Finite Group Databasebeta

← #11994755

Subgroups — #11994755

Order 1280.

536 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#442C211yesmaximal, characteristic
2#10614035C211yesmaximal, characteristic, complemented
3#10602394C211yesmaximal, characteristic, complemented
4#10602390C211yesmaximal, characteristic, complemented
5#10602390C211yesmaximal, characteristic, complemented
6#10598152C211yesmaximal, characteristic, complemented
7#10598151C211yesmaximal, characteristic, complemented
8C22×C5×D8C411yescharacteristic
9C2×C4×C5×D4C2211yescharacteristic
10C2×C4×C5×D4C2211yescharacteristic
11C5×#442—22no—
12C5×#442—22no—
13C2×C5×#106C411yescharacteristic
14C2×C5×#102C411yescharacteristic
15C2×C5×#102C411yescharacteristic
16C2×C5×#97C2211yescharacteristic
17#65496—22no—
18#65301—22no—
19#65301—22no—
20#65214C2211yescharacteristic
21#65214C2211yescharacteristic
22#65214C2211yescharacteristic
23#65214C2211yescharacteristic
24D4⋊#168—22no—
25D4⋊#168—22no—
26#64745—22no—
27#9093—51nomaximal, Sylow
28C22×C5×D4C2×C411yescharacteristic
29C22×C5×D4C2×C411yescharacteristic
30C23×C4×C5—21no—
31C23×C4×C5—21no—
32C2×C5×D8—22no—
33C2×C5×D8—22no—
34C2×C5×D8—22no—
35C22×C5×C8C2×C411yescharacteristic
36C22×C5×C8C2×C411yescharacteristic
37C4×C5×D4—21no—
38C4×C5×D4—21no—
39C4×C5×D4—21no—
40C4×C5×D4—21no—
41C4×C5×D4—21no—
42C4×C5×D4—21no—
43C4×C5×D4D412yes—
44C4×C5×D4D412yes—
45C2×C5×C4⋊C4C2×C411yescharacteristic
46C2×C5×C4⋊C4C2×C411yescharacteristic
47C2×C5×C22⋊C4—21no—
48C2×C5×C22⋊C4—21no—
49C2×C42×C5C2311yescharacteristic
50C2×#681—24no—
51C5×#106—22no—
52C5×#102—22no—
53C5×#102—22no—
54C5×#97—21no—
55C5×#97—21no—
56C22⋊#168—24no—
57C22⋊#168—21no—
58C22⋊#168—21no—
59C22⋊#168—21no—
60C22⋊#168D412yes—
61C4⋊#168—21no—
62C4⋊#168—21no—
63C4⋊#168—21no—
64C4⋊#168—21no—
65C4×#168—21no—
66C4×#168—21no—
67C4×#168—21no—
68C4×#168D412yes—
69#2975—51no—
70C2×#442D511yescharacteristic
71#1478—51no—
72#1478—51no—
73#1460—51no—
74#1281—51no—
75#1275—51no—
76C24×C5—21no—
77C24×C5—21no—
78C2×C5×D4—21no—
79C2×C5×D4—21no—
80C2×C5×D4—21no—
81C2×C5×D4—21no—
82C2×C5×D4—21no—
83C2×C5×D4—21no—
84C2×C5×D4—21no—
85C2×C5×D4—21no—
86C2×C5×D4—21no—
87C2×C5×D4—21no—
88C2×C5×D4C22⋊C412yes—
89C2×C5×D4M1612yescomplemented
90C22×C4×C5—21no—
91C22×C4×C5—22no—
92C22×C4×C5—22no—
93C22×C4×C5—21no—
94C22×C4×C5—41no—
95C22×C4×C5—41no—
96C22×C4×C5—82no—
97C22×C4×C5—82no—
98C22×C4×C5C22×C411yescharacteristic
99C22×C4×C5C2×D411yescharacteristic
100C22×C4×C5#4111yescharacteristic
101C5×D8—28no—
102C2×C5×C8—21no—
103C2×C5×C8—21no—
104C2×C5×C8—21no—
105C2×C5×C8—21no—
106C2×C5×C8—21no—
107C2×C5×C8M1612yescomplemented
108C5×C4⋊C4—21no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—21no—
111C5×C4⋊C4C22⋊C412yes—
112C5×C22⋊C4—22no—
113C5×C22⋊C4—22no—
114C5×C22⋊C4—41no—
115C5×C22⋊C4—41no—
116C42×C5C2×D411yescharacteristic
117C42×C5C2×D411yescharacteristic
118C42×C5C2×D411yescharacteristic
119C42×C5#4111yescharacteristic
120#681—84no—
121C2×#168—22no—
122C2×#168—22no—
123C2×#168—41no—
124C2×#168—41no—
125C22×D8Dic511yescharacteristic
126C2×C4×D4C2×D511yescharacteristic
127C2×C4×D4C2×D511yescharacteristic
128#442—22no—
129#442—22no—
130#436—102no—
131#436—102no—
132#431—51no—
133#431—51no—
134#431—51no—
135#431—51no—
136C2×#106Dic511yescharacteristic
137C2×#102Dic511yescharacteristic
138C2×#102Dic511yescharacteristic
139#407—102no—
140C2×#97C2×D511yescharacteristic
141D4⋊C8—102no—
142D4⋊C8—102no—
143#323—102no—
144C23×C5—22no—
145C23×C5—22no—
146C23×C5—41no—
147C23×C5—41no—
148C23×C5—41no—
149C23×C5—41no—
150C23×C5—81no—
151C23×C5—81no—
152C23×C5—81no—
153C23×C5—81no—
154C23×C5C4×D411yescharacteristic
155C5×D4—22no—
156C5×D4—22no—
157C5×D4—22no—
158C5×D4—22no—
159C5×D4—41no—
160C5×D4—41no—
161C5×D4—41no—
162C5×D4—41no—
163C2×C4×C5—22no—
164C2×C4×C5—41no—
165C2×C4×C5—41no—
166C2×C4×C5—44no—
167C2×C4×C5—41no—
168C2×C4×C5—82no—
169C2×C4×C5—82no—
170C2×C4×C5—82no—
171C2×C4×C5—81no—
172C2×C4×C5—81no—
173C2×C4×C5C2×C22⋊C411yescharacteristic
174C2×C4×C5C4×D411yescharacteristic
175C2×C4×C5#12011yescharacteristic
176C2×C4×C5#12111yescharacteristic
177C2×C4×C5#12111yescharacteristic
178C2×C4×C5#12311yescharacteristic
179C2×C4×C5C2×M1611yescharacteristic
180C2×C4×C5C2×M1611yescharacteristic
181C2×C4×C5#13111yescharacteristic
182C2×C4×C5#13111yescharacteristic
183C5×C8—22no—
184C5×C8—41no—
185#168—42no—
186#168—42no—
187#168—81no—
188#168—81no—
189C22×D4C2×Dic511yescharacteristic
190C22×D4C2×Dic511yescharacteristic
191C23×C4—21no—
192C23×C4—21no—
193C2×D8—22no—
194C2×D8—22no—
195C2×D8—22no—
196C2×M16—104no—
197C22×C8C2×Dic511yescharacteristic
198C22×C8C2×Dic511yescharacteristic
199C4×D4—21no—
200C4×D4—21no—
201C4×D4—21no—
202C4×D4—21no—
203C4×D4—21no—
204C4×D4—21no—
205C4×D4C22⋊D512yes—
206C4×D4C22⋊D512yes—
207C2×C4⋊C4C2×Dic511yescharacteristic
208C2×C4⋊C4C2×Dic511yescharacteristic
209C2×C22⋊C4—21no—
210C2×C22⋊C4—21no—
211C2×C42C22×D511yescharacteristic
212#106—22no—
213C4⋊C8—101no—
214C4⋊C8—101no—
215C4⋊C8—101no—
216C4⋊C8—101no—
217#102—22no—
218#102—22no—
219C22⋊C8—52no—
220C22⋊C8—104no—
221C22⋊C8—101no—
222C22⋊C8—101no—
223C22⋊C8—101no—
224#97—21no—
225#97—21no—
226C4×C8—52no—
227C4×C8—101no—
228C4×C8—101no—
229C4×C8—101no—
230C22×C5—21no—
231C22×C5—21no—
232C22×C5—42no—
233C22×C5—42no—
234C22×C5—42no—
235C22×C5—42no—
236C22×C5—82no—
237C22×C5—82no—
238C22×C5—82no—
239C22×C5—82no—
240C22×C5—81no—
241C22×C5—81no—
242C22×C5#38611yescharacteristic
243C22×C5#43511yescharacteristic
244C22×C5#43611yescharacteristic
245C4×C5—21no—
246C4×C5—21no—
247C4×C5—21no—
248C4×C5—21no—
249C4×C5—42no—
250C4×C5—81no—
251C4×C5#40711yescharacteristic
252C4×C5#40811yescharacteristic
253C4×C5#43511yescharacteristic
254C4×C5#43611yescharacteristic
255C24—21no—
256C24—21no—
257C2×D4—21no—
258C2×D4—21no—
259C2×D4—21no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4#68112yescomplemented
268C2×D4C22⋊Dic512yes—
269C22×C4—21no—
270C22×C4—22no—
271C22×C4—22no—
272C22×C4—21no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—82no—
276C22×C4—82no—
277C22×C4D4×D511yescharacteristic
278C22×C4#71111yescharacteristic
279C22×C4C22×Dic511yescharacteristic
280D8—28no—
281M16—404no—
282C2×C8—21no—
283C2×C8—21no—
284C2×C8—21no—
285C2×C8—21no—
286C2×C8—21no—
287C2×C8—102no—
288C2×C8—102no—
289C2×C8—201no—
290C2×C8—201no—
291C2×C8#68112yescomplemented
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C4⋊C4C22⋊Dic512yes—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—41no—
299C22⋊C4—41no—
300C42D4×D511yescharacteristic
301C42#71111yescharacteristic
302C42C2×C22⋊D511yescharacteristic
303C42C2×C22⋊D511yescharacteristic
304C2×C5—21no—
305C2×C5—21no—
306C2×C5—82no—
307C2×C5—82no—
308C2×C5#187011yescharacteristic
309C2×C5#190311yescharacteristic
310C2×C5#190411yescharacteristic
311C23—22no—
312C23—22no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—81no—
318C23—81no—
319C23—81no—
320C23—81no—
321C23D4×Dic511yescharacteristic
322D4—22no—
323D4—22no—
324D4—22no—
325D4—22no—
326D4—41no—
327D4—41no—
328D4—41no—
329D4—41no—
330C2×C4—22no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—44no—
334C2×C4—41no—
335C2×C4—82no—
336C2×C4—82no—
337C2×C4—82no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4C2×#68111yescharacteristic
341C2×C4C2×#68111yescharacteristic
342C2×C4D4×Dic511yescharacteristic
343C2×C4#408111yescharacteristic
344C2×C4#408311yescharacteristic
345C2×C4#408511yescharacteristic
346C2×C4#408511yescharacteristic
347C2×C4#409411yescharacteristic
348C2×C4#409411yescharacteristic
349C2×C4C2×C22⋊Dic511yescharacteristic
350C8—22no—
351C8—41no—
352C8—202no—
353C8—202no—
354C8—401no—
355C8—401no—
356C5#909311yescharacteristic, complemented, Sylow
357C22—21no—
358C22—21no—
359C22—42no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—82no—
364C22—82no—
365C22—82no—
366C22—82no—
367C22—81no—
368C22—81no—
369C22#6530011yescharacteristic
370C22#6530111yescharacteristic
371C22#6550911yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—42no—
377C4—81no—
378C4#6530011yescharacteristic
379C4#6530111yescharacteristic
380C4#6549611yescharacteristic
381C4#6552311yescharacteristic
382C2—21no—
383C2—21no—
384C2—82no—
385C2—82no—
386C2#1060240411yescharacteristic
387C2#1060288211yescharacteristic
388C2#1060288311yescharacteristic
subgroupG/H
centerC22#65509
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC2×C5×#442C2
socleC22×C5#386
prime radicalC22×C5×D8C4
cosocleC2×C42×C5C23
hypercenterC2×#442D5
hypocenterC5#9093
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
2. #10614035C2semidirect
3. #10602394C2semidirect
4. #10602390C2semidirect
5. #10602390C2semidirect
6. #10598152C2semidirect
7. #10598151C2semidirect
89. C2×C5×D4M16semidirect
107. C2×C5×C8M16semidirect
267. C2×D4#681semidirect
291. C2×C8#681semidirect
356. C5#9093semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#4422
#106140352
#106023942
#106023902
#105981522
#105981512
#90935