Finite Group Databasebeta

← #11987366

Subgroups — #11987366

Order 1280.

578 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#4070C211yesmaximal, characteristic
2C5×#1797C211yesmaximal, characteristic
3C2×#64744C211yesmaximal, characteristic
4#10597971C212yesmaximal, complemented
5#10597968C212yesmaximal, complemented
6C22×C42×C5C2211yescharacteristic
7C2×#4070C411yescharacteristic
8C23×#168—21no—
9C2×C4×Dic10C411yescharacteristic
10C2×C5×C4⋊C8—21no—
11C2×C5×C22⋊C8—21no—
12#65501C411yescharacteristic
13#65499—21no—
14C4×C22⋊Dic5—21no—
15C4×C4⋊Dic5C411yescharacteristic
16#65222—21no—
17C4×#683—21no—
18#65218C2211yescharacteristic
19#65217C2211yescharacteristic
20C5×#336C2212yes—
21#64744—21no—
22#64744C2212yes—
23#7589—51nomaximal, Sylow
24C23×C4×C5C2×C411yescharacteristic
25C23×C4×C5D411yescharacteristic
26C23×C4×C5D411yescharacteristic
27C22×Dic10C2×C411yescharacteristic
28C22×C5×C8—22no—
29C2×C42×C5—42no—
30C2×C42×C5C2×C411yescharacteristic
31C2×C42×C5D411yescharacteristic
32C2×C42×C5D411yescharacteristic
33C2×C42×C5C2311yescharacteristic
34C2×C22⋊Dic5—21no—
35C2×C22⋊Dic5—21no—
36C2×C4⋊Dic5C2×C411yescharacteristic
37C2×C4⋊Dic5C2×C411yescharacteristic
38C2×C4⋊Dic5C2×C411yescharacteristic
39#4070—22no—
40#4070C814yescomplemented
41C2×#683—21no—
42C2×#683—21no—
43C2×#683—21no—
44C2×C4×Dic5—21no—
45C2×C4×Dic5—21no—
46C22×#168—24no—
47C22×#168—22no—
48C22×#168—42no—
49C22×#168—42no—
50C4×Dic10—42no—
51C5×C4⋊C8—42no—
52C5×C22⋊C8—42no—
53#3963—21no—
54#3963—21no—
55#3963—21no—
56#3963—21no—
57#3963—21no—
58C4×C22⋊Q8—51no—
59#1797D511yescharacteristic
60C2×#336—51no—
61#1272—52no—
62#1271—52no—
63C24×C5C22⋊C411yescharacteristic
64C22×C4×C5—22no—
65C22×C4×C5—22no—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5—41no—
69C22×C4×C5—41no—
70C22×C4×C5—41no—
71C22×C4×C5—41no—
72C22×C4×C5C22⋊C411yescharacteristic
73C22×C4×C5C22⋊C411yescharacteristic
74C22×C4×C5C22⋊C411yescharacteristic
75C22×C4×C5C2×C812yes—
76C22×C4×C5M1612yes—
77C22×C4×C5SD1612yes—
78C22×C4×C5Q1612yes—
79C22×C4×C5C22×C411yescharacteristic
80C22×C4×C5C2×D411yescharacteristic
81C22×C4×C5C2×D411yescharacteristic
82C22×Dic5—21no—
83C22×Dic5—21no—
84C22×Dic5—21no—
85C22×Dic5—21no—
86C2×Dic10—21no—
87C2×Dic10—41no—
88C2×Dic10—41no—
89C2×Dic10C2×C812yescomplemented
90C2×C5×C8—42no—
91C2×C5×C8—42no—
92C2×C5×C8—42no—
93C42×C5—22no—
94C42×C5—22no—
95C42×C5—41no—
96C42×C5—41no—
97C22⋊Dic5—24no—
98C22⋊Dic5—42no—
99C4⋊Dic5—21no—
100C4⋊Dic5—41no—
101C4⋊Dic5—41no—
102C4⋊Dic5C2×C812yescomplemented
103#683—24no—
104#683—42no—
105#683—41no—
106#683—41no—
107C4×Dic5—42no—
108C4×Dic5—42no—
109C2×#168—24no—
110C2×#168—48no—
111C2×#168—42no—
112C2×#168—42no—
113C23×C8—101no—
114C2×C22⋊Q8—51no—
115C2×C4×Q8—51no—
116C22×C42C2×D511yescharacteristic
117C2×C4⋊C8—21no—
118C2×C22⋊C8—21no—
119#391—51no—
120#389—51no—
121#387—101no—
122#385—101no—
123#380—51no—
124C4×C4⋊C4—51no—
125C4×C4⋊C4—101no—
126C4×C22⋊C4—101no—
127#336—52no—
128#336—101no—
129#336C2×D512yes—
130C23×C5—21no—
131C23×C5—21no—
132C23×C5—21no—
133C23×C5—21no—
134C23×C5C22⋊C812yes—
135C23×C5#10312yes—
136C23×C5#10412yes—
137C23×C5C2×C22⋊C411yescharacteristic
138C2×C4×C5—24no—
139C2×C4×C5—24no—
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×C5C22⋊C812yes—
157C2×C4×C5#9912yes—
158C2×C4×C5#10312yes—
159C2×C4×C5C22×C811yescharacteristic
160C2×C4×C5C2×M1611yescharacteristic
161C2×C4×C5C2×SD1611yescharacteristic
162C2×C4×C5C2×Q1611yescharacteristic
163C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C5#13711yescharacteristic
165C2×Dic5—22no—
166C2×Dic5—22no—
167C2×Dic5—41no—
168C2×Dic5—41no—
169C2×Dic5—41no—
170C2×Dic5—41no—
171C2×Dic5—41no—
172C2×Dic5—41no—
173C2×Dic5—41no—
174C2×Dic5—41no—
175C2×Dic5—41no—
176C2×Dic5—41no—
177Dic10—42no—
178Dic10—42no—
179C5×C8—82no—
180#168—44no—
181C22×Q8—51no—
182C23×C4C4×D511yescharacteristic
183C23×C4D2011yescharacteristic
184C23×C4C22⋊D511yescharacteristic
185C22×C8—22no—
186C22×C8—104no—
187C22×C8—102no—
188C22×C8—202no—
189C22×C8—202no—
190C22⋊Q8—54no—
191C22⋊Q8—102no—
192C4×Q8—202no—
193C2×C4⋊C4—51no—
194C2×C4⋊C4—51no—
195C2×C4⋊C4—51no—
196C2×C4⋊C4—101no—
197C2×C4⋊C4—101no—
198C2×C4⋊C4—101no—
199C2×C22⋊C4—101no—
200C2×C22⋊C4—101no—
201C2×C42—42no—
202C2×C42—101no—
203C2×C42—101no—
204C2×C42C4×D511yescharacteristic
205C2×C42D2011yescharacteristic
206C2×C42C22⋊D511yescharacteristic
207C2×C42C22×D511yescharacteristic
208C4⋊C8—42no—
209C22⋊C8—42no—
210#95—101no—
211#95—101no—
212#95—101no—
213#95—101no—
214#95—101no—
215C22×C5—22no—
216C22×C5—22no—
217C22×C5—22no—
218C22×C5—22no—
219C22×C5—22no—
220C22×C5—22no—
221C22×C5Q8⋊C814yes—
222C22×C5C2×C22⋊C811yescharacteristic
223C22×C5C2×#9911yescharacteristic
224C22×C5#41311yescharacteristic
225C22×C5C2×#10311yescharacteristic
226C22×C5#41711yescharacteristic
227C22×C5C2×#10411yescharacteristic
228C22×C5#42111yescharacteristic
229C4×C5—21no—
230C4×C5—21no—
231C4×C5—22no—
232C4×C5—21no—
233C4×C5—22no—
234C4×C5—21no—
235C4×C5—21no—
236C4×C5—22no—
237C4×C5—21no—
238Dic5—42no—
239Dic5—42no—
240Dic5—81no—
241Dic5—81no—
242C24#68511yescharacteristic
243C2×Q8—52no—
244C2×Q8—101no—
245C2×Q8—201no—
246C2×Q8—201no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—101no—
256C22×C4—101no—
257C22×C4—101no—
258C22×C4—101no—
259C22×C4C8×D512yes—
260C22×C4#67612yes—
261C22×C4#68511yescharacteristic
262C22×C4#68511yescharacteristic
263C22×C4#68511yescharacteristic
264C22×C4#68712yes—
265C22×C4#68912yes—
266C22×C4C2×C4×D511yescharacteristic
267C22×C4C2×D2011yescharacteristic
268C22×C4C2×C22⋊D511yescharacteristic
269C2×C8—42no—
270C2×C8—42no—
271C2×C8—42no—
272C2×C8—104no—
273C2×C8—208no—
274C2×C8—202no—
275C2×C8—202no—
276C4⋊C4—52no—
277C4⋊C4—104no—
278C4⋊C4—101no—
279C4⋊C4—201no—
280C4⋊C4—201no—
281C4⋊C4—202no—
282C4⋊C4—201no—
283C4⋊C4—201no—
284C22⋊C4—104no—
285C22⋊C4—202no—
286C42—22no—
287C42—22no—
288C42—41no—
289C42—41no—
290C42—202no—
291C42—202no—
292C2×C5—24no—
293C2×C5#145911yescharacteristic
294C2×C5C2×Q8⋊C811yescharacteristic
295C2×C5#147711yescharacteristic
296C2×C5#150411yescharacteristic
297C2×C5#152011yescharacteristic
298C2×C5#153211yescharacteristic
299C2×C5#155011yescharacteristic
300C23—21no—
301C23—21no—
302C23—21no—
303C23—21no—
304C23#394212yes—
305C23#395212yes—
306C23#395712yes—
307C23C2×#68511yescharacteristic
308Q8—202no—
309Q8—202no—
310C2×C4—24no—
311C2×C4—24no—
312C2×C4—21no—
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—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—102no—
329C2×C4—102no—
330C2×C4—201no—
331C2×C4—201no—
332C2×C4—201no—
333C2×C4—201no—
334C2×C4—201no—
335C2×C4—201no—
336C2×C4—201no—
337C2×C4—201no—
338C2×C4—201no—
339C2×C4—201no—
340C2×C4#393812yes—
341C2×C4#394212yes—
342C2×C4#395212yes—
343C2×C4C2×C8×D511yescharacteristic
344C2×C4C2×#67611yescharacteristic
345C2×C4#405411yescharacteristic
346C2×C4#405511yescharacteristic
347C2×C4C2×#68711yescharacteristic
348C2×C4C2×#68911yescharacteristic
349C8—82no—
350C8—204no—
351C5#758911yescharacteristic, complemented, Sylow
352C22—22no—
353C22—22no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—22no—
358C22#6470414yes—
359C22C2×#393811yescharacteristic
360C22C2×#394211yescharacteristic
361C22#6529411yescharacteristic
362C22C2×#395211yescharacteristic
363C22#6542111yescharacteristic
364C22#6542211yescharacteristic
365C22C2×#395711yescharacteristic
366C4—22no—
367C4—21no—
368C4—21no—
369C4—21no—
370C4—22no—
371C4—21no—
372C4—21no—
373C4—22no—
374C4—21no—
375C4—202no—
376C4—202no—
377C4—401no—
378C4—401no—
379C2—24no—
380C2#1060030311yescharacteristic
381C2#1060071211yescharacteristic
382C2#1060076911yescharacteristic
383C2C2×#6470411yescharacteristic
384C2#1060130211yescharacteristic
385C2#1060154811yescharacteristic
386C2#1060160011yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC2×C4×C5C22×C8
FrattiniC2×C42C22×D5
FittingC5×#1797C2
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1797D5
hypocenterC5#7589
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1797

Complements

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

NH ≅ G/Ntype
4. #10597971C2semidirect
5. #10597968C2semidirect
40. #4070C8semidirect
89. C2×Dic10C2×C8semidirect
102. C4⋊Dic5C2×C8semidirect
351. C5#7589semidirect

Maximal subgroups

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

subgroupindex
C4×#40702
C5×#17972
C2×#647442
#105979712
#105979682
#75895