Finite Group Databasebeta

← #11997583

Subgroups — #11997583

Order 1280.

394 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10601265C211yesmaximal, characteristic
2#10601261C211yesmaximal, characteristic
3C2×#64704C211yesmaximal, characteristic
4C4×#3948C211yesmaximal, characteristic
5C2×#64674C211yesmaximal, characteristic
6C5×#1277C211yesmaximal, characteristic
7#10598195C211yesmaximal, characteristic
8C2×C4×Dic10C2211yescharacteristic
9C2×C5×C4⋊C8C2211yescharacteristic
10C2×C5×C4⋊C8C2211yescharacteristic
11C2×C4×C5×C8C2211yescharacteristic
12C2×#3948C411yescharacteristic
13C2×#3948C411yescharacteristic
14C2×#3946—21no—
15C4×C4⋊Dic5C2211yescharacteristic
16C2×C4×#168C2211yescharacteristic
17C2×C4×#168C2211yescharacteristic
18#64771C411yescharacteristic
19#64771C411yescharacteristic
20#64770—21no—
21#64770—21no—
22#64770—21no—
23#64704—22no—
24#64674—22no—
25#9557—51nomaximal, Sylow
26C22×Dic10C2×C411yescharacteristic
27C22×C5×C8—21no—
28C22×C5×C8—21no—
29C22×C5×C8C2×C411yescharacteristic
30C22×C5×C8C2×C411yescharacteristic
31C2×C42×C5C2311yescharacteristic
32C2×C4⋊Dic5C2×C411yescharacteristic
33C2×C4⋊Dic5C2×C411yescharacteristic
34C2×C4⋊Dic5C2×C411yescharacteristic
35C2×#683—21no—
36C2×C4×Dic5—21no—
37C2×C4×Dic5—21no—
38C22×#168—21no—
39C22×#168D411yescharacteristic
40C22×#168D411yescharacteristic
41C4×Dic10—21no—
42C4×Dic10—21no—
43C4×Dic10—21no—
44C4×Dic10—21no—
45C5×C4⋊C8—21no—
46C5×C4⋊C8—21no—
47C5×C4⋊C8—21no—
48C5×C4⋊C8—21no—
49C4×C5×C8—21no—
50C4×C5×C8—21no—
51#3963—21no—
52#3948—22no—
53#3948—22no—
54#3946—42no—
55C4×#168—21no—
56C4×#168—21no—
57C4×#168—21no—
58C4×#168D412yes—
59#1984—51no—
60#1939—51no—
61C4×#103—51no—
62C2×Q8⋊C8—51no—
63C2×#322—51no—
64#1279—51no—
65#1277D511yescharacteristic
66C22×C4×C5C22×C411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C22×C4×C5#4111yescharacteristic
69C22×Dic5—21no—
70C22×Dic5—21no—
71C22×Dic5—21no—
72C22×Dic5—21no—
73C2×Dic10—21no—
74C2×Dic10—21no—
75C2×Dic10—21no—
76C2×Dic10—21no—
77C2×Dic10—21no—
78C2×Dic10M1612yes—
79C2×C5×C8—21no—
80C2×C5×C8—21no—
81C2×C5×C8—21no—
82C2×C5×C8—21no—
83C2×C5×C8—21no—
84C2×C5×C8—21no—
85C2×C5×C8—41no—
86C2×C5×C8—41no—
87C2×C5×C8—41no—
88C2×C5×C8—41no—
89C2×C5×C8—41no—
90C2×C5×C8—41no—
91C42×C5C2×D411yescharacteristic
92C42×C5#4111yescharacteristic
93C42×C5#4111yescharacteristic
94C42×C5#4111yescharacteristic
95C4⋊Dic5—21no—
96C4⋊Dic5—21no—
97C4⋊Dic5—21no—
98C4⋊Dic5—21no—
99C4⋊Dic5—21no—
100C4⋊Dic5M1612yes—
101#683—41no—
102#683—41no—
103C4×Dic5—41no—
104C4×Dic5—41no—
105C4×Dic5—41no—
106C4×Dic5—41no—
107C2×#168—21no—
108C2×#168—21no—
109C2×#168—21no—
110C2×#168—21no—
111C2×#168—22no—
112C2×#168—41no—
113C2×#168—41no—
114C2×#168SD1612yes—
115C2×#168Q1612yes—
116C2×C4×Q8—51no—
117C2×C4⋊C8—101no—
118C2×C4⋊C8C2×D511yescharacteristic
119C2×C4⋊C8C2×D511yescharacteristic
120C2×#103—51no—
121C2×#103—51no—
122C2×C4×C8—51no—
123C2×C4×C8—51no—
124C2×C4×C8C2×D511yescharacteristic
125C4×C4⋊C4—51no—
126#340—51no—
127#340—51no—
128#336—101no—
129#336—101no—
130#336—101no—
131Q8⋊C8—102no—
132#322—102no—
133C23×C5C4×D411yescharacteristic
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5#11711yescharacteristic
137C2×C4×C5C4×D411yescharacteristic
138C2×C4×C5#12111yescharacteristic
139C2×C4×C5#12311yescharacteristic
140C2×C4×C5#12411yescharacteristic
141C2×C4×C5#12611yescharacteristic
142C2×C4×C5C2×M1611yescharacteristic
143C2×C4×C5C2×M1611yescharacteristic
144C2×C4×C5#13111yescharacteristic
145C2×C4×C5#13111yescharacteristic
146C2×C4×C5C2×SD1611yescharacteristic
147C2×C4×C5C2×Q1611yescharacteristic
148C2×C4×C5#13511yescharacteristic
149C2×C4×C5#13511yescharacteristic
150C2×Dic5—22no—
151C2×Dic5—22no—
152C2×Dic5—41no—
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—
162Dic10—22no—
163Dic10—22no—
164Dic10—41no—
165Dic10—41no—
166C5×C8—41no—
167C5×C8—41no—
168C5×C8—81no—
169C5×C8—81no—
170#168—22no—
171#168—22no—
172#168—42no—
173C22×Q8—51no—
174C22×C8—21no—
175C22×C8—21no—
176C22×C8—51no—
177C22×C8—51no—
178C22×C8—101no—
179C22×C8C4×D511yescharacteristic
180C22×C8C4×D511yescharacteristic
181C4×Q8—101no—
182C4×Q8—101no—
183C4×Q8—101no—
184C4×Q8—101no—
185C2×C4⋊C4—51no—
186C2×C4⋊C4—51no—
187C2×C4⋊C4—51no—
188C2×C4⋊C4—101no—
189C2×C42—101no—
190C2×C42—101no—
191C2×C42C22×D511yescharacteristic
192C4⋊C8—21no—
193C4⋊C8—21no—
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8—202no—
197#103—102no—
198#103—102no—
199C4×C8—21no—
200C4×C8—21no—
201C4×C8—52no—
202C4×C8—101no—
203C4×C8—101no—
204C4×C8—101no—
205#95—101no—
206C22×C5#38811yescharacteristic
207C22×C5#43511yescharacteristic
208C22×C5#43511yescharacteristic
209C22×C5C4×SD1611yescharacteristic
210C22×C5C4×Q1611yescharacteristic
211C22×C5#44411yescharacteristic
212C22×C5#44411yescharacteristic
213C4×C5—21no—
214C4×C5—21no—
215C4×C5#43211yescharacteristic
216C4×C5#43311yescharacteristic
217C4×C5#43511yescharacteristic
218C4×C5#43611yescharacteristic
219C4×C5#46511yescharacteristic
220C4×C5#46711yescharacteristic
221C4×C5#48711yescharacteristic
222C4×C5#48811yescharacteristic
223Dic5—42no—
224Dic5—42no—
225Dic5—81no—
226Dic5—81no—
227C2×Q8—52no—
228C2×Q8—101no—
229C2×Q8—101no—
230C2×Q8—101no—
231C2×Q8—101no—
232C2×Q8—101no—
233C22×C4—101no—
234C22×C4—101no—
235C22×C4—101no—
236C22×C4—101no—
237C22×C4C2×C4×D511yescharacteristic
238C22×C4D4×D511yescharacteristic
239C22×C4#71311yescharacteristic
240C2×C8—21no—
241C2×C8—21no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—41no—
251C2×C8—41no—
252C2×C8—52no—
253C2×C8—52no—
254C2×C8—101no—
255C2×C8—101no—
256C2×C8—101no—
257C2×C8—101no—
258C2×C8—102no—
259C2×C8—201no—
260C2×C8—201no—
261C4⋊C4—52no—
262C4⋊C4—101no—
263C4⋊C4—101no—
264C4⋊C4—101no—
265C4⋊C4—101no—
266C4⋊C4—101no—
267C4⋊C4—201no—
268C4⋊C4—201no—
269C42—201no—
270C42—201no—
271C42—201no—
272C42—201no—
273C42#70911yescharacteristic
274C42#70911yescharacteristic
275C42D4×D511yescharacteristic
276C42#71111yescharacteristic
277C2×C5#158211yescharacteristic
278C2×C5#158311yescharacteristic
279C2×C5#158411yescharacteristic
280C2×C5#158411yescharacteristic
281C2×C5#192411yescharacteristic
282C2×C5#193311yescharacteristic
283C2×C5#193811yescharacteristic
284C23#403911yescharacteristic
285Q8—102no—
286Q8—102no—
287Q8—201no—
288Q8—201no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—102no—
292C2×C4—102no—
293C2×C4—201no—
294C2×C4—201no—
295C2×C4—201no—
296C2×C4—201no—
297C2×C4—201no—
298C2×C4—201no—
299C2×C4—201no—
300C2×C4—201no—
301C2×C4—201no—
302C2×C4—201no—
303C2×C4#401811yescharacteristic
304C2×C4#402711yescharacteristic
305C2×C4#403011yescharacteristic
306C2×C4#403111yescharacteristic
307C2×C4#404011yescharacteristic
308C2×C4#404411yescharacteristic
309C2×C4#404711yescharacteristic
310C2×C4#404711yescharacteristic
311C2×C4D5×M1611yescharacteristic
312C2×C4D5×M1611yescharacteristic
313C2×C4#405811yescharacteristic
314C2×C4D5×SD1611yescharacteristic
315C2×C4#406211yescharacteristic
316C2×C4D5×Q1611yescharacteristic
317C8—41no—
318C8—41no—
319C8—81no—
320C8—81no—
321C8—102no—
322C8—102no—
323C8—202no—
324C5#955711yescharacteristic, complemented, Sylow
325C22#6495811yescharacteristic
326C22#6512511yescharacteristic
327C22#6512511yescharacteristic
328C22#6514111yescharacteristic
329C22#6516211yescharacteristic
330C22#6518311yescharacteristic
331C22#6518311yescharacteristic
332C4—21no—
333C4—21no—
334C4—202no—
335C4—202no—
336C4—401no—
337C4—401no—
338C4#6497911yescharacteristic
339C4#6499411yescharacteristic
340C4#6501711yescharacteristic
341C4#6501811yescharacteristic
342C4#6505711yescharacteristic
343C4#6506711yescharacteristic
344C4#6508111yescharacteristic
345C4#6510211yescharacteristic
346C2#1059931211yescharacteristic
347C2#1059931311yescharacteristic
348C2#1059935311yescharacteristic
349C2#1059935311yescharacteristic
350C2#1059945111yescharacteristic
351C2#1059964311yescharacteristic
352C2#1059971211yescharacteristic
subgroupG/H
centerC22×C4D4×D5
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1277C2
socle, prime radicalC23×C5C4×D4
cosocleC2×C42×C5C23
hypercenter#1277D5
hypocenterC5#9557
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
324. C5#9557semidirect

Maximal subgroups

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

subgroupindex
#106012652
#106012612
C2×#647042
C4×#39482
C2×#646742
C5×#12772
#105981952
#95575