Finite Group Databasebeta

← #11993619

Subgroups — #11993619

Order 1280.

392 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10614246C211yesmaximal, characteristic
2C5×#1806C211yesmaximal, characteristic
3#10602431C211yesmaximal, characteristic
4#10601287C211yesmaximal, characteristic, complemented
5#10601283C211yesmaximal, characteristic, complemented
6#10598111C211yesmaximal, characteristic, complemented
7#10598110C211yesmaximal, characteristic, complemented
8C4×C5×#41C2211yescharacteristic
9C5×#423C2211yescharacteristic
10C2×C5×#104—21no—
11C4×C5×C4⋊C4C2211yescharacteristic
12#65523—21no—
13#65289—22no—
14#65286—21no—
15#65215—21no—
16#65214—21no—
17#65214C2211yescharacteristic
18#65213C2211yescharacteristic
19C2×C4⋊#168C2211yescharacteristic
20C2×C4×#168C2211yescharacteristic
21C5×#339—21no—
22Q8⋊#168C411yescharacteristic, complemented
23Q8⋊#168C411yescharacteristic, complemented
24D4⋊#168C411yescharacteristic, complemented
25D4⋊#168C411yescharacteristic, complemented
26#64700—22no—
27#64699—21no—
28#64699—21no—
29#8905—51nomaximal, Sylow
30C2×C5×#41D411yescharacteristic
31C2×C5×M16—21no—
32C4×C5×Q8C2×C411yescharacteristic
33C4×C5×Q8Q811yescharacteristic
34C4×C5×D4—21no—
35C4×C5×D4—21no—
36C4×C5×D4C2×C411yescharacteristic
37C4×C5×D4Q811yescharacteristic
38C5×#117—21no—
39C5×#117D411yescharacteristic
40C2×C5×C4⋊C4—21no—
41C2×C42×C5—21no—
42C2×C42×C5—21no—
43C2×C42×C5C2311yescharacteristic
44C2×#681—21no—
45C22×#168—21no—
46C22×#168—21no—
47C5×C4⋊C8—21no—
48C5×C4⋊C8—21no—
49C5×#104—42no—
50C5×#95—21no—
51C22⋊#168—22no—
52C22⋊#168—22no—
53C22⋊#168—21no—
54C4⋊#168—21no—
55C4⋊#168—21no—
56C4⋊#168C2×C411yescharacteristic
57C4⋊#168C2×C411yescharacteristic
58C4⋊#168D412yes—
59C4⋊#168D411yescharacteristic
60C4⋊#168D411yescharacteristic
61#3935—22no—
62C4×#168—22no—
63C4×#168—21no—
64C4×#168—21no—
65C4×#168C2×C411yescharacteristic
66C4×#168C2×C411yescharacteristic
67#2925—51no—
68#1806D511yescharacteristic
69#1571—51no—
70#1566—51no—
71#1476—51no—
72#1303—51no—
73#1279—51no—
74C5×#41—21no—
75C5×#41—21no—
76C5×#41—21no—
77C5×#41—21no—
78C2×C5×Q8C4⋊C411yescharacteristic
79C2×C5×D4—21no—
80C2×C5×D4C4⋊C411yescharacteristic
81C22×C4×C5—21no—
82C22×C4×C5—21no—
83C22×C4×C5—21no—
84C22×C4×C5—41no—
85C22×C4×C5C2×D411yescharacteristic
86C22×C4×C5#4111yescharacteristic
87C22×C4×C5#4111yescharacteristic
88C5×M16—41no—
89C5×M16—41no—
90C2×C5×C8—41no—
91C5×C4⋊C4—21no—
92C5×C4⋊C4—21no—
93C5×C4⋊C4—22no—
94C5×C4⋊C4—41no—
95C5×C4⋊C4C4⋊C411yescharacteristic
96C5×C4⋊C4C4⋊C411yescharacteristic
97C5×C22⋊C4—21no—
98C5×C22⋊C4—21no—
99C5×C22⋊C4—21no—
100C42×C5—21no—
101C42×C5—21no—
102C42×C5—21no—
103C42×C5—41no—
104C42×C5—41no—
105C42×C5C22×C411yescharacteristic
106C42×C5C2×D411yescharacteristic
107C42×C5C2×D411yescharacteristic
108C42×C5C2×Q811yescharacteristic
109#681—41no—
110#681—41no—
111C2×#168—21no—
112C2×#168—21no—
113C2×#168—21no—
114C2×#168—21no—
115C2×#168—21no—
116C2×#168—22no—
117C2×#168—21no—
118C2×#168—42no—
119C2×#168—41no—
120C2×#168—41no—
121C4×#41C2×D511yescharacteristic
122#433—102no—
123#432—101no—
124#431—51no—
125#431—101no—
126#423—51no—
127#423C2×D511yescharacteristic
128C2×C4⋊C8—51no—
129C2×#104—21no—
130#408—101no—
131#405—101no—
132C2×C4×C8—51no—
133C4×C4⋊C4C2×D511yescharacteristic
134#339—21no—
135#335—101no—
136#335—101no—
137#334—102no—
138Q8⋊C8—51no—
139Q8⋊C8—51no—
140D4⋊C8—51no—
141D4⋊C8—51no—
142C23×C5—21no—
143C23×C5#12311yescharacteristic
144C5×Q8—21no—
145C5×Q8—21no—
146C5×D4—21no—
147C5×D4—21no—
148C5×D4—41no—
149C5×D4—41no—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—42no—
161C2×C4×C5—81no—
162C2×C4×C5—81no—
163C2×C4×C5—81no—
164C2×C4×C5C2×C4⋊C411yescharacteristic
165C2×C4×C5C4×D411yescharacteristic
166C2×C4×C5C4×D411yescharacteristic
167C2×C4×C5#12011yescharacteristic
168C2×C4×C5C22⋊Q811yescharacteristic
169C2×C4×C5C22⋊Q811yescharacteristic
170C2×C4×C5#13511yescharacteristic
171C2×C4×C5#13511yescharacteristic
172C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
173C2×C4×C5#13711yescharacteristic
174C5×C8—81no—
175#168—22no—
176#168—41no—
177#168—41no—
178#168—41no—
179#168—41no—
180#168—41no—
181#168—42no—
182C2×#41C22⋊D511yescharacteristic
183C2×M16—21no—
184C2×M16—101no—
185C22×C8—101no—
186C22×C8—101no—
187C4×Q8Dic1011yescharacteristic
188C4×Q8C4×D511yescharacteristic
189C4×D4—21no—
190C4×D4—21no—
191C4×D4Dic1011yescharacteristic
192C4×D4C4×D511yescharacteristic
193#117—21no—
194#117C22⋊D511yescharacteristic
195C2×C4⋊C4—21no—
196C2×C42—21no—
197C2×C42—21no—
198C2×C42C22×D511yescharacteristic
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—51no—
202C4⋊C8—51no—
203C4⋊C8—52no—
204C4⋊C8—51no—
205C4⋊C8—51no—
206C4⋊C8—101no—
207C4⋊C8—101no—
208#104—42no—
209C22⋊C8—102no—
210C22⋊C8—102no—
211C22⋊C8—101no—
212#97—102no—
213C4×C8—51no—
214C4×C8—51no—
215C4×C8—102no—
216C4×C8—101no—
217C4×C8—101no—
218#95—21no—
219C22×C5—21no—
220C22×C5—21no—
221C22×C5—41no—
222C22×C5—41no—
223C22×C5—41no—
224C22×C5#38511yescharacteristic
225C22×C5#48211yescharacteristic
226C22×C5#48511yescharacteristic
227C4×C5—21no—
228C4×C5—21no—
229C4×C5—21no—
230C4×C5—41no—
231C4×C5—41no—
232C4×C5—41no—
233C4×C5—82no—
234C4×C5#42711yescharacteristic
235C4×C5#42811yescharacteristic
236C4×C5#44311yescharacteristic
237C4×C5#44411yescharacteristic
238C4×C5#44911yescharacteristic
239C4×C5#45211yescharacteristic
240#41—21no—
241#41—21no—
242#41—21no—
243#41—21no—
244C2×Q8#68311yescharacteristic
245C2×D4—21no—
246C2×D4#68311yescharacteristic
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—41no—
251C22×C4#71111yescharacteristic
252C22×C4#71111yescharacteristic
253C22×C4C2×C22⋊D511yescharacteristic
254M16—41no—
255M16—41no—
256M16—201no—
257M16—201no—
258C2×C8—41no—
259C2×C8—101no—
260C2×C8—101no—
261C2×C8—101no—
262C2×C8—101no—
263C2×C8—101no—
264C2×C8—102no—
265C2×C8—101no—
266C2×C8—202no—
267C2×C8—201no—
268C2×C8—201no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—22no—
272C4⋊C4—41no—
273C4⋊C4#68311yescharacteristic
274C4⋊C4#68311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C42—21no—
279C42—21no—
280C42—21no—
281C42—41no—
282C42—41no—
283C42C2×Dic1011yescharacteristic
284C42C2×C4×D511yescharacteristic
285C42D4×D511yescharacteristic
286C42D4×D511yescharacteristic
287C2×C5—21no—
288C2×C5—21no—
289C2×C5—81no—
290C2×C5#185411yescharacteristic
291C2×C5#186111yescharacteristic
292C2×C5#186611yescharacteristic
293C23—21no—
294C23#408111yescharacteristic
295Q8—21no—
296Q8—21no—
297D4—21no—
298D4—21no—
299D4—41no—
300D4—41no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—41no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4#402411yescharacteristic
316C2×C4#402411yescharacteristic
317C2×C4#402711yescharacteristic
318C2×C4#402711yescharacteristic
319C2×C4C2×#68311yescharacteristic
320C2×C4#407811yescharacteristic
321C2×C4#408311yescharacteristic
322C2×C4#408811yescharacteristic
323C2×C4#409611yescharacteristic
324C2×C4#409611yescharacteristic
325C8—81no—
326C8—102no—
327C8—201no—
328C8—201no—
329C8—201no—
330C8—202no—
331C8—201no—
332C8—201no—
333C5#890511yescharacteristic, complemented, Sylow
334C22—21no—
335C22—21no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22#6523511yescharacteristic
340C22#6532411yescharacteristic
341C22#6533411yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—82no—
349C4#6511211yescharacteristic
350C4#6511311yescharacteristic
351C4#6525311yescharacteristic
352C4#6528711yescharacteristic
353C4#6532611yescharacteristic
354C4#6533611yescharacteristic
355C2—21no—
356C2—21no—
357C2—81no—
358C2#1060029911yescharacteristic
359C2#1060116911yescharacteristic
360C2#1060119111yescharacteristic
subgroupG/H
centerC2×C4#4083
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1806C2
socleC22×C5#385
prime radicalC2×C5×#41D4
cosocleC2×C42×C5C23
hypercenter#1806D5
hypocenterC5#8905
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1806

Complements

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

NH ≅ G/Ntype
4. #10601287C2semidirect
5. #10601283C2semidirect
6. #10598111C2semidirect
7. #10598110C2semidirect
22. Q8⋊#168C4semidirect
23. Q8⋊#168C4semidirect
24. D4⋊#168C4semidirect
25. D4⋊#168C4semidirect
333. C5#8905semidirect

Maximal subgroups

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

subgroupindex
#106142462
C5×#18062
#106024312
#106012872
#106012832
#105981112
#105981102
#89055