Finite Group Databasebeta

← #11987686

Subgroups — #11987686

Order 1280.

438 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2860C211yesmaximal, characteristic
2#10600185C211yesmaximal, characteristic, complemented
3#10600181C211yesmaximal, characteristic, complemented
4#10598130C212yesmaximal
5#10598129C212yesmaximal, complemented
6C2×C5×#126—21no—
7C5×#390C411yescharacteristic
8C5×#390C411yescharacteristic
9C5×#390C2211yescharacteristic
10C5×#389C411yescharacteristic
11C5×#389C411yescharacteristic
12C5×#389C2211yescharacteristic
13C5×#388—21no—
14C5×#388—21no—
15C5×#388—21no—
16C43×C5C2211yescharacteristic
17C2×C4⋊#168—21no—
18C2×C4×#168—21no—
19#64744—21no—
20#64744—21no—
21#64744C2212yes—
22#64744C2212yes—
23#7666—51nomaximal, Sylow
24C22×C5×D4C2×C411yescharacteristic
25C5×#126—42no—
26C5×#126—42no—
27C2×C5×C4⋊C4—21no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4—21no—
30C2×C5×C4⋊C4C2×C411yescharacteristic
31C2×C5×C4⋊C4C2×C411yescharacteristic
32C2×C5×C4⋊C4C2×C411yescharacteristic
33C2×C5×C22⋊C4—21no—
34C2×C5×C22⋊C4—21no—
35C2×C5×C22⋊C4—21no—
36C2×C5×C22⋊C4—21no—
37C2×C5×C22⋊C4—21no—
38C2×C5×C22⋊C4—21no—
39C2×C42×C5C2×C411yescharacteristic
40C2×C42×C5C2×C411yescharacteristic
41C2×C42×C5D411yescharacteristic
42C2×C42×C5D411yescharacteristic
43C2×C42×C5D411yescharacteristic
44C2×C42×C5D411yescharacteristic
45C2×C42×C5C2311yescharacteristic
46C22×#168—22no—
47C22×#168—22no—
48C5×#95—21no—
49C5×#95—21no—
50C5×#95—21no—
51C4⋊#168—42no—
52C4×#168—24no—
53#2860D511yescharacteristic
54#1831—51no—
55#1744—51no—
56#1271—52no—
57#1270—52no—
58C24×C5—21no—
59C2×C5×D4—22no—
60C2×C5×D4—41no—
61C2×C5×D4—41no—
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5—21no—
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22⋊C411yescharacteristic
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22⋊C411yescharacteristic
69C22×C4×C5C22×C411yescharacteristic
70C22×C4×C5C2×D411yescharacteristic
71C22×C4×C5C2×D411yescharacteristic
72C5×C4⋊C4—22no—
73C5×C4⋊C4—41no—
74C5×C4⋊C4—41no—
75C5×C4⋊C4—42no—
76C5×C4⋊C4—42no—
77C5×C4⋊C4—41no—
78C5×C4⋊C4—41no—
79C5×C22⋊C4—42no—
80C5×C22⋊C4—42no—
81C5×C22⋊C4—42no—
82C5×C22⋊C4—42no—
83C5×C22⋊C4—41no—
84C5×C22⋊C4—41no—
85C5×C22⋊C4—42no—
86C42×C5—22no—
87C42×C5—22no—
88C42×C5—22no—
89C42×C5—41no—
90C42×C5—41no—
91C42×C5—41no—
92C42×C5D812yes—
93C42×C5SD1612yes—
94C2×#168—24no—
95C2×#168—42no—
96C2×#168—42no—
97C2×#168—42no—
98C2×#168—42no—
99C2×#168—42no—
100C2×#126—21no—
101C2×C4⋊C8—101no—
102C2×C4×C8—101no—
103#390Dic511yescharacteristic
104#390Dic511yescharacteristic
105#390C2×D511yescharacteristic
106#389Dic511yescharacteristic
107#389Dic511yescharacteristic
108#389C2×D511yescharacteristic
109#388—21no—
110#388—21no—
111#388—21no—
112C43C2×D511yescharacteristic
113#336—52no—
114#336—52no—
115#336—101no—
116#336—101no—
117C23×C5—41no—
118C23×C5—41no—
119C23×C5—41no—
120C23×C5—41no—
121C23×C5—41no—
122C23×C5—41no—
123C23×C5—41no—
124C23×C5C2×C22⋊C411yescharacteristic
125C5×D4—82no—
126C2×C4×C5—21no—
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—21no—
134C2×C4×C5—21no—
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—41no—
142C2×C4×C5—41no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
145C2×C4×C5—41no—
146C2×C4×C5—41no—
147C2×C4×C5—41no—
148C2×C4×C5—41no—
149C2×C4×C5—41no—
150C2×C4×C5#10212yes—
151C2×C4×C5#10212yes—
152C2×C4×C5#10412yes—
153C2×C4×C5#13112yes—
154C2×C4×C5C2×D811yescharacteristic
155C2×C4×C5C2×SD1611yescharacteristic
156C2×C4×C5#13512yes—
157#168—44no—
158#168—82no—
159C22×D4C2×Dic511yescharacteristic
160C22×C8—102no—
161C22×C8—102no—
162#126—42no—
163#126—42no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—21no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4C2×Dic511yescharacteristic
168C2×C4⋊C4C2×Dic511yescharacteristic
169C2×C4⋊C4C2×Dic511yescharacteristic
170C2×C22⋊C4—21no—
171C2×C22⋊C4—21no—
172C2×C22⋊C4—21no—
173C2×C22⋊C4—21no—
174C2×C22⋊C4—21no—
175C2×C22⋊C4—21no—
176C2×C42C2×Dic511yescharacteristic
177C2×C42C2×Dic511yescharacteristic
178C2×C42C22⋊D511yescharacteristic
179C2×C42C22⋊D511yescharacteristic
180C2×C42C22⋊D511yescharacteristic
181C2×C42C22⋊D511yescharacteristic
182C2×C42C22×D511yescharacteristic
183C4⋊C8—202no—
184C4×C8—104no—
185#95—21no—
186#95—21no—
187#95—21no—
188C22×C5—81no—
189C22×C5—81no—
190C22×C5—81no—
191C22×C5—81no—
192C22×C5—81no—
193C22×C5—81no—
194C22×C5—81no—
195C22×C5#40811yescharacteristic
196C22×C5#41011yescharacteristic
197C22×C5#41311yescharacteristic
198C22×C5C2×#10211yescharacteristic
199C22×C5#41611yescharacteristic
200C22×C5C2×#10411yescharacteristic
201C22×C5#42111yescharacteristic
202C4×C5—22no—
203C4×C5—22no—
204C4×C5—22no—
205C4×C5—22no—
206C4×C5—21no—
207C4×C5—21no—
208C4×C5—22no—
209C4×C5—41no—
210C4×C5—81no—
211C4×C5—81no—
212C4×C5—81no—
213C24—21no—
214C2×D4—22no—
215C2×D4—41no—
216C2×D4—41no—
217C22×C4—21no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4C22⋊Dic511yescharacteristic
221C22×C4C22⋊Dic511yescharacteristic
222C22×C4C22⋊Dic511yescharacteristic
223C22×C4C22⋊Dic511yescharacteristic
224C22×C4C22×Dic511yescharacteristic
225C22×C4C2×C22⋊D511yescharacteristic
226C22×C4C2×C22⋊D511yescharacteristic
227C2×C8—104no—
228C2×C8—202no—
229C2×C8—202no—
230C2×C8—202no—
231C2×C8—202no—
232C2×C8—202no—
233C4⋊C4—22no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C22⋊C4—42no—
241C22⋊C4—42no—
242C22⋊C4—42no—
243C22⋊C4—42no—
244C22⋊C4—42no—
245C22⋊C4—41no—
246C22⋊C4—41no—
247C42—22no—
248C42—22no—
249C42—22no—
250C42—41no—
251C42—41no—
252C42—41no—
253C42#68612yes—
254C42#68712yes—
255C2×C5—161no—
256C2×C5#147311yescharacteristic
257C2×C5#148211yescharacteristic
258C2×C5#149211yescharacteristic
259C2×C5#150011yescharacteristic
260C2×C5#151711yescharacteristic
261C2×C5#153211yescharacteristic
262C2×C5#154011yescharacteristic
263C23—41no—
264C23—41no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23—41no—
270C23C2×C22⋊Dic511yescharacteristic
271D4—82no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4#396412yes—
297C2×C4#396412yes—
298C2×C4#396912yes—
299C2×C4C2×#68611yescharacteristic
300C2×C4C2×#68711yescharacteristic
301C2×C4#409412yes—
302C2×C4#409612yes—
303C8—204no—
304C8—402no—
305C5#766611yescharacteristic, complemented, Sylow
306C22—81no—
307C22—81no—
308C22—81no—
309C22—81no—
310C22—81no—
311C22—81no—
312C22—81no—
313C22C2×#396411yescharacteristic
314C22#6552211yescharacteristic
315C22#6552311yescharacteristic
316C22C2×#396911yescharacteristic
317C22#6552511yescharacteristic
318C22#6552611yescharacteristic
319C22#6552911yescharacteristic
320C4—22no—
321C4—22no—
322C4—22no—
323C4—22no—
324C4—22no—
325C4—21no—
326C4—21no—
327C4—41no—
328C4—81no—
329C4—81no—
330C4—81no—
331C2—161no—
332C2#1060253811yescharacteristic
333C2#1060254111yescharacteristic
334C2#1060254311yescharacteristic
335C2#1060254711yescharacteristic
336C2#1060259511yescharacteristic
337C2#1060259711yescharacteristic
338C2#1060260711yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic5
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2860C2
socleC23×C5C2×C22⋊C4
prime radicalC22×C5×D4C2×C4
cosocleC2×C42×C5C23
hypercenter#2860D5
hypocenterC5#7666
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C43 ◁ #2860

Complements

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

NH ≅ G/Ntype
2. #10600185C2semidirect
3. #10600181C2semidirect
5. #10598129C2semidirect
305. C5#7666semidirect

Maximal subgroups

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

subgroupindex
C5×#28602
#106001852
#106001812
#105981302
#105981292
#76665