Finite Group Databasebeta

← #11997604

Subgroups — #11997604

Order 1280.

446 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10601263C211yesmaximal, characteristic
2#10601261C211yesmaximal, characteristic, complemented
3C2×#64703C211yesmaximal, characteristic
4C4×#3953C211yesmaximal, characteristic
5C2×#64674C211yesmaximal, characteristic, complemented
6C5×#1277C211yesmaximal, characteristic, complemented
7#10598195C211yesmaximal, characteristic, complemented
8C2×C4×D20C2211yescharacteristic
9C2×C5×C4⋊C8C2211yescharacteristic
10C2×C5×C4⋊C8C2211yescharacteristic
11C2×C4×C5×C8C2211yescharacteristic
12C2×#3953C411yescharacteristic
13C2×#3953C411yescharacteristic
14C2×#3952—21no—
15C2×#3952—21no—
16C2×#3946—21no—
17C4×C4⋊Dic5C2211yescharacteristic
18C2×C4×#168C2211yescharacteristic
19C2×C4×#168C2211yescharacteristic
20#64771C411yescharacteristic
21#64771C411yescharacteristic
22#64770—21no—
23#64703—22no—
24#64674—22no—
25#9560—51nomaximal, Sylow
26C22×D20C2×C411yescharacteristic
27C22×C4×D5—21no—
28C22×C5×C8—21no—
29C22×C5×C8—21no—
30C22×C5×C8C2×C411yescharacteristic
31C22×C5×C8C2×C411yescharacteristic
32C2×C42×C5C2311yescharacteristic
33C2×#685—21no—
34C2×C4⋊Dic5C2×C411yescharacteristic
35C2×C4⋊Dic5C2×C411yescharacteristic
36C2×C4⋊Dic5C2×C411yescharacteristic
37C2×C4×Dic5—21no—
38C22×#168—21no—
39C22×#168D411yescharacteristic
40C22×#168D411yescharacteristic
41C4×D20—21no—
42C4×D20—21no—
43C4×D20—21no—
44C4×D20—21no—
45C5×C4⋊C8—21no—
46C5×C4⋊C8—21no—
47C5×C4⋊C8—21no—
48C5×C4⋊C8—21no—
49C4×C5×C8—21no—
50C4×C5×C8—21no—
51#3963—21no—
52#3953—22no—
53#3953—22no—
54#3952—42no—
55#3952—42no—
56#3946—42no—
57C4×#168—21no—
58C4×#168—21no—
59C4×#168—21no—
60C4×#168D412yes—
61#1954—51no—
62#1939—51no—
63C4×#102—51no—
64C2×D4⋊C8—51no—
65C2×#322—51no—
66#1279—51no—
67#1277D511yescharacteristic, complemented
68C23×D5—21no—
69C22×C4×C5C22×C411yescharacteristic
70C22×C4×C5C2×D411yescharacteristic
71C22×C4×C5#4111yescharacteristic
72C22×Dic5—21no—
73C22×Dic5—21no—
74C22×Dic5—21no—
75C2×D20—21no—
76C2×D20—21no—
77C2×D20—21no—
78C2×D20—21no—
79C2×D20—21no—
80C2×D20M1612yes—
81C2×C4×D5—41no—
82C2×C4×D5—41no—
83C2×C4×D5—41no—
84C2×C4×D5—41no—
85C2×C4×D5—41no—
86C2×C4×D5—41no—
87C2×C5×C8—21no—
88C2×C5×C8—21no—
89C2×C5×C8—21no—
90C2×C5×C8—21no—
91C2×C5×C8—21no—
92C2×C5×C8—21no—
93C2×C5×C8—41no—
94C2×C5×C8—41no—
95C2×C5×C8—41no—
96C2×C5×C8—41no—
97C2×C5×C8—41no—
98C2×C5×C8—41no—
99C42×C5C2×D411yescharacteristic
100C42×C5#4111yescharacteristic
101C42×C5#4111yescharacteristic
102C42×C5#4111yescharacteristic
103#685—41no—
104#685—41no—
105C4⋊Dic5—21no—
106C4⋊Dic5—21no—
107C4⋊Dic5—21no—
108C4⋊Dic5—21no—
109C4⋊Dic5—21no—
110C4⋊Dic5M1612yes—
111C4×Dic5—41no—
112C4×Dic5—41no—
113C2×#168—22no—
114C2×#168—22no—
115C2×#168—22no—
116C2×#168—21no—
117C2×#168—21no—
118C2×#168—21no—
119C2×#168—21no—
120C2×#168—21no—
121C2×#168—21no—
122C2×C4×D4—51no—
123C2×C4⋊C8—101no—
124C2×C4⋊C8C2×D511yescharacteristic
125C2×C4⋊C8C2×D511yescharacteristic
126C2×#102—51no—
127C2×#102—51no—
128C2×C22⋊C8—101no—
129C2×C22⋊C8—101no—
130C2×C4×C8—51no—
131C2×C4×C8—51no—
132C2×C4×C8C2×D511yescharacteristic
133C4×C4⋊C4—51no—
134#340—51no—
135#340—51no—
136#336—101no—
137D4⋊C8—102no—
138#322—102no—
139C23×C5C4×D411yescharacteristic
140C22×D5—22no—
141C22×D5—41no—
142C22×D5—41no—
143C22×D5—41no—
144C22×D5—41no—
145C22×D5—41no—
146C22×D5—41no—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5#11711yescharacteristic
150C2×C4×C5C4×D411yescharacteristic
151C2×C4×C5#12111yescharacteristic
152C2×C4×C5#12311yescharacteristic
153C2×C4×C5#12411yescharacteristic
154C2×C4×C5#12611yescharacteristic
155C2×C4×C5C2×M1611yescharacteristic
156C2×C4×C5C2×M1611yescharacteristic
157C2×C4×C5#13111yescharacteristic
158C2×C4×C5#13111yescharacteristic
159C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
162C2×C4×C5#13711yescharacteristic
163C2×Dic5—22no—
164C2×Dic5—41no—
165C2×Dic5—41no—
166C2×Dic5—41no—
167C2×Dic5—41no—
168C2×Dic5—41no—
169C2×Dic5—41no—
170C2×Dic5—41no—
171C2×Dic5—41no—
172D20—22no—
173D20—22no—
174D20—41no—
175D20—41no—
176C4×D5—81no—
177C4×D5—81no—
178C4×D5—81no—
179C4×D5—81no—
180C5×C8—41no—
181C5×C8—41no—
182C5×C8—81no—
183C5×C8—81no—
184#168—24no—
185#168—41no—
186#168—41no—
187C22×D4—51no—
188C23×C4—101no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—51no—
192C22×C8—51no—
193C22×C8—101no—
194C22×C8C4×D511yescharacteristic
195C22×C8C4×D511yescharacteristic
196C4×D4—101no—
197C4×D4—101no—
198C4×D4—101no—
199C4×D4—101no—
200C2×C4⋊C4—51no—
201C2×C4⋊C4—51no—
202C2×C4⋊C4—51no—
203C2×C22⋊C4—101no—
204C2×C42—101no—
205C2×C42C22×D511yescharacteristic
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8—21no—
210C4⋊C8—202no—
211#102—102no—
212#102—102no—
213C22⋊C8—202no—
214C22⋊C8—202no—
215C4×C8—21no—
216C4×C8—21no—
217C4×C8—52no—
218C4×C8—101no—
219C4×C8—101no—
220C4×C8—101no—
221#95—101no—
222C22×C5#38811yescharacteristic
223C22×C5#43511yescharacteristic
224C22×C5#43511yescharacteristic
225C22×C5#44011yescharacteristic
226C22×C5#44211yescharacteristic
227C22×C5#44311yescharacteristic
228C22×C5#44311yescharacteristic
229C2×D5—42no—
230C2×D5—42no—
231C2×D5—42no—
232C2×D5—81no—
233C2×D5—81no—
234C2×D5—81no—
235C2×D5—81no—
236C4×C5—21no—
237C4×C5—21no—
238C4×C5#43211yescharacteristic
239C4×C5#43311yescharacteristic
240C4×C5#43511yescharacteristic
241C4×C5#43611yescharacteristic
242C4×C5#46811yescharacteristic
243C4×C5#46911yescharacteristic
244C4×C5#48911yescharacteristic
245C4×C5#49011yescharacteristic
246Dic5—42no—
247Dic5—81no—
248Dic5—81no—
249C24—101no—
250C2×D4—52no—
251C2×D4—101no—
252C2×D4—101no—
253C2×D4—101no—
254C2×D4—101no—
255C2×D4—101no—
256C22×C4—101no—
257C22×C4—101no—
258C22×C4—101no—
259C22×C4—201no—
260C22×C4—201no—
261C22×C4—201no—
262C22×C4—201no—
263C22×C4—201no—
264C22×C4—201no—
265C22×C4C2×C4×D511yescharacteristic
266C22×C4D4×D511yescharacteristic
267C22×C4#71311yescharacteristic
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—41no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—41no—
280C2×C8—102no—
281C2×C8—102no—
282C2×C8—102no—
283C2×C8—101no—
284C2×C8—101no—
285C2×C8—101no—
286C2×C8—101no—
287C2×C8—101no—
288C2×C8—101no—
289C4⋊C4—52no—
290C4⋊C4—101no—
291C4⋊C4—101no—
292C4⋊C4—101no—
293C4⋊C4—101no—
294C4⋊C4—101no—
295C22⋊C4—201no—
296C22⋊C4—201no—
297C42—201no—
298C42—201no—
299C42#70911yescharacteristic
300C42#70911yescharacteristic
301C42D4×D511yescharacteristic
302C42#71111yescharacteristic
303C2×C5#158511yescharacteristic
304C2×C5#158611yescharacteristic
305C2×C5#158611yescharacteristic
306C2×C5#158811yescharacteristic
307C2×C5#192411yescharacteristic
308C2×C5#193611yescharacteristic
309C2×C5#193711yescharacteristic
310D5—82no—
311C23—102no—
312C23—201no—
313C23—201no—
314C23—201no—
315C23—201no—
316C23—201no—
317C23—201no—
318C23#403911yescharacteristic
319D4—102no—
320D4—102no—
321D4—201no—
322D4—201no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—102no—
326C2×C4—201no—
327C2×C4—201no—
328C2×C4—201no—
329C2×C4—201no—
330C2×C4—201no—
331C2×C4—201no—
332C2×C4—201no—
333C2×C4—201no—
334C2×C4—401no—
335C2×C4—401no—
336C2×C4—401no—
337C2×C4—401no—
338C2×C4#401811yescharacteristic
339C2×C4#402711yescharacteristic
340C2×C4#403011yescharacteristic
341C2×C4#403111yescharacteristic
342C2×C4#404011yescharacteristic
343C2×C4#404411yescharacteristic
344C2×C4#404711yescharacteristic
345C2×C4#404711yescharacteristic
346C2×C4D5×M1611yescharacteristic
347C2×C4D5×M1611yescharacteristic
348C2×C4#405711yescharacteristic
349C2×C4#406011yescharacteristic
350C2×C4#406011yescharacteristic
351C2×C4#406411yescharacteristic
352C8—41no—
353C8—41no—
354C8—81no—
355C8—81no—
356C8—104no—
357C8—201no—
358C8—201no—
359C5#956011yescharacteristic, complemented, Sylow
360C22—202no—
361C22—202no—
362C22—202no—
363C22—401no—
364C22—401no—
365C22—401no—
366C22—401no—
367C22#6495811yescharacteristic
368C22#6512511yescharacteristic
369C22#6512511yescharacteristic
370C22#6515811yescharacteristic
371C22#6517811yescharacteristic
372C22#6518411yescharacteristic
373C22#6518411yescharacteristic
374C4—21no—
375C4—21no—
376C4—202no—
377C4—401no—
378C4—401no—
379C4#6497911yescharacteristic
380C4#6499411yescharacteristic
381C4#6501711yescharacteristic
382C4#6501811yescharacteristic
383C4#6505311yescharacteristic
384C4#6507111yescharacteristic
385C4#6508411yescharacteristic
386C4#6510111yescharacteristic
387C2—402no—
388C2#1059931411yescharacteristic
389C2#1059931411yescharacteristic
390C2#1059935411yescharacteristic
391C2#1059935511yescharacteristic
392C2#1059945111yescharacteristic
393C2#1059964911yescharacteristic
394C2#1059971111yescharacteristic
subgroupG/H
centerC22×C4D4×D5
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1277C2
socleC23×C5C4×D4
prime radicalC22×D20C2×C4
cosocleC2×C42×C5C23
hypercenter#1277D5
hypocenterC5#9560
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
2. #10601261C2semidirect
5. C2×#64674C2semidirect
6. C5×#1277C2semidirect
7. #10598195C2semidirect
67. #1277D5semidirect
359. C5#9560semidirect

Maximal subgroups

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

subgroupindex
#106012632
#106012612
C2×#647032
C4×#39532
C2×#646742
C5×#12772
#105981952
#95605