Finite Group Databasebeta

← #12008699

Subgroups — #12008699

Order 1280.

578 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 578 conjugacy classes of subgroups — too many to draw. Only its 95 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×#65265C211yesmaximal, characteristic
2C5×#1463C211yesmaximal, characteristic
3#10602345C211yesmaximal, characteristic
4#10597944C214yesmaximal, complemented
5C22×C5×C4⋊C4C2211yescharacteristic
6C22×C4⋊Dic5C411yescharacteristic
7C22×#683—21no—
8C22×#683—21no—
9C22×C4×Dic5C411yescharacteristic
10C5×#407—21no—
11#65496—21no—
12#65265—21no—
13#65265—21no—
14#65265C412yes—
15#65265C2212yes—
16C5×#324—21no—
17C5×#324C2212yes—
18#64748—21no—
19#64748C2212yes—
20#11512—51nomaximal, Sylow
21C23×C4×C5C2×C411yescharacteristic
22C23×C4×C5D411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×Dic5—21no—
25C23×Dic5—21no—
26C2×C5×M16—41no—
27C2×C5×C4⋊C4—41no—
28C2×C5×C4⋊C4—41no—
29C2×C5×C4⋊C4C2×C411yescharacteristic
30C2×C5×C4⋊C4D411yescharacteristic
31C2×C5×C4⋊C4D411yescharacteristic
32C2×C5×C4⋊C4C2311yescharacteristic
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5—41no—
35C2×C4⋊Dic5—41no—
36C2×C4⋊Dic5C2×C412yes—
37C2×#683—22no—
38C2×#683—22no—
39C2×#683—22no—
40C2×#683—22no—
41C2×#683—44no—
42C2×#683—44no—
43C2×C4×Dic5—21no—
44C2×C4×Dic5—24no—
45C2×C4×Dic5C2×C412yes—
46C2×#681—41no—
47C5×C22⋊C8—22no—
48C5×C22⋊C8—41no—
49C22⋊#168—22no—
50C22⋊#168—41no—
51C2×#384—51no—
52#1463—51no—
53#1463D511yescharacteristic
54#1325—54no—
55C24×C5C22⋊C411yescharacteristic
56C22×C4×C5—21no—
57C22×C4×C5—21no—
58C22×C4×C5—22no—
59C22×C4×C5—22no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5—42no—
65C22×C4×C5—42no—
66C22×C4×C5C22⋊C411yescharacteristic
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22⋊C411yescharacteristic
69C22×C4×C5C22×C411yescharacteristic
70C22×C4×C5C2×D411yescharacteristic
71C22×C4×C5C2×D411yescharacteristic
72C22×Dic5—24no—
73C22×Dic5—24no—
74C22×Dic5—24no—
75C22×Dic5—22no—
76C22×Dic5—22no—
77C22×Dic5—42no—
78C22×Dic5—42no—
79C22×Dic5—41no—
80C22×Dic5—41no—
81C5×M16—82no—
82C2×C5×C8—42no—
83C5×C4⋊C4—41no—
84C5×C4⋊C4—41no—
85C5×C4⋊C4—41no—
86C5×C4⋊C4—41no—
87C4⋊Dic5—42no—
88C4⋊Dic5—42no—
89#683—44no—
90#683—44no—
91#683—44no—
92#683—44no—
93C4×Dic5—24no—
94C4×Dic5—22no—
95C4×Dic5M1614yescomplemented
96#681—82no—
97C2×#168—42no—
98C22×C4⋊C4—51no—
99C22×C4⋊C4—101no—
100C22×C4⋊C4—101no—
101C22×C4⋊C4C2×D511yescharacteristic
102C22×C42—51no—
103#407—21no—
104#407—101no—
105#384—52no—
106#384—52no—
107#384—101no—
108#384—101no—
109#324—21no—
110#324—52no—
111#324—101no—
112#324C2×D512yes—
113C23×C5—22no—
114C23×C5—22no—
115C23×C5—21no—
116C23×C5—21no—
117C23×C5#9911yescharacteristic
118C23×C5#9911yescharacteristic
119C23×C5C2×C22⋊C411yescharacteristic
120C2×C4×C5—24no—
121C2×C4×C5—24no—
122C2×C4×C5—21no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—42no—
131C2×C4×C5—42no—
132C2×C4×C5—41no—
133C2×C4×C5—41no—
134C2×C4×C5—41no—
135C2×C4×C5—41no—
136C2×C4×C5—81no—
137C2×C4×C5—81no—
138C2×C4×C5#10112yes—
139C2×C4×C5C2×M1612yes—
140C2×Dic5—24no—
141C2×Dic5—216no—
142C2×Dic5—24no—
143C2×Dic5—24no—
144C2×Dic5—42no—
145C2×Dic5—42no—
146C2×Dic5—42no—
147C2×Dic5—82no—
148C2×Dic5—82no—
149C5×C8—82no—
150#168—82no—
151C23×C4—101no—
152C23×C4—101no—
153C23×C4C4×D511yescharacteristic
154C23×C4D2011yescharacteristic
155C23×C4C22⋊D511yescharacteristic
156C2×M16—41no—
157C2×M16—201no—
158C2×C4⋊C4—41no—
159C2×C4⋊C4—41no—
160C2×C4⋊C4—52no—
161C2×C4⋊C4—101no—
162C2×C4⋊C4—102no—
163C2×C4⋊C4—102no—
164C2×C4⋊C4—102no—
165C2×C4⋊C4—102no—
166C2×C4⋊C4—201no—
167C2×C4⋊C4—201no—
168C2×C4⋊C4—204no—
169C2×C4⋊C4—204no—
170C2×C4⋊C4C4×D511yescharacteristic
171C2×C4⋊C4D2011yescharacteristic
172C2×C4⋊C4C22⋊D511yescharacteristic
173C2×C4⋊C4C22×D511yescharacteristic
174C2×C42—52no—
175C2×C42—104no—
176C2×C42—101no—
177C22⋊C8—22no—
178C22⋊C8—41no—
179C22⋊C8—102no—
180C22⋊C8—201no—
181C22×C5—24no—
182C22×C5—24no—
183C22×C5—21no—
184C22×C5—21no—
185C22×C5—21no—
186C22×C5—21no—
187C22×C5—21no—
188C22×C5—21no—
189C22×C5#35312yes—
190C22×C5#35612yes—
191C22×C5#40711yescharacteristic
192C22×C5C2×#9911yescharacteristic
193C22×C5C2×#10111yescharacteristic
194C4×C5—22no—
195C4×C5—22no—
196C4×C5—41no—
197C4×C5—41no—
198C4×C5—41no—
199C4×C5—41no—
200Dic5—28no—
201Dic5—82no—
202C24#68511yescharacteristic
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—104no—
214C22×C4—104no—
215C22×C4—104no—
216C22×C4—102no—
217C22×C4—102no—
218C22×C4—202no—
219C22×C4—202no—
220C22×C4—201no—
221C22×C4—201no—
222C22×C4#68511yescharacteristic
223C22×C4#68511yescharacteristic
224C22×C4#68511yescharacteristic
225C22×C4C2×C4×D511yescharacteristic
226C22×C4C2×D2011yescharacteristic
227C22×C4C2×C22⋊D511yescharacteristic
228M16—82no—
229M16—402no—
230C2×C8—42no—
231C2×C8—202no—
232C4⋊C4—41no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—202no—
237C4⋊C4—202no—
238C4⋊C4—204no—
239C4⋊C4—204no—
240C4⋊C4—204no—
241C4⋊C4—204no—
242C42—54no—
243C42—104no—
244C42—102no—
245C2×C5—21no—
246C2×C5—22no—
247C2×C5—22no—
248C2×C5—21no—
249C2×C5#146311yescharacteristic
250C2×C5C2×#35311yescharacteristic
251C2×C5C2×#35611yescharacteristic
252C23—21no—
253C23—21no—
254C23—22no—
255C23—22no—
256C23#393811yescharacteristic
257C23#393811yescharacteristic
258C23C2×#68511yescharacteristic
259C2×C4—24no—
260C2×C4—24no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—81no—
276C2×C4—81no—
277C2×C4—104no—
278C2×C4—1016no—
279C2×C4—104no—
280C2×C4—104no—
281C2×C4—202no—
282C2×C4—202no—
283C2×C4—202no—
284C2×C4—402no—
285C2×C4—402no—
286C2×C4#395612yes—
287C2×C4D5×M1612yes—
288C8—82no—
289C8—402no—
290C5#1151211yescharacteristic, complemented, Sylow
291C22—24no—
292C22—24no—
293C22—21no—
294C22—21no—
295C22—21no—
296C22—21no—
297C22—21no—
298C22—21no—
299C22#6469412yes—
300C22#6469812yes—
301C22C2×#393811yescharacteristic
302C22#6541511yescharacteristic
303C22C2×#395611yescharacteristic
304C4—22no—
305C4—22no—
306C4—41no—
307C4—41no—
308C4—41no—
309C4—41no—
310C4—108no—
311C4—402no—
312C2—21no—
313C2—21no—
314C2—22no—
315C2—22no—
316C2#1060076411yescharacteristic
317C2C2×#6469411yescharacteristic
318C2C2×#6469811yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#1463C2
socleC22×C5C2×#99
prime radicalC24×C5C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#1463D5
hypocenterC5#11512
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
4. #10597944C2semidirect
95. C4×Dic5M16semidirect
290. C5#11512semidirect

Maximal subgroups

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

subgroupindex
C2×#652652
C5×#14632
#106023452
#105979442
#115125