Finite Group Databasebeta

← #11991034

Subgroups — #11991034

Order 1280.

738 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 738 conjugacy classes of subgroups — too many to draw. Only its 127 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×#65876C211yesmaximal, characteristic
2C5×#1800C211yesmaximal, characteristic
3#10602394C211yesmaximal, characteristic
4#10601299C212yesmaximal, complemented
5#10601293C212yesmaximal, complemented
6C2×C4×C5×D4C2211yescharacteristic
7C2×#4082—21no—
8C2×#4072C412yes—
9C2×#4070C412yes—
10#65876—24no—
11#65876—24no—
12C2×#4033—21no—
13C2×#4025—22no—
14C2×#4015C2211yescharacteristic
15C2×C4×Dic10C2211yescharacteristic
16C5×#423C2212yes—
17C2×C5×#100—21no—
18#65214C2212yes—
19C5×#343—21no—
20#64745—22no—
21#64704—24no—
22#64702—24no—
23#8389—51nomaximal, Sylow
24C22×C5×D4D411yescharacteristic
25C23×C4×C5C2×C412yes—
26C22×Dic10—21no—
27C22×Dic10C2×C411yescharacteristic
28C2×C5×M16—22no—
29C4×C5×D4—22no—
30C4×C5×D4—22no—
31C2×C5×C4⋊C4D411yescharacteristic
32C2×C5×C22⋊C4D412yes—
33C2×C42×C5C2311yescharacteristic
34C2×C22⋊Dic5—22no—
35C2×C22⋊Dic5—22no—
36#4082—28no—
37#4072—24no—
38#4072—24no—
39C2×C4⋊Dic5—21no—
40C2×C4⋊Dic5C2×C411yescharacteristic
41C2×C4⋊Dic5C2×C412yes—
42#4070—24no—
43#4070—24no—
44C2×#683—22no—
45C2×#683—21no—
46C2×C4×Dic5—22no—
47C2×C4×Dic5—21no—
48#4033—28no—
49#4025—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×#556—51no—
61#1800D511yescharacteristic
62#1546—52no—
63#1487—52no—
64#1460—51no—
65C24×C5C22⋊C412yes—
66C2×C5×D4—22no—
67C2×C5×D4—22no—
68C2×C5×D4—21no—
69C2×C5×D4—21no—
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—22no—
78C22×Dic5—21no—
79C22×Dic5—21no—
80C2×Dic10—21no—
81C2×Dic10—24no—
82C2×Dic10—42no—
83C2×Dic10—42no—
84C2×Dic10—41no—
85C2×Dic10—41no—
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—
95C22⋊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—28no—
104C4×Dic5—24no—
105C2×#168—42no—
106#556—104no—
107#556—104no—
108C2×C4⋊Q8—51no—
109C2×#126—102no—
110C2×#124—101no—
111C2×C22⋊Q8—52no—
112C2×C4×Q8—51no—
113C2×C4×Q8—101no—
114C2×C4×D4C2×D511yescharacteristic
115C2×#117—52no—
116#431—52no—
117#423C2×D512yes—
118C2×#100—21no—
119#343—21no—
120#332—104no—
121Q8⋊C8—104no—
122#323—102no—
123C23×C5—22no—
124C23×C5—22no—
125C23×C5—22no—
126C23×C5—42no—
127C23×C5—42no—
128C23×C5C2×C22⋊C411yescharacteristic
129C5×D4—42no—
130C5×D4—42no—
131C2×C4×C5—22no—
132C2×C4×C5—22no—
133C2×C4×C5—41no—
134C2×C4×C5—44no—
135C2×C4×C5—44no—
136C2×C4×C5—42no—
137C2×C4×C5C2×C22⋊C411yescharacteristic
138C2×C4×C5C2×C22⋊C411yescharacteristic
139C2×C4×C5#12012yes—
140C2×C4×C5#12012yes—
141C2×C4×C5#13512yes—
142C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C5#13711yescharacteristic
144C2×Dic5—22no—
145C2×Dic5—22no—
146C2×Dic5—24no—
147C2×Dic5—42no—
148C2×Dic5—42no—
149C2×Dic5—42no—
150C2×Dic5—42no—
151Dic10—24no—
152Dic10—42no—
153Dic10—44no—
154Dic10—44no—
155C5×C8—82no—
156#168—82no—
157C22×Q8—51no—
158C22×Q8—101no—
159C22×D4C22⋊D511yescharacteristic
160C23×C4C4×D512yes—
161C2×M16—22no—
162C4⋊Q8—54no—
163C4⋊Q8—102no—
164#126—1016no—
165#124—108no—
166C22⋊Q8—104no—
167C22⋊Q8—104no—
168C4×Q8—54no—
169C4×Q8—108no—
170C4×Q8—102no—
171C4×D4—22no—
172C4×D4—22no—
173#117—104no—
174#117—104no—
175C2×C4⋊C4—51no—
176C2×C4⋊C4—52no—
177C2×C4⋊C4—102no—
178C2×C4⋊C4—101no—
179C2×C4⋊C4—101no—
180C2×C4⋊C4C22⋊D511yescharacteristic
181C2×C22⋊C4—102no—
182C2×C22⋊C4—102no—
183C2×C22⋊C4D2012yes—
184C2×C42—102no—
185C2×C42—101no—
186C2×C42C22×D511yescharacteristic
187C4⋊C8—22no—
188C4⋊C8—22no—
189C4⋊C8—102no—
190#100—42no—
191C22⋊C8—102no—
192C4×C8—102no—
193C22×C5—21no—
194C22×C5—21no—
195C22×C5—42no—
196C22×C5—42no—
197C22×C5—42no—
198C22×C5—82no—
199C22×C5—82no—
200C22×C5#37911yescharacteristic
201C22×C5#41611yescharacteristic
202C22×C5#41711yescharacteristic
203C4×C5—22no—
204C4×C5—21no—
205C4×C5—42no—
206C4×C5#41312yes—
207C4×C5#44912yes—
208C4×C5#45212yes—
209Dic5—42no—
210Dic5—42no—
211Dic5—44no—
212C24#68512yes—
213C2×Q8—52no—
214C2×Q8—101no—
215C2×Q8—104no—
216C2×Q8—202no—
217C2×Q8—202no—
218C2×Q8—201no—
219C2×Q8—201no—
220C2×D4—22no—
221C2×D4—21no—
222C2×D4—22no—
223C2×D4—21no—
224C22×C4—22no—
225C22×C4—22no—
226C22×C4—44no—
227C22×C4—101no—
228C22×C4—102no—
229C22×C4—101no—
230C22×C4#68512yes—
231C22×C4C2×C4×D511yescharacteristic
232C22×C4C2×D2011yescharacteristic
233C22×C4C2×C22⋊D511yescharacteristic
234M16—42no—
235M16—42no—
236C2×C8—42no—
237C2×C8—202no—
238C4⋊C4—22no—
239C4⋊C4—52no—
240C4⋊C4—54no—
241C4⋊C4—108no—
242C4⋊C4—101no—
243C4⋊C4—102no—
244C4⋊C4—104no—
245C4⋊C4—104no—
246C22⋊C4—24no—
247C22⋊C4—108no—
248C22⋊C4—108no—
249C42—108no—
250C42—104no—
251C42D4×D512yes—
252C42D4×D512yes—
253C2×C5—21no—
254C2×C5—21no—
255C2×C5—82no—
256C2×C5#178511yescharacteristic
257C2×C5#178811yescharacteristic
258C2×C5#179611yescharacteristic
259C23—22no—
260C23—22no—
261C23—22no—
262C23—42no—
263C23—42no—
264C23C2×#68511yescharacteristic
265Q8—104no—
266Q8—202no—
267Q8—204no—
268Q8—204no—
269D4—42no—
270D4—42no—
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—44no—
275C2×C4—44no—
276C2×C4—42no—
277C2×C4—102no—
278C2×C4—104no—
279C2×C4—102no—
280C2×C4—202no—
281C2×C4—202no—
282C2×C4—202no—
283C2×C4—202no—
284C2×C4D5×C22⋊C411yescharacteristic
285C2×C4D5×C22⋊C411yescharacteristic
286C2×C4#402812yes—
287C2×C4#407811yescharacteristic
288C2×C4#408312yes—
289C2×C4#408811yescharacteristic
290C2×C4#409612yes—
291C8—82no—
292C8—402no—
293C5#838911yescharacteristic, complemented, Sylow
294C22—21no—
295C22—21no—
296C22—42no—
297C22—42no—
298C22—42no—
299C22—82no—
300C22—82no—
301C22#6524411yescharacteristic
302C22#6525511yescharacteristic
303C22#6529111yescharacteristic
304C4—21no—
305C4—22no—
306C4—42no—
307C4—204no—
308C4—202no—
309C4—202no—
310C4#6503412yes—
311C4#6532612yes—
312C4#6533612yes—
313C2—21no—
314C2—21no—
315C2—82no—
316C2#1060031511yescharacteristic
317C2#1060087311yescharacteristic
318C2#1060093411yescharacteristic
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#8389
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. #10601299C2semidirect
5. #10601293C2semidirect
293. C5#8389semidirect

Maximal subgroups

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

subgroupindex
C2×#658762
C5×#18002
#106023942
#106012992
#106012932
#83895