Finite Group Databasebeta

← #11995957

Subgroups — #11995957

Order 1280.

490 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2932C211yesmaximal, characteristic
2#10615048C211yesmaximal, characteristic
3#10602607C211yesmaximal, characteristic
4#10601301C211yesmaximal, characteristic, complemented
5#10600621C211yesmaximal, characteristic, complemented
6#10598204C211yesmaximal, characteristic, complemented
7#10598151C211yesmaximal, characteristic, complemented
8C2×C5×#131—21no—
9C5×#532C2211yescharacteristic
10C2×#4015C2211yescharacteristic
11C5×#435—22no—
12C5×#435—22no—
13C5×#423C2211yescharacteristic
14C5×#408—21no—
15C2×C5×#97C2211yescharacteristic
16#65382C412yescomplemented
17#65365C412yescomplemented
18#65329—22no—
19#65308—22no—
20#65225C2211yescharacteristic
21#65214C2211yescharacteristic
22#65214C2211yescharacteristic
23#64771—21no—
24#64771—21no—
25#64757—22no—
26#64706—22no—
27#9289—51nomaximal, Sylow
28C2×C5×#41—21no—
29C22×Dic10—21no—
30C5×#131—42no—
31C5×#131—42no—
32C2×C5×M16—22no—
33C2×C5×M16—21no—
34C22×C5×C8—22no—
35C22×C5×C8D411yescharacteristic
36C22×C5×C8D411yescharacteristic
37C5×C4⋊Q8C2×C411yescharacteristic
38C5×#127C2×C411yescharacteristic
39C5×#124—21no—
40C5×#121—21no—
41C5×#121D412yes—
42C4×C5×D4—21no—
43C4×C5×D4D412yes—
44C2×C42×C5C2311yescharacteristic
45C2×#687—24no—
46C2×C4⋊Dic5—21no—
47C2×C4⋊Dic5—21no—
48C2×C4⋊Dic5—21no—
49#4015—21no—
50#4015—21no—
51#4015—21no—
52#4015C2×C412yes—
53C5×C4⋊C8—21no—
54C5×C4⋊C8D412yes—
55C5×C22⋊C8—24no—
56C5×#97—21no—
57C5×#97—21no—
58#3963—21no—
59#3963—21no—
60C22⋊#168—21no—
61C22⋊#168—21no—
62#3942—24no—
63C4⋊#168—21no—
64C4⋊#168—21no—
65C4×#168—21no—
66C4×#168C2×C412yes—
67#3206—51no—
68#2932D511yescharacteristic
69#1993—51no—
70#1549—51no—
71#1517—51no—
72#1286—51no—
73#1275—51no—
74C5×#41—41no—
75C5×#41—41no—
76C5×#41—41no—
77C5×#41—41no—
78C2×C5×Q8—21no—
79C2×C5×D4—22no—
80C2×C5×D4—21no—
81C2×C5×D4—21no—
82C2×C5×D4C22⋊C412yes—
83C22×C4×C5—22no—
84C22×C4×C5C2×D411yescharacteristic
85C22×C4×C5C2×D411yescharacteristic
86C22×C4×C5#4111yescharacteristic
87C22×Dic5—41no—
88C22×Dic5—41no—
89C2×Dic10—22no—
90C2×Dic10—41no—
91C2×Dic10—82no—
92C5×M16—44no—
93C5×M16—41no—
94C5×M16—41no—
95C2×C5×C8—21no—
96C2×C5×C8—21no—
97C2×C5×C8—22no—
98C2×C5×C8—21no—
99C2×C5×C8—21no—
100C2×C5×C8—21no—
101C2×C5×C8—44no—
102C2×C5×C8SD1612yescomplemented
103C5×C4⋊C4—21no—
104C5×C4⋊C4C22⋊C412yes—
105C5×C22⋊C4—22no—
106C5×C22⋊C4—22no—
107C42×C5C22×C411yescharacteristic
108C42×C5C2×D411yescharacteristic
109C42×C5C2×D411yescharacteristic
110C42×C5#4111yescharacteristic
111#687—84no—
112C4⋊Dic5—22no—
113C4⋊Dic5—22no—
114C4⋊Dic5—41no—
115C4⋊Dic5—41no—
116C4⋊Dic5—41no—
117C4⋊Dic5—41no—
118C2×#168—22no—
119C2×#168—41no—
120C2×#131—21no—
121#532C2×D511yescharacteristic
122C2×C4⋊Q8—51no—
123#492—52no—
124#487—52no—
125#461—102no—
126#448—102no—
127#435—22no—
128#435—22no—
129#431—51no—
130#431—51no—
131#423C2×D511yescharacteristic
132#408—21no—
133C2×#97C2×D511yescharacteristic
134#382—51no—
135#340—101no—
136#340—101no—
137#332—102no—
138#327—102no—
139C23×C5—22no—
140C23×C5#12111yescharacteristic
141C5×Q8—41no—
142C5×Q8—41no—
143C5×D4—42no—
144C5×D4—42no—
145C5×D4—42no—
146C5×D4—41no—
147C5×D4—41no—
148C5×D4—81no—
149C2×C4×C5—22no—
150C2×C4×C5—41no—
151C2×C4×C5—41no—
152C2×C4×C5—42no—
153C2×C4×C5—42no—
154C2×C4×C5C2×C22⋊C411yescharacteristic
155C2×C4×C5C4×D411yescharacteristic
156C2×C4×C5C4×D411yescharacteristic
157C2×C4×C5#12011yescharacteristic
158C2×C4×C5#12111yescharacteristic
159C2×C4×C5#12311yescharacteristic
160C2×C4×C5C2×SD1611yescharacteristic
161C2×C4×C5#13511yescharacteristic
162C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C2×C4×C5#13711yescharacteristic
164C2×Dic5—42no—
165C2×Dic5—82no—
166C2×Dic5—81no—
167C2×Dic5—81no—
168C2×Dic5—81no—
169Dic10—44no—
170Dic10—82no—
171C5×C8—22no—
172C5×C8—42no—
173C5×C8—41no—
174#168—42no—
175#168—81no—
176C2×#41—21no—
177C22×Q8—101no—
178C2×SD16—104no—
179#131—42no—
180#131—42no—
181C2×M16—22no—
182C2×M16—21no—
183C22×C8—22no—
184C22×C8C22⋊D511yescharacteristic
185C22×C8C22⋊D511yescharacteristic
186C4⋊Q8—52no—
187C4⋊Q8—101no—
188C4⋊Q8—101no—
189C4⋊Q8—101no—
190C4⋊Q8C4×D511yescharacteristic
191#127C4×D511yescharacteristic
192#124—21no—
193#121—21no—
194#121D2012yes—
195C4×D4—21no—
196C4×D4C22⋊D512yes—
197C2×C4⋊C4—101no—
198C2×C4⋊C4—101no—
199C2×C4⋊C4—101no—
200C2×C42C22×D511yescharacteristic
201C4⋊C8—21no—
202C4⋊C8—101no—
203C4⋊C8—101no—
204C4⋊C8C22⋊D512yes—
205#103—104no—
206C22⋊C8—24no—
207C22⋊C8—101no—
208C22⋊C8—101no—
209#97—21no—
210#97—21no—
211C4×C8—52no—
212C4×C8—101no—
213#95—101no—
214#95—101no—
215C22×C5—21no—
216C22×C5—21no—
217C22×C5—42no—
218C22×C5—42no—
219C22×C5—42no—
220C22×C5#38611yescharacteristic
221C22×C5#46111yescharacteristic
222C22×C5#46311yescharacteristic
223C4×C5—21no—
224C4×C5—21no—
225C4×C5—21no—
226C4×C5—21no—
227C4×C5—42no—
228C4×C5C4×SD1611yescharacteristic
229C4×C5#44011yescharacteristic
230C4×C5#45011yescharacteristic
231C4×C5#45211yescharacteristic
232Dic5—82no—
233Dic5—161no—
234#41—41no—
235#41—41no—
236#41—41no—
237#41—41no—
238C2×Q8—21no—
239C2×Q8—102no—
240C2×Q8—201no—
241C2×Q8—402no—
242C2×D4—22no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4#68512yes—
246C22×C4—22no—
247C22×C4—201no—
248C22×C4—201no—
249C22×C4C2×D2011yescharacteristic
250C22×C4#70911yescharacteristic
251C22×C4C2×C22⋊D511yescharacteristic
252SD16—404no—
253M16—44no—
254M16—41no—
255M16—41no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—22no—
262C2×C8—44no—
263C2×C8—102no—
264C2×C8—201no—
265C2×C8#68712yescomplemented
266C4⋊C4—21no—
267C4⋊C4—102no—
268C4⋊C4—102no—
269C4⋊C4—201no—
270C4⋊C4—201no—
271C4⋊C4—201no—
272C4⋊C4—201no—
273C4⋊C4#68512yes—
274C22⋊C4—22no—
275C22⋊C4—22no—
276C42C2×C4×D511yescharacteristic
277C42#70911yescharacteristic
278C42C2×C22⋊D511yescharacteristic
279C42C2×C22⋊D511yescharacteristic
280C2×C5—21no—
281C2×C5—21no—
282C2×C5—82no—
283C2×C5#187711yescharacteristic
284C2×C5#190211yescharacteristic
285C2×C5#191011yescharacteristic
286C23—22no—
287C23#407611yescharacteristic
288Q8—41no—
289Q8—41no—
290Q8—204no—
291Q8—402no—
292D4—42no—
293D4—42no—
294D4—42no—
295D4—41no—
296D4—41no—
297D4—81no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—41no—
301C2×C4—42no—
302C2×C4—42no—
303C2×C4—202no—
304C2×C4—402no—
305C2×C4—401no—
306C2×C4—401no—
307C2×C4—401no—
308C2×C4C2×#68511yescharacteristic
309C2×C4C4×C22⋊D511yescharacteristic
310C2×C4C4×C22⋊D511yescharacteristic
311C2×C4#407511yescharacteristic
312C2×C4#407611yescharacteristic
313C2×C4#407811yescharacteristic
314C2×C4C2×#68711yescharacteristic
315C2×C4#409611yescharacteristic
316C2×C4#409711yescharacteristic
317C2×C4#409911yescharacteristic
318C8—22no—
319C8—42no—
320C8—41no—
321C8—202no—
322C8—401no—
323C5#928911yescharacteristic, complemented, Sylow
324C22—21no—
325C22—21no—
326C22—42no—
327C22—42no—
328C22—42no—
329C22#6530511yescharacteristic
330C22#6530811yescharacteristic
331C22#6550211yescharacteristic
332C4—21no—
333C4—21no—
334C4—21no—
335C4—21no—
336C4—42no—
337C4—402no—
338C4—801no—
339C4C4×#68711yescharacteristic
340C4#6530711yescharacteristic
341C4#6550711yescharacteristic
342C4#6552811yescharacteristic
343C2—21no—
344C2—21no—
345C2—82no—
346C2#1060240511yescharacteristic
347C2#1060281511yescharacteristic
348C2#1060281811yescharacteristic
subgroupG/H
centerC22#65502
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2932C2
socleC22×C5#386
prime radicalC5×#532C22
cosocleC2×C42×C5C23
hypercenter#2932D5
hypocenterC5#9289
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2932

Complements

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

NH ≅ G/Ntype
4. #10601301C2semidirect
5. #10600621C2semidirect
6. #10598204C2semidirect
7. #10598151C2semidirect
16. #65382C4semidirect
17. #65365C4semidirect
102. C2×C5×C8SD16semidirect
265. C2×C8#687semidirect
323. C5#9289semidirect

Maximal subgroups

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

subgroupindex
C5×#29322
#106150482
#106026072
#106013012
#106006212
#105982042
#105981512
#92895