Finite Group Databasebeta

← #11991044

Subgroups — #11991044

Order 1280.

966 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 966 conjugacy classes of subgroups — too many to draw. Only its 147 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×D4×Dic10C211yesmaximal, characteristic
2C5×#1800C211yesmaximal, characteristic
3#10602394C211yesmaximal, characteristic
4#10601300C212yesmaximal, complemented
5#10601293C212yesmaximal, complemented
6C23×Dic10C412yes—
7C2×C4×C5×D4C2211yescharacteristic
8C2×D4×Dic5—21no—
9C2×#4070C412yes—
10D4×Dic10—24no—
11D4×Dic10—24no—
12C2×#4034—21no—
13C2×#4024—22no—
14C2×#4015C2211yescharacteristic
15C2×C4×Dic10C2211yescharacteristic
16C5×#423C2212yes—
17C2×C5×#100—21no—
18#65214C2212yes—
19C5×#343—21no—
20#64745—22no—
21#64704—24no—
22#64701—24no—
23#8391—51nomaximal, Sylow
24C22×C5×D4D411yescharacteristic
25C23×C4×C5C2×C412yes—
26C23×Dic5—22no—
27C22×Dic10—22no—
28C22×Dic10—24no—
29C22×Dic10—24no—
30C22×Dic10—48no—
31C22×Dic10C2×C411yescharacteristic
32C22×Dic10C2×C412yes—
33C2×C5×M16—22no—
34C4×C5×D4—22no—
35C4×C5×D4—22no—
36C2×C5×C4⋊C4D411yescharacteristic
37C2×C5×C22⋊C4D412yes—
38C2×C42×C5C2311yescharacteristic
39C2×C22⋊Dic5—22no—
40D4×Dic5—28no—
41C2×C4⋊Dic5—21no—
42C2×C4⋊Dic5—21no—
43C2×C4⋊Dic5C2×C411yescharacteristic
44#4070—24no—
45#4070—24no—
46C2×#683—22no—
47C2×#683—21no—
48C2×C4×Dic5—21no—
49#4034—28no—
50#4024—216no—
51#4015—22no—
52#4015D414yes—
53C4×Dic10—22no—
54C4×Dic10D414yes—
55C5×C4⋊C8—22no—
56C5×C4⋊C8—22no—
57C5×#100—42no—
58C22⋊#168—22no—
59C4⋊#168—22no—
60C4×#168—22no—
61C2×D4×Q8—51no—
62#1800D511yescharacteristic
63#1548—52no—
64#1487—52no—
65#1460—51no—
66C24×C5C22⋊C412yes—
67C2×C5×D4—22no—
68C2×C5×D4—22no—
69C2×C5×D4SD1612yes—
70C2×C5×D4Q1612yes—
71C22×C4×C5—22no—
72C22×C4×C5—22no—
73C22×C4×C5—44no—
74C22×C4×C5C22⋊C412yes—
75C22×C4×C5C22×C411yescharacteristic
76C22×C4×C5C2×D411yescharacteristic
77C22×C4×C5C2×D411yescharacteristic
78C22×Dic5—21no—
79C22×Dic5—28no—
80C22×Dic5—21no—
81C22×Dic5—22no—
82C22×Dic5—48no—
83C2×Dic10—21no—
84C2×Dic10—24no—
85C2×Dic10—28no—
86C2×Dic10—22no—
87C2×Dic10—416no—
88C2×Dic10—48no—
89C2×Dic10—48no—
90C2×Dic10—48no—
91C2×Dic10—44no—
92C2×Dic10C22⋊C412yes—
93C2×Dic10C22⋊C414yes—
94C5×M16—42no—
95C5×M16—42no—
96C2×C5×C8—42no—
97C5×C4⋊C4—22no—
98C5×C22⋊C4—24no—
99C42×C5C2×D412yes—
100C42×C5C2×D412yes—
101C22⋊Dic5—28no—
102C4⋊Dic5—21no—
103C4⋊Dic5—24no—
104C4⋊Dic5—24no—
105C4⋊Dic5C22⋊C412yes—
106#683—28no—
107#683—24no—
108C4×Dic5—24no—
109C2×#168—42no—
110C23×Q8—52no—
111D4×Q8—104no—
112D4×Q8—104no—
113C2×C4⋊Q8—51no—
114C2×C4⋊Q8—101no—
115C2×C22⋊Q8—52no—
116C2×C22⋊Q8—102no—
117C2×C4×Q8—51no—
118C2×C4×D4—101no—
119C2×C4×D4C2×D511yescharacteristic
120#431—52no—
121#423C2×D512yes—
122C2×#100—21no—
123#343—21no—
124#333—104no—
125Q8⋊C8—104no—
126#323—102no—
127C23×C5—22no—
128C23×C5—22no—
129C23×C5—42no—
130C23×C5—42no—
131C23×C5#10314yes—
132C23×C5C2×C22⋊C411yescharacteristic
133C5×D4—24no—
134C5×D4—24no—
135C2×C4×C5—22no—
136C2×C4×C5—22no—
137C2×C4×C5—41no—
138C2×C4×C5—44no—
139C2×C4×C5—44no—
140C2×C4×C5—42no—
141C2×C4×C5C2×C22⋊C411yescharacteristic
142C2×C4×C5C2×C22⋊C411yescharacteristic
143C2×C4×C5#12012yes—
144C2×C4×C5#12012yes—
145C2×C4×C5C2×SD1611yescharacteristic
146C2×C4×C5C2×Q1611yescharacteristic
147C2×C4×C5#13712yes—
148C2×Dic5—24no—
149C2×Dic5—22no—
150C2×Dic5—22no—
151C2×Dic5—24no—
152C2×Dic5—416no—
153C2×Dic5—44no—
154C2×Dic5—42no—
155Dic10—24no—
156Dic10—22no—
157Dic10—416no—
158Dic10—44no—
159Dic10—44no—
160Dic10#10014yescomplemented
161C5×C8—82no—
162#168—82no—
163C22×Q8—51no—
164C22×Q8—52no—
165C22×Q8—104no—
166C22×Q8—104no—
167C22×Q8—102no—
168C22×Q8—208no—
169C22×D4C22⋊D511yescharacteristic
170C23×C4—102no—
171C23×C4C4×D512yes—
172C2×M16—22no—
173C4⋊Q8—54no—
174C4⋊Q8—108no—
175C4⋊Q8—102no—
176C22⋊Q8—1016no—
177C22⋊Q8—104no—
178C22⋊Q8—104no—
179C4×Q8—54no—
180C4×Q8—102no—
181C4×D4—22no—
182C4×D4—22no—
183C4×D4—108no—
184C2×C4⋊C4—51no—
185C2×C4⋊C4—102no—
186C2×C4⋊C4—101no—
187C2×C4⋊C4—101no—
188C2×C4⋊C4—101no—
189C2×C4⋊C4C22⋊D511yescharacteristic
190C2×C22⋊C4—102no—
191C2×C22⋊C4D2012yes—
192C2×C42—101no—
193C2×C42C22×D511yescharacteristic
194C4⋊C8—22no—
195C4⋊C8—22no—
196C4⋊C8—102no—
197#100—42no—
198C22⋊C8—102no—
199C4×C8—102no—
200C22×C5—21no—
201C22×C5—21no—
202C22×C5—24no—
203C22×C5—44no—
204C22×C5—44no—
205C22×C5—42no—
206C22×C5—42no—
207C22×C5#37911yescharacteristic
208C22×C5C2×#10311yescharacteristic
209C22×C5#41911yescharacteristic
210C4×C5—22no—
211C4×C5—21no—
212C4×C5—42no—
213C4×C5C2×#10012yes—
214C4×C5#44812yes—
215C4×C5#45112yes—
216Dic5—24no—
217Dic5—42no—
218Dic5—44no—
219C24#68512yes—
220C2×Q8—52no—
221C2×Q8—54no—
222C2×Q8—104no—
223C2×Q8—108no—
224C2×Q8—101no—
225C2×Q8—102no—
226C2×Q8—204no—
227C2×Q8—208no—
228C2×Q8—208no—
229C2×Q8—2016no—
230C2×Q8—208no—
231C2×D4—22no—
232C2×D4—22no—
233C2×D4#68712yes—
234C2×D4#68912yes—
235C22×C4—22no—
236C22×C4—22no—
237C22×C4—44no—
238C22×C4—101no—
239C22×C4—108no—
240C22×C4—101no—
241C22×C4—102no—
242C22×C4—208no—
243C22×C4#68512yes—
244C22×C4C2×C4×D511yescharacteristic
245C22×C4C2×D2011yescharacteristic
246C22×C4C2×C22⋊D511yescharacteristic
247M16—42no—
248M16—42no—
249C2×C8—42no—
250C2×C8—202no—
251C4⋊C4—22no—
252C4⋊C4—52no—
253C4⋊C4—108no—
254C4⋊C4—101no—
255C4⋊C4—104no—
256C4⋊C4—104no—
257C4⋊C4—104no—
258C22⋊C4—24no—
259C22⋊C4—108no—
260C42—104no—
261C42D4×D512yes—
262C42D4×D512yes—
263C2×C5—21no—
264C2×C5—21no—
265C2×C5—44no—
266C2×C5#178311yescharacteristic
267C2×C5#178711yescharacteristic
268C2×C5#179611yescharacteristic
269C23—22no—
270C23—22no—
271C23—42no—
272C23—42no—
273C23#394214yes—
274C23C2×#68511yescharacteristic
275Q8—54no—
276Q8—104no—
277Q8—102no—
278Q8—204no—
279Q8—2016no—
280Q8—204no—
281D4—24no—
282D4—24no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—41no—
286C2×C4—44no—
287C2×C4—44no—
288C2×C4—42no—
289C2×C4—104no—
290C2×C4—102no—
291C2×C4—102no—
292C2×C4—104no—
293C2×C4—2016no—
294C2×C4—204no—
295C2×C4—202no—
296C2×C4D5×C22⋊C411yescharacteristic
297C2×C4D5×C22⋊C411yescharacteristic
298C2×C4#402812yes—
299C2×C4C2×#68711yescharacteristic
300C2×C4#408312yes—
301C2×C4C2×#68911yescharacteristic
302C2×C4#409712yes—
303C8—82no—
304C8—402no—
305C5#839111yescharacteristic, complemented, Sylow
306C22—21no—
307C22—21no—
308C22—24no—
309C22—44no—
310C22—44no—
311C22—42no—
312C22—42no—
313C22#6524411yescharacteristic
314C22C2×#394211yescharacteristic
315C22#6529311yescharacteristic
316C4—21no—
317C4—22no—
318C4—42no—
319C4—104no—
320C4—204no—
321C4—202no—
322C4D5×#10012yes—
323C4#6532912yes—
324C4#6533912yes—
325C2—21no—
326C2—21no—
327C2—44no—
328C2#1060031811yescharacteristic
329C2#1060087211yescharacteristic
330C2#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#8391
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. #10601300C2semidirect
5. #10601293C2semidirect
160. Dic10#100semidirect
305. C5#8391semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic102
C5×#18002
#106023942
#106013002
#106012932
#83915