Finite Group Databasebeta

← #11991039

Subgroups — #11991039

Order 1280.

706 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 706 conjugacy classes of subgroups — too many to draw. Only its 131 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×#65901C211yesmaximal, characteristic
2C5×#1801C211yesmaximal, characteristic
3#10602417C211yesmaximal, characteristic
4#10601299C212yesmaximal
5#10601293C212yesmaximal
6C2×C4×C5×Q8C2211yescharacteristic
7C2×#4090—21no—
8#65901—24no—
9#65901—24no—
10C2×#4035—22no—
11C2×#4033—21no—
12C2×#4016C412yes—
13C2×#4015C2211yescharacteristic
14C2×C4×Dic10C412yes—
15C2×C4×Dic10C2211yescharacteristic
16C5×#423C2212yes—
17C2×C5×#101—21no—
18#65214C2212yes—
19C5×#343—21no—
20#64748—22no—
21#64704—24no—
22#64702—24no—
23#8390—51nomaximal, Sylow
24C22×C5×Q8D411yescharacteristic
25C22×Dic10—21no—
26C22×Dic10C2×C411yescharacteristic
27C2×C5×M16—22no—
28C4×C5×Q8—22no—
29C4×C5×Q8—22no—
30C2×C5×C4⋊C4D412yes—
31C2×C5×C4⋊C4D411yescharacteristic
32C2×C42×C5C2×C412yes—
33C2×C42×C5C2311yescharacteristic
34#4090—28no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5C2×C412yes—
37C2×C4⋊Dic5C2×C411yescharacteristic
38C2×#683—22no—
39C2×#683—22no—
40C2×#683—22no—
41C2×#683—21no—
42C2×C4×Dic5—22no—
43C2×C4×Dic5—21no—
44#4035—216no—
45#4033—28no—
46#4016—24no—
47#4016—24no—
48#4015—22no—
49#4015D414yes—
50C4×Dic10—24no—
51C4×Dic10—22no—
52C4×Dic10—24no—
53C4×Dic10D414yes—
54C5×C4⋊C8—22no—
55C5×C4⋊C8—22no—
56C5×#101—42no—
57C22⋊#168—22no—
58C4⋊#168—22no—
59C4×#168—22no—
60C2×#557—51no—
61#1801D511yescharacteristic
62#1546—52no—
63#1487—52no—
64#1461—51no—
65C2×C5×Q8—22no—
66C2×C5×Q8—22no—
67C2×C5×Q8—21no—
68C2×C5×Q8—21no—
69C22×C4×C5C22⋊C412yes—
70C22×C4×C5C22⋊C412yes—
71C22×C4×C5C22×C411yescharacteristic
72C22×C4×C5C2×D411yescharacteristic
73C22×C4×C5C2×D411yescharacteristic
74C22×Dic5—21no—
75C22×Dic5—22no—
76C22×Dic5—21no—
77C2×Dic10—21no—
78C2×Dic10—24no—
79C2×Dic10—24no—
80C2×Dic10—42no—
81C2×Dic10—41no—
82C2×Dic10—41no—
83C2×Dic10C22⋊C412yes—
84C5×M16—42no—
85C5×M16—42no—
86C2×C5×C8—42no—
87C5×C4⋊C4—22no—
88C5×C4⋊C4—24no—
89C42×C5—22no—
90C42×C5—22no—
91C42×C5C2×D412yes—
92C42×C5C2×D412yes—
93C4⋊Dic5—22no—
94C4⋊Dic5—21no—
95C4⋊Dic5—24no—
96C4⋊Dic5C22⋊C414yes—
97C4⋊Dic5C22⋊C412yes—
98#683—28no—
99#683—28no—
100#683—28no—
101#683—24no—
102C4×Dic5—28no—
103C4×Dic5—24no—
104C2×#168—42no—
105#557—104no—
106#557—104no—
107C2×C4⋊Q8—51no—
108C2×C4⋊Q8—101no—
109C2×#125—52no—
110C2×#125—102no—
111C2×C4×Q8—52no—
112C2×C4×Q8—51no—
113C2×C4×Q8—101no—
114C2×C4×Q8C2×D511yescharacteristic
115#431—52no—
116#423C2×D512yes—
117C2×#101—21no—
118#343—21no—
119#332—104no—
120Q8⋊C8—104no—
121#324—102no—
122C23×C5C2×C22⋊C411yescharacteristic
123C5×Q8—42no—
124C5×Q8—42no—
125C2×C4×C5—22no—
126C2×C4×C5—22no—
127C2×C4×C5—22no—
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5—41no—
131C2×C4×C5—42no—
132C2×C4×C5C2×C22⋊C411yescharacteristic
133C2×C4×C5C2×C22⋊C411yescharacteristic
134C2×C4×C5#12012yes—
135C2×C4×C5#12012yes—
136C2×C4×C5#13512yes—
137C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C5#13711yescharacteristic
139C2×Dic5—24no—
140C2×Dic5—22no—
141C2×Dic5—22no—
142C2×Dic5—24no—
143C2×Dic5—42no—
144C2×Dic5—42no—
145C2×Dic5—42no—
146Dic10—24no—
147Dic10—22no—
148Dic10—44no—
149Dic10—44no—
150Dic10#10114yescomplemented
151C5×C8—82no—
152#168—82no—
153C22×Q8—51no—
154C22×Q8—101no—
155C22×Q8C22⋊D511yescharacteristic
156C2×M16—22no—
157C4⋊Q8—54no—
158C4⋊Q8—108no—
159C4⋊Q8—102no—
160#125—104no—
161#125—104no—
162#125—1016no—
163C4×Q8—22no—
164C4×Q8—22no—
165C4×Q8—54no—
166C4×Q8—104no—
167C4×Q8—104no—
168C4×Q8—108no—
169C4×Q8—102no—
170C2×C4⋊C4—51no—
171C2×C4⋊C4—52no—
172C2×C4⋊C4—102no—
173C2×C4⋊C4—102no—
174C2×C4⋊C4—102no—
175C2×C4⋊C4—101no—
176C2×C4⋊C4—101no—
177C2×C4⋊C4D2012yes—
178C2×C4⋊C4C22⋊D511yescharacteristic
179C2×C42—102no—
180C2×C42—101no—
181C2×C42C4×D512yes—
182C2×C42C22×D511yescharacteristic
183C4⋊C8—22no—
184C4⋊C8—22no—
185C4⋊C8—102no—
186#101—42no—
187C22⋊C8—102no—
188C4×C8—102no—
189C22×C5—21no—
190C22×C5—21no—
191C22×C5#37911yescharacteristic
192C22×C5#41611yescharacteristic
193C22×C5#41711yescharacteristic
194C4×C5—22no—
195C4×C5—21no—
196C4×C5—42no—
197C4×C5—42no—
198C4×C5C2×#10112yes—
199C4×C5#44912yes—
200C4×C5#45212yes—
201Dic5—24no—
202Dic5—42no—
203Dic5—44no—
204C2×Q8—22no—
205C2×Q8—21no—
206C2×Q8—22no—
207C2×Q8—21no—
208C2×Q8—52no—
209C2×Q8—104no—
210C2×Q8—101no—
211C2×Q8—104no—
212C2×Q8—202no—
213C2×Q8—201no—
214C2×Q8—201no—
215C22×C4—101no—
216C22×C4—101no—
217C22×C4—102no—
218C22×C4#68512yes—
219C22×C4#68512yes—
220C22×C4C2×C4×D511yescharacteristic
221C22×C4C2×D2011yescharacteristic
222C22×C4C2×C22⋊D511yescharacteristic
223M16—42no—
224M16—42no—
225C2×C8—42no—
226C2×C8—202no—
227C4⋊C4—24no—
228C4⋊C4—22no—
229C4⋊C4—52no—
230C4⋊C4—54no—
231C4⋊C4—108no—
232C4⋊C4—108no—
233C4⋊C4—108no—
234C4⋊C4—101no—
235C4⋊C4—102no—
236C4⋊C4—104no—
237C4⋊C4—104no—
238C42—22no—
239C42—22no—
240C42—108no—
241C42—104no—
242C42D4×D512yes—
243C42D4×D512yes—
244C2×C5—21no—
245C2×C5—21no—
246C2×C5#178411yescharacteristic
247C2×C5#178811yescharacteristic
248C2×C5#179611yescharacteristic
249C23C2×#68511yescharacteristic
250Q8—42no—
251Q8—42no—
252Q8—54no—
253Q8—104no—
254Q8—102no—
255Q8—204no—
256Q8—204no—
257C2×C4—22no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—22no—
262C2×C4—41no—
263C2×C4—42no—
264C2×C4—104no—
265C2×C4—102no—
266C2×C4—102no—
267C2×C4—104no—
268C2×C4—202no—
269C2×C4—202no—
270C2×C4—202no—
271C2×C4D5×C22⋊C411yescharacteristic
272C2×C4D5×C22⋊C411yescharacteristic
273C2×C4#402812yes—
274C2×C4#407811yescharacteristic
275C2×C4#408312yes—
276C2×C4#408811yescharacteristic
277C2×C4#409612yes—
278C8—82no—
279C8—402no—
280C5#839011yescharacteristic, complemented, Sylow
281C22—21no—
282C22—21no—
283C22#6524411yescharacteristic
284C22#6525511yescharacteristic
285C22#6529111yescharacteristic
286C4—21no—
287C4—22no—
288C4—42no—
289C4—42no—
290C4—104no—
291C4—204no—
292C4—202no—
293C4D5×#10112yes—
294C4#6532612yes—
295C4#6533612yes—
296C2—21no—
297C2—21no—
298C2#1060031511yescharacteristic
299C2#1060090611yescharacteristic
300C2#1060093411yescharacteristic
subgroupG/H
centerC22#65244
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1801C2
socleC22×C5#379
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1801D5
hypocenterC5#8390
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1801

Complements

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

NH ≅ G/Ntype
150. Dic10#101semidirect
280. C5#8390semidirect

Maximal subgroups

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

subgroupindex
C2×#659012
C5×#18012
#106024172
#106012992
#106012932
#83905