Finite Group Databasebeta

← #11995981

Subgroups — #11995981

Order 1280.

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

normal subgroups only

This group has 426 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#10614954C211yesmaximal, characteristic
2#10610211C211yesmaximal, characteristic
3C5×#1960C211yesmaximal, characteristic
4#10602566C211yesmaximal, characteristic
5#10600339C211yesmaximal, characteristic
6#10598151C211yesmaximal, characteristic
7#10598122C211yesmaximal, characteristic
8C2×C5×C4⋊Q8C2211yescharacteristic
9#65804C2211yescharacteristic
10C2×C5×#103—21no—
11C2×C5×#103—21no—
12C2×C5×#97C2211yescharacteristic
13C5×#382C2211yescharacteristic
14#65391—21no—
15#65390—21no—
16#65383—22no—
17#65382C412yescomplemented
18#65368C412yescomplemented
19#65260—22no—
20#65214C2211yescharacteristic
21#65214C2211yescharacteristic
22#65213C2211yescharacteristic
23#64990—22no—
24#64990—22no—
25#64767—22no—
26#64672—22no—
27#9292—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×#103—42no—
49C5×#103—42no—
50C5×#97—21no—
51C5×#97—21no—
52C5×#95—21no—
53C5×#95—21no—
54C22⋊#168—21no—
55C22⋊#168—21no—
56#3947—22no—
57#3946—24no—
58C8×Dic5—22no—
59#3942—24no—
60#3940—24no—
61C4⋊#168—21no—
62C4⋊#168—21no—
63C4⋊#168—21no—
64C4⋊#168D412yes—
65C4×#168—21no—
66C4×#168C2×C412yes—
67#3229—51no—
68#2961—51no—
69#1960D511yescharacteristic
70#1546—51no—
71#1518—51no—
72#1286—51no—
73#1275—51no—
74C2×C5×Q8—22no—
75C2×C5×Q8—41no—
76C2×C5×Q8—41no—
77C2×C5×Q8—41no—
78C2×C5×Q8—41no—
79C2×C5×Q8—41no—
80C22×C4×C5—41no—
81C22×C4×C5—41no—
82C22×C4×C5C2×D411yescharacteristic
83C22×C4×C5C2×D411yescharacteristic
84C22×C4×C5#4111yescharacteristic
85C2×Dic10—21no—
86C2×Dic10C22⋊C412yes—
87C2×C5×C8—21no—
88C2×C5×C8—21no—
89C2×C5×C8—21no—
90C2×C5×C8—21no—
91C2×C5×C8—21no—
92C2×C5×C8SD1612yes—
93C5×C4⋊C4—22no—
94C5×C4⋊C4—22no—
95C5×C4⋊C4—41no—
96C5×C4⋊C4—41no—
97C5×C4⋊C4—41no—
98C5×C4⋊C4—41no—
99C42×C5C22×C411yescharacteristic
100C42×C5C2×D411yescharacteristic
101C42×C5C2×D411yescharacteristic
102C42×C5#4111yescharacteristic
103C22⋊Dic5—22no—
104C4⋊Dic5—21no—
105C4⋊Dic5—21no—
106C4⋊Dic5—21no—
107C4⋊Dic5C22⋊C412yes—
108#683—22no—
109#683—22no—
110C4×Dic5—22no—
111#681—41no—
112#681—41no—
113C2×#168—22no—
114C2×#168—22no—
115C2×#168—41no—
116#533—51no—
117C2×C4⋊Q8C2×D511yescharacteristic
118#498—52no—
119#487—52no—
120#483—102no—
121#475—102no—
122#446—102no—
123#446—102no—
124#431—51no—
125#431—51no—
126#424—101no—
127#423—51no—
128C2×#103—21no—
129C2×#103—21no—
130#405—101no—
131C2×#97C2×D511yescharacteristic
132#382C2×D511yescharacteristic
133#332—102no—
134#328—102no—
135C23×C5#12111yescharacteristic
136C5×Q8—42no—
137C5×Q8—42no—
138C5×Q8—81no—
139C5×Q8—81no—
140C2×C4×C5—41no—
141C2×C4×C5—41no—
142C2×C4×C5—42no—
143C2×C4×C5—81no—
144C2×C4×C5—81no—
145C2×C4×C5—81no—
146C2×C4×C5—81no—
147C2×C4×C5—81no—
148C2×C4×C5C2×C22⋊C411yescharacteristic
149C2×C4×C5C4×D411yescharacteristic
150C2×C4×C5C4×D411yescharacteristic
151C2×C4×C5#12011yescharacteristic
152C2×C4×C5#12111yescharacteristic
153C2×C4×C5#12311yescharacteristic
154C2×C4×C5C2×SD1611yescharacteristic
155C2×C4×C5#13511yescharacteristic
156C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
157C2×C4×C5#13711yescharacteristic
158C2×Dic5—22no—
159C2×Dic5—22no—
160Dic10—42no—
161Dic10—81no—
162C5×C8—22no—
163C5×C8—41no—
164#168—42no—
165#168—42no—
166#168—81no—
167C22×Q8—21no—
168C2×M16—101no—
169C22×C8C22⋊D511yescharacteristic
170C22×C8C22⋊D511yescharacteristic
171C4⋊Q8—21no—
172C4⋊Q8—21no—
173C4⋊Q8—21no—
174C4⋊Q8—51no—
175C4⋊Q8—51no—
176C4⋊Q8C4×D512yes—
177#125—101no—
178C22⋊Q8—52no—
179C22⋊Q8—101no—
180C4×Q8—52no—
181C4×Q8—101no—
182#117—101no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—21no—
186C2×C42C22×D511yescharacteristic
187#106—104no—
188C4⋊C8—52no—
189C4⋊C8—104no—
190C4⋊C8—101no—
191C4⋊C8—101no—
192C4⋊C8—101no—
193#103—42no—
194#103—42no—
195#103—104no—
196C22⋊C8—101no—
197C22⋊C8—101no—
198#97—21no—
199#97—21no—
200#97—102no—
201C4×C8—52no—
202C4×C8—102no—
203C4×C8—101no—
204#95—21no—
205#95—21no—
206C22×C5—21no—
207C22×C5—21no—
208C22×C5#38611yescharacteristic
209C22×C5#46011yescharacteristic
210C22×C5#46411yescharacteristic
211C4×C5—21no—
212C4×C5—21no—
213C4×C5—21no—
214C4×C5—21no—
215C4×C5—82no—
216C4×C5—161no—
217C4×C5C4×SD1611yescharacteristic
218C4×C5#44011yescharacteristic
219C4×C5#44811yescharacteristic
220C4×C5#44911yescharacteristic
221Dic5—42no—
222Dic5—42no—
223C2×Q8—22no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—52no—
230C2×Q8—101no—
231C22×C4—41no—
232C22×C4—41no—
233C22×C4D4×D511yescharacteristic
234C22×C4#71111yescharacteristic
235C22×C4C2×C22⋊D511yescharacteristic
236M16—201no—
237M16—201no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—102no—
244C2×C8—102no—
245C2×C8—201no—
246C2×C8#68712yes—
247C4⋊C4—22no—
248C4⋊C4—22no—
249C4⋊C4—41no—
250C4⋊C4—41no—
251C4⋊C4—41no—
252C4⋊C4—41no—
253C4⋊C4—52no—
254C4⋊C4—101no—
255C4⋊C4—102no—
256C4⋊C4—102no—
257C4⋊C4—101no—
258C4⋊C4—101no—
259C22⋊C4—102no—
260C42—102no—
261C42C2×C4×D511yescharacteristic
262C42#70911yescharacteristic
263C42D4×D511yescharacteristic
264C42D4×D511yescharacteristic
265C2×C5—21no—
266C2×C5—21no—
267C2×C5#188011yescharacteristic
268C2×C5#190211yescharacteristic
269C2×C5#190911yescharacteristic
270C23#408411yescharacteristic
271Q8—42no—
272Q8—42no—
273Q8—81no—
274Q8—81no—
275Q8—202no—
276Q8—401no—
277C2×C4—41no—
278C2×C4—41no—
279C2×C4—42no—
280C2×C4—81no—
281C2×C4—81no—
282C2×C4—81no—
283C2×C4—81no—
284C2×C4—81no—
285C2×C4—102no—
286C2×C4—102no—
287C2×C4D5×C22⋊C411yescharacteristic
288C2×C4#402711yescharacteristic
289C2×C4#402911yescharacteristic
290C2×C4#403011yescharacteristic
291C2×C4C4×C22⋊D511yescharacteristic
292C2×C4#407811yescharacteristic
293C2×C4C2×#68711yescharacteristic
294C2×C4#408311yescharacteristic
295C2×C4#409611yescharacteristic
296C2×C4#409711yescharacteristic
297C8—22no—
298C8—41no—
299C8—202no—
300C8—202no—
301C8—401no—
302C5#929211yescharacteristic, complemented, Sylow
303C22—21no—
304C22—21no—
305C22#6524511yescharacteristic
306C22#6534311yescharacteristic
307C22#6536411yescharacteristic
308C4—21no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—82no—
313C4—161no—
314C4—202no—
315C4—202no—
316C4C4×#68711yescharacteristic
317C4#6530711yescharacteristic
318C4#6532611yescharacteristic
319C4#6532911yescharacteristic
320C2—21no—
321C2—21no—
322C2#1060045311yescharacteristic
323C2#1060114211yescharacteristic
324C2#1060114311yescharacteristic
subgroupG/H
centerC22#65245
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1960C2
socleC22×C5#386
prime radicalC23×C5#121
cosocleC2×C42×C5C23
hypercenter#1960D5
hypocenterC5#9292
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
17. #65382C4semidirect
18. #65368C4semidirect
302. C5#9292semidirect

Maximal subgroups

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

subgroupindex
#106149542
#106102112
C5×#19602
#106025662
#106003392
#105981512
#105981222
#92925