Finite Group Databasebeta

← #12009855

Subgroups — #12009855

Order 1280.

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

normal subgroups only

This group has 482 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#10614104C211yesmaximal, characteristic
2C4×C5×#99C211yesmaximal, characteristic
3#10602396C211yesmaximal, characteristic
4#10597982C214yesmaximal, complemented
5C2×C4×C5×D4C2211yescharacteristic
6C2×#4081—21no—
7C22×C4⋊Dic5C411yescharacteristic, complemented
8C2×C5×#99—21no—
9C4×C5×C22⋊C4—21no—
10#65501—21no—
11#65501C411yescharacteristic, complemented
12#65272C412yescomplemented
13#65242C2212yes—
14#65232—21no—
15#65217—21no—
16#65215—21no—
17C5×#342C2212yes—
18#64745—21no—
19#64745C2212yes—
20#11773—51nomaximal, Sylow
21C22×C5×D4D411yescharacteristic
22C23×C4×C5C2×C411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×Dic5—21no—
25C4×C5×D4—41no—
26C4×C5×D4—41no—
27C2×C5×C4⋊C4C2×C411yescharacteristic
28C2×C5×C22⋊C4—22no—
29C2×C5×C22⋊C4D411yescharacteristic
30C2×C5×C22⋊C4C2311yescharacteristic
31C2×C42×C5—41no—
32C2×C42×C5D411yescharacteristic
33C2×C22⋊Dic5—21no—
34C2×C22⋊Dic5—22no—
35#4081—44no—
36C2×C4⋊Dic5—21no—
37C2×C4⋊Dic5—21no—
38C2×C4⋊Dic5—41no—
39C2×C4⋊Dic5—41no—
40C2×C4⋊Dic5C2×C412yes—
41C2×#683—22no—
42C5×#99—24no—
43C5×#95—41no—
44#3963—22no—
45#3963—22no—
46#3963C2×C412yes—
47C22⋊#168—22no—
48C4⋊#168—41no—
49#3935—41no—
50#2486—51no—
51C4×#99D511yescharacteristic
52#1466—51no—
53#1344—54no—
54C24×C5C22⋊C411yescharacteristic
55C24×C5C2×D411yescharacteristic
56C2×C5×D4—22no—
57C2×C5×D4—22no—
58C2×C5×D4—41no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—42no—
64C22×C4×C5—42no—
65C22×C4×C5—42no—
66C22×C4×C5C22⋊C411yescharacteristic
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22⋊C411yescharacteristic
69C22×C4×C5C22×C411yescharacteristic
70C22×C4×C5C2×D411yescharacteristic
71C22×Dic5—22no—
72C22×Dic5—22no—
73C22×Dic5—42no—
74C22×Dic5—42no—
75C22×Dic5—42no—
76C5×C4⋊C4—41no—
77C5×C22⋊C4—24no—
78C5×C22⋊C4—41no—
79C5×C22⋊C4—41no—
80C5×C22⋊C4—42no—
81C42×C5—21no—
82C42×C5—21no—
83C42×C5—82no—
84C22⋊Dic5—42no—
85C22⋊Dic5—44no—
86C4⋊Dic5—42no—
87C4⋊Dic5—41no—
88C4⋊Dic5—41no—
89C4⋊Dic5—42no—
90#683—44no—
91C2×#168—42no—
92C2×#123—101no—
93C2×C4×D4C2×D511yescharacteristic
94C22×C4⋊C4—51no—
95#432—101no—
96C2×#99—21no—
97#398—52no—
98#397—52no—
99#389—101no—
100#381—101no—
101#380—51no—
102#380—101no—
103C4×C22⋊C4—21no—
104#342C2×D512yes—
105#323—52no—
106#323—101no—
107C23×C5—21no—
108C23×C5—21no—
109C23×C5—21no—
110C23×C5—21no—
111C23×C5—41no—
112C23×C5—41no—
113C23×C5—41no—
114C23×C5—41no—
115C23×C5#10412yes—
116C23×C5C2×C22⋊C411yescharacteristic
117C23×C5AGL(1,ℤ/8)12yes—
118C5×D4—44no—
119C2×C4×C5—22no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—21no—
126C2×C4×C5—42no—
127C2×C4×C5—42no—
128C2×C4×C5—42no—
129C2×C4×C5—41no—
130C2×C4×C5—41no—
131C2×C4×C5—41no—
132C2×C4×C5—44no—
133C2×C4×C5—81no—
134C2×C4×C5—82no—
135C2×C4×C5—82no—
136C2×C4×C5#9911yescharacteristic
137C2×C4×C5#9911yescharacteristic
138C2×Dic5—42no—
139C2×Dic5—42no—
140C2×Dic5—42no—
141C2×Dic5—42no—
142C2×Dic5—42no—
143C2×Dic5—42no—
144C2×Dic5—84no—
145#168—82no—
146C22×D4C22⋊D511yescharacteristic
147C23×C4—101no—
148C23×C4C4×D511yescharacteristic
149C23×C4C22⋊D511yescharacteristic
150#123—204no—
151C4×D4—41no—
152C4×D4—41no—
153C2×C4⋊C4—52no—
154C2×C4⋊C4—102no—
155C2×C4⋊C4—101no—
156C2×C4⋊C4—101no—
157C2×C4⋊C4—201no—
158C2×C4⋊C4—201no—
159C2×C4⋊C4C4×D511yescharacteristic
160C2×C22⋊C4—22no—
161C2×C22⋊C4—101no—
162C2×C22⋊C4—102no—
163C2×C22⋊C4D2011yescharacteristic
164C2×C22⋊C4C22×D511yescharacteristic
165C2×C42—41no—
166C2×C42D2011yescharacteristic
167C4⋊C8—201no—
168#99—24no—
169C22⋊C8—102no—
170#97—201no—
171#95—41no—
172#95—52no—
173#95—102no—
174#95—102no—
175C22×C5—21no—
176C22×C5—21no—
177C22×C5—22no—
178C22×C5—22no—
179C22×C5—42no—
180C22×C5—42no—
181C22×C5—42no—
182C22×C5—41no—
183C22×C5—41no—
184C22×C5—41no—
185C22×C5—41no—
186C22×C5—81no—
187C22×C5C2×#9911yescharacteristic
188C22×C5#41811yescharacteristic
189C22×C5C2×#10411yescharacteristic
190C4×C5—21no—
191C4×C5—41no—
192C4×C5—41no—
193C4×C5—41no—
194C4×C5—41no—
195C4×C5—84no—
196C4×C5#35212yes—
197Dic5—82no—
198Dic5—82no—
199C24#68511yescharacteristic
200C24C2×C22⋊D511yescharacteristic
201C2×D4—22no—
202C2×D4—22no—
203C2×D4—41no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—42no—
209C22×C4—42no—
210C22×C4—42no—
211C22×C4—102no—
212C22×C4—102no—
213C22×C4—202no—
214C22×C4—202no—
215C22×C4—202no—
216C22×C4#68511yescharacteristic
217C22×C4#68511yescharacteristic
218C22×C4#68511yescharacteristic
219C22×C4C2×C4×D511yescharacteristic
220C22×C4C2×D2011yescharacteristic
221C2×C8—202no—
222C4⋊C4—41no—
223C4⋊C4—202no—
224C4⋊C4—204no—
225C4⋊C4—202no—
226C4⋊C4—201no—
227C4⋊C4—201no—
228C22⋊C4—24no—
229C22⋊C4—41no—
230C22⋊C4—41no—
231C22⋊C4—42no—
232C22⋊C4—202no—
233C22⋊C4—204no—
234C42—21no—
235C42—21no—
236C42—82no—
237C2×C5—21no—
238C2×C5—21no—
239C2×C5—42no—
240C2×C5—42no—
241C2×C5#150711yescharacteristic
242C2×C5C2×#35211yescharacteristic
243C2×C5#212911yescharacteristic
244C23—21no—
245C23—21no—
246C23—21no—
247C23—21no—
248C23—41no—
249C23—41no—
250C23—41no—
251C23—41no—
252C23#393712yes—
253C23C2×#68511yescharacteristic
254C23#409512yes—
255D4—44no—
256C2×C4—22no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—44no—
270C2×C4—81no—
271C2×C4—82no—
272C2×C4—82no—
273C2×C4—202no—
274C2×C4—202no—
275C2×C4—202no—
276C2×C4—202no—
277C2×C4—202no—
278C2×C4—202no—
279C2×C4—404no—
280C2×C4#393811yescharacteristic
281C2×C4#393811yescharacteristic
282C8—402no—
283C5#1177311yescharacteristic, complemented, Sylow
284C22—21no—
285C22—21no—
286C22—22no—
287C22—22no—
288C22—42no—
289C22—42no—
290C22—42no—
291C22—41no—
292C22—41no—
293C22—41no—
294C22—41no—
295C22—81no—
296C22C2×#393711yescharacteristic
297C22C2×#393811yescharacteristic
298C22#6529011yescharacteristic
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—41no—
304C4—84no—
305C4—402no—
306C4—402no—
307C4#6469212yes—
308C2—21no—
309C2—21no—
310C2—42no—
311C2—42no—
312C2#1060023711yescharacteristic
313C2C2×#6469211yescharacteristic
314C2#1060085211yescharacteristic
subgroupG/H
centerC22C2×#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#11773
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
4. #10597982C2semidirect
7. C22×C4⋊Dic5C4semidirect
11. #65501C4semidirect
12. #65272C4semidirect
283. C5#11773semidirect

Maximal subgroups

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

subgroupindex
#106141042
C4×C5×#992
#106023962
#105979822
#117735