Finite Group Databasebeta

← #12009637

Subgroups — #12009637

Order 1280.

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

normal subgroups only

This group has 470 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#10614079C211yesmaximal, characteristic
2C4×C5×#99C211yesmaximal, characteristic
3#10602393C211yesmaximal, characteristic
4#10597982C212yesmaximal, complemented
5#10597981C212yesmaximal, complemented
6C2×C4×C5×D4C2211yescharacteristic
7C2×C4×Dic10C411yescharacteristic, complemented
8C2×C5×#99—21no—
9C4×C5×C22⋊C4—21no—
10#65511—21no—
11C4×C22⋊Dic5—21no—
12C4×C22⋊Dic5—21no—
13C2×C22⋊#168—21no—
14#65271—21no—
15#65242C411yescharacteristic, complemented
16#65242C2211yescharacteristic
17#65236C411yescharacteristic, complemented
18#65236C2211yescharacteristic
19#65221C411yescharacteristic, complemented
20C5×#342C2212yes—
21#64748—21no—
22#64745C2212yes—
23#11728—51nomaximal, Sylow
24C22×C5×D4D411yescharacteristic
25C23×C4×C5D411yescharacteristic
26C23×C4×C5D411yescharacteristic
27C22×Dic10C2×C411yescharacteristic
28C4×C5×D4—41no—
29C4×C5×D4—41no—
30C2×C5×C4⋊C4D411yescharacteristic
31C2×C5×C22⋊C4—22no—
32C2×C5×C22⋊C4C2×C411yescharacteristic
33C2×C5×C22⋊C4C2311yescharacteristic
34C2×C42×C5—41no—
35C2×C42×C5C2×C411yescharacteristic
36C2×C22⋊Dic5—21no—
37C2×C22⋊Dic5—21no—
38C2×C22⋊Dic5—21no—
39C2×C22⋊Dic5—21no—
40C2×C4⋊Dic5C2×C411yescharacteristic
41C2×#683—21no—
42C2×C4×Dic5—21no—
43C2×C4×Dic5—21no—
44C22×#168—41no—
45C4×Dic10—41no—
46C4×Dic10—41no—
47C5×#99—24no—
48C5×#95—41no—
49#3963—21no—
50#3963—21no—
51#3963—21no—
52#3963—21no—
53#3963—21no—
54#3963C2×C411yescharacteristic
55#3963C2×C411yescharacteristic
56C22⋊#168—22no—
57C22⋊#168—41no—
58#2398—51no—
59C4×#99D511yescharacteristic
60#1459—51no—
61#1351—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—
84C2×Dic10—41no—
85C2×Dic10—42no—
86C5×C4⋊C4—41no—
87C5×C22⋊C4—24no—
88C5×C22⋊C4—41no—
89C5×C22⋊C4—41no—
90C5×C22⋊C4—42no—
91C42×C5—21no—
92C42×C5—21no—
93C42×C5—82no—
94C22⋊Dic5—42no—
95C22⋊Dic5—42no—
96C22⋊Dic5—42no—
97C22⋊Dic5—42no—
98C4⋊Dic5—41no—
99#683—42no—
100C4×Dic5—42no—
101C4×Dic5—41no—
102C4×Dic5—41no—
103C2×#168—42no—
104C2×#168—82no—
105C2×C4×Q8—51no—
106C2×C4×D4C2×D511yescharacteristic
107C2×#99—21no—
108C2×C22⋊C8—101no—
109#400—101no—
110#397—51no—
111#397—51no—
112#394—101no—
113#393—51no—
114#393—51no—
115C4×C22⋊C4—21no—
116C4×C22⋊C4—101no—
117C4×C22⋊C4—101no—
118#376—51no—
119#342C2×D512yes—
120#324—101no—
121#323—52no—
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×C5#10412yes—
131C23×C5C2×C22⋊C411yescharacteristic
132C23×C5#13512yes—
133C5×D4—44no—
134C2×C4×C5—22no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5—42no—
142C2×C4×C5—42no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
145C2×C4×C5—41no—
146C2×C4×C5—44no—
147C2×C4×C5—81no—
148C2×C4×C5—81no—
149C2×C4×C5—82no—
150C2×C4×C5—82no—
151C2×C4×C5#9911yescharacteristic
152C2×C4×C5#9911yescharacteristic
153C2×Dic5—22no—
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—
164C2×Dic5—41no—
165Dic10—42no—
166Dic10—42no—
167#168—82no—
168C22×Q8—51no—
169C22×D4C22⋊D511yescharacteristic
170C23×C4D2011yescharacteristic
171C23×C4C22⋊D511yescharacteristic
172C22×C8—201no—
173C4×Q8—201no—
174C4×Q8—201no—
175C4×D4—41no—
176C4×D4—41no—
177C2×C4⋊C4—51no—
178C2×C4⋊C4—101no—
179C2×C4⋊C4D2011yescharacteristic
180C2×C22⋊C4—22no—
181C2×C22⋊C4—101no—
182C2×C22⋊C4—101no—
183C2×C22⋊C4—101no—
184C2×C22⋊C4—101no—
185C2×C22⋊C4C4×D511yescharacteristic
186C2×C22⋊C4C22×D511yescharacteristic
187C2×C42—41no—
188C2×C42—101no—
189C2×C42—101no—
190C2×C42C4×D511yescharacteristic
191#99—24no—
192C22⋊C8—102no—
193C22⋊C8—201no—
194#95—41no—
195#95—51no—
196#95—51no—
197#95—101no—
198#95—101no—
199#95—101no—
200#95—101no—
201#95—101no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5—22no—
205C22×C5—22no—
206C22×C5—42no—
207C22×C5—42no—
208C22×C5—41no—
209C22×C5—41no—
210C22×C5—41no—
211C22×C5—41no—
212C22×C5—81no—
213C22×C5—81no—
214C22×C5C2×#9911yescharacteristic
215C22×C5#41611yescharacteristic
216C22×C5C2×#10411yescharacteristic
217C4×C5—21no—
218C4×C5—41no—
219C4×C5—41no—
220C4×C5—41no—
221C4×C5—41no—
222C4×C5—84no—
223C4×C5#35412yes—
224Dic5—42no—
225Dic5—81no—
226Dic5—81no—
227Dic5—81no—
228C24#68511yescharacteristic
229C24C2×C22⋊D511yescharacteristic
230C2×Q8—201no—
231C2×Q8—202no—
232C2×D4—22no—
233C2×D4—22no—
234C2×D4—41no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—42no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—101no—
243C22×C4—101no—
244C22×C4—101no—
245C22×C4—101no—
246C22×C4#68511yescharacteristic
247C22×C4#68511yescharacteristic
248C22×C4#68511yescharacteristic
249C22×C4C2×C4×D511yescharacteristic
250C22×C4C2×D2011yescharacteristic
251C2×C8—202no—
252C2×C8—402no—
253C4⋊C4—41no—
254C4⋊C4—201no—
255C4⋊C4—202no—
256C22⋊C4—24no—
257C22⋊C4—41no—
258C22⋊C4—41no—
259C22⋊C4—42no—
260C22⋊C4—202no—
261C22⋊C4—202no—
262C22⋊C4—202no—
263C22⋊C4—202no—
264C42—21no—
265C42—21no—
266C42—82no—
267C42—202no—
268C42—201no—
269C42—201no—
270C2×C5—21no—
271C2×C5—21no—
272C2×C5—42no—
273C2×C5—42no—
274C2×C5#150111yescharacteristic
275C2×C5#212011yescharacteristic
276C2×C5C2×#35411yescharacteristic
277C23—21no—
278C23—21no—
279C23—21no—
280C23—21no—
281C23—41no—
282C23—41no—
283C23—41no—
284C23—41no—
285C23#393712yes—
286C23C2×#68511yescharacteristic
287C23#409612yes—
288Q8—202no—
289Q8—202no—
290D4—44no—
291C2×C4—22no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—42no—
299C2×C4—42no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—44no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—82no—
307C2×C4—82no—
308C2×C4—102no—
309C2×C4—201no—
310C2×C4—201no—
311C2×C4—201no—
312C2×C4—201no—
313C2×C4—201no—
314C2×C4—201no—
315C2×C4—201no—
316C2×C4—201no—
317C2×C4—201no—
318C2×C4—201no—
319C2×C4—201no—
320C2×C4#393811yescharacteristic
321C2×C4#393811yescharacteristic
322C8—402no—
323C5#1172811yescharacteristic, complemented, Sylow
324C22—21no—
325C22—21no—
326C22—22no—
327C22—22no—
328C22—42no—
329C22—42no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—81no—
335C22—81no—
336C22C2×#393711yescharacteristic
337C22C2×#393811yescharacteristic
338C22#6529111yescharacteristic
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—84no—
345C4—202no—
346C4—401no—
347C4—401no—
348C4—401no—
349C4#6469312yes—
350C2—21no—
351C2—21no—
352C2—42no—
353C2—42no—
354C2#1060023611yescharacteristic
355C2C2×#6469311yescharacteristic
356C2#1060084911yescharacteristic
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#11728
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. #10597982C2semidirect
5. #10597981C2semidirect
7. C2×C4×Dic10C4semidirect
15. #65242C4semidirect
17. #65236C4semidirect
19. #65221C4semidirect
323. C5#11728semidirect

Maximal subgroups

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

subgroupindex
#106140792
C4×C5×#992
#106023932
#105979822
#105979812
#117285