Finite Group Databasebeta

← #12008580

Subgroups — #12008580

Order 1280.

428 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C4×#4090C211yesmaximal, characteristic
2C5×#1461C211yesmaximal, characteristic
3#10602417C211yesmaximal, characteristic
4#10597946C212yesmaximal
5#10597944C212yesmaximal
6C2×C4×C5×Q8C2211yescharacteristic
7C2×#4090C411yescharacteristic
8C2×C4×Dic10C411yescharacteristic
9C5×#431—21no—
10#65519C411yescharacteristic
11#65265C2211yescharacteristic
12#65263C2211yescharacteristic
13#65261—21no—
14#65261—21no—
15C4×#683—21no—
16C4×#683—21no—
17C42×Dic5C411yescharacteristic
18#65214—21no—
19C5×#324—21no—
20C5×#324C2212yes—
21#64748—21no—
22#64748C2212yes—
23#11478—51nomaximal, Sylow
24C22×C5×Q8C2×C411yescharacteristic
25C22×Dic10C2×C411yescharacteristic
26C4×C5×Q8—41no—
27C4×C5×Q8—41no—
28C2×C5×C4⋊C4D411yescharacteristic
29C2×C5×C4⋊C4D411yescharacteristic
30C2×C5×C4⋊C4C2311yescharacteristic
31C2×C42×C5C2×C411yescharacteristic
32C2×C42×C5D411yescharacteristic
33C2×C42×C5D411yescharacteristic
34#4090—22no—
35#4090C814yescomplemented
36C2×C4⋊Dic5C2×C411yescharacteristic
37C2×#683—21no—
38C2×#683—21no—
39C2×#683—21no—
40C2×#683—21no—
41C2×#683—21no—
42C2×C4×Dic5—21no—
43C2×C4×Dic5—21no—
44C2×C4×Dic5—21no—
45C2×C4×Dic5C2×C411yescharacteristic
46C2×C4×Dic5C2×C411yescharacteristic
47C4×Dic10—41no—
48C4×Dic10—41no—
49C5×C4⋊C8—41no—
50C5×C22⋊C8—22no—
51C4×C5×C8—41no—
52#3963—21no—
53#3963—21no—
54#3963—21no—
55#3963—21no—
56C22⋊#168—22no—
57C4⋊#168—41no—
58C4×#168—41no—
59C4×C4⋊Q8—51no—
60#1461—51no—
61#1461D511yescharacteristic
62#1325—52no—
63#1319—52no—
64C2×C5×Q8—41no—
65C2×C5×Q8—41no—
66C2×C5×Q8C2×C812yes—
67C2×C5×Q8M1612yes—
68C22×C4×C5C22⋊C411yescharacteristic
69C22×C4×C5C22⋊C411yescharacteristic
70C22×C4×C5C22⋊C411yescharacteristic
71C22×C4×C5C22⋊C411yescharacteristic
72C22×C4×C5C22×C411yescharacteristic
73C22×C4×C5C2×D411yescharacteristic
74C22×C4×C5C2×D411yescharacteristic
75C22×Dic5—21no—
76C22×Dic5—21no—
77C22×Dic5—21no—
78C22×Dic5—21no—
79C2×Dic10—21no—
80C2×Dic10—41no—
81C2×Dic10—41no—
82C2×Dic10C2×C812yes—
83C2×C5×C8—42no—
84C5×C4⋊C4—41no—
85C5×C4⋊C4—41no—
86C5×C4⋊C4—41no—
87C42×C5—21no—
88C42×C5—21no—
89C42×C5—21no—
90C42×C5—21no—
91C42×C5—21no—
92C42×C5—21no—
93C4⋊Dic5—41no—
94#683—24no—
95#683—24no—
96#683—42no—
97#683—42no—
98#683—42no—
99C4×Dic5—24no—
100C4×Dic5—21no—
101C4×Dic5—42no—
102C4×Dic5—41no—
103C4×Dic5—41no—
104C4×Dic5—41no—
105C4×Dic5C2×C812yes—
106C2×#168—42no—
107C2×C4⋊Q8—51no—
108C2×C4×Q8—51no—
109C2×C4×Q8C2×D511yescharacteristic
110#431—21no—
111#431—101no—
112#391—51no—
113#391—51no—
114#389—101no—
115#389—101no—
116#384—51no—
117C4×C4⋊C4—101no—
118C4×C4⋊C4—101no—
119C43—51no—
120#324—21no—
121#324—52no—
122#324—101no—
123#324C2×D512yes—
124C23×C5C2×C22⋊C411yescharacteristic
125C5×Q8—42no—
126C5×Q8—42no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—22no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—41no—
138C2×C4×C5—41no—
139C2×C4×C5—41no—
140C2×C4×C5C22⋊C812yes—
141C2×C4×C5C22⋊C812yes—
142C2×C4×C5#9911yescharacteristic
143C2×C4×C5#9911yescharacteristic
144C2×C4×C5C22×C811yescharacteristic
145C2×C4×C5C2×M1611yescharacteristic
146C2×Dic5—22no—
147C2×Dic5—22no—
148C2×Dic5—22no—
149C2×Dic5—22no—
150C2×Dic5—22no—
151C2×Dic5—41no—
152C2×Dic5—41no—
153C2×Dic5—41no—
154C2×Dic5—41no—
155C2×Dic5—41no—
156C2×Dic5—41no—
157C2×Dic5—41no—
158Dic10—42no—
159Dic10—42no—
160C5×C8—82no—
161#168—82no—
162C22×Q8—51no—
163C22×Q8C4×D511yescharacteristic
164C4⋊Q8—54no—
165C4⋊Q8—102no—
166C4×Q8—41no—
167C4×Q8—41no—
168C4×Q8—201no—
169C4×Q8—201no—
170C2×C4⋊C4—51no—
171C2×C4⋊C4—101no—
172C2×C4⋊C4—101no—
173C2×C4⋊C4—101no—
174C2×C4⋊C4—101no—
175C2×C4⋊C4—101no—
176C2×C4⋊C4D2011yescharacteristic
177C2×C4⋊C4C22⋊D511yescharacteristic
178C2×C4⋊C4C22×D511yescharacteristic
179C2×C42—51no—
180C2×C42—51no—
181C2×C42—101no—
182C2×C42—101no—
183C2×C42—101no—
184C2×C42C4×D511yescharacteristic
185C2×C42D2011yescharacteristic
186C2×C42C22⋊D511yescharacteristic
187C4⋊C8—41no—
188C4⋊C8—201no—
189C22⋊C8—22no—
190C22⋊C8—102no—
191C4×C8—41no—
192C4×C8—201no—
193#95—101no—
194#95—101no—
195#95—101no—
196#95—101no—
197C22×C5—21no—
198C22×C5—21no—
199C22×C5C2×C22⋊C811yescharacteristic
200C22×C5C2×#9911yescharacteristic
201C22×C5#41311yescharacteristic
202C4×C5—21no—
203C4×C5—21no—
204C4×C5—21no—
205C4×C5—22no—
206C4×C5—22no—
207C4×C5—41no—
208C4×C5—41no—
209C4×C5—41no—
210C4×C5#35612yes—
211Dic5—24no—
212Dic5—42no—
213Dic5—42no—
214Dic5—81no—
215C2×Q8—41no—
216C2×Q8—41no—
217C2×Q8—52no—
218C2×Q8—101no—
219C2×Q8—201no—
220C2×Q8—201no—
221C2×Q8C8×D512yes—
222C2×Q8#67612yes—
223C22×C4—101no—
224C22×C4—101no—
225C22×C4—101no—
226C22×C4—101no—
227C22×C4#68511yescharacteristic
228C22×C4#68511yescharacteristic
229C22×C4#68511yescharacteristic
230C22×C4#68511yescharacteristic
231C22×C4C2×C4×D511yescharacteristic
232C22×C4C2×D2011yescharacteristic
233C22×C4C2×C22⋊D511yescharacteristic
234C2×C8—42no—
235C2×C8—202no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—104no—
240C4⋊C4—104no—
241C4⋊C4—201no—
242C4⋊C4—202no—
243C4⋊C4—202no—
244C4⋊C4—202no—
245C42—21no—
246C42—21no—
247C42—21no—
248C42—21no—
249C42—21no—
250C42—21no—
251C42—52no—
252C42—104no—
253C42—101no—
254C42—201no—
255C42—202no—
256C42—201no—
257C42—201no—
258C2×C5—21no—
259C2×C5—21no—
260C2×C5#145911yescharacteristic
261C2×C5#212611yescharacteristic
262C2×C5C2×#35611yescharacteristic
263C23C2×#68511yescharacteristic
264Q8—42no—
265Q8—42no—
266Q8—202no—
267Q8—202no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—22no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—102no—
282C2×C4—102no—
283C2×C4—102no—
284C2×C4—102no—
285C2×C4—102no—
286C2×C4—201no—
287C2×C4—201no—
288C2×C4—201no—
289C2×C4—201no—
290C2×C4—201no—
291C2×C4—201no—
292C2×C4—201no—
293C2×C4#393811yescharacteristic
294C2×C4#393811yescharacteristic
295C2×C4#395212yes—
296C2×C4#395212yes—
297C2×C4C2×C8×D511yescharacteristic
298C2×C4C2×#67611yescharacteristic
299C8—82no—
300C8—402no—
301C5#1147811yescharacteristic, complemented, Sylow
302C22—21no—
303C22—21no—
304C22C2×#393811yescharacteristic
305C22C2×#395211yescharacteristic
306C22#6542111yescharacteristic
307C4—22no—
308C4—22no—
309C4—21no—
310C4—21no—
311C4—21no—
312C4—41no—
313C4—41no—
314C4—41no—
315C4—104no—
316C4—202no—
317C4—202no—
318C4—401no—
319C4#6469812yes—
320C2—21no—
321C2—21no—
322C2#1060071211yescharacteristic
323C2#1060085311yescharacteristic
324C2C2×#6469811yescharacteristic
subgroupG/H
centerC2×C4#3938
commutatorC2×C4×C5C22×C8
FrattiniC2×C4⋊C4C22×D5
FittingC5×#1461C2
socleC22×C5C2×#99
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C5×C4⋊C4C23
hypercenter#1461D5
hypocenterC5#11478
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1461

Complements

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

NH ≅ G/Ntype
35. #4090C8semidirect
301. C5#11478semidirect

Maximal subgroups

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

subgroupindex
C4×#40902
C5×#14612
#106024172
#105979462
#105979442
#114785