Finite Group Databasebeta

← #12014472

Subgroups — #12014472

Order 1280.

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

normal subgroups only

This group has 564 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#10614684C211yesmaximal, characteristic
2C2×C5×#354C211yesmaximal, characteristic
3C2×#64761C211yesmaximal, characteristic
4Dic5×#99C212yesmaximal
5#10598186C212yesmaximal
6C2×C5×#124C2211yescharacteristic
7C2×Q8×Dic5C411yescharacteristic, complemented
8C2×D4×Dic5C2211yescharacteristic
9C2×C5×#99C2212yes—
10#65519C411yescharacteristic, complemented
11#65510C2211yescharacteristic
12C2×#3966C2212yes—
13#65240—22no—
14#65239—22no—
15C22⋊C4×Dic5—22no—
16#65224C411yescharacteristic, complemented
17#65221C411yescharacteristic, complemented
18C5×#354C414yescomplemented
19#64761C414yescomplemented
20#64747—22no—
21#12627—51nomaximal, Sylow
22C22×C5×Q8C2×C411yescharacteristic
23C22×C5×D4C2311yescharacteristic
24C23×Dic5D412yes—
25C5×#124—22no—
26C5×#124C2×C412yes—
27C5×#124C2×C412yes—
28C2×C5×C22⋊C4—22no—
29C2×C5×C22⋊C4—22no—
30C2×C42×C5C2×C411yescharacteristic
31C2×C22⋊Dic5—22no—
32C2×C22⋊Dic5—22no—
33C2×C22⋊Dic5D412yes—
34Q8×Dic5—42no—
35D4×Dic5—42no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—22no—
38C2×C4⋊Dic5C2×C411yescharacteristic
39C2×C4⋊Dic5C2×C411yescharacteristic
40C2×C4×Dic5—21no—
41C2×C4×Dic5—42no—
42C2×C4×Dic5C2×C411yescharacteristic
43C2×C4×Dic5C2×C411yescharacteristic
44C5×#99—22no—
45C5×#99C2×C414yes—
46#3966—22no—
47#3966C2×C414yes—
48#3963—21no—
49#3963—21no—
50#3963—22no—
51#3963—42no—
52#2326—51no—
53C2×#354—51no—
54C2×#354D511yescharacteristic
55C4×#99—52no—
56#1393—52no—
57C24×C5C2×D412yes—
58C2×C5×Q8—21no—
59C2×C5×Q8—41no—
60C2×C5×Q8—41no—
61C2×C5×Q8C4212yescomplemented
62C2×C5×D4—41no—
63C2×C5×D4—41no—
64C2×C5×D4C22×C411yescharacteristic
65C2×C5×D4C22×C411yescharacteristic
66C2×C5×D4#4112yes—
67C22×C4×C5—21no—
68C22×C4×C5—21no—
69C22×C4×C5—42no—
70C22×C4×C5C22×C411yescharacteristic
71C22×Dic5—22no—
72C22×Dic5—22no—
73C22×Dic5—21no—
74C22×Dic5—21no—
75C22×Dic5—42no—
76C22×Dic5—82no—
77C22×Dic5C22⋊C411yescharacteristic
78C22×Dic5C22⋊C412yes—
79C22×Dic5C22⋊C411yescharacteristic
80C5×C22⋊C4—24no—
81C5×C22⋊C4—24no—
82C5×C22⋊C4—24no—
83C5×C22⋊C4—42no—
84C42×C5—21no—
85C42×C5C4212yescomplemented
86C22⋊Dic5—24no—
87C22⋊Dic5—42no—
88C22⋊Dic5—42no—
89C22⋊Dic5—82no—
90C4⋊Dic5—41no—
91C4⋊Dic5—42no—
92C4⋊Dic5—41no—
93C4⋊Dic5—82no—
94C4×Dic5—22no—
95C4×Dic5—42no—
96C4×Dic5—41no—
97C4×Dic5—84no—
98C2×#124C2×D511yescharacteristic
99C2×C4×Q8—51no—
100C2×C4×D4—51no—
101C2×#99—52no—
102C2×#99C2×D512yes—
103#391—51no—
104#390—51no—
105#388—102no—
106#385—102no—
107#384—51no—
108C4×C22⋊C4—102no—
109#376—51no—
110#354—54no—
111#354Dic514yescomplemented
112#342—102no—
113C23×C5—22no—
114C23×C5—22no—
115C23×C5—42no—
116C23×C5—42no—
117C23×C5C2×C22⋊C411yescharacteristic
118C23×C5C4×D412yes—
119C23×C5C4×D412yes—
120C5×Q8—42no—
121C5×Q8—42no—
122C5×D4—41no—
123C5×D4—41no—
124C5×D4—42no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—22no—
128C2×C4×C5—22no—
129C2×C4×C5—41no—
130C2×C4×C5—41no—
131C2×C4×C5—41no—
132C2×C4×C5—41no—
133C2×C4×C5—44no—
134C2×C4×C5—82no—
135C2×C4×C5—82no—
136C2×C4×C5C2×C4211yescharacteristic
137C2×C4×C5#11711yescharacteristic
138C2×Dic5—21no—
139C2×Dic5—22no—
140C2×Dic5—41no—
141C2×Dic5—44no—
142C2×Dic5—42no—
143C2×Dic5—41no—
144C2×Dic5—42no—
145C2×Dic5—44no—
146C2×Dic5—41no—
147C2×Dic5—41no—
148C2×Dic5—41no—
149C2×Dic5—41no—
150C2×Dic5—82no—
151C2×Dic5—82no—
152C2×Dic5—82no—
153C2×Dic5#9912yes—
154C22×Q8C4×D511yescharacteristic
155C22×D4C22×D511yescharacteristic
156C23×C4—52no—
157#124—22no—
158#124C4×D512yes—
159#124C2×Dic512yes—
160C4×Q8—202no—
161C4×D4—202no—
162C2×C4⋊C4—51no—
163C2×C4⋊C4—51no—
164C2×C4⋊C4—101no—
165C2×C4⋊C4—102no—
166C2×C22⋊C4—22no—
167C2×C22⋊C4—22no—
168C2×C22⋊C4—52no—
169C2×C22⋊C4—102no—
170C2×C22⋊C4—102no—
171C2×C42—51no—
172C2×C42—51no—
173C2×C42—101no—
174C2×C42—202no—
175C2×C42C4×D511yescharacteristic
176#99—22no—
177#99—54no—
178#99—102no—
179#99C2×Dic514yes—
180#95—101no—
181#95—101no—
182#95—102no—
183#95—202no—
184C22×C5—21no—
185C22×C5—21no—
186C22×C5—22no—
187C22×C5—22no—
188C22×C5—42no—
189C22×C5—42no—
190C22×C5—42no—
191C22×C5—42no—
192C22×C5—82no—
193C22×C5C4×C22⋊C411yescharacteristic
194C22×C5C2×#9911yescharacteristic
195C22×C5#41011yescharacteristic
196C4×C5—21no—
197C4×C5—21no—
198C4×C5—42no—
199C4×C5—42no—
200C4×C5—84no—
201Dic5—22no—
202Dic5—42no—
203Dic5—41no—
204Dic5—81no—
205Dic5—84no—
206Dic5—81no—
207C24D4×D512yes—
208C2×Q8—21no—
209C2×Q8—41no—
210C2×Q8—41no—
211C2×Q8C4×Dic512yescomplemented
212C2×D4—41no—
213C2×D4—41no—
214C2×D4C2×C4×D511yescharacteristic
215C2×D4#71112yes—
216C2×D4C22×Dic511yescharacteristic
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—42no—
220C22×C4—51no—
221C22×C4—51no—
222C22×C4—52no—
223C22×C4—102no—
224C22×C4—102no—
225C22×C4—101no—
226C22×C4—101no—
227C22×C4—202no—
228C22×C4—402no—
229C22×C4C2×C4×D511yescharacteristic
230C4⋊C4—201no—
231C4⋊C4—201no—
232C4⋊C4—202no—
233C4⋊C4—402no—
234C22⋊C4—24no—
235C22⋊C4—24no—
236C22⋊C4—24no—
237C22⋊C4—42no—
238C22⋊C4—104no—
239C22⋊C4—202no—
240C22⋊C4—202no—
241C22⋊C4—402no—
242C42—21no—
243C42—102no—
244C42—201no—
245C42—202no—
246C42—404no—
247C42C4×Dic512yescomplemented
248C2×C5—21no—
249C2×C5—21no—
250C2×C5—42no—
251C2×C5—42no—
252C2×C5C4×#9911yescharacteristic
253C2×C5#212711yescharacteristic
254C2×C5#212911yescharacteristic
255C23—22no—
256C23—22no—
257C23—42no—
258C23—42no—
259C23D5×C22⋊C411yescharacteristic
260C23#402712yes—
261C23D4×Dic512yes—
262Q8—42no—
263Q8—42no—
264D4—41no—
265D4—42no—
266D4—41no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—44no—
276C2×C4—52no—
277C2×C4—82no—
278C2×C4—82no—
279C2×C4—101no—
280C2×C4—102no—
281C2×C4—201no—
282C2×C4—204no—
283C2×C4—202no—
284C2×C4—201no—
285C2×C4—204no—
286C2×C4—201no—
287C2×C4—202no—
288C2×C4—201no—
289C2×C4—201no—
290C2×C4—201no—
291C2×C4—402no—
292C2×C4—402no—
293C2×C4—402no—
294C2×C4#402311yescharacteristic
295C2×C4C2×C4×Dic511yescharacteristic
296C5#1262711yescharacteristic, complemented, Sylow
297C22—21no—
298C22—21no—
299C22—22no—
300C22—22no—
301C22—42no—
302C22—42no—
303C22—42no—
304C22—42no—
305C22—82no—
306C22#6502911yescharacteristic
307C22D5×#9911yescharacteristic
308C22C22⋊C4×Dic511yescharacteristic
309C4—21no—
310C4—21no—
311C4—42no—
312C4—42no—
313C4—84no—
314C4—102no—
315C4—202no—
316C4—201no—
317C4—401no—
318C4—404no—
319C4—401no—
320C2—21no—
321C2—21no—
322C2—42no—
323C2—42no—
324C2#1059995011yescharacteristic
325C2#1059995211yescharacteristic
326C2Dic5×#9911yescharacteristic
subgroupG/H
centerC22D5×#99
commutatorC2×C4×C5C2×C42
FrattiniC22×D4C22×D5
FittingC2×C5×#354C2
socleC22×C5C2×#99
prime radical, cosocleC22×C5×D4C23
hypercenterC2×#354D5
hypocenterC5#12627
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×D4 ◁ C2×#354

Complements

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

NH ≅ G/Ntype
7. C2×Q8×Dic5C4semidirect
10. #65519C4semidirect
16. #65224C4semidirect
17. #65221C4semidirect
18. C5×#354C4semidirect
19. #64761C4semidirect
61. C2×C5×Q8C42semidirect
85. C42×C5C42semidirect
111. #354Dic5semidirect
211. C2×Q8C4×Dic5semidirect
247. C42C4×Dic5semidirect
296. C5#12627semidirect

Maximal subgroups

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

subgroupindex
#106146842
C2×C5×#3542
C2×#647612
Dic5×#992
#105981862
#126275