Finite Group Databasebeta

← #12014488

Subgroups — #12014488

Order 1280.

464 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 125 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
1#10614958C211yesmaximal, characteristic
2C2×C5×#356C211yesmaximal, characteristic
3C2×#64768C211yesmaximal, characteristic
4Dic5×#101C212yesmaximal
5#10598190C212yesmaximal
6C2×C5×C4⋊Q8C2211yescharacteristic
7C2×Q8×Dic5C411yescharacteristic
8C2×Q8×Dic5C2211yescharacteristic
9C2×C5×#101C2212yes—
10#65519C411yescharacteristic
11#65519C2211yescharacteristic
12C2×#3968C2212yes—
13M16×Dic5—22no—
14#65270—22no—
15#65270—22no—
16#65225C411yescharacteristic
17#65221C411yescharacteristic
18C5×#356C414yescomplemented
19#64774—22no—
20#64768C414yescomplemented
21#12631—51nomaximal, Sylow
22C22×C5×Q8C2×C411yescharacteristic
23C22×C5×Q8C2311yescharacteristic
24C2×C5×M16—22no—
25C5×C4⋊Q8—22no—
26C5×C4⋊Q8C2×C412yes—
27C5×C4⋊Q8C2×C412yes—
28C2×C5×C4⋊C4—22no—
29C2×C42×C5C2×C411yescharacteristic
30Q8×Dic5—42no—
31Q8×Dic5—42no—
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5C2×C411yescharacteristic
34C2×C4⋊Dic5C2×C411yescharacteristic
35C2×C4⋊Dic5D412yes—
36C2×C4×Dic5—21no—
37C2×C4×Dic5C2×C411yescharacteristic
38C2×C4×Dic5C2×C411yescharacteristic
39C2×C4×Dic5D412yes—
40C2×#681—22no—
41C5×#101—22no—
42C5×#101C2×C414yes—
43#3968—22no—
44#3968C2×C414yes—
45#3963—22no—
46#3963—21no—
47#3963—21no—
48#3963—22no—
49#3963—22no—
50#3947—42no—
51C8×Dic5—42no—
52#2327—51no—
53C2×#356—51no—
54C2×#356D511yescharacteristic
55C4×#101—52no—
56#1394—52no—
57C2×C5×Q8—21no—
58C2×C5×Q8—41no—
59C2×C5×Q8—41no—
60C2×C5×Q8—41no—
61C2×C5×Q8—41no—
62C2×C5×Q8C4212yes—
63C2×C5×Q8C22×C411yescharacteristic
64C2×C5×Q8C22×C411yescharacteristic
65C2×C5×Q8#4112yes—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5C22×C411yescharacteristic
69C22×C4×C5C2×D412yes—
70C22×Dic5—21no—
71C22×Dic5—21no—
72C22×Dic5C22⋊C412yes—
73C22×Dic5C22⋊C411yescharacteristic
74C22×Dic5C22⋊C411yescharacteristic
75C5×M16—24no—
76C5×M16—42no—
77C2×C5×C8—42no—
78C5×C4⋊C4—24no—
79C5×C4⋊C4—24no—
80C42×C5—21no—
81C42×C5C4212yes—
82C4⋊Dic5—41no—
83C4⋊Dic5—42no—
84C4⋊Dic5—42no—
85C4⋊Dic5—41no—
86C4×Dic5—22no—
87C4×Dic5—22no—
88C4×Dic5—22no—
89C4×Dic5—42no—
90C4×Dic5—41no—
91#681—24no—
92#681—42no—
93C2×#168—42no—
94C2×C4⋊Q8C2×D511yescharacteristic
95C2×C4×Q8—51no—
96C2×C4×Q8—51no—
97C2×#101—52no—
98C2×#101C2×D512yes—
99C4×M16—102no—
100#391—51no—
101#391—51no—
102#387—102no—
103#387—102no—
104#382—51no—
105#376—51no—
106#356—54no—
107#356Dic514yescomplemented
108#343—102no—
109C23×C5C2×C22⋊C411yescharacteristic
110C5×Q8—41no—
111C5×Q8—41no—
112C5×Q8—42no—
113C5×Q8—42no—
114C5×Q8—42no—
115C2×C4×C5—22no—
116C2×C4×C5—21no—
117C2×C4×C5—22no—
118C2×C4×C5—21no—
119C2×C4×C5—22no—
120C2×C4×C5—22no—
121C2×C4×C5—41no—
122C2×C4×C5—41no—
123C2×C4×C5—41no—
124C2×C4×C5—41no—
125C2×C4×C5C2×C4211yescharacteristic
126C2×C4×C5#11711yescharacteristic
127C2×C4×C5C4×D412yes—
128C2×C4×C5C4×D412yes—
129C2×Dic5—21no—
130C2×Dic5—22no—
131C2×Dic5—41no—
132C2×Dic5—42no—
133C2×Dic5—41no—
134C2×Dic5—41no—
135C2×Dic5—41no—
136C2×Dic5—42no—
137C2×Dic5—41no—
138C2×Dic5—41no—
139C2×Dic5#9912yes—
140C5×C8—44no—
141#168—44no—
142C22×Q8C4×D511yescharacteristic
143C22×Q8C22×D511yescharacteristic
144C2×M16—22no—
145C2×M16—102no—
146C4⋊Q8—22no—
147C4⋊Q8C4×D512yes—
148C4⋊Q8C2×Dic512yes—
149C4×Q8—202no—
150C4×Q8—202no—
151C2×C4⋊C4—22no—
152C2×C4⋊C4—51no—
153C2×C4⋊C4—52no—
154C2×C4⋊C4—51no—
155C2×C4⋊C4—101no—
156C2×C42—51no—
157C2×C42—52no—
158C2×C42—51no—
159C2×C42—101no—
160C2×C42C4×D511yescharacteristic
161#101—22no—
162#101—54no—
163#101—102no—
164#101C2×Dic514yes—
165#97—202no—
166C4×C8—202no—
167#95—101no—
168#95—101no—
169#95—102no—
170#95—102no—
171#95—102no—
172C22×C5—21no—
173C22×C5—21no—
174C22×C5C4×C22⋊C411yescharacteristic
175C22×C5C2×#9911yescharacteristic
176C22×C5#41011yescharacteristic
177C4×C5—22no—
178C4×C5—22no—
179C4×C5—21no—
180C4×C5—21no—
181C4×C5—42no—
182C4×C5—42no—
183Dic5—22no—
184Dic5—41no—
185Dic5—42no—
186Dic5—81no—
187Dic5—81no—
188C2×Q8—21no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—41no—
193C2×Q8C4×Dic512yes—
194C2×Q8C2×C4×D511yescharacteristic
195C2×Q8#71112yes—
196C2×Q8C22×Dic511yescharacteristic
197C22×C4—21no—
198C22×C4—21no—
199C22×C4—51no—
200C22×C4—52no—
201C22×C4—51no—
202C22×C4—101no—
203C22×C4—101no—
204C22×C4C2×C4×D511yescharacteristic
205C22×C4D4×D512yes—
206M16—24no—
207M16—42no—
208M16—104no—
209M16—202no—
210C2×C8—42no—
211C2×C8—202no—
212C4⋊C4—24no—
213C4⋊C4—24no—
214C4⋊C4—201no—
215C4⋊C4—202no—
216C4⋊C4—201no—
217C4⋊C4—202no—
218C42—21no—
219C42—102no—
220C42—102no—
221C42—102no—
222C42—201no—
223C42—202no—
224C42C4×Dic512yes—
225C2×C5—21no—
226C2×C5—21no—
227C2×C5C4×#9911yescharacteristic
228C2×C5#213311yescharacteristic
229C2×C5#213511yescharacteristic
230C23D5×C22⋊C411yescharacteristic
231Q8—41no—
232Q8—42no—
233Q8—41no—
234Q8—42no—
235Q8—42no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—22no—
241C2×C4—22no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—52no—
247C2×C4—101no—
248C2×C4—102no—
249C2×C4—201no—
250C2×C4—202no—
251C2×C4—201no—
252C2×C4—201no—
253C2×C4—201no—
254C2×C4—202no—
255C2×C4—201no—
256C2×C4—201no—
257C2×C4#402311yescharacteristic
258C2×C4#402712yes—
259C2×C4C2×C4×Dic511yescharacteristic
260C2×C4D4×Dic512yes—
261C8—44no—
262C8—204no—
263C5#1263111yescharacteristic, complemented, Sylow
264C22—21no—
265C22—21no—
266C22#6502911yescharacteristic
267C22D5×#9911yescharacteristic
268C22C22⋊C4×Dic511yescharacteristic
269C4—22no—
270C4—22no—
271C4—21no—
272C4—21no—
273C4—42no—
274C4—42no—
275C4—102no—
276C4—201no—
277C4—202no—
278C4—401no—
279C4—401no—
280C2—21no—
281C2—21no—
282C2#1059996411yescharacteristic
283C2#1059996611yescharacteristic
284C2Dic5×#9911yescharacteristic
subgroupG/H
centerC22D5×#99
commutatorC2×C4×C5C2×C42
FrattiniC22×Q8C22×D5
FittingC2×C5×#356C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC22×C5×Q8C23
hypercenterC2×#356D5
hypocenterC5#12631
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#356

Complements

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

NH ≅ G/Ntype
18. C5×#356C4semidirect
20. #64768C4semidirect
107. #356Dic5semidirect
263. C5#12631semidirect

Maximal subgroups

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

subgroupindex
#106149582
C2×C5×#3562
C2×#647682
Dic5×#1012
#105981902
#126315