Finite Group Databasebeta

← #11997513

Subgroups — #11997513

Order 1280.

392 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
2C2×#64700C211yesmaximal, characteristic
3C2×#64676C211yesmaximal, characteristic
4#10600270C211yesmaximal, characteristic
5C4×#3942C211yesmaximal, characteristic
6C5×#1279C211yesmaximal, characteristic
7#10598144C211yesmaximal, characteristic
8C2×C4×Dic10C2211yescharacteristic
9C2×C5×C4⋊C8C2211yescharacteristic
10C2×C4×C5×C8C2211yescharacteristic
11C4×C5×C4⋊C4C2211yescharacteristic
12C2×#3942C411yescharacteristic
13C2×#3942C411yescharacteristic
14C2×C4⋊#168C2211yescharacteristic
15C2×#3935—21no—
16C2×C4×#168C2211yescharacteristic
17C2×C4×#168C2211yescharacteristic
18#64770—21no—
19#64770—21no—
20#64749C411yescharacteristic
21#64749C411yescharacteristic
22#64744—21no—
23#64700—22no—
24#64676—22no—
25#9547—51nomaximal, Sylow
26C22×Dic10C2×C411yescharacteristic
27C22×C5×C8—21no—
28C22×C5×C8—21no—
29C2×C5×C4⋊C4C2×C411yescharacteristic
30C2×C5×C4⋊C4C2×C411yescharacteristic
31C2×C42×C5—21no—
32C2×C42×C5C2311yescharacteristic
33C2×C4⋊Dic5C2×C411yescharacteristic
34C2×#683—21no—
35C2×C4×Dic5—21no—
36C22×#168—21no—
37C22×#168C2×C411yescharacteristic
38C22×#168C2×C411yescharacteristic
39C22×#168D411yescharacteristic
40C22×#168D411yescharacteristic
41C4×Dic10—21no—
42C4×Dic10—21no—
43C4×Dic10—21no—
44C4×Dic10—21no—
45C5×C4⋊C8—21no—
46C5×C4⋊C8—21no—
47C4×C5×C8—21no—
48C4×C5×C8—21no—
49C5×#95—21no—
50#3942—22no—
51#3942—22no—
52C4⋊#168—21no—
53C4⋊#168D412yes—
54#3935—42no—
55C4×#168—21no—
56C4×#168—21no—
57C4×#168—21no—
58C4×#168—21no—
59#1984—51no—
60#1770—51no—
61C4×#103—51no—
62C2×#334—51no—
63C2×Q8⋊C8—51no—
64#1279D511yescharacteristic
65#1273—51no—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5C22×C411yescharacteristic
69C22×C4×C5C2×D411yescharacteristic
70C22×C4×C5#4111yescharacteristic
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—22no—
80C2×C5×C8—41no—
81C2×C5×C8—41no—
82C2×C5×C8—41no—
83C2×C5×C8—41no—
84C2×C5×C8—41no—
85C5×C4⋊C4—21no—
86C5×C4⋊C4—21no—
87C5×C4⋊C4—21no—
88C5×C4⋊C4—21no—
89C42×C5—41no—
90C42×C5—41no—
91C42×C5C2×D411yescharacteristic
92C42×C5#4111yescharacteristic
93C42×C5#4111yescharacteristic
94C42×C5#4111yescharacteristic
95C4⋊Dic5—21no—
96C4⋊Dic5—21no—
97#683—41no—
98#683—41no—
99C4×Dic5—41no—
100C4×Dic5—41no—
101C2×#168—21no—
102C2×#168—21no—
103C2×#168—21no—
104C2×#168—21no—
105C2×#168—21no—
106C2×#168—22no—
107C2×#168—21no—
108C2×#168—21no—
109C2×#168—21no—
110C2×#168—21no—
111C2×#168—21no—
112C2×#168—41no—
113C2×#168—41no—
114C2×#168M1612yes—
115C2×#168SD1612yes—
116C2×C4×Q8—51no—
117C2×C4⋊C8—51no—
118C2×C4⋊C8C2×D511yescharacteristic
119C2×#103—51no—
120C2×#103—51no—
121C2×#97—101no—
122C2×C4×C8—51no—
123C2×C4×C8—51no—
124C2×C4×C8C2×D511yescharacteristic
125C4×C4⋊C4C2×D511yescharacteristic
126#340—51no—
127#340—51no—
128#336—101no—
129#336—101no—
130#336—101no—
131#334—102no—
132Q8⋊C8—102no—
133C23×C5C4×D411yescharacteristic
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—41no—
137C2×C4×C5—41no—
138C2×C4×C5—41no—
139C2×C4×C5—41no—
140C2×C4×C5—41no—
141C2×C4×C5—41no—
142C2×C4×C5#11711yescharacteristic
143C2×C4×C5C4×D411yescharacteristic
144C2×C4×C5#12111yescharacteristic
145C2×C4×C5#12311yescharacteristic
146C2×C4×C5#12411yescharacteristic
147C2×C4×C5#12611yescharacteristic
148C2×C4×C5C2×M1611yescharacteristic
149C2×C4×C5C2×M1611yescharacteristic
150C2×C4×C5#13111yescharacteristic
151C2×C4×C5#13111yescharacteristic
152C2×C4×C5C2×SD1611yescharacteristic
153C2×C4×C5#13511yescharacteristic
154C2×C4×C5#13711yescharacteristic
155C2×C4×C5#13711yescharacteristic
156C2×Dic5—22no—
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—42no—
167C5×C8—81no—
168#168—22no—
169#168—22no—
170#168—41no—
171#168—42no—
172#168—41no—
173C22×Q8—51no—
174C22×C8—21no—
175C22×C8—21no—
176C22×C8—51no—
177C22×C8—51no—
178C22×C8—51no—
179C22×C8—51no—
180C22×C8—101no—
181C4×Q8—101no—
182C4×Q8—101no—
183C4×Q8—101no—
184C4×Q8—101no—
185C2×C4⋊C4—51no—
186C2×C4⋊C4—101no—
187C2×C4⋊C4C4×D511yescharacteristic
188C2×C4⋊C4C4×D511yescharacteristic
189C2×C42—21no—
190C2×C42—101no—
191C2×C42C22×D511yescharacteristic
192C4⋊C8—21no—
193C4⋊C8—21no—
194C4⋊C8—52no—
195C4⋊C8—101no—
196#103—102no—
197#103—102no—
198#97—202no—
199C4×C8—21no—
200C4×C8—21no—
201C4×C8—101no—
202C4×C8—101no—
203C4×C8—101no—
204C4×C8—101no—
205#95—21no—
206C22×C5#38811yescharacteristic
207C22×C5#43511yescharacteristic
208C22×C5#43611yescharacteristic
209C22×C5C4×SD1611yescharacteristic
210C22×C5#44111yescharacteristic
211C22×C5#44311yescharacteristic
212C22×C5#44411yescharacteristic
213C4×C5—21no—
214C4×C5—21no—
215C4×C5—81no—
216C4×C5—81no—
217C4×C5#43211yescharacteristic
218C4×C5#43311yescharacteristic
219C4×C5#43511yescharacteristic
220C4×C5#43511yescharacteristic
221C4×C5#46111yescharacteristic
222C4×C5#46411yescharacteristic
223C4×C5#48311yescharacteristic
224C4×C5#48511yescharacteristic
225Dic5—42no—
226Dic5—81no—
227C2×Q8—52no—
228C2×Q8—101no—
229C2×Q8—101no—
230C2×Q8—101no—
231C2×Q8—101no—
232C2×Q8—101no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—101no—
236C22×C4—101no—
237C22×C4C2×C4×D511yescharacteristic
238C22×C4D4×D511yescharacteristic
239C22×C4#71111yescharacteristic
240C2×C8—22no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—52no—
247C2×C8—52no—
248C2×C8—101no—
249C2×C8—101no—
250C2×C8—101no—
251C2×C8—101no—
252C2×C8—102no—
253C2×C8—101no—
254C2×C8—101no—
255C2×C8—101no—
256C2×C8—101no—
257C2×C8—101no—
258C2×C8—101no—
259C2×C8—201no—
260C2×C8—201no—
261C4⋊C4—21no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—101no—
266C4⋊C4—101no—
267C4⋊C4—201no—
268C4⋊C4—201no—
269C42—41no—
270C42—41no—
271C42—201no—
272C42—201no—
273C42#70911yescharacteristic
274C42#70911yescharacteristic
275C42D4×D511yescharacteristic
276C42#71311yescharacteristic
277C2×C5#158311yescharacteristic
278C2×C5#158711yescharacteristic
279C2×C5#159011yescharacteristic
280C2×C5#159311yescharacteristic
281C2×C5#192411yescharacteristic
282C2×C5#192711yescharacteristic
283C2×C5#192911yescharacteristic
284C23#402711yescharacteristic
285Q8—102no—
286Q8—102no—
287Q8—201no—
288Q8—201no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—102no—
298C2×C4—201no—
299C2×C4—201no—
300C2×C4—201no—
301C2×C4—201no—
302C2×C4—201no—
303C2×C4#401811yescharacteristic
304C2×C4#403011yescharacteristic
305C2×C4#403111yescharacteristic
306C2×C4#403911yescharacteristic
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#406111yescharacteristic
316C2×C4#406411yescharacteristic
317C8—42no—
318C8—81no—
319C8—102no—
320C8—102no—
321C8—202no—
322C8—201no—
323C8—201no—
324C5#954711yescharacteristic, complemented, Sylow
325C22#6495811yescharacteristic
326C22#6501711yescharacteristic
327C22#6501811yescharacteristic
328C22#6504711yescharacteristic
329C22#6507811yescharacteristic
330C22#6511211yescharacteristic
331C22#6511311yescharacteristic
332C4—21no—
333C4—21no—
334C4—81no—
335C4—81no—
336C4—202no—
337C4—401no—
338C4#6497911yescharacteristic
339C4#6499411yescharacteristic
340C4#6505611yescharacteristic
341C4#6510711yescharacteristic
342C4#6512511yescharacteristic
343C4#6512511yescharacteristic
344C4#6515111yescharacteristic
345C4#6517711yescharacteristic
346C2#1059894811yescharacteristic
347C2#1059895411yescharacteristic
348C2#1059901511yescharacteristic
349C2#1059902011yescharacteristic
350C2#1059945111yescharacteristic
351C2#1059953711yescharacteristic
352C2#1059958611yescharacteristic
subgroupG/H
centerC22×C4D4×D5
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1279C2
socle, prime radicalC23×C5C4×D4
cosocleC2×C42×C5C23
hypercenter#1279D5
hypocenterC5#9547
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
324. C5#9547semidirect

Maximal subgroups

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

subgroupindex
#106012652
C2×#647002
C2×#646762
#106002702
C4×#39422
C5×#12792
#105981442
#95475