Finite Group Databasebeta

← #12009632

Subgroups — #12009632

Order 1280.

456 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 87 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#10614077C211yesmaximal, characteristic
2C4×C5×#99C211yesmaximal, characteristic
3#10602394C211yesmaximal, characteristic
4#10597983C212yesmaximal, complemented
5#10597982C212yesmaximal, complemented
6C2×C4×C5×D4C2211yescharacteristic
7C2×#4072C411yescharacteristic, complemented
8C2×C5×#99—21no—
9C4×C5×C22⋊C4—21no—
10#65511—21no—
11C4×C22⋊Dic5—21no—
12C4×C22⋊Dic5C411yescharacteristic, complemented
13#65275C411yescharacteristic, complemented
14#65272C411yescharacteristic, complemented
15#65242C2211yescharacteristic
16#65241—21no—
17#65238C2211yescharacteristic
18C4×#683—21no—
19#65214—21no—
20C5×#342C2212yes—
21#64745—21no—
22#64745C2212yes—
23#11727—51nomaximal, Sylow
24C22×C5×D4D411yescharacteristic
25C23×C4×C5C2×C411yescharacteristic
26C23×C4×C5D411yescharacteristic
27C4×C5×D4—41no—
28C4×C5×D4—41no—
29C2×C5×C4⋊C4C2×C411yescharacteristic
30C2×C5×C22⋊C4—22no—
31C2×C5×C22⋊C4D411yescharacteristic
32C2×C5×C22⋊C4C2311yescharacteristic
33C2×C42×C5—41no—
34C2×C42×C5D411yescharacteristic
35C2×C22⋊Dic5—21no—
36C2×C22⋊Dic5—21no—
37C2×C22⋊Dic5—21no—
38C2×C22⋊Dic5—21no—
39#4072—41no—
40#4072—41no—
41C2×C4⋊Dic5C2×C411yescharacteristic
42C2×C4⋊Dic5C2×C411yescharacteristic
43C2×#683—21no—
44C2×#683—21no—
45C2×C4×Dic5—21no—
46C2×C4×Dic5—21no—
47C5×#99—24no—
48C5×#95—41no—
49#3963—21no—
50#3963—21no—
51#3963—21no—
52#3963—21no—
53#3963C2×C411yescharacteristic
54#3963C2×C411yescharacteristic
55C22⋊#168—22no—
56C4⋊#168—41no—
57C4×#168—41no—
58#2395—51no—
59C4×#99D511yescharacteristic
60#1460—51no—
61#1352—52no—
62#1344—52no—
63C24×C5C22⋊C411yescharacteristic
64C24×C5C2×D411yescharacteristic
65C2×C5×D4—22no—
66C2×C5×D4—22no—
67C2×C5×D4—41no—
68C22×C4×C5—21no—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—42no—
73C22×C4×C5—42no—
74C22×C4×C5—42no—
75C22×C4×C5C22⋊C411yescharacteristic
76C22×C4×C5C22⋊C411yescharacteristic
77C22×C4×C5C22⋊C411yescharacteristic
78C22×C4×C5C22×C411yescharacteristic
79C22×C4×C5C2×D411yescharacteristic
80C22×Dic5—21no—
81C22×Dic5—21no—
82C22×Dic5—21no—
83C22×Dic5—21no—
84C5×C4⋊C4—41no—
85C5×C22⋊C4—24no—
86C5×C22⋊C4—41no—
87C5×C22⋊C4—41no—
88C5×C22⋊C4—42no—
89C42×C5—21no—
90C42×C5—21no—
91C42×C5—82no—
92C22⋊Dic5—42no—
93C22⋊Dic5—42no—
94C22⋊Dic5—42no—
95C22⋊Dic5—42no—
96C4⋊Dic5—41no—
97C4⋊Dic5—41no—
98#683—42no—
99#683—42no—
100C4×Dic5—42no—
101C4×Dic5—41no—
102C4×Dic5—41no—
103C2×#168—42no—
104C2×C4×D4C2×D511yescharacteristic
105C2×#117—51no—
106#431—101no—
107C2×#99—21no—
108#400—51no—
109#399—51no—
110#398—51no—
111#397—51no—
112#397—101no—
113#394—101no—
114C4×C4⋊C4—101no—
115C4×C22⋊C4—21no—
116C4×C22⋊C4—51no—
117C4×C22⋊C4—101no—
118#342C2×D512yes—
119#323—52no—
120#323—101no—
121C23×C5—21no—
122C23×C5—21no—
123C23×C5—21no—
124C23×C5—21no—
125C23×C5—21no—
126C23×C5—41no—
127C23×C5—41no—
128C23×C5—41no—
129C23×C5—41no—
130C23×C5C2×C22⋊C411yescharacteristic
131C23×C5#13512yes—
132C5×D4—44no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—22no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—42no—
140C2×C4×C5—42no—
141C2×C4×C5—42no—
142C2×C4×C5—41no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
145C2×C4×C5—44no—
146C2×C4×C5—81no—
147C2×C4×C5—82no—
148C2×C4×C5—82no—
149C2×C4×C5#9911yescharacteristic
150C2×C4×C5#9911yescharacteristic
151C2×C4×C5#10412yes—
152C2×Dic5—22no—
153C2×Dic5—41no—
154C2×Dic5—41no—
155C2×Dic5—41no—
156C2×Dic5—41no—
157C2×Dic5—41no—
158C2×Dic5—41no—
159C2×Dic5—41no—
160C2×Dic5—41no—
161C2×Dic5—41no—
162C2×Dic5—41no—
163C2×Dic5—41no—
164#168—82no—
165C22×D4C22⋊D511yescharacteristic
166C23×C4C4×D511yescharacteristic
167C23×C4C22⋊D511yescharacteristic
168C4×D4—41no—
169C4×D4—41no—
170#117—201no—
171#117—201no—
172C2×C4⋊C4—51no—
173C2×C4⋊C4—51no—
174C2×C4⋊C4—101no—
175C2×C4⋊C4—101no—
176C2×C4⋊C4C4×D511yescharacteristic
177C2×C22⋊C4—22no—
178C2×C22⋊C4—101no—
179C2×C22⋊C4—101no—
180C2×C22⋊C4—101no—
181C2×C22⋊C4—101no—
182C2×C22⋊C4D2011yescharacteristic
183C2×C22⋊C4C22×D511yescharacteristic
184C2×C42—41no—
185C2×C42—101no—
186C2×C42—101no—
187C2×C42D2011yescharacteristic
188C4⋊C8—201no—
189#99—24no—
190C22⋊C8—102no—
191C4×C8—201no—
192#95—41no—
193#95—51no—
194#95—51no—
195#95—101no—
196#95—101no—
197#95—101no—
198#95—101no—
199C22×C5—21no—
200C22×C5—21no—
201C22×C5—22no—
202C22×C5—42no—
203C22×C5—41no—
204C22×C5—41no—
205C22×C5—41no—
206C22×C5—41no—
207C22×C5—41no—
208C22×C5—81no—
209C22×C5—81no—
210C22×C5—81no—
211C22×C5C2×#9911yescharacteristic
212C22×C5#41611yescharacteristic
213C22×C5C2×#10411yescharacteristic
214C4×C5—21no—
215C4×C5—22no—
216C4×C5—41no—
217C4×C5—41no—
218C4×C5—41no—
219C4×C5—84no—
220C4×C5#35212yes—
221Dic5—42no—
222Dic5—81no—
223Dic5—81no—
224Dic5—81no—
225C24#68511yescharacteristic
226C24C2×C22⋊D511yescharacteristic
227C2×D4—22no—
228C2×D4—22no—
229C2×D4—41no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—42no—
235C22×C4—42no—
236C22×C4—42no—
237C22×C4—101no—
238C22×C4—101no—
239C22×C4—101no—
240C22×C4—101no—
241C22×C4#68511yescharacteristic
242C22×C4#68511yescharacteristic
243C22×C4#68511yescharacteristic
244C22×C4C2×C4×D511yescharacteristic
245C22×C4C2×D2011yescharacteristic
246C2×C8—202no—
247C4⋊C4—41no—
248C4⋊C4—201no—
249C4⋊C4—201no—
250C4⋊C4—202no—
251C4⋊C4—202no—
252C22⋊C4—24no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C22⋊C4—42no—
256C22⋊C4—202no—
257C22⋊C4—202no—
258C22⋊C4—202no—
259C22⋊C4—202no—
260C42—21no—
261C42—21no—
262C42—82no—
263C42—202no—
264C42—201no—
265C42—201no—
266C2×C5—21no—
267C2×C5—21no—
268C2×C5—42no—
269C2×C5—81no—
270C2×C5#150111yescharacteristic
271C2×C5C2×#35211yescharacteristic
272C2×C5#212611yescharacteristic
273C23—21no—
274C23—21no—
275C23—21no—
276C23—21no—
277C23—21no—
278C23—41no—
279C23—41no—
280C23—41no—
281C23—41no—
282C23C2×#68511yescharacteristic
283C23#409612yes—
284D4—44no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—22no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—44no—
298C2×C4—81no—
299C2×C4—82no—
300C2×C4—82no—
301C2×C4—102no—
302C2×C4—201no—
303C2×C4—201no—
304C2×C4—201no—
305C2×C4—201no—
306C2×C4—201no—
307C2×C4—201no—
308C2×C4—201no—
309C2×C4—201no—
310C2×C4—201no—
311C2×C4—201no—
312C2×C4—201no—
313C2×C4#393712yes—
314C2×C4#393811yescharacteristic
315C2×C4#393811yescharacteristic
316C8—402no—
317C5#1172711yescharacteristic, complemented, Sylow
318C22—21no—
319C22—21no—
320C22—22no—
321C22—42no—
322C22—41no—
323C22—41no—
324C22—41no—
325C22—41no—
326C22—41no—
327C22—81no—
328C22—81no—
329C22—81no—
330C22C2×#393711yescharacteristic
331C22C2×#393811yescharacteristic
332C22#6529111yescharacteristic
333C4—22no—
334C4—21no—
335C4—41no—
336C4—41no—
337C4—41no—
338C4—84no—
339C4—202no—
340C4—401no—
341C4—401no—
342C4—401no—
343C4#6469212yes—
344C2—21no—
345C2—21no—
346C2—42no—
347C2—81no—
348C2#1060023611yescharacteristic
349C2C2×#6469211yescharacteristic
350C2#1060085311yescharacteristic
subgroupG/H
centerC2×C4#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C22⋊C4C22×D5
FittingC4×C5×#99C2
socleC22×C5C2×#99
prime radicalC22×C5×D4D4
cosocleC2×C5×C22⋊C4C23
hypercenterC4×#99D5
hypocenterC5#11727
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
4. #10597983C2semidirect
5. #10597982C2semidirect
7. C2×#4072C4semidirect
12. C4×C22⋊Dic5C4semidirect
13. #65275C4semidirect
14. #65272C4semidirect
317. C5#11727semidirect

Maximal subgroups

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

subgroupindex
#106140772
C4×C5×#992
#106023942
#105979832
#105979822
#117275