Finite Group Databasebeta

← #11993623

Subgroups — #11993623

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×#1476C211yesmaximal, characteristic
3#10602439C211yesmaximal, characteristic
4#10601543C211yesmaximal, characteristic, complemented
5#10600523C211yesmaximal, characteristic, complemented
6#10598237C211yesmaximal, characteristic, complemented
7#10598146C211yesmaximal, characteristic, complemented
8C4×C5×#41C2211yescharacteristic
9C5×#431C2211yescharacteristic
10C2×C4×C5×C8C2211yescharacteristic
11C2×#3969—21no—
12#65523—21no—
13#65289—22no—
14#65286—21no—
15C4×C4⋊Dic5C2211yescharacteristic
16#65215—21no—
17#65214—21no—
18#65213C2211yescharacteristic
19#65213C2211yescharacteristic
20C2×C4⋊#168C2211yescharacteristic
21C5×Q8⋊C8C411yescharacteristic, complemented
22C5×Q8⋊C8C411yescharacteristic, complemented
23C5×D4⋊C8C411yescharacteristic, complemented
24C5×D4⋊C8C411yescharacteristic, complemented
25#64752—21no—
26#64678—21no—
27#64678—21no—
28#64677—22no—
29#8905—51nomaximal, Sylow
30C2×C5×#41D411yescharacteristic
31C22×C5×C8—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×C42×C5—21no—
41C2×C42×C5C2311yescharacteristic
42C2×C4⋊Dic5—21no—
43C2×C4×Dic5—21no—
44C2×#681—21no—
45C2×#681—21no—
46C22×#168—21no—
47C5×C4⋊C8C2×C411yescharacteristic
48C5×C4⋊C8C2×C411yescharacteristic
49C5×C22⋊C8—21no—
50C4×C5×C8—21no—
51C4×C5×C8—21no—
52C4×C5×C8C2×C411yescharacteristic
53C4×C5×C8C2×C411yescharacteristic
54#3969—42no—
55#3963—21no—
56C22⋊#168—22no—
57C22⋊#168—22no—
58C4⋊#168—21no—
59C4⋊#168—21no—
60C4⋊#168—21no—
61C4⋊#168—21no—
62C4⋊#168D412yes—
63C4⋊#168D411yescharacteristic
64C4⋊#168D411yescharacteristic
65#3935—22no—
66C4×#168—22no—
67#2925—51no—
68#1806—51no—
69#1571—51no—
70#1566—51no—
71#1476D511yescharacteristic
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×C5C2×D411yescharacteristic
85C22×C4×C5#4111yescharacteristic
86C22×C4×C5#4111yescharacteristic
87C22×Dic5—41no—
88C2×C5×C8—21no—
89C2×C5×C8—21no—
90C2×C5×C8—21no—
91C2×C5×C8—21no—
92C2×C5×C8—42no—
93C5×C4⋊C4—21no—
94C5×C4⋊C4—21no—
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×C5C22×C411yescharacteristic
104C42×C5C2×D411yescharacteristic
105C42×C5C2×D411yescharacteristic
106C42×C5C2×Q811yescharacteristic
107C4⋊Dic5—22no—
108C4⋊Dic5—41no—
109C4×Dic5—41no—
110C4×Dic5—41no—
111#681—41no—
112#681—41no—
113#681—41no—
114#681—41no—
115C2×#168—21no—
116C2×#168—22no—
117C2×#168—21no—
118C2×#168—41no—
119C2×#168—41no—
120C2×#168—41no—
121C4×#41C2×D511yescharacteristic
122#433—102no—
123#432—101no—
124#431—101no—
125#431C2×D511yescharacteristic
126#423—51no—
127#423—51no—
128C2×C4⋊C8—51no—
129C2×#104—101no—
130#408—101no—
131#405—101no—
132C2×C4×C8C2×D511yescharacteristic
133C4×C4⋊C4—51no—
134#339—101no—
135#335—101no—
136#335—101no—
137#334—102no—
138Q8⋊C8Dic511yescharacteristic, complemented
139Q8⋊C8Dic511yescharacteristic, complemented
140D4⋊C8Dic511yescharacteristic, complemented
141D4⋊C8Dic511yescharacteristic, complemented
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—81no—
161C2×C4×C5C2×C4⋊C411yescharacteristic
162C2×C4×C5C4×D411yescharacteristic
163C2×C4×C5C4×D411yescharacteristic
164C2×C4×C5#12011yescharacteristic
165C2×C4×C5C22⋊Q811yescharacteristic
166C2×C4×C5C22⋊Q811yescharacteristic
167C2×C4×C5#13511yescharacteristic
168C2×C4×C5#13511yescharacteristic
169C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C5#13711yescharacteristic
171C2×Dic5—42no—
172C2×Dic5—81no—
173C2×Dic5—81no—
174C5×C8—22no—
175C5×C8—41no—
176C5×C8—41no—
177C5×C8—41no—
178#168—41no—
179#168—41no—
180#168—42no—
181#168—81no—
182C2×#41D2011yescharacteristic
183C2×M16—101no—
184C2×M16—101no—
185C22×C8—21no—
186C22×C8—101no—
187C4×Q8Dic1011yescharacteristic
188C4×Q8C2×Dic511yescharacteristic
189C4×D4—21no—
190C4×D4—21no—
191C4×D4Dic1011yescharacteristic
192C4×D4C2×Dic511yescharacteristic
193#117—21no—
194#117D2011yescharacteristic
195C2×C4⋊C4—101no—
196C2×C42—21no—
197C2×C42—101no—
198C2×C42C22×D511yescharacteristic
199C4⋊C8—52no—
200C4⋊C8—51no—
201C4⋊C8—51no—
202C4⋊C8—101no—
203C4⋊C8—101no—
204C4⋊C8—101no—
205C4⋊C8—101no—
206C4⋊C8C2×Dic511yescharacteristic
207C4⋊C8C2×Dic511yescharacteristic
208#104—202no—
209C22⋊C8—21no—
210C22⋊C8—102no—
211C22⋊C8—102no—
212#97—102no—
213C4×C8—21no—
214C4×C8—21no—
215C4×C8—102no—
216C4×C8C2×Dic511yescharacteristic
217C4×C8C2×Dic511yescharacteristic
218#95—101no—
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#42711yescharacteristic
234C4×C5#42811yescharacteristic
235C4×C5#44311yescharacteristic
236C4×C5#44411yescharacteristic
237C4×C5#44911yescharacteristic
238C4×C5#45211yescharacteristic
239Dic5—82no—
240#41—21no—
241#41—21no—
242#41—21no—
243#41—21no—
244C2×Q8C4⋊Dic511yescharacteristic
245C2×D4—21no—
246C2×D4C4⋊Dic511yescharacteristic
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—201no—
251C22×C4C2×D2011yescharacteristic
252C22×C4#71111yescharacteristic
253C22×C4#71111yescharacteristic
254M16—201no—
255M16—201no—
256M16—201no—
257M16—201no—
258C2×C8—21no—
259C2×C8—21no—
260C2×C8—21no—
261C2×C8—21no—
262C2×C8—42no—
263C2×C8—101no—
264C2×C8—102no—
265C2×C8—101no—
266C2×C8—201no—
267C2×C8—201no—
268C2×C8—201no—
269C4⋊C4—21no—
270C4⋊C4—21no—
271C4⋊C4—102no—
272C4⋊C4—201no—
273C4⋊C4C4⋊Dic511yescharacteristic
274C4⋊C4C4⋊Dic511yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C42—21no—
279C42—21no—
280C42—21no—
281C42—201no—
282C42—201no—
283C42C2×Dic1011yescharacteristic
284C42D4×D511yescharacteristic
285C42D4×D511yescharacteristic
286C42C22×Dic511yescharacteristic
287C2×C5—21no—
288C2×C5—21no—
289C2×C5—81no—
290C2×C5#185411yescharacteristic
291C2×C5#186111yescharacteristic
292C2×C5#186611yescharacteristic
293C23—21no—
294C23#403211yescharacteristic
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—81no—
312C2×C4—202no—
313C2×C4—401no—
314C2×C4—401no—
315C2×C4#402411yescharacteristic
316C2×C4#402411yescharacteristic
317C2×C4#402811yescharacteristic
318C2×C4#405011yescharacteristic
319C2×C4#405011yescharacteristic
320C2×C4#405411yescharacteristic
321C2×C4#405511yescharacteristic
322C2×C4C2×C4⋊Dic511yescharacteristic
323C2×C4D4×Dic511yescharacteristic
324C2×C4D4×Dic511yescharacteristic
325C8—22no—
326C8—41no—
327C8—41no—
328C8—41no—
329C8—202no—
330C8—201no—
331C8—201no—
332C8—401no—
333C5#890511yescharacteristic, complemented, Sylow
334C22—21no—
335C22—21no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22#6501211yescharacteristic
340C22#6502611yescharacteristic
341C22#6523911yescharacteristic
342C4—21no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4—402no—
349C4#6502211yescharacteristic
350C4#6502311yescharacteristic
351C4#6539511yescharacteristic
352C4#6541011yescharacteristic
353C4#6548511yescharacteristic
354C4#6548611yescharacteristic
355C2—21no—
356C2—21no—
357C2—81no—
358C2#1060072211yescharacteristic
359C2#1060108511yescharacteristic
360C2#1060116811yescharacteristic
subgroupG/H
centerC2×C4#4028
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1476C2
socleC22×C5#385
prime radicalC2×C5×#41D4
cosocleC2×C42×C5C23
hypercenter#1476D5
hypocenterC5#8905
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1476

Complements

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

NH ≅ G/Ntype
4. #10601543C2semidirect
5. #10600523C2semidirect
6. #10598237C2semidirect
7. #10598146C2semidirect
21. C5×Q8⋊C8C4semidirect
22. C5×Q8⋊C8C4semidirect
23. C5×D4⋊C8C4semidirect
24. C5×D4⋊C8C4semidirect
138. Q8⋊C8Dic5semidirect
139. Q8⋊C8Dic5semidirect
140. D4⋊C8Dic5semidirect
141. D4⋊C8Dic5semidirect
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×#14762
#106024392
#106015432
#106005232
#105982372
#105981462
#89055