Finite Group Databasebeta

← #11998690

Subgroups — #11998690

Order 1280.

370 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
1#10615070C211yesmaximal, characteristic
2C5×#1518C211yesmaximal, characteristic
3#10602631C211yesmaximal, characteristic
4#10601586C211yesmaximal, characteristic
5#10601535C211yesmaximal, characteristic
6#10600340C211yesmaximal, characteristic
7#10600339C211yesmaximal, characteristic
8C5×#533C2211yescharacteristic
9#65804C2211yescharacteristic
10C5×#431C2211yescharacteristic
11C5×#382C2211yescharacteristic
12#65368C411yescharacteristic, complemented
13#65368C411yescharacteristic, complemented
14#65367C411yescharacteristic, complemented
15#65367C411yescharacteristic, complemented
16#65353—21no—
17#65353—21no—
18#65287—21no—
19#65287—21no—
20#65225C2211yescharacteristic
21#65214C2211yescharacteristic
22C2×C4×#168C2211yescharacteristic
23C5×#328—22no—
24#64758—22no—
25#64749—21no—
26#64749—21no—
27#64687—22no—
28#64675—21no—
29#64674—21no—
30#64672—22no—
31#9759—51nomaximal, Sylow
32C5×C4⋊Q8C2×C411yescharacteristic
33C5×C4⋊Q8C2×C411yescharacteristic
34C5×#125—21no—
35C5×C22⋊Q8—21no—
36C5×C22⋊Q8—21no—
37C4×C5×Q8—21no—
38C4×C5×Q8—21no—
39C5×#117—21no—
40C2×C5×C4⋊C4—21no—
41C2×C42×C5C2311yescharacteristic
42#4072—21no—
43C2×C4⋊Dic5—21no—
44#4070—21no—
45#4070—21no—
46C22×#168D411yescharacteristic
47C22×#168D411yescharacteristic
48#4016—21no—
49#4015C2×C411yescharacteristic
50#4015C2×C411yescharacteristic
51C4×Dic10—21no—
52C4×Dic10—21no—
53C5×C4⋊C8—21no—
54C5×C22⋊C8D412yes—
55C4×C5×C8—21no—
56C5×#95—21no—
57C5×#95—21no—
58#3963—21no—
59#3963—21no—
60C22⋊#168D412yes—
61#3940—21no—
62#3940—21no—
63#3940—21no—
64#3940—21no—
65#3939—21no—
66#3939—21no—
67#3939—21no—
68#3939—21no—
69C4⋊#168—21no—
70C4×#168—21no—
71C4×#168C2×C411yescharacteristic
72C4×#168C2×C411yescharacteristic
73C4×#168D411yescharacteristic
74C4×#168D411yescharacteristic
75#3160—51no—
76#1835—51no—
77#1518—51no—
78#1518—51no—
79#1518—51no—
80#1518D511yescharacteristic
81#1452—51no—
82C2×C5×Q8—21no—
83C2×C5×Q8—21no—
84C22×C4×C5—41no—
85C22×C4×C5C2×D411yescharacteristic
86C22×C4×C5C2×D411yescharacteristic
87C22×C4×C5C2×D411yescharacteristic
88C22×Dic5—41no—
89C2×Dic10—21no—
90C2×Dic10—21no—
91C2×C5×C8—22no—
92C5×C4⋊C4—21no—
93C5×C4⋊C4—21no—
94C5×C4⋊C4—21no—
95C5×C4⋊C4—21no—
96C5×C4⋊C4—41no—
97C5×C4⋊C4—41no—
98C5×C4⋊C4—41no—
99C5×C4⋊C4—41no—
100C5×C22⋊C4—41no—
101C42×C5—41no—
102C42×C5C22×C411yescharacteristic
103C42×C5C2×D411yescharacteristic
104C42×C5#4111yescharacteristic
105C42×C5#4111yescharacteristic
106C22⋊Dic5—41no—
107C4⋊Dic5—21no—
108C4⋊Dic5—21no—
109C4⋊Dic5—21no—
110C4⋊Dic5—21no—
111C4⋊Dic5—41no—
112C4⋊Dic5—41no—
113#683—41no—
114#683—41no—
115C4×Dic5—41no—
116C2×#168—21no—
117C2×#168—21no—
118C2×#168—21no—
119C2×#168—21no—
120C2×#168—22no—
121C2×#168C22⋊C411yescharacteristic
122C2×#168C22⋊C411yescharacteristic
123C2×#168C22⋊C411yescharacteristic
124C2×#168C22⋊C411yescharacteristic
125#533—51no—
126#533C2×D511yescharacteristic
127#500—51no—
128#500—51no—
129#499—101no—
130#499—101no—
131#498—51no—
132#498—51no—
133#431—51no—
134#431C2×D511yescharacteristic
135#427—101no—
136#427—101no—
137C2×C4×C8—51no—
138#382—51no—
139#382C2×D511yescharacteristic
140#340—101no—
141#340—101no—
142#328—22no—
143#328—102no—
144#328—102no—
145#328—102no—
146#322—101no—
147#322—101no—
148C23×C5#12711yescharacteristic
149C5×Q8—81no—
150C5×Q8—81no—
151C2×C4×C5—41no—
152C2×C4×C5—41no—
153C2×C4×C5—41no—
154C2×C4×C5—41no—
155C2×C4×C5—81no—
156C2×C4×C5—81no—
157C2×C4×C5—81no—
158C2×C4×C5C2×C22⋊C411yescharacteristic
159C2×C4×C5C4×D411yescharacteristic
160C2×C4×C5C4×D411yescharacteristic
161C2×C4×C5#12111yescharacteristic
162C2×C4×C5#12111yescharacteristic
163C2×C4×C5#12411yescharacteristic
164C2×C4×C5#13711yescharacteristic
165C2×C4×C5#13711yescharacteristic
166C2×C4×C5#13711yescharacteristic
167C2×C4×C5#13711yescharacteristic
168C2×Dic5—41no—
169C2×Dic5—41no—
170C2×Dic5—81no—
171C2×Dic5—81no—
172C2×Dic5—81no—
173Dic10—81no—
174Dic10—81no—
175C5×C8—42no—
176#168—21no—
177#168—21no—
178#168—21no—
179#168—21no—
180#168—42no—
181C22×C8—51no—
182C22×C8—51no—
183C4⋊Q8—51no—
184C4⋊Q8—51no—
185C4⋊Q8C4×D511yescharacteristic
186C4⋊Q8C4×D511yescharacteristic
187#125—21no—
188#125—101no—
189C22⋊Q8—21no—
190C22⋊Q8—21no—
191C22⋊Q8—101no—
192C22⋊Q8—101no—
193C4×Q8—21no—
194C4×Q8—21no—
195C4×Q8—101no—
196C4×Q8—101no—
197#117—21no—
198#117—101no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—101no—
201C2×C42C22×D511yescharacteristic
202#107—101no—
203#107—101no—
204#107—101no—
205#107—101no—
206#106—101no—
207#106—101no—
208#106—101no—
209#106—101no—
210C4⋊C8—21no—
211C4⋊C8—101no—
212C22⋊C8—52no—
213C22⋊C8C22⋊D512yes—
214C4×C8—21no—
215C4×C8—51no—
216C4×C8—51no—
217C4×C8—51no—
218C4×C8—51no—
219C4×C8—101no—
220#95—21no—
221#95—21no—
222#95—101no—
223#95—101no—
224C22×C5—21no—
225C22×C5—21no—
226C22×C5#39011yescharacteristic
227C22×C5#49711yescharacteristic
228C22×C5#49711yescharacteristic
229C4×C5—21no—
230C4×C5—21no—
231C4×C5—21no—
232C4×C5—21no—
233C4×C5—81no—
234C4×C5—81no—
235C4×C5—161no—
236C4×C5#41911yescharacteristic
237C4×C5#41911yescharacteristic
238C4×C5#49111yescharacteristic
239C4×C5#49111yescharacteristic
240Dic5—81no—
241Dic5—81no—
242Dic5—161no—
243C2×Q8—21no—
244C2×Q8—21no—
245C2×Q8—101no—
246C2×Q8—101no—
247C22×C4—41no—
248C22×C4—201no—
249C22×C4D4×D511yescharacteristic
250C22×C4D4×D511yescharacteristic
251C22×C4C2×C22⋊D511yescharacteristic
252C2×C8—22no—
253C2×C8—51no—
254C2×C8—51no—
255C2×C8—51no—
256C2×C8—51no—
257C2×C8—101no—
258C2×C8—101no—
259C2×C8—101no—
260C2×C8—101no—
261C2×C8—102no—
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—41no—
269C4⋊C4—41no—
270C4⋊C4—101no—
271C4⋊C4—101no—
272C4⋊C4—101no—
273C4⋊C4—101no—
274C4⋊C4—201no—
275C4⋊C4—201no—
276C4⋊C4—201no—
277C4⋊C4—201no—
278C22⋊C4—41no—
279C22⋊C4—201no—
280C42—41no—
281C42—201no—
282C42C2×C4×D511yescharacteristic
283C42#70911yescharacteristic
284C42D4×D511yescharacteristic
285C42#71111yescharacteristic
286C2×C5—21no—
287C2×C5—21no—
288C2×C5#196011yescharacteristic
289C2×C5#197611yescharacteristic
290C2×C5#197611yescharacteristic
291C23#408611yescharacteristic
292Q8—81no—
293Q8—81no—
294Q8—401no—
295Q8—401no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—81no—
301C2×C4—81no—
302C2×C4—81no—
303C2×C4—201no—
304C2×C4—201no—
305C2×C4—401no—
306C2×C4—401no—
307C2×C4—401no—
308C2×C4D5×C22⋊C411yescharacteristic
309C2×C4#402711yescharacteristic
310C2×C4#403011yescharacteristic
311C2×C4#403111yescharacteristic
312C2×C4#406111yescharacteristic
313C2×C4#406111yescharacteristic
314C2×C4#406411yescharacteristic
315C2×C4#406411yescharacteristic
316C2×C4C4×C22⋊D511yescharacteristic
317C2×C4#408511yescharacteristic
318C8—42no—
319C8—101no—
320C8—101no—
321C8—101no—
322C8—101no—
323C8—202no—
324C5#975911yescharacteristic, complemented, Sylow
325C22—21no—
326C22—21no—
327C22#6524611yescharacteristic
328C22#6545611yescharacteristic
329C22#6547911yescharacteristic
330C4—21no—
331C4—21no—
332C4—21no—
333C4—21no—
334C4—81no—
335C4—81no—
336C4—161no—
337C4—401no—
338C4—401no—
339C4—801no—
340C4#6508611yescharacteristic
341C4#6508611yescharacteristic
342C4#6509111yescharacteristic
343C4#6509111yescharacteristic
344C2—21no—
345C2—21no—
346C2#1060083511yescharacteristic
347C2#1060102111yescharacteristic
348C2#1060119011yescharacteristic
subgroupG/H
centerC22#65246
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1518C2
socleC22×C5#390
prime radicalC23×C5#127
cosocleC2×C42×C5C23
hypercenter#1518D5
hypocenterC5#9759
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1518

Complements

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

NH ≅ G/Ntype
12. #65368C4semidirect
13. #65368C4semidirect
14. #65367C4semidirect
15. #65367C4semidirect
324. C5#9759semidirect

Maximal subgroups

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

subgroupindex
#106150702
C5×#15182
#106026312
#106015862
#106015352
#106003402
#106003392
#97595