Finite Group Databasebeta

← #11991064

Subgroups — #11991064

Order 1280.

782 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 782 conjugacy classes of subgroups — too many to draw. Only its 143 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
1C2×#65877C211yesmaximal, characteristic
2C5×#1800C211yesmaximal, characteristic
3#10602394C211yesmaximal, characteristic
4#10601301C212yesmaximal, complemented
5#10601293C212yesmaximal, complemented
6C2×C4×C5×D4C2211yescharacteristic
7C2×D4×Dic5—21no—
8C22×C4⋊Dic5C412yes—
9C2×#4070C412yes—
10#65877—24no—
11#65877—24no—
12C2×#4036—21no—
13C2×#4024—22no—
14C2×#4015C2211yescharacteristic
15C2×C4×Dic10C2211yescharacteristic
16C5×#423C2212yes—
17C2×C5×#100—21no—
18#65214C2212yes—
19C5×#343—21no—
20#64745—22no—
21#64706—24no—
22#64704—24no—
23#8395—51nomaximal, Sylow
24C22×C5×D4D411yescharacteristic
25C23×C4×C5C2×C412yes—
26C23×Dic5—22no—
27C22×Dic10—21no—
28C22×Dic10C2×C411yescharacteristic
29C2×C5×M16—22no—
30C4×C5×D4—22no—
31C4×C5×D4—22no—
32C2×C5×C4⋊C4D411yescharacteristic
33C2×C5×C22⋊C4D412yes—
34C2×C42×C5C2311yescharacteristic
35C2×C22⋊Dic5—22no—
36D4×Dic5—28no—
37C2×C4⋊Dic5—22no—
38C2×C4⋊Dic5—21no—
39C2×C4⋊Dic5—24no—
40C2×C4⋊Dic5—24no—
41C2×C4⋊Dic5C2×C411yescharacteristic
42C2×C4⋊Dic5C2×C412yes—
43#4070—24no—
44#4070—24no—
45C2×#683—22no—
46C2×#683—21no—
47C2×C4×Dic5—21no—
48#4036—28no—
49#4024—216no—
50#4015—22no—
51#4015D414yes—
52C4×Dic10—22no—
53C4×Dic10D414yes—
54C5×C4⋊C8—22no—
55C5×C4⋊C8—22no—
56C5×#100—42no—
57C22⋊#168—22no—
58C4⋊#168—22no—
59C4×#168—22no—
60C2×#554—51no—
61#1800D511yescharacteristic
62#1549—52no—
63#1487—52no—
64#1460—51no—
65C24×C5C22⋊C412yes—
66C2×C5×D4—22no—
67C2×C5×D4—22no—
68C2×C5×D4SD1612yes—
69C2×C5×D4Q1612yes—
70C22×C4×C5—22no—
71C22×C4×C5—22no—
72C22×C4×C5—44no—
73C22×C4×C5C22⋊C412yes—
74C22×C4×C5C22×C411yescharacteristic
75C22×C4×C5C2×D411yescharacteristic
76C22×C4×C5C2×D411yescharacteristic
77C22×Dic5—21no—
78C22×Dic5—22no—
79C22×Dic5—21no—
80C22×Dic5—28no—
81C22×Dic5—84no—
82C2×Dic10—21no—
83C2×Dic10—24no—
84C2×Dic10—42no—
85C2×Dic10—82no—
86C2×Dic10C22⋊C412yes—
87C5×M16—42no—
88C5×M16—42no—
89C2×C5×C8—42no—
90C5×C4⋊C4—22no—
91C5×C22⋊C4—24no—
92C42×C5C2×D412yes—
93C42×C5C2×D412yes—
94C22⋊Dic5—28no—
95C4⋊Dic5—28no—
96C4⋊Dic5—21no—
97C4⋊Dic5—22no—
98C4⋊Dic5—24no—
99C4⋊Dic5C22⋊C412yes—
100C4⋊Dic5C22⋊C414yes—
101#683—28no—
102#683—24no—
103C4×Dic5—24no—
104C2×#168—42no—
105#554—104no—
106#554—104no—
107C2×C4⋊Q8—51no—
108C2×#125—101no—
109C2×C22⋊Q8—52no—
110C2×C22⋊Q8—102no—
111C2×C4×Q8—51no—
112C2×C4×D4—101no—
113C2×C4×D4C2×D511yescharacteristic
114C22×C4⋊C4—52no—
115#431—52no—
116#423C2×D512yes—
117C2×#100—21no—
118#343—21no—
119#332—104no—
120Q8⋊C8—104no—
121#323—102no—
122C23×C5—22no—
123C23×C5—22no—
124C23×C5—42no—
125C23×C5—42no—
126C23×C5#10314yes—
127C23×C5C2×C22⋊C411yescharacteristic
128C5×D4—24no—
129C5×D4—24no—
130C2×C4×C5—22no—
131C2×C4×C5—22no—
132C2×C4×C5—41no—
133C2×C4×C5—44no—
134C2×C4×C5—44no—
135C2×C4×C5—42no—
136C2×C4×C5C2×C22⋊C411yescharacteristic
137C2×C4×C5C2×C22⋊C411yescharacteristic
138C2×C4×C5#12012yes—
139C2×C4×C5#12012yes—
140C2×C4×C5C2×SD1611yescharacteristic
141C2×C4×C5C2×Q1611yescharacteristic
142C2×C4×C5#13712yes—
143C2×Dic5—22no—
144C2×Dic5—22no—
145C2×Dic5—24no—
146C2×Dic5—42no—
147C2×Dic5—44no—
148C2×Dic5—42no—
149C2×Dic5—88no—
150Dic10—24no—
151Dic10—42no—
152Dic10—84no—
153C5×C8—82no—
154#168—82no—
155C22×Q8—51no—
156C22×Q8—101no—
157C22×D4C22⋊D511yescharacteristic
158C23×C4—102no—
159C23×C4C4×D512yes—
160C2×M16—22no—
161C4⋊Q8—54no—
162C4⋊Q8—102no—
163#125—108no—
164C22⋊Q8—1016no—
165C22⋊Q8—104no—
166C22⋊Q8—104no—
167C4×Q8—54no—
168C4×Q8—102no—
169C4×D4—22no—
170C4×D4—22no—
171C4×D4—108no—
172C2×C4⋊C4—51no—
173C2×C4⋊C4—52no—
174C2×C4⋊C4—104no—
175C2×C4⋊C4—104no—
176C2×C4⋊C4—102no—
177C2×C4⋊C4—102no—
178C2×C4⋊C4—101no—
179C2×C4⋊C4—101no—
180C2×C4⋊C4C22⋊D511yescharacteristic
181C2×C22⋊C4—102no—
182C2×C22⋊C4D2012yes—
183C2×C42—101no—
184C2×C42C22×D511yescharacteristic
185C4⋊C8—22no—
186C4⋊C8—22no—
187C4⋊C8—102no—
188#100—42no—
189C22⋊C8—102no—
190C4×C8—102no—
191C22×C5—21no—
192C22×C5—21no—
193C22×C5—24no—
194C22×C5—44no—
195C22×C5—44no—
196C22×C5—42no—
197C22×C5—42no—
198C22×C5#37911yescharacteristic
199C22×C5C2×#10311yescharacteristic
200C22×C5#41911yescharacteristic
201C4×C5—22no—
202C4×C5—21no—
203C4×C5—42no—
204C4×C5#41312yes—
205C4×C5#44812yes—
206C4×C5#45112yes—
207Dic5—44no—
208Dic5—42no—
209Dic5—42no—
210C24#68512yes—
211C2×Q8—52no—
212C2×Q8—101no—
213C2×Q8—104no—
214C2×Q8—202no—
215C2×Q8—402no—
216C2×D4—22no—
217C2×D4—22no—
218C2×D4#68712yes—
219C2×D4#68912yes—
220C22×C4—22no—
221C22×C4—22no—
222C22×C4—44no—
223C22×C4—101no—
224C22×C4—101no—
225C22×C4—102no—
226C22×C4—108no—
227C22×C4—404no—
228C22×C4#68512yes—
229C22×C4C2×C4×D511yescharacteristic
230C22×C4C2×D2011yescharacteristic
231C22×C4C2×C22⋊D511yescharacteristic
232M16—42no—
233M16—42no—
234C2×C8—42no—
235C2×C8—202no—
236C4⋊C4—22no—
237C4⋊C4—52no—
238C4⋊C4—54no—
239C4⋊C4—108no—
240C4⋊C4—108no—
241C4⋊C4—101no—
242C4⋊C4—102no—
243C4⋊C4—104no—
244C4⋊C4—104no—
245C22⋊C4—24no—
246C22⋊C4—108no—
247C42—104no—
248C42D4×D512yes—
249C42D4×D512yes—
250C2×C5—21no—
251C2×C5—21no—
252C2×C5—44no—
253C2×C5#178511yescharacteristic
254C2×C5#178711yescharacteristic
255C2×C5#179511yescharacteristic
256C23—22no—
257C23—22no—
258C23—42no—
259C23—42no—
260C23#394214yes—
261C23C2×#68511yescharacteristic
262Q8—104no—
263Q8—202no—
264Q8—404no—
265D4—24no—
266D4—24no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—41no—
270C2×C4—44no—
271C2×C4—44no—
272C2×C4—42no—
273C2×C4—102no—
274C2×C4—102no—
275C2×C4—104no—
276C2×C4—202no—
277C2×C4—204no—
278C2×C4—202no—
279C2×C4—408no—
280C2×C4D5×C22⋊C411yescharacteristic
281C2×C4D5×C22⋊C411yescharacteristic
282C2×C4#402812yes—
283C2×C4C2×#68711yescharacteristic
284C2×C4#408312yes—
285C2×C4C2×#68911yescharacteristic
286C2×C4#409712yes—
287C8—82no—
288C8—402no—
289C5#839511yescharacteristic, complemented, Sylow
290C22—21no—
291C22—21no—
292C22—24no—
293C22—44no—
294C22—44no—
295C22—42no—
296C22—42no—
297C22#6524411yescharacteristic
298C22C2×#394211yescharacteristic
299C22#6529311yescharacteristic
300C4—21no—
301C4—22no—
302C4—42no—
303C4—202no—
304C4—202no—
305C4—204no—
306C4#6503412yes—
307C4#6532912yes—
308C4#6533912yes—
309C2—21no—
310C2—21no—
311C2—44no—
312C2#1060031811yescharacteristic
313C2#1060087311yescharacteristic
314C2#1060093211yescharacteristic
subgroupG/H
centerC22#65244
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1800C2
socleC22×C5#379
prime radicalC22×C5×D4D4
cosocleC2×C42×C5C23
hypercenter#1800D5
hypocenterC5#8395
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1800

Complements

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

NH ≅ G/Ntype
4. #10601301C2semidirect
5. #10601293C2semidirect
289. C5#8395semidirect

Maximal subgroups

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

subgroupindex
C2×#658772
C5×#18002
#106023942
#106013012
#106012932
#83955