Finite Group Databasebeta

← #11999346

Subgroups — #11999346

Order 1280.

572 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
1C2×#65222C211yesmaximal, characteristic
2C5×#1797C211yesmaximal, characteristic
3C4×C22⋊#168C211yesmaximal, characteristic
4#10598165C212yesmaximal
5#10598165C212yesmaximal
6C22×C42×C5C2211yescharacteristic
7C22×#683C411yescharacteristic
8C22×#683C411yescharacteristic
9C2×C5×C4⋊C8—21no—
10C2×C5×C22⋊C8C2212yes—
11C2×#3963C411yescharacteristic
12C2×#3963C411yescharacteristic
13C2×#3963C2211yescharacteristic
14C2×#3963C2211yescharacteristic
15C2×C22⋊#168C2212yes—
16#65222—21no—
17#65222—21no—
18#65222—21no—
19#65222—21no—
20C2×C4×#168—21no—
21C5×#336—21no—
22#64744—21no—
23#9880—51nomaximal, Sylow
24C23×C4×C5C2×C411yescharacteristic
25C23×C4×C5C2×C411yescharacteristic
26C23×C4×C5C2311yescharacteristic
27C23×Dic5C2×C411yescharacteristic
28C23×Dic5C2×C411yescharacteristic
29C23×Dic5C2×C411yescharacteristic
30C23×Dic5C2×C411yescharacteristic
31C22×C5×C8—22no—
32C2×C42×C5—42no—
33C2×C42×C5D411yescharacteristic
34C2×C42×C5D411yescharacteristic
35C2×C42×C5D411yescharacteristic
36C2×C42×C5D411yescharacteristic
37C2×#683—21no—
38C2×#683—21no—
39C2×#683—22no—
40C2×#683—21no—
41C2×#683—21no—
42C2×#683—42no—
43C2×#683C814yescomplemented
44C22×#168—22no—
45C5×C4⋊C8—42no—
46C5×C22⋊C8—24no—
47#3963—21no—
48#3963—21no—
49#3963—21no—
50#3963—21no—
51#3963—21no—
52#3963—21no—
53#3963—21no—
54#3963—21no—
55C22⋊#168—22no—
56C22⋊#168Q814yes—
57C4×#168—42no—
58C2×#387—51no—
59#1797D511yescharacteristic
60C4×C22⋊C8—51no—
61#1280—52no—
62#1280—52no—
63C24×C5C22×C411yescharacteristic
64C22×C4×C5—22no—
65C22×C4×C5—22no—
66C22×C4×C5—41no—
67C22×C4×C5—41no—
68C22×C4×C5—41no—
69C22×C4×C5—41no—
70C22×C4×C5—41no—
71C22×C4×C5C22⋊C411yescharacteristic
72C22×C4×C5C22⋊C411yescharacteristic
73C22×C4×C5C22⋊C411yescharacteristic
74C22×C4×C5C22⋊C411yescharacteristic
75C22×C4×C5C2×C812yes—
76C22×C4×C5M1612yes—
77C22×C4×C5C2×D411yescharacteristic
78C22×C4×C5C2×D411yescharacteristic
79C22×C4×C5C2×Q812yes—
80C22×C4×C5#4112yes—
81C22×Dic5—21no—
82C22×Dic5—21no—
83C22×Dic5—21no—
84C22×Dic5—21no—
85C22×Dic5—21no—
86C22×Dic5—21no—
87C22×Dic5—22no—
88C22×Dic5—22no—
89C22×Dic5—41no—
90C22×Dic5—41no—
91C22×Dic5—41no—
92C22×Dic5—41no—
93C22×Dic5—41no—
94C22×Dic5—41no—
95C22×Dic5—41no—
96C22×Dic5—41no—
97C22×Dic5C2×C812yes—
98C22×Dic5C2×C812yes—
99C2×C5×C8—42no—
100C2×C5×C8—42no—
101C2×C5×C8—42no—
102C42×C5—22no—
103C42×C5—22no—
104C42×C5—41no—
105C42×C5—41no—
106#683—24no—
107#683—24no—
108#683—42no—
109#683—42no—
110C2×#168—24no—
111C2×#168—42no—
112C2×#168—42no—
113C22×C4⋊C4—51no—
114C22×C4⋊C4—51no—
115C22×C42C2×D511yescharacteristic
116C2×C4⋊C8—21no—
117C2×C22⋊C8—52no—
118C2×C22⋊C8C2×D512yes—
119C2×C4×C8—101no—
120#387—101no—
121#387—101no—
122#387—101no—
123#387—101no—
124C2×#95—51no—
125C2×#95—51no—
126C2×#95—51no—
127C2×#95—51no—
128#336—21no—
129#336—101no—
130C23×C5—21no—
131C23×C5—21no—
132C23×C5—21no—
133C23×C5—21no—
134C23×C5C2×C22⋊C411yescharacteristic
135C23×C5C4×Q812yes—
136C23×C5C22×C811yescharacteristic
137C23×C5C2×M1611yescharacteristic
138C23×C5#13112yes—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5—42no—
153C2×C4×C5—42no—
154C2×C4×C5—42no—
155C2×C4×C5—42no—
156C2×C4×C5—44no—
157C2×C4×C5C22⋊C812yes—
158C2×C4×C5C22⋊C812yes—
159C2×C4×C5#9912yes—
160C2×C4×C5C22⋊Q812yes—
161C2×C4×C5#12411yescharacteristic
162C2×C4×C5C4⋊Q811yescharacteristic
163C2×Dic5—22no—
164C2×Dic5—22no—
165C2×Dic5—42no—
166C2×Dic5—42no—
167C2×Dic5—41no—
168C2×Dic5—41no—
169C2×Dic5—41no—
170C2×Dic5—41no—
171C2×Dic5—42no—
172C2×Dic5—42no—
173C2×Dic5—41no—
174C2×Dic5—41no—
175C2×Dic5—41no—
176C2×Dic5—41no—
177C2×Dic5—41no—
178C2×Dic5—41no—
179C2×Dic5—82no—
180C2×Dic5—82no—
181C5×C8—82no—
182#168—44no—
183C23×C4—51no—
184C23×C4—51no—
185C23×C4—51no—
186C23×C4—51no—
187C23×C4C4×D511yescharacteristic
188C23×C4C4×D511yescharacteristic
189C23×C4C22×D511yescharacteristic
190C22×C8—22no—
191C22×C8—102no—
192C2×C4⋊C4—54no—
193C2×C4⋊C4—102no—
194C2×C4⋊C4—101no—
195C2×C4⋊C4—101no—
196C2×C4⋊C4—101no—
197C2×C4⋊C4—101no—
198C2×C4⋊C4—202no—
199C2×C42—42no—
200C2×C42D2011yescharacteristic
201C2×C42D2011yescharacteristic
202C2×C42C22⋊D511yescharacteristic
203C2×C42C22⋊D511yescharacteristic
204C4⋊C8—42no—
205C22⋊C8—24no—
206C22⋊C8—54no—
207C22⋊C8—102no—
208C4×C8—202no—
209#95—101no—
210#95—101no—
211#95—101no—
212#95—101no—
213#95—101no—
214#95—101no—
215#95—101no—
216#95—101no—
217C22×C5—21no—
218C22×C5—21no—
219C22×C5—21no—
220C22×C5—21no—
221C22×C5—22no—
222C22×C5—22no—
223C22×C5—22no—
224C22×C5—22no—
225C22×C5#39111yescharacteristic
226C22×C5C2×C22⋊C811yescharacteristic
227C22×C5#40811yescharacteristic
228C22×C5C2×#9911yescharacteristic
229C22×C5#41011yescharacteristic
230C22×C5#41311yescharacteristic
231C22×C5#41311yescharacteristic
232C22×C5C8×Q812yes—
233C22×C5#44612yes—
234C4×C5—22no—
235C4×C5—22no—
236C4×C5—22no—
237C4×C5—22no—
238C4×C5—21no—
239C4×C5—21no—
240C4×C5—41no—
241Dic5—42no—
242Dic5—42no—
243Dic5—81no—
244Dic5—81no—
245C24C2×C4×D511yescharacteristic
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—52no—
254C22×C4—52no—
255C22×C4—101no—
256C22×C4—101no—
257C22×C4—101no—
258C22×C4—101no—
259C22×C4—101no—
260C22×C4—101no—
261C22×C4—102no—
262C22×C4—102no—
263C22×C4—201no—
264C22×C4—201no—
265C22×C4—201no—
266C22×C4—201no—
267C22×C4—201no—
268C22×C4—201no—
269C22×C4—201no—
270C22×C4—201no—
271C22×C4C8×D512yes—
272C22×C4#67612yes—
273C22×C4#68511yescharacteristic
274C22×C4#68511yescharacteristic
275C22×C4#68511yescharacteristic
276C22×C4#68511yescharacteristic
277C22×C4C2×D2011yescharacteristic
278C22×C4#71112yes—
279C22×C4Q8×D512yes—
280C22×C4C2×C22⋊D511yescharacteristic
281C2×C8—42no—
282C2×C8—42no—
283C2×C8—42no—
284C2×C8—104no—
285C2×C8—202no—
286C2×C8—202no—
287C4⋊C4—104no—
288C4⋊C4—104no—
289C4⋊C4—202no—
290C4⋊C4—202no—
291C42—22no—
292C42—22no—
293C42—41no—
294C42—41no—
295C2×C5—22no—
296C2×C5—22no—
297C2×C5#145811yescharacteristic
298C2×C5#145911yescharacteristic
299C2×C5#146811yescharacteristic
300C2×C5#147311yescharacteristic
301C2×C5#198411yescharacteristic
302C2×C5#199611yescharacteristic
303C2×C5#199811yescharacteristic
304C23—21no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23#403312yes—
309C23C2×C8×D511yescharacteristic
310C23C2×#67611yescharacteristic
311C23#405312yes—
312C23C2×#68511yescharacteristic
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—44no—
331C2×C4—102no—
332C2×C4—102no—
333C2×C4—202no—
334C2×C4—202no—
335C2×C4—201no—
336C2×C4—201no—
337C2×C4—201no—
338C2×C4—201no—
339C2×C4—202no—
340C2×C4—202no—
341C2×C4—201no—
342C2×C4—201no—
343C2×C4—201no—
344C2×C4—201no—
345C2×C4—201no—
346C2×C4—201no—
347C2×C4—402no—
348C2×C4—402no—
349C2×C4#393812yes—
350C2×C4#395212yes—
351C2×C4#395212yes—
352C2×C4#404312yes—
353C2×C4#408211yescharacteristic
354C2×C4#409011yescharacteristic
355C8—82no—
356C8—204no—
357C5#988011yescharacteristic, complemented, Sylow
358C22—21no—
359C22—21no—
360C22—22no—
361C22—22no—
362C22—21no—
363C22—21no—
364C22—22no—
365C22—22no—
366C22#6511912yes—
367C22#6512012yes—
368C22C2×#393811yescharacteristic
369C22#6526311yescharacteristic
370C22#6529511yescharacteristic
371C22C2×#395211yescharacteristic
372C22#6541811yescharacteristic
373C22#6542111yescharacteristic
374C22#6542111yescharacteristic
375C4—22no—
376C4—22no—
377C4—22no—
378C4—21no—
379C4—22no—
380C4—21no—
381C4—41no—
382C4—202no—
383C4—202no—
384C4—401no—
385C4—401no—
386C2—22no—
387C2—22no—
388C2#1060032211yescharacteristic
389C2#1060071211yescharacteristic
390C2#1060076211yescharacteristic
391C2#1060126511yescharacteristic
392C2#1060131811yescharacteristic
393C2#1060157511yescharacteristic
394C2#1060162211yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC23×C5C22×C8
FrattiniC23×C4C22×D5
FittingC5×#1797C2
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C22×C4
cosocleC23×C4×C5C23
hypercenter#1797D5
hypocenterC5#9880
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
43. C2×#683C8semidirect
357. C5#9880semidirect

Maximal subgroups

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

subgroupindex
C2×#652222
C5×#17972
C4×C22⋊#1682
#105981652
#98805