Finite Group Databasebeta

← #11993776

Subgroups — #11993776

Order 1280.

426 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2935C211yesmaximal, characteristic
2#10602597C211yesmaximal, characteristic
3#10602595C211yesmaximal, characteristic
4#10601215C211yesmaximal, characteristic, complemented
5#10600668C211yesmaximal, characteristic, complemented
6#10598194C211yesmaximal, characteristic, complemented
7#10598158C211yesmaximal, characteristic, complemented
8C2×C5×#131—21no—
9C5×#532C2211yescharacteristic
10C5×#436—21no—
11C5×#435—22no—
12C5×C8×D4—21no—
13C2×C5×C4⋊C8C2211yescharacteristic
14C5×#408—21no—
15C4×C5×M16C2211yescharacteristic
16C2×#3954—21no—
17#65214C2211yescharacteristic
18#65213C2211yescharacteristic
19C2×C4⋊#168C2211yescharacteristic
20C2×C4×#168C2211yescharacteristic
21#64778—21no—
22#64767C411yescharacteristic
23#64767C411yescharacteristic
24#64764C411yescharacteristic
25#64764C411yescharacteristic
26D4⋊#168—22no—
27#64699—21no—
28#64699—21no—
29#8930—51nomaximal, Sylow
30C2×C5×#41—21no—
31C5×#131—42no—
32C5×#131—42no—
33C2×C5×M16—22no—
34C2×C5×M16D411yescharacteristic
35C2×C5×M16D411yescharacteristic
36C22×C5×C8—22no—
37C22×C5×C8—21no—
38C5×C4⋊Q8C2×C411yescharacteristic
39C5×#127C2×C411yescharacteristic
40C5×#124—21no—
41C5×#121—21no—
42C5×#121Q812yes—
43C4×C5×D4—21no—
44C4×C5×D4D412yes—
45C2×C42×C5C2311yescharacteristic
46C2×#681—21no—
47C22×#168—21no—
48C22×#168—21no—
49C5×C4⋊C8—21no—
50C5×C4⋊C8D411yescharacteristic
51C5×C4⋊C8D411yescharacteristic
52C5×C22⋊C8—22no—
53C5×C22⋊C8—22no—
54C5×#97—21no—
55C4×C5×C8—21no—
56C22⋊#168—21no—
57#3954—42no—
58C4⋊#168—21no—
59C4⋊#168—21no—
60C4⋊#168—21no—
61C4⋊#168C2×C411yescharacteristic
62C4⋊#168C2×C411yescharacteristic
63C4⋊#168C2×C411yescharacteristic
64C4⋊#168C2×C411yescharacteristic
65C4×#168—21no—
66C4×#168—21no—
67C4×#168—21no—
68#2935D511yescharacteristic
69#1950—51no—
70#1571—51no—
71#1540—51no—
72#1492—51no—
73#1278—51no—
74#1277—51no—
75C5×#41—41no—
76C5×#41—41no—
77C5×#41—41no—
78C5×#41—41no—
79C2×C5×Q8—21no—
80C2×C5×D4—22no—
81C2×C5×D4—21no—
82C2×C5×D4—21no—
83C2×C5×D4C4⋊C412yes—
84C22×C4×C5—22no—
85C22×C4×C5C2×D411yescharacteristic
86C22×C4×C5C2×Q811yescharacteristic
87C22×C4×C5#4111yescharacteristic
88C5×M16—21no—
89C5×M16—21no—
90C5×M16—21no—
91C5×M16—44no—
92C5×M16D812yes—
93C2×C5×C8—21no—
94C2×C5×C8—21no—
95C2×C5×C8—21no—
96C2×C5×C8—21no—
97C2×C5×C8—44no—
98C2×C5×C8—41no—
99C2×C5×C8—41no—
100C5×C4⋊C4—21no—
101C5×C4⋊C4C4⋊C412yes—
102C5×C22⋊C4—22no—
103C5×C22⋊C4—22no—
104C42×C5C22×C411yescharacteristic
105C42×C5C2×D411yescharacteristic
106C42×C5C2×D411yescharacteristic
107C42×C5#4111yescharacteristic
108#681—41no—
109#681—41no—
110C2×#168—22no—
111C2×#168—21no—
112C2×#168—21no—
113C2×#168—21no—
114C2×#168—21no—
115C2×#168—41no—
116C2×#168—41no—
117C2×#168—41no—
118C2×#168—41no—
119C2×#168—41no—
120C2×#131—21no—
121#532C2×D511yescharacteristic
122#436—21no—
123#435—22no—
124C8×D4—21no—
125#431—51no—
126C2×#108—101no—
127#423—51no—
128C2×C4⋊C8—51no—
129C2×C4⋊C8C2×D511yescharacteristic
130#408—21no—
131C4×M16C2×D511yescharacteristic
132C2×C4×C8—51no—
133#341—101no—
134#335—101no—
135#335—101no—
136#332—51no—
137#332—51no—
138#331—51no—
139#331—51no—
140D4⋊C8—102no—
141C23×C5—22no—
142C23×C5C22⋊Q811yescharacteristic
143C5×Q8—41no—
144C5×Q8—41no—
145C5×D4—42no—
146C5×D4—42no—
147C5×D4—42no—
148C5×D4—41no—
149C5×D4—41no—
150C5×D4—41no—
151C5×D4—41no—
152C2×C4×C5—21no—
153C2×C4×C5—21no—
154C2×C4×C5—22no—
155C2×C4×C5—41no—
156C2×C4×C5—42no—
157C2×C4×C5—42no—
158C2×C4×C5C2×C4⋊C411yescharacteristic
159C2×C4×C5C4×D411yescharacteristic
160C2×C4×C5C4×D411yescharacteristic
161C2×C4×C5#12011yescharacteristic
162C2×C4×C5C22⋊Q811yescharacteristic
163C2×C4×C5#12311yescharacteristic
164C2×C4×C5C2×D811yescharacteristic
165C2×C4×C5#13511yescharacteristic
166C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C5#13711yescharacteristic
168C5×C8—22no—
169C5×C8—41no—
170C5×C8—41no—
171C5×C8—41no—
172#168—42no—
173#168—41no—
174#168—41no—
175#168—41no—
176#168—41no—
177#168—81no—
178C2×#41—21no—
179#131—42no—
180#131—42no—
181C2×M16—22no—
182C2×M16—101no—
183C2×M16C22⋊D511yescharacteristic
184C2×M16C22⋊D511yescharacteristic
185C22×C8—22no—
186C22×C8—21no—
187C22×C8—101no—
188C22×C8—101no—
189C4⋊Q8C4×D511yescharacteristic
190#127C4×D511yescharacteristic
191#124—21no—
192#121—21no—
193#121Dic1012yes—
194C4×D4—21no—
195C4×D4C22⋊D512yes—
196C2×C42C22×D511yescharacteristic
197#108—202no—
198C4⋊C8—21no—
199C4⋊C8—51no—
200C4⋊C8—51no—
201C4⋊C8—51no—
202C4⋊C8—51no—
203C4⋊C8—101no—
204C4⋊C8—101no—
205C4⋊C8—101no—
206C4⋊C8C22⋊D511yescharacteristic
207C4⋊C8C22⋊D511yescharacteristic
208C22⋊C8—22no—
209C22⋊C8—22no—
210C22⋊C8—101no—
211#97—21no—
212C4×C8—21no—
213C4×C8—101no—
214C4×C8—101no—
215C4×C8—101no—
216C22×C5—21no—
217C22×C5—21no—
218C22×C5—42no—
219C22×C5—42no—
220C22×C5—42no—
221C22×C5#38511yescharacteristic
222C22×C5#47411yescharacteristic
223C22×C5#47811yescharacteristic
224C4×C5—21no—
225C4×C5—21no—
226C4×C5—21no—
227C4×C5—42no—
228C4×C5C4×D811yescharacteristic
229C4×C5#44011yescharacteristic
230C4×C5#44311yescharacteristic
231C4×C5#44411yescharacteristic
232C4×C5#44711yescharacteristic
233C4×C5#45211yescharacteristic
234#41—41no—
235#41—41no—
236#41—41no—
237#41—41no—
238C2×Q8—21no—
239C2×D4—22no—
240C2×D4—21no—
241C2×D4—21no—
242C2×D4#68312yes—
243C22×C4—22no—
244C22×C4C2×Dic1011yescharacteristic
245C22×C4#70911yescharacteristic
246C22×C4C2×C22⋊D511yescharacteristic
247M16—21no—
248M16—21no—
249M16—21no—
250M16—44no—
251M16—201no—
252M16—201no—
253M16#68612yes—
254C2×C8—21no—
255C2×C8—21no—
256C2×C8—21no—
257C2×C8—21no—
258C2×C8—44no—
259C2×C8—41no—
260C2×C8—41no—
261C2×C8—102no—
262C2×C8—101no—
263C2×C8—101no—
264C2×C8—101no—
265C2×C8—101no—
266C2×C8—201no—
267C2×C8—201no—
268C2×C8—201no—
269C2×C8—201no—
270C2×C8—201no—
271C4⋊C4—21no—
272C4⋊C4#68312yes—
273C22⋊C4—22no—
274C22⋊C4—22no—
275C42C2×C4×D511yescharacteristic
276C42#70911yescharacteristic
277C42C2×C22⋊D511yescharacteristic
278C42C2×C22⋊D511yescharacteristic
279C2×C5—21no—
280C2×C5—21no—
281C2×C5—82no—
282C2×C5#185811yescharacteristic
283C2×C5#186211yescharacteristic
284C2×C5#186611yescharacteristic
285C23—22no—
286C23#407011yescharacteristic
287Q8—41no—
288Q8—41no—
289D4—42no—
290D4—42no—
291D4—42no—
292D4—41no—
293D4—41no—
294D4—41no—
295D4—41no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4C2×#68311yescharacteristic
303C2×C4#407011yescharacteristic
304C2×C4C4×C22⋊D511yescharacteristic
305C2×C4C4×C22⋊D511yescharacteristic
306C2×C4#407511yescharacteristic
307C2×C4C2×#68611yescharacteristic
308C2×C4#407811yescharacteristic
309C2×C4#409611yescharacteristic
310C2×C4#409711yescharacteristic
311C2×C4#409911yescharacteristic
312C8—22no—
313C8—41no—
314C8—41no—
315C8—41no—
316C8—202no—
317C8—201no—
318C8—201no—
319C8—201no—
320C8—201no—
321C8—401no—
322C5#893011yescharacteristic, complemented, Sylow
323C22—21no—
324C22—21no—
325C22—42no—
326C22—42no—
327C22—42no—
328C22#6529611yescharacteristic
329C22#6529811yescharacteristic
330C22#6549911yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—42no—
335C4C4×#68611yescharacteristic
336C4#6530711yescharacteristic
337C4#6543311yescharacteristic
338C4#6543411yescharacteristic
339C4#6550611yescharacteristic
340C4#6552811yescharacteristic
341C2—21no—
342C2—21no—
343C2—82no—
344C2#1060239911yescharacteristic
345C2#1060281011yescharacteristic
346C2#1060282011yescharacteristic
subgroupG/H
centerC2×C4#4099
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#2935C2
socleC22×C5#385
prime radicalC5×#532C22
cosocleC2×C42×C5C23
hypercenter#2935D5
hypocenterC5#8930
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2935

Complements

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

NH ≅ G/Ntype
4. #10601215C2semidirect
5. #10600668C2semidirect
6. #10598194C2semidirect
7. #10598158C2semidirect
322. C5#8930semidirect

Maximal subgroups

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

subgroupindex
C5×#29352
#106025972
#106025952
#106012152
#106006682
#105981942
#105981582
#89305