Finite Group Databasebeta

← #12008696

Subgroups — #12008696

Order 1280.

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

normal subgroups only

This group has 490 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×#65266C211yesmaximal, characteristic
2C5×#1463C211yesmaximal, characteristic
3#10602345C211yesmaximal, characteristic
4#10597943C214yesmaximal, complemented
5C22×C5×C4⋊C4C2211yescharacteristic
6C22×C4⋊Dic5C411yescharacteristic
7C22×C4×Dic5C411yescharacteristic
8C5×#407—21no—
9C2×#3963—21no—
10C2×#3963—21no—
11#65496—21no—
12#65266—21no—
13#65266—21no—
14#65266C412yes—
15#65266C2212yes—
16C5×#324—21no—
17C5×#324C2212yes—
18#64748—21no—
19#64748C2212yes—
20#11511—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×C4×Dic5—21no—
38C2×C4×Dic5—24no—
39C2×C4×Dic5C2×C412yes—
40C2×#681—41no—
41C5×C22⋊C8—22no—
42C5×C22⋊C8—41no—
43#3963—22no—
44#3963—22no—
45#3963—22no—
46#3963—22no—
47C22⋊#168—22no—
48C22⋊#168—41no—
49C2×#382—51no—
50#1463—51no—
51#1463D511yescharacteristic
52#1324—54no—
53C24×C5C22⋊C411yescharacteristic
54C22×C4×C5—21no—
55C22×C4×C5—21no—
56C22×C4×C5—22no—
57C22×C4×C5—22no—
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—42no—
63C22×C4×C5—42no—
64C22×C4×C5C22⋊C411yescharacteristic
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22⋊C411yescharacteristic
67C22×C4×C5C22×C411yescharacteristic
68C22×C4×C5C2×D411yescharacteristic
69C22×C4×C5C2×D411yescharacteristic
70C22×Dic5—24no—
71C22×Dic5—22no—
72C22×Dic5—22no—
73C22×Dic5—42no—
74C22×Dic5—42no—
75C22×Dic5—44no—
76C22×Dic5—41no—
77C22×Dic5—41no—
78C5×M16—82no—
79C2×C5×C8—42no—
80C5×C4⋊C4—41no—
81C5×C4⋊C4—41no—
82C5×C4⋊C4—41no—
83C5×C4⋊C4—41no—
84C4⋊Dic5—42no—
85C4⋊Dic5—42no—
86C4×Dic5—24no—
87C4×Dic5—22no—
88C4×Dic5M1614yescomplemented
89#681—82no—
90C2×#168—42no—
91C22×C4⋊C4—51no—
92C22×C4⋊C4C2×D511yescharacteristic
93C22×C42—51no—
94#407—21no—
95#407—101no—
96#382—52no—
97#382—52no—
98#382—101no—
99#382—101no—
100C2×#95—101no—
101C2×#95—101no—
102#324—21no—
103#324—52no—
104#324—101no—
105#324C2×D512yes—
106C23×C5—22no—
107C23×C5—22no—
108C23×C5—21no—
109C23×C5—21no—
110C23×C5#9911yescharacteristic
111C23×C5#9911yescharacteristic
112C23×C5C2×C22⋊C411yescharacteristic
113C2×C4×C5—24no—
114C2×C4×C5—24no—
115C2×C4×C5—21no—
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5—42no—
124C2×C4×C5—42no—
125C2×C4×C5—41no—
126C2×C4×C5—41no—
127C2×C4×C5—41no—
128C2×C4×C5—41no—
129C2×C4×C5—81no—
130C2×C4×C5—81no—
131C2×C4×C5#10112yes—
132C2×C4×C5C2×M1612yes—
133C2×Dic5—24no—
134C2×Dic5—48no—
135C2×Dic5—42no—
136C2×Dic5—42no—
137C2×Dic5—44no—
138C2×Dic5—42no—
139C2×Dic5—82no—
140C2×Dic5—82no—
141C5×C8—82no—
142#168—82no—
143C23×C4—101no—
144C23×C4—101no—
145C23×C4C4×D511yescharacteristic
146C23×C4D2011yescharacteristic
147C23×C4C22⋊D511yescharacteristic
148C2×M16—41no—
149C2×M16—201no—
150C2×C4⋊C4—41no—
151C2×C4⋊C4—41no—
152C2×C4⋊C4—52no—
153C2×C4⋊C4—101no—
154C2×C4⋊C4—201no—
155C2×C4⋊C4—201no—
156C2×C4⋊C4C4×D511yescharacteristic
157C2×C4⋊C4D2011yescharacteristic
158C2×C4⋊C4C22⋊D511yescharacteristic
159C2×C4⋊C4C22×D511yescharacteristic
160C2×C42—52no—
161C2×C42—104no—
162C2×C42—101no—
163C22⋊C8—22no—
164C22⋊C8—41no—
165C22⋊C8—102no—
166C22⋊C8—201no—
167#95—102no—
168#95—102no—
169#95—102no—
170#95—102no—
171C22×C5—24no—
172C22×C5—24no—
173C22×C5—21no—
174C22×C5—21no—
175C22×C5—21no—
176C22×C5—21no—
177C22×C5—21no—
178C22×C5—21no—
179C22×C5#35412yes—
180C22×C5#35512yes—
181C22×C5#40711yescharacteristic
182C22×C5C2×#9911yescharacteristic
183C22×C5C2×#10111yescharacteristic
184C4×C5—22no—
185C4×C5—22no—
186C4×C5—41no—
187C4×C5—41no—
188C4×C5—41no—
189C4×C5—41no—
190Dic5—44no—
191Dic5—82no—
192C24#68511yescharacteristic
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—22no—
196C22×C4—22no—
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—21no—
200C22×C4—21no—
201C22×C4—42no—
202C22×C4—42no—
203C22×C4—104no—
204C22×C4—102no—
205C22×C4—102no—
206C22×C4—202no—
207C22×C4—202no—
208C22×C4—204no—
209C22×C4—201no—
210C22×C4—201no—
211C22×C4#68511yescharacteristic
212C22×C4#68511yescharacteristic
213C22×C4#68511yescharacteristic
214C22×C4C2×C4×D511yescharacteristic
215C22×C4C2×D2011yescharacteristic
216C22×C4C2×C22⋊D511yescharacteristic
217M16—82no—
218M16—402no—
219C2×C8—42no—
220C2×C8—202no—
221C4⋊C4—41no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—202no—
226C4⋊C4—202no—
227C42—54no—
228C42—104no—
229C42—102no—
230C2×C5—21no—
231C2×C5—22no—
232C2×C5—22no—
233C2×C5—21no—
234C2×C5#146311yescharacteristic
235C2×C5C2×#35411yescharacteristic
236C2×C5C2×#35511yescharacteristic
237C23—21no—
238C23—21no—
239C23—22no—
240C23—22no—
241C23#393811yescharacteristic
242C23#393811yescharacteristic
243C23C2×#68511yescharacteristic
244C2×C4—24no—
245C2×C4—24no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—81no—
261C2×C4—81no—
262C2×C4—104no—
263C2×C4—208no—
264C2×C4—202no—
265C2×C4—202no—
266C2×C4—204no—
267C2×C4—202no—
268C2×C4—402no—
269C2×C4—402no—
270C2×C4#395612yes—
271C2×C4D5×M1612yes—
272C8—82no—
273C8—402no—
274C5#1151111yescharacteristic, complemented, Sylow
275C22—24no—
276C22—24no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—21no—
281C22—21no—
282C22—21no—
283C22#6469312yes—
284C22#6469712yes—
285C22C2×#393811yescharacteristic
286C22#6541511yescharacteristic
287C22C2×#395611yescharacteristic
288C4—22no—
289C4—22no—
290C4—41no—
291C4—41no—
292C4—41no—
293C4—41no—
294C4—204no—
295C4—402no—
296C2—21no—
297C2—21no—
298C2—22no—
299C2—22no—
300C2#1060076411yescharacteristic
301C2C2×#6469311yescharacteristic
302C2C2×#6469711yescharacteristic
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#11511
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. #10597943C2semidirect
88. C4×Dic5M16semidirect
274. C5#11511semidirect

Maximal subgroups

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

subgroupindex
C2×#652662
C5×#14632
#106023452
#105979432
#115115