Finite Group Databasebeta

← #11997607

Subgroups — #11997607

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
2C2×#64679C211yesmaximal, characteristic
3C2×#64675C211yesmaximal, characteristic, complemented
4#10600277C211yesmaximal, characteristic, complemented
5C4×#3941C211yesmaximal, characteristic
6C5×#1279C211yesmaximal, characteristic, complemented
7#10598194C211yesmaximal, characteristic, complemented
8C2×C4×D20C2211yescharacteristic
9C2×C5×C4⋊C8C2211yescharacteristic
10C2×C4×C5×C8C2211yescharacteristic
11C4×C5×C4⋊C4C2211yescharacteristic
12C2×#3952—21no—
13C2×#3952—21no—
14C2×#3941C411yescharacteristic
15C2×#3941C411yescharacteristic
16C2×C4⋊#168—21no—
17C2×C4⋊#168C2211yescharacteristic
18C2×C4×#168C2211yescharacteristic
19C2×C4×#168C2211yescharacteristic
20#64749C411yescharacteristic
21#64749C411yescharacteristic
22#64744—21no—
23#64679—22no—
24#64675—22no—
25#9560—51nomaximal, Sylow
26C22×D20C2×C411yescharacteristic
27C22×C4×D5—21no—
28C22×C5×C8—21no—
29C22×C5×C8—21no—
30C2×C5×C4⋊C4C2×C411yescharacteristic
31C2×C5×C4⋊C4C2×C411yescharacteristic
32C2×C42×C5—21no—
33C2×C42×C5C2311yescharacteristic
34C2×#685—21no—
35C2×C4⋊Dic5C2×C411yescharacteristic
36C22×#168—21no—
37C22×#168C2×C411yescharacteristic
38C22×#168C2×C411yescharacteristic
39C22×#168D411yescharacteristic
40C22×#168D411yescharacteristic
41C4×D20—21no—
42C4×D20—21no—
43C4×D20—21no—
44C4×D20—21no—
45C5×C4⋊C8—21no—
46C5×C4⋊C8—21no—
47C4×C5×C8—21no—
48C4×C5×C8D412yes—
49C5×#95—21no—
50#3952—42no—
51#3952—42no—
52#3941—22no—
53#3941—22no—
54C4⋊#168—21no—
55C4⋊#168—21no—
56C4⋊#168—42no—
57C4×#168—21no—
58C4×#168—21no—
59C4×#168—21no—
60C4×#168—21no—
61#1954—51no—
62#1939—51no—
63C4×#102—51no—
64C2×D4⋊C8—51no—
65C2×#322—51no—
66#1279D511yescharacteristic, complemented
67#1277—51no—
68C23×D5—21no—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5C22×C411yescharacteristic
72C22×C4×C5C2×D411yescharacteristic
73C22×C4×C5#4111yescharacteristic
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—22no—
88C2×C5×C8—22no—
89C2×C5×C8—22no—
90C2×C5×C8—41no—
91C2×C5×C8—41no—
92C2×C5×C8—41no—
93C5×C4⋊C4—21no—
94C5×C4⋊C4—21no—
95C5×C4⋊C4—21no—
96C5×C4⋊C4M1612yes—
97C42×C5—41no—
98C42×C5—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—
107C2×#168—21no—
108C2×#168—21no—
109C2×#168—21no—
110C2×#168—21no—
111C2×#168—21no—
112C2×#168—21no—
113C2×#168—21no—
114C2×#168—21no—
115C2×#168—21no—
116C2×#168—21no—
117C2×#168—21no—
118C2×#168—21no—
119C2×#168—41no—
120C2×#168—41no—
121C2×#168—41no—
122C2×C4×D4—51no—
123C2×C4⋊C8—51no—
124C2×C4⋊C8—101no—
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⋊C4C2×D511yescharacteristic
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—22no—
150C2×C4×C5—41no—
151C2×C4×C5—41no—
152C2×C4×C5—41no—
153C2×C4×C5—41no—
154C2×C4×C5—41no—
155C2×C4×C5#11711yescharacteristic
156C2×C4×C5C4×D411yescharacteristic
157C2×C4×C5#12111yescharacteristic
158C2×C4×C5#12311yescharacteristic
159C2×C4×C5#12411yescharacteristic
160C2×C4×C5#12611yescharacteristic
161C2×C4×C5C2×M1611yescharacteristic
162C2×C4×C5C2×M1611yescharacteristic
163C2×C4×C5#13111yescharacteristic
164C2×C4×C5#13111yescharacteristic
165C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C5#13711yescharacteristic
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—24no—
181C5×C8—81no—
182#168—41no—
183#168—41no—
184#168—41no—
185#168—41no—
186#168—81no—
187C22×D4—51no—
188C23×C4—101no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—51no—
192C22×C8—51no—
193C22×C8—51no—
194C22×C8—51no—
195C22×C8—101no—
196C4×D4—101no—
197C4×D4—101no—
198C4×D4—101no—
199C4×D4—101no—
200C2×C4⋊C4—51no—
201C2×C4⋊C4C4×D511yescharacteristic
202C2×C4⋊C4C4×D511yescharacteristic
203C2×C22⋊C4—101no—
204C2×C42—21no—
205C2×C42C22×D511yescharacteristic
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—101no—
209C4⋊C8—101no—
210C4⋊C8—202no—
211#102—102no—
212#102—102no—
213C22⋊C8—202no—
214C22⋊C8—202no—
215C4×C8—21no—
216C4×C8—101no—
217C4×C8—101no—
218C4×C8—101no—
219C4×C8—101no—
220C4×C8D2012yes—
221#95—21no—
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—42no—
239C4×C5—81no—
240C4×C5#43211yescharacteristic
241C4×C5#43311yescharacteristic
242C4×C5#43511yescharacteristic
243C4×C5#43611yescharacteristic
244C4×C5#46811yescharacteristic
245C4×C5#46911yescharacteristic
246C4×C5#48911yescharacteristic
247C4×C5#49011yescharacteristic
248Dic5—81no—
249C24—101no—
250C2×D4—52no—
251C2×D4—101no—
252C2×D4—101no—
253C2×D4—101no—
254C2×D4—101no—
255C2×D4—101no—
256C22×C4—21no—
257C22×C4—21no—
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#71111yescharacteristic
268C2×C8—22no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—101no—
275C2×C8—101no—
276C2×C8—101no—
277C2×C8—101no—
278C2×C8—101no—
279C2×C8—101no—
280C2×C8—101no—
281C2×C8—101no—
282C2×C8—101no—
283C2×C8—101no—
284C2×C8—101no—
285C2×C8—101no—
286C2×C8—201no—
287C2×C8—201no—
288C2×C8—201no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—101no—
293C4⋊C4—101no—
294C4⋊C4#67612yes—
295C22⋊C4—201no—
296C22⋊C4—201no—
297C42—41no—
298C42—41no—
299C42C2×D2011yescharacteristic
300C42#70911yescharacteristic
301C42#71111yescharacteristic
302C42#71311yescharacteristic
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#402711yescharacteristic
319D4—102no—
320D4—102no—
321D4—201no—
322D4—201no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—22no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—201no—
332C2×C4—201no—
333C2×C4—201no—
334C2×C4—401no—
335C2×C4—401no—
336C2×C4—401no—
337C2×C4—401no—
338C2×C4C4×D2011yescharacteristic
339C2×C4#403111yescharacteristic
340C2×C4#403211yescharacteristic
341C2×C4#403811yescharacteristic
342C2×C4#404111yescharacteristic
343C2×C4#404411yescharacteristic
344C2×C4C2×#67611yescharacteristic
345C2×C4#404711yescharacteristic
346C2×C4D5×M1611yescharacteristic
347C2×C4#405311yescharacteristic
348C2×C4#405711yescharacteristic
349C2×C4#406011yescharacteristic
350C2×C4#406011yescharacteristic
351C2×C4#406411yescharacteristic
352C8—24no—
353C8—81no—
354C8—201no—
355C8—201no—
356C8—201no—
357C8—201no—
358C8—401no—
359C5#956011yescharacteristic, complemented, Sylow
360C22—202no—
361C22—202no—
362C22—202no—
363C22—401no—
364C22—401no—
365C22—401no—
366C22—401no—
367C22#6495911yescharacteristic
368C22#6501711yescharacteristic
369C22#6501911yescharacteristic
370C22#6507411yescharacteristic
371C22#6510611yescharacteristic
372C22#6511311yescharacteristic
373C22#6511311yescharacteristic
374C4—21no—
375C4—21no—
376C4—42no—
377C4—81no—
378C4—401no—
379C4#6497711yescharacteristic
380C4#6499511yescharacteristic
381C4#6505311yescharacteristic
382C4#6508411yescharacteristic
383C4#6512411yescharacteristic
384C4#6512911yescharacteristic
385C4#6515411yescharacteristic
386C4#6517511yescharacteristic
387C2—402no—
388C2#1059895011yescharacteristic
389C2#1059895111yescharacteristic
390C2#1059901311yescharacteristic
391C2#1059901611yescharacteristic
392C2#1059940911yescharacteristic
393C2#1059953811yescharacteristic
394C2#1059965011yescharacteristic
subgroupG/H
centerC22×C4D4×D5
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1279C2
socleC23×C5C4×D4
prime radicalC22×D20C2×C4
cosocleC2×C42×C5C23
hypercenter#1279D5
hypocenterC5#9560
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
3. C2×#64675C2semidirect
4. #10600277C2semidirect
6. C5×#1279C2semidirect
7. #10598194C2semidirect
66. #1279D5semidirect
359. C5#9560semidirect

Maximal subgroups

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

subgroupindex
#106012632
C2×#646792
C2×#646752
#106002772
C4×#39412
C5×#12792
#105981942
#95605