Finite Group Databasebeta

← #12014492

Subgroups — #12014492

Order 1280.

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

normal subgroups only

This group has 512 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×#355C211yesmaximal, characteristic
3C2×#64762C211yesmaximal, characteristic
4Dic5×#101C212yesmaximal, complemented
5#10598190C212yesmaximal, complemented
6C2×C5×#124C2211yescharacteristic
7C2×Q8×Dic5C2211yescharacteristic
8C2×D4×Dic5C411yescharacteristic
9C2×C5×#101C2212yes—
10#65519C2211yescharacteristic
11C2×#3968C2212yes—
12#65510C411yescharacteristic
13M16×Dic5—22no—
14#65240—22no—
15#65239—22no—
16#65224C411yescharacteristic
17#65221C411yescharacteristic
18C5×#355C414yescomplemented
19#64774—22no—
20#64762C414yescomplemented
21#12632—51nomaximal, Sylow
22C22×C5×Q8C2311yescharacteristic
23C22×C5×D4C2×C411yescharacteristic
24C23×Dic5—21no—
25C2×C5×M16—22no—
26C5×#124—22no—
27C5×#124C2×C412yes—
28C5×#124C2×C412yes—
29C2×C5×C22⋊C4—22no—
30C2×C42×C5C2×C411yescharacteristic
31C2×C22⋊Dic5—21no—
32C2×C22⋊Dic5—22no—
33Q8×Dic5—42no—
34D4×Dic5—42no—
35C2×C4⋊Dic5—22no—
36C2×C4⋊Dic5C2×C411yescharacteristic
37C2×C4⋊Dic5C2×C411yescharacteristic
38C2×C4⋊Dic5D412yes—
39C2×C4×Dic5C2×C411yescharacteristic
40C2×C4×Dic5C2×C411yescharacteristic
41C2×C4×Dic5D412yes—
42C2×#681—22no—
43C5×#101—22no—
44C5×#101C2×C414yescomplemented
45#3968—22no—
46#3968C2×C414yescomplemented
47#3963—22no—
48#3963—21no—
49#3963—21no—
50#3947—42no—
51C8×Dic5—42no—
52#2326—51no—
53C2×#355—51no—
54C2×#355D511yescharacteristic
55C4×#101—52no—
56#1394—52no—
57C24×C5—21no—
58C2×C5×Q8—41no—
59C2×C5×Q8—41no—
60C2×C5×Q8C22×C411yescharacteristic
61C2×C5×Q8C22×C411yescharacteristic
62C2×C5×Q8#4112yes—
63C2×C5×D4—21no—
64C2×C5×D4—41no—
65C2×C5×D4—41no—
66C2×C5×D4C4212yes—
67C22×C4×C5—21no—
68C22×C4×C5C22×C411yescharacteristic
69C22×C4×C5C2×D412yes—
70C22×Dic5—21no—
71C22×Dic5—21no—
72C22×Dic5—42no—
73C22×Dic5—82no—
74C22×Dic5C22⋊C412yes—
75C22×Dic5C22⋊C411yescharacteristic
76C22×Dic5C22⋊C411yescharacteristic
77C5×M16—24no—
78C5×M16—42no—
79C2×C5×C8—42no—
80C5×C22⋊C4—24no—
81C5×C22⋊C4—24no—
82C42×C5—21no—
83C42×C5C4212yes—
84C22⋊Dic5—42no—
85C22⋊Dic5—82no—
86C4⋊Dic5—41no—
87C4⋊Dic5—42no—
88C4⋊Dic5—41no—
89C4⋊Dic5—82no—
90C4×Dic5—22no—
91C4×Dic5—22no—
92C4×Dic5—22no—
93C4×Dic5—41no—
94#681—24no—
95#681—42no—
96C2×#168—42no—
97C2×#124C2×D511yescharacteristic
98C2×C4×Q8—51no—
99C2×C4×D4—51no—
100C2×#101—52no—
101C2×#101C2×D512yes—
102C4×M16—102no—
103#391—51no—
104#390—51no—
105#388—102no—
106#385—102no—
107#384—51no—
108#376—51no—
109#355—54no—
110#355Dic514yescomplemented
111#343—102no—
112C23×C5—22no—
113C23×C5—42no—
114C23×C5—42no—
115C23×C5—41no—
116C23×C5—41no—
117C23×C5C2×C22⋊C411yescharacteristic
118C5×Q8—41no—
119C5×Q8—41no—
120C5×Q8—42no—
121C5×D4—42no—
122C5×D4—42no—
123C2×C4×C5—22no—
124C2×C4×C5—21no—
125C2×C4×C5—22no—
126C2×C4×C5—21no—
127C2×C4×C5—22no—
128C2×C4×C5—41no—
129C2×C4×C5—41no—
130C2×C4×C5C2×C4211yescharacteristic
131C2×C4×C5#11711yescharacteristic
132C2×C4×C5C4×D412yes—
133C2×C4×C5C4×D412yes—
134C2×Dic5—21no—
135C2×Dic5—22no—
136C2×Dic5—41no—
137C2×Dic5—42no—
138C2×Dic5—41no—
139C2×Dic5—42no—
140C2×Dic5—41no—
141C2×Dic5—41no—
142C2×Dic5—41no—
143C2×Dic5—41no—
144C2×Dic5—84no—
145C2×Dic5#9912yes—
146C5×C8—44no—
147#168—44no—
148C22×Q8C22×D511yescharacteristic
149C22×D4C4×D511yescharacteristic
150C23×C4—101no—
151C2×M16—22no—
152C2×M16—102no—
153#124—22no—
154#124C4×D512yes—
155#124C2×Dic512yes—
156C4×Q8—202no—
157C4×D4—202no—
158C2×C4⋊C4—51no—
159C2×C4⋊C4—52no—
160C2×C4⋊C4—51no—
161C2×C4⋊C4—102no—
162C2×C22⋊C4—22no—
163C2×C22⋊C4—101no—
164C2×C22⋊C4—102no—
165C2×C42—51no—
166C2×C42—52no—
167C2×C42—51no—
168C2×C42C4×D511yescharacteristic
169#101—22no—
170#101—54no—
171#101—102no—
172#101C2×Dic514yescomplemented
173#97—202no—
174C4×C8—202no—
175#95—101no—
176#95—101no—
177#95—102no—
178C22×C5—21no—
179C22×C5—21no—
180C22×C5—44no—
181C22×C5—42no—
182C22×C5—82no—
183C22×C5—81no—
184C22×C5—81no—
185C22×C5C4×C22⋊C411yescharacteristic
186C22×C5C2×#9911yescharacteristic
187C22×C5#41011yescharacteristic
188C4×C5—22no—
189C4×C5—22no—
190C4×C5—21no—
191C4×C5—21no—
192C4×C5—42no—
193Dic5—22no—
194Dic5—42no—
195Dic5—41no—
196Dic5—81no—
197Dic5—81no—
198C24—21no—
199C2×Q8—41no—
200C2×Q8—41no—
201C2×Q8C2×C4×D511yescharacteristic
202C2×Q8#71112yes—
203C2×Q8C22×Dic511yescharacteristic
204C2×D4—21no—
205C2×D4—41no—
206C2×D4—41no—
207C2×D4C4×Dic512yes—
208C22×C4—21no—
209C22×C4—51no—
210C22×C4—51no—
211C22×C4—52no—
212C22×C4—101no—
213C22×C4—101no—
214C22×C4—202no—
215C22×C4—402no—
216C22×C4C2×C4×D511yescharacteristic
217C22×C4D4×D512yes—
218M16—24no—
219M16—42no—
220M16—104no—
221M16—202no—
222C2×C8—42no—
223C2×C8—202no—
224C4⋊C4—201no—
225C4⋊C4—202no—
226C4⋊C4—201no—
227C4⋊C4—402no—
228C22⋊C4—24no—
229C22⋊C4—24no—
230C22⋊C4—202no—
231C22⋊C4—402no—
232C42—21no—
233C42—102no—
234C42—102no—
235C42—102no—
236C42—201no—
237C42C4×Dic512yes—
238C2×C5—21no—
239C2×C5—21no—
240C2×C5—82no—
241C2×C5C4×#9911yescharacteristic
242C2×C5#213311yescharacteristic
243C2×C5#213411yescharacteristic
244C23—22no—
245C23—42no—
246C23—42no—
247C23—41no—
248C23—41no—
249C23D5×C22⋊C411yescharacteristic
250Q8—41no—
251Q8—42no—
252Q8—41no—
253D4—42no—
254D4—42no—
255C2×C4—21no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—52no—
263C2×C4—101no—
264C2×C4—102no—
265C2×C4—201no—
266C2×C4—202no—
267C2×C4—201no—
268C2×C4—201no—
269C2×C4—202no—
270C2×C4—201no—
271C2×C4—201no—
272C2×C4—201no—
273C2×C4—404no—
274C2×C4#402311yescharacteristic
275C2×C4#402712yes—
276C2×C4C2×C4×Dic511yescharacteristic
277C2×C4D4×Dic512yes—
278C8—44no—
279C8—204no—
280C5#1263211yescharacteristic, complemented, Sylow
281C22—21no—
282C22—21no—
283C22—44no—
284C22—42no—
285C22—82no—
286C22—81no—
287C22—81no—
288C22#6502911yescharacteristic
289C22D5×#9911yescharacteristic
290C22C22⋊C4×Dic511yescharacteristic
291C4—22no—
292C4—22no—
293C4—21no—
294C4—21no—
295C4—42no—
296C4—102no—
297C4—201no—
298C4—202no—
299C4—401no—
300C4—401no—
301C2—21no—
302C2—21no—
303C2—82no—
304C2#1059995711yescharacteristic
305C2#1059995911yescharacteristic
306C2Dic5×#9911yescharacteristic
subgroupG/H
centerC22D5×#99
commutatorC2×C4×C5C2×C42
FrattiniC22×Q8C22×D5
FittingC2×C5×#355C2
socleC22×C5C2×#99
prime radicalC22×C5×D4C2×C4
cosocleC22×C5×Q8C23
hypercenterC2×#355D5
hypocenterC5#12632
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#355

Complements

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

NH ≅ G/Ntype
4. Dic5×#101C2semidirect
5. #10598190C2semidirect
18. C5×#355C4semidirect
20. #64762C4semidirect
44. C5×#101C2×C4semidirect
46. #3968C2×C4semidirect
110. #355Dic5semidirect
172. #101C2×Dic5semidirect
280. C5#12632semidirect

Maximal subgroups

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

subgroupindex
#106146842
C2×C5×#3552
C2×#647622
Dic5×#1012
#105981902
#126325