Finite Group Databasebeta

← #11998672

Subgroups — #11998672

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#10615070C211yesmaximal, characteristic
2C5×#1518C211yesmaximal, characteristic
3#10602631C211yesmaximal, characteristic
4#10601586C211yesmaximal, characteristic
5#10601533C211yesmaximal, characteristic
6#10600342C211yesmaximal, 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—
20C2×#3940—21no—
21C2×#3939—21no—
22#65225C2211yescharacteristic
23#65214C2211yescharacteristic
24C2×C4×#168C2211yescharacteristic
25C5×#328—22no—
26#64758—22no—
27#64687—22no—
28#64674—21no—
29C8×#168—21no—
30#64672—22no—
31#9755—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#3940—42no—
66#3939—21no—
67#3939—21no—
68#3939—21no—
69#3939—21no—
70#3939—42no—
71C4⋊#168—21no—
72C4×#168—21no—
73C4×#168C2×C411yescharacteristic
74C4×#168C2×C411yescharacteristic
75C4×#168D411yescharacteristic
76C4×#168D411yescharacteristic
77#3160—51no—
78#1846—51no—
79#1518—51no—
80#1518—51no—
81#1518—51no—
82#1518D511yescharacteristic
83#1450—51no—
84C2×C5×Q8—21no—
85C2×C5×Q8—21no—
86C22×C4×C5—41no—
87C22×C4×C5C2×D411yescharacteristic
88C22×C4×C5C2×D411yescharacteristic
89C22×C4×C5C2×D411yescharacteristic
90C22×Dic5—41no—
91C2×Dic10—21no—
92C2×Dic10—21no—
93C2×C5×C8—22no—
94C5×C4⋊C4—21no—
95C5×C4⋊C4—21no—
96C5×C4⋊C4—21no—
97C5×C4⋊C4—21no—
98C5×C4⋊C4—41no—
99C5×C4⋊C4—41no—
100C5×C4⋊C4—41no—
101C5×C4⋊C4—41no—
102C5×C22⋊C4—41no—
103C42×C5—41no—
104C42×C5C22×C411yescharacteristic
105C42×C5C2×D411yescharacteristic
106C42×C5#4111yescharacteristic
107C42×C5#4111yescharacteristic
108C22⋊Dic5—41no—
109C4⋊Dic5—21no—
110C4⋊Dic5—21no—
111C4⋊Dic5—21no—
112C4⋊Dic5—21no—
113C4⋊Dic5—41no—
114C4⋊Dic5—41no—
115#683—41no—
116#683—41no—
117C4×Dic5—41no—
118C2×#168—22no—
119C2×#168C22⋊C411yescharacteristic
120C2×#168C22⋊C411yescharacteristic
121C2×#168C22⋊C411yescharacteristic
122C2×#168C22⋊C411yescharacteristic
123C2×#168SD1612yes—
124C2×#168SD1612yes—
125C2×#168Q1612yes—
126C2×#168Q1612yes—
127#533—51no—
128#533C2×D511yescharacteristic
129#500—51no—
130#500—51no—
131#499—101no—
132#499—101no—
133#498—51no—
134#498—51no—
135#431—51no—
136#431C2×D511yescharacteristic
137#427—101no—
138#427—101no—
139C2×#107—101no—
140C2×#106—101no—
141C2×C4×C8—51no—
142#382—51no—
143#382C2×D511yescharacteristic
144#328—22no—
145#328—102no—
146#328—102no—
147#328—102no—
148#322—101no—
149C82—101no—
150C23×C5#12711yescharacteristic
151C5×Q8—81no—
152C5×Q8—81no—
153C2×C4×C5—41no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—81no—
158C2×C4×C5—81no—
159C2×C4×C5—81no—
160C2×C4×C5C2×C22⋊C411yescharacteristic
161C2×C4×C5C4×D411yescharacteristic
162C2×C4×C5C4×D411yescharacteristic
163C2×C4×C5#12111yescharacteristic
164C2×C4×C5#12111yescharacteristic
165C2×C4×C5#12411yescharacteristic
166C2×C4×C5C2×SD1611yescharacteristic
167C2×C4×C5C2×SD1611yescharacteristic
168C2×C4×C5C2×Q1611yescharacteristic
169C2×C4×C5C2×Q1611yescharacteristic
170C2×Dic5—41no—
171C2×Dic5—41no—
172C2×Dic5—81no—
173C2×Dic5—81no—
174C2×Dic5—81no—
175Dic10—81no—
176Dic10—81no—
177C5×C8—42no—
178#168—42no—
179#168#10312yes—
180#168#10312yes—
181#168#10312yes—
182#168#10312yes—
183C22×C8—51no—
184C22×C8—51no—
185C4⋊Q8—51no—
186C4⋊Q8—51no—
187C4⋊Q8C4×D511yescharacteristic
188C4⋊Q8C4×D511yescharacteristic
189#125—21no—
190#125—101no—
191C22⋊Q8—21no—
192C22⋊Q8—21no—
193C22⋊Q8—101no—
194C22⋊Q8—101no—
195C4×Q8—21no—
196C4×Q8—21no—
197C4×Q8—101no—
198C4×Q8—101no—
199#117—21no—
200#117—101no—
201C2×C4⋊C4—21no—
202C2×C4⋊C4—101no—
203C2×C42C22×D511yescharacteristic
204#107—101no—
205#107—101no—
206#107—101no—
207#107—101no—
208#107—202no—
209#106—101no—
210#106—101no—
211#106—101no—
212#106—101no—
213#106—202no—
214C4⋊C8—21no—
215C4⋊C8—101no—
216C22⋊C8—52no—
217C22⋊C8C22⋊D512yes—
218C4×C8—21no—
219C4×C8—51no—
220C4×C8—51no—
221C4×C8—51no—
222C4×C8—51no—
223C4×C8—101no—
224#95—21no—
225#95—21no—
226#95—101no—
227#95—101no—
228C22×C5—21no—
229C22×C5—21no—
230C22×C5#39011yescharacteristic
231C22×C5#49211yescharacteristic
232C22×C5#49411yescharacteristic
233C4×C5—21no—
234C4×C5—21no—
235C4×C5—21no—
236C4×C5—21no—
237C4×C5—81no—
238C4×C5—81no—
239C4×C5—161no—
240C4×C5C2×#10311yescharacteristic
241C4×C5C2×#10311yescharacteristic
242C4×C5#48711yescharacteristic
243C4×C5#48711yescharacteristic
244Dic5—81no—
245Dic5—81no—
246Dic5—161no—
247C2×Q8—21no—
248C2×Q8—21no—
249C2×Q8—101no—
250C2×Q8—101no—
251C22×C4—41no—
252C22×C4—201no—
253C22×C4D4×D511yescharacteristic
254C22×C4D4×D511yescharacteristic
255C22×C4C2×C22⋊D511yescharacteristic
256C2×C8—22no—
257C2×C8—51no—
258C2×C8—51no—
259C2×C8—51no—
260C2×C8—51no—
261C2×C8—52no—
262C2×C8—52no—
263C2×C8—52no—
264C2×C8—52no—
265C2×C8—102no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—41no—
271C4⋊C4—41no—
272C4⋊C4—41no—
273C4⋊C4—41no—
274C4⋊C4—101no—
275C4⋊C4—101no—
276C4⋊C4—101no—
277C4⋊C4—101no—
278C4⋊C4—201no—
279C4⋊C4—201no—
280C4⋊C4—201no—
281C4⋊C4—201no—
282C22⋊C4—41no—
283C22⋊C4—201no—
284C42—41no—
285C42—201no—
286C42C2×C4×D511yescharacteristic
287C42#70911yescharacteristic
288C42D4×D511yescharacteristic
289C42#71111yescharacteristic
290C2×C5—21no—
291C2×C5—21no—
292C2×C5#195611yescharacteristic
293C2×C5#197611yescharacteristic
294C2×C5#197611yescharacteristic
295C23#408611yescharacteristic
296Q8—81no—
297Q8—81no—
298Q8—401no—
299Q8—401no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—81no—
307C2×C4—201no—
308C2×C4—201no—
309C2×C4—401no—
310C2×C4—401no—
311C2×C4—401no—
312C2×C4D5×C22⋊C411yescharacteristic
313C2×C4#402711yescharacteristic
314C2×C4#403011yescharacteristic
315C2×C4#403111yescharacteristic
316C2×C4D5×SD1611yescharacteristic
317C2×C4D5×SD1611yescharacteristic
318C2×C4D5×Q1611yescharacteristic
319C2×C4D5×Q1611yescharacteristic
320C2×C4C4×C22⋊D511yescharacteristic
321C2×C4#408511yescharacteristic
322C8—42no—
323C8—52no—
324C8—52no—
325C8—52no—
326C8—52no—
327C8—202no—
328C5#975511yescharacteristic, complemented, Sylow
329C22—21no—
330C22—21no—
331C22#6524611yescharacteristic
332C22#6546411yescharacteristic
333C22#6547011yescharacteristic
334C4—21no—
335C4—21no—
336C4—21no—
337C4—21no—
338C4—81no—
339C4—81no—
340C4—161no—
341C4—401no—
342C4—401no—
343C4—801no—
344C4#6508111yescharacteristic
345C4#6508111yescharacteristic
346C4D5×#10311yescharacteristic
347C4D5×#10311yescharacteristic
348C2—21no—
349C2—21no—
350C2#1060083511yescharacteristic
351C2#1060101811yescharacteristic
352C2#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#9755
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
328. C5#9755semidirect

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
#106015332
#106003422
#106003392
#97555