211yescharacteristic
20#65213C2211yescharacteristic
21#64990—22no—
22#64990—22no—
23C5×#340—21no—
24C5×#340—21no—
25#64766—22no—
26#64672—22no—
27#9288—51nomaximal, Sylow
28C22×C5×Q8—21no—
29C22×C5×C8D411yescharacteristic
30C22×C5×C8D411yescharacteristic
31C5×C4⋊Q8—21no—
32C5×C4⋊Q8—21no—
33C5×C4⋊Q8—21no—
34C5×C4⋊Q8C2×C412yes—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4—21no—
37C2×C5×C4⋊C4—21no—
38C2×C42×C5C2311yescharacteristic
39#4072—21no—
40#4070—21no—
41#4070D412yes—
42C2×#681—21no—
43#4016—21no—
44#4015C2×C411yescharacteristic
45#4015C2×C411yescharacteristic
46C4×Dic10—21no—
47C4×Dic10D412yes—
48C5×#97—21no—
49C5×#97—21no—
50C5×#95—21no—
51C5×#95—21no—
52C22⋊#168—21no—
53C22⋊#168—21no—
54#3947—22no—
55#3946—24no—
56C8×Dic5—22no—
57#3942—24no—
58#3939—24no—
59C4⋊#168—21no—
60C4⋊#168—21no—
61C4⋊#168—21no—
62C4⋊#168D412yes—
63C4×#168—21no—
64C4×#168C2×C412yes—
65#3230—51no—
66#2961—51no—
67#1993D511yescharacteristic
68#1548—51no—
69#1518—51no—
70#1286—51no—
71#1275—51no—
72C2×C5×Q8—22no—
73C2×C5×Q8—41no—
74C2×C5×Q8—82no—
75C22×C4×C5—41no—
76C22×C4×C5—41no—
77C22×C4×C5C2×D411yescharacteristic
78C22×C4×C5C2×D411yescharacteristic
79C22×C4×C5#4111yescharacteristic
80C2×Dic10—21no—
81C2×Dic10C22⋊C412yes—
82C2×C5×C8—21no—
83C2×C5×C8—21no—
84C2×C5×C8—21no—
85C2×C5×C8—21no—
86C2×C5×C8—21no—
87C2×C5×C8Q1612yes—
88C5×C4⋊C4—22no—
89C5×C4⋊C4—22no—
90C5×C4⋊C4—41no—
91C5×C4⋊C4—41no—
92C5×C4⋊C4—41no—
93C5×C4⋊C4—41no—
94C42×C5C22×C411yescharacteristic
95C42×C5C2×D411yescharacteristic
96C42×C5C2×D411yescharacteristic
97C42×C5#4111yescharacteristic
98C22⋊Dic5—22no—
99C4⋊Dic5—21no—
100C4⋊Dic5—21no—
101C4⋊Dic5—21no—
102C4⋊Dic5C22⋊C412yes—
103#683—22no—
104#683—22no—
105C4×Dic5—22no—
106#681—41no—
107#681—41no—
108C2×#168—22no—
109C2×#168—22no—
110C2×#168—41no—
111#533—51no—
112C2×C4⋊Q8C2×D511yescharacteristic
113#500—52no—
114#487—52no—
115#484—102no—
116#477—102no—
117#446—102no—
118#446—102no—
119#431—51no—
120#431—51no—
121#424—101no—
122#423—51no—
123#405—101no—
124C2×#97C2×D511yescharacteristic
125#382C2×D511yescharacteristic
126#340—21no—
127#340—21no—
128#333—102no—
129#328—102no—
130C23×C5#12111yescharacteristic
131C5×Q8—82no—
132C5×Q8—82no—
133C2×C4×C5—41no—
134C2×C4×C5—41no—
135C2×C4×C5—42no—
136C2×C4×C5—82no—
137C2×C4×C5—81no—
138C2×C4×C5—81no—
139C2×C4×C5—81no—
140C2×C4×C5C2×C22⋊C411yescharacteristic
141C2×C4×C5C4×D411yescharacteristic
142C2×C4×C5C4×D411yescharacteristic
143C2×C4×C5#12011yescharacteristic
144C2×C4×C5#12111yescharacteristic
145C2×C4×C5#12311yescharacteristic
146C2×C4×C5C2×Q1611yescharacteristic
147C2×C4×C5#13511yescharacteristic
148C2×C4×C5#13711yescharacteristic
149C2×C4×C5#13711yescharacteristic
150C2×Dic5—22no—
151C2×Dic5—22no—
152Dic10—42no—
153Dic10—81no—
154C5×C8—22no—
155C5×C8—41no—
156#168—42no—
157#168—42no—
158#168—81no—
159C22×Q8—21no—
160C2×M16—101no—
161C22×C8C22⋊D511yescharacteristic
162C22×C8C22⋊D511yescharacteristic
163C4⋊Q8—21no—
164C4⋊Q8—21no—
165C4⋊Q8—21no—
166C4⋊Q8—51no—
167C4⋊Q8—51no—
168C4⋊Q8C4×D512yes—
169#125—101no—
170C22⋊Q8—52no—
171C22⋊Q8—101no—
172C4×Q8—52no—
173C4×Q8—101no—
174#117—101no—
175C2×C4⋊C4—21no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C42C22×D511yescharacteristic
179#107—104no—
180C4⋊C8—52no—
181C4⋊C8—104no—
182C4⋊C8—101no—
183C4⋊C8—101no—
184C4⋊C8—101no—
185#103—104no—
186C22⋊C8—101no—
187C22⋊C8—101no—
188#97—21no—
189#97—21no—
190#97—102no—
191C4×C8—52no—
192C4×C8—102no—
193C4×C8—101no—
194#95—21no—
195#95—21no—
196C22×C5—21no—
197C22×C5—21no—
198C22×C5#38611yescharacteristic
199C22×C5#46211yescharacteristic
200C22×C5#46411yescharacteristic
201C4×C5—21no—
202C4×C5—21no—
203C4×C5—21no—
204C4×C5—21no—
205C4×C5—82no—
206C4×C5—161no—
207C4×C5C4×Q1611yescharacteristic
208C4×C5#44111yescharacteristic
209C4×C5#45111yescharacteristic
210C4×C5#45211yescharacteristic
211Dic5—42no—
212Dic5—42no—
213C2×Q8—22no—
214C2×Q8—41no—
215C2×Q8—52no—
216C2×Q8—82no—
217C2×Q8—101no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4D4×D511yescharacteristic
221C22×C4#71111yescharacteristic
222C22×C4C2×C22⋊D511yescharacteristic
223M16—201no—
224M16—201no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—102no—
231C2×C8—102no—
232C2×C8—201no—
233C2×C8#68912yes—
234C4⋊C4—22no—
235C4⋊C4—22no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—52no—
241C4⋊C4—101no—
242C4⋊C4—102no—
243C4⋊C4—102no—
244C4⋊C4—101no—
245C4⋊C4—101no—
246C22⋊C4—102no—
247C42—102no—
248C42C2×C4×D511yescharacteristic
249C42#70911yescharacteristic
250C42D4×D511yescharacteristic
251C42D4×D511yescharacteristic
252C2×C5—21no—
253C2×C5—21no—
254C2×C5#187811yescharacteristic
255C2×C5#190311yescharacteristic
256C2×C5#190911yescharacteristic
257C23#408411yescharacteristic
258Q8—82no—
259Q8—82no—
260Q8—202no—
261Q8—401no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—42no—
265C2×C4—82no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—81no—
269C2×C4—102no—
270C2×C4—102no—
271C2×C4D5×C22⋊C411yescharacteristic
272C2×C4#402711yescharacteristic
273C2×C4#402911yescharacteristic
274C2×C4#403011yescharacteristic
275C2×C4C4×C22⋊D511yescharacteristic
276C2×C4#408311yescharacteristic
277C2×C4#408811yescharacteristic
278C2×C4C2×#68911yescharacteristic
279C2×C4#409611yescharacteristic
280C2×C4#409711yescharacteristic
281C8—22no—
282C8—41no—
283C8—202no—
284C8—202no—
285C8—401no—
286C5#928811yescharacteristic, complemented, Sylow
287C22—21no—
288C22—21no—
289C22#6524511yescharacteristic
290C22#6534311yescharacteristic
291C22#6537911yescharacteristic
292C4—21no—
293C4—21no—
294C4—21no—
295C4—21no—
296C4—82no—
297C4—161no—
298C4—202no—
299C4—202no—
300C4C4×#68911yescharacteristic
301C4#6531911yescharacteristic
302C4#6533611yescharacteristic
303C4#6533911yescharacteristic
304C2—21no—
305C2—21no—
306C2#1060048311yescharacteristic
307C2#1060112211yescharacteristic
308C2#1060114311yescharacteristic
subgroupG/H
centerC22#65245
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1993C2
socleC22×C5#386
prime radicalC23×C5#121
cosocleC2×C42×C5C23
hypercenter#1993D5
hypocenterC5#9288
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1993

Complements

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

NH ≅ G/Ntype
14. #65382C4semidirect
16. #65367C4semidirect
286. C5#9288semidirect

Maximal subgroups

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

subgroupindex
#106149552
#106102112
C5×#19932
#106025672
#106003392
#105981512
#105981222
#92885