Finite Group Databasebeta

← #11995399

Subgroups — #11995399

Order 1280.

456 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3076C211yesmaximal, characteristic
2#10614248C211yesmaximal, characteristic
3#10602628C211yesmaximal, characteristic, complemented
4#10602619C211yesmaximal, characteristic, complemented
5#10602439C211yesmaximal, characteristic
6#10598198C211yesmaximal, characteristic, complemented
7#10598195C211yesmaximal, characteristic, complemented
8C5×#533C2211yescharacteristic
9C4×C5×#41C2211yescharacteristic
10C5×#479—21no—
11C5×#478—21no—
12C5×#477C411yescharacteristic, complemented
13C5×#476C411yescharacteristic, complemented
14C5×#475C411yescharacteristic, complemented
15C5×#474C411yescharacteristic, complemented
16C5×#427—21no—
17C2×C5×C4⋊C8C2211yescharacteristic
18C5×#416—21no—
19C2×#3969—21no—
20#65313—21no—
21#65301—21no—
22#65300—22no—
23C4×C4⋊Dic5C2211yescharacteristic
24#65214—21no—
25#65214C2211yescharacteristic
26#65213C2211yescharacteristic
27C4×#681—21no—
28C2×C4×#168C2211yescharacteristic
29#64758—22no—
30Q8⋊#168—21no—
31Q8⋊#168—21no—
32#64752—21no—
33#9209—51nomaximal, Sylow
34C2×C5×#41D411yescharacteristic
35C22×C5×C8—21no—
36C5×C4⋊Q8C2×C411yescharacteristic
37C5×C4⋊Q8C2×C411yescharacteristic
38C5×#125—21no—
39C5×C22⋊Q8—21no—
40C5×C22⋊Q8—21no—
41C4×C5×Q8—21no—
42C4×C5×Q8—21no—
43C4×C5×Q8C2×C411yescharacteristic
44C4×C5×Q8D411yescharacteristic
45C4×C5×D4—21no—
46C4×C5×D4—21no—
47C4×C5×D4C2×C411yescharacteristic
48C4×C5×D4D411yescharacteristic
49C5×#117—21no—
50C5×#117—21no—
51C5×#117D411yescharacteristic
52C2×C42×C5—21no—
53C2×C42×C5C2311yescharacteristic
54C2×C4⋊Dic5—21no—
55C2×C4×Dic5—21no—
56C2×#681—22no—
57C2×#681—21no—
58C22×#168—21no—
59C5×#107—21no—
60C5×#107—21no—
61C5×#106—21no—
62C5×#106—21no—
63C5×C4⋊C8—21no—
64C5×C4⋊C8C2×C411yescharacteristic
65C5×C4⋊C8C2×C411yescharacteristic
66C5×#103—21no—
67C5×#103—21no—
68C5×#102—21no—
69C5×#102—21no—
70#3969—42no—
71#3963—21no—
72C22⋊#168—22no—
73C22⋊#168D412yes—
74C4⋊#168—22no—
75C4⋊#168—21no—
76C4⋊#168—21no—
77C4⋊#168—21no—
78#3935—22no—
79C4×#168—21no—
80C4×#168—21no—
81C4×#168D411yescharacteristic
82C4×#168D411yescharacteristic
83#3076D511yescharacteristic
84#2965—51no—
85#1806—51no—
86#1503—51no—
87#1493—51no—
88#1301—51no—
89#1279—51no—
90C5×#41—21no—
91C5×#41—21no—
92C5×#41—21no—
93C5×#41—21no—
94C2×C5×Q8—21no—
95C2×C5×Q8—21no—
96C2×C5×Q8C22⋊C411yescharacteristic
97C2×C5×D4—21no—
98C2×C5×D4C22⋊C411yescharacteristic
99C22×C4×C5—21no—
100C22×C4×C5—21no—
101C22×C4×C5—21no—
102C22×C4×C5C2×D411yescharacteristic
103C22×C4×C5C2×D411yescharacteristic
104C22×C4×C5#4111yescharacteristic
105C22×Dic5—41no—
106C2×C5×C8—21no—
107C2×C5×C8—21no—
108C2×C5×C8—41no—
109C2×C5×C8—41no—
110C5×C4⋊C4—21no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—21no—
113C5×C4⋊C4—21no—
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—41no—
117C5×C4⋊C4—41no—
118C5×C4⋊C4C22⋊C411yescharacteristic
119C5×C4⋊C4C22⋊C411yescharacteristic
120C5×C22⋊C4—21no—
121C5×C22⋊C4—21no—
122C5×C22⋊C4—21no—
123C5×C22⋊C4—41no—
124C42×C5—21no—
125C42×C5—21no—
126C42×C5—21no—
127C42×C5—41no—
128C42×C5C22×C411yescharacteristic
129C42×C5C2×D411yescharacteristic
130C42×C5C2×D411yescharacteristic
131C42×C5#4111yescharacteristic
132C4⋊Dic5—22no—
133C4⋊Dic5—41no—
134C4×Dic5—41no—
135C4×Dic5—41no—
136#681—44no—
137#681—41no—
138#681—41no—
139C2×#168—21no—
140C2×#168—21no—
141C2×#168—22no—
142C2×#168—42no—
143C2×#168—41no—
144#533C2×D511yescharacteristic
145C4×#41C2×D511yescharacteristic
146#479—21no—
147#478—21no—
148#477Dic511yescharacteristic, complemented
149#476Dic511yescharacteristic, complemented
150#475Dic511yescharacteristic, complemented
151#474Dic511yescharacteristic, complemented
152#446—101no—
153#436—101no—
154#435—102no—
155#431—51no—
156#431—101no—
157#427—21no—
158#423—51no—
159C2×C4⋊C8C2×D511yescharacteristic
160C2×#104—101no—
161#416—21no—
162C4×M16—101no—
163C2×C4×C8—51no—
164C4×C4⋊C4—51no—
165#339—101no—
166#328—102no—
167Q8⋊C8—101no—
168Q8⋊C8—101no—
169C23×C5—21no—
170C23×C5#12111yescharacteristic
171C5×Q8—21no—
172C5×Q8—21no—
173C5×Q8—41no—
174C5×Q8—41no—
175C5×Q8—81no—
176C5×D4—21no—
177C5×D4—21no—
178C5×D4—41no—
179C5×D4—41no—
180C2×C4×C5—21no—
181C2×C4×C5—21no—
182C2×C4×C5—21no—
183C2×C4×C5—21no—
184C2×C4×C5—21no—
185C2×C4×C5—41no—
186C2×C4×C5—42no—
187C2×C4×C5—41no—
188C2×C4×C5—41no—
189C2×C4×C5—41no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5C2×C22⋊C411yescharacteristic
194C2×C4×C5C4×D411yescharacteristic
195C2×C4×C5C4×D411yescharacteristic
196C2×C4×C5#12011yescharacteristic
197C2×C4×C5#12111yescharacteristic
198C2×C4×C5#12311yescharacteristic
199C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
200C2×C4×C5#13711yescharacteristic
201C2×C4×C5#13711yescharacteristic
202C2×C4×C5#13711yescharacteristic
203C2×Dic5—42no—
204C2×Dic5—81no—
205C2×Dic5—81no—
206C5×C8—41no—
207C5×C8—41no—
208#168—22no—
209#168—41no—
210#168—42no—
211#168—81no—
212C2×#41C22⋊D511yescharacteristic
213C2×M16—102no—
214C2×M16—101no—
215C22×C8—21no—
216C22×C8—101no—
217C4⋊Q8C2×Dic511yescharacteristic
218C4⋊Q8C2×Dic511yescharacteristic
219#125—21no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222C4×Q8—21no—
223C4×Q8—21no—
224C4×Q8C2×Dic511yescharacteristic
225C4×Q8C22⋊D511yescharacteristic
226C4×D4—21no—
227C4×D4—21no—
228C4×D4C2×Dic511yescharacteristic
229C4×D4C22⋊D511yescharacteristic
230#117—21no—
231#117—21no—
232#117C22⋊D511yescharacteristic
233C2×C4⋊C4—101no—
234C2×C42—21no—
235C2×C42—101no—
236C2×C42C22×D511yescharacteristic
237#107—21no—
238#107—21no—
239#106—21no—
240#106—21no—
241C4⋊C8—21no—
242C4⋊C8—102no—
243C4⋊C8—101no—
244C4⋊C8—101no—
245C4⋊C8—101no—
246C4⋊C8C2×Dic511yescharacteristic
247C4⋊C8C2×Dic511yescharacteristic
248#104—202no—
249#103—21no—
250#103—21no—
251#102—21no—
252#102—21no—
253C22⋊C8—52no—
254C22⋊C8—102no—
255#97—102no—
256C4×C8—51no—
257C4×C8—51no—
258C4×C8—101no—
259C4×C8—101no—
260#95—101no—
261C22×C5—21no—
262C22×C5—21no—
263C22×C5—41no—
264C22×C5—41no—
265C22×C5—41no—
266C22×C5#38611yescharacteristic
267C22×C5#46811yescharacteristic
268C22×C5#47011yescharacteristic
269C4×C5—21no—
270C4×C5—21no—
271C4×C5—21no—
272C4×C5—41no—
273C4×C5—41no—
274C4×C5—41no—
275C4×C5—81no—
276C4×C5—81no—
277C4×C5#41711yescharacteristic
278C4×C5#41911yescharacteristic
279C4×C5#44311yescharacteristic
280C4×C5#44411yescharacteristic
281C4×C5#46811yescharacteristic
282C4×C5#47011yescharacteristic
283Dic5—82no—
284#41—21no—
285#41—21no—
286#41—21no—
287#41—21no—
288C2×Q8—21no—
289C2×Q8—21no—
290C2×Q8C22⋊Dic511yescharacteristic
291C2×D4—21no—
292C2×D4C22⋊Dic511yescharacteristic
293C22×C4—21no—
294C22×C4—21no—
295C22×C4—21no—
296C22×C4—201no—
297C22×C4D4×D511yescharacteristic
298C22×C4#71111yescharacteristic
299C22×C4C2×C22⋊D511yescharacteristic
300M16—204no—
301M16—201no—
302M16—201no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8—101no—
308C2×C8—101no—
309C2×C8—102no—
310C2×C8—202no—
311C2×C8—201no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—21no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—41no—
319C4⋊C4—41no—
320C4⋊C4—102no—
321C4⋊C4—201no—
322C4⋊C4C22⋊Dic511yescharacteristic
323C4⋊C4C22⋊Dic511yescharacteristic
324C22⋊C4—21no—
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—41no—
328C42—21no—
329C42—21no—
330C42—21no—
331C42—41no—
332C42—201no—
333C42—201no—
334C42D4×D511yescharacteristic
335C42#71111yescharacteristic
336C42C22×Dic511yescharacteristic
337C42C2×C22⋊D511yescharacteristic
338C2×C5—21no—
339C2×C5—21no—
340C2×C5—81no—
341C2×C5#187611yescharacteristic
342C2×C5#189411yescharacteristic
343C2×C5#190611yescharacteristic
344C23—21no—
345C23#408511yescharacteristic
346Q8—21no—
347Q8—21no—
348Q8—41no—
349Q8—41no—
350Q8—81no—
351D4—21no—
352D4—21no—
353D4—41no—
354D4—41no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—41no—
361C2×C4—42no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—202no—
369C2×C4—401no—
370C2×C4—401no—
371C2×C4D4×Dic511yescharacteristic
372C2×C4D4×Dic511yescharacteristic
373C2×C4#408111yescharacteristic
374C2×C4#408311yescharacteristic
375C2×C4#408511yescharacteristic
376C2×C4#408811yescharacteristic
377C2×C4#408811yescharacteristic
378C2×C4#409511yescharacteristic
379C2×C4#409711yescharacteristic
380C2×C4C2×C22⋊Dic511yescharacteristic
381C8—41no—
382C8—41no—
383C8—102no—
384C8—201no—
385C8—202no—
386C8—401no—
387C5#920911yescharacteristic, complemented, Sylow
388C22—21no—
389C22—21no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22#6533811yescharacteristic
394C22#6534111yescharacteristic
395C22#6550911yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—41no—
400C4—41no—
401C4—41no—
402C4—81no—
403C4—81no—
404C4—402no—
405C4#6533811yescharacteristic
406C4#6534111yescharacteristic
407C4#6548511yescharacteristic
408C4#6548611yescharacteristic
409C4#6551411yescharacteristic
410C4#6552111yescharacteristic
411C2—21no—
412C2—21no—
413C2—81no—
414C2#1060249011yescharacteristic
415C2#1060288011yescharacteristic
416C2#1060290711yescharacteristic
subgroupG/H
centerC2×C4#4085
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#3076C2
socleC22×C5#386
prime radicalC2×C5×#41D4
cosocleC2×C42×C5C23
hypercenter#3076D5
hypocenterC5#9209
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3076

Complements

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

NH ≅ G/Ntype
3. #10602628C2semidirect
4. #10602619C2semidirect
6. #10598198C2semidirect
7. #10598195C2semidirect
12. C5×#477C4semidirect
13. C5×#476C4semidirect
14. C5×#475C4semidirect
15. C5×#474C4semidirect
148. #477Dic5semidirect
149. #476Dic5semidirect
150. #475Dic5semidirect
151. #474Dic5semidirect
387. C5#9209semidirect

Maximal subgroups

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

subgroupindex
C5×#30762
#106142482
#106026282
#106026192
#106024392
#105981982
#105981952
#92095