Finite Group Databasebeta

← #11987608

Subgroups — #11987608

Order 1280.

500 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#4070C211yesmaximal, characteristic
2C5×#1797C211yesmaximal, characteristic
3#10602324C211yesmaximal, characteristic
4#10597971C212yesmaximal, complemented
5#10597968C212yesmaximal, complemented
6C22×C42×C5C2211yescharacteristic
7C2×#4070C411yescharacteristic
8C2×C4×Dic10C411yescharacteristic
9C2×C5×C4⋊C8—21no—
10C2×C5×C22⋊C8—21no—
11#65501C411yescharacteristic
12#65499—21no—
13C4×C22⋊Dic5—21no—
14C2×C22⋊#168—21no—
15C4×C4⋊Dic5C411yescharacteristic
16#65222—21no—
17C4×#683—21no—
18#65218C2211yescharacteristic
19#65217C2211yescharacteristic
20C5×#336C2212yes—
21#64744—21no—
22#64744C2212yes—
23#7648—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#4070—22no—
41C2×#683—21no—
42C2×#683—21no—
43C2×#683—21no—
44C2×C4×Dic5—21no—
45C2×C4×Dic5—21no—
46C22×#168—22no—
47C4×Dic10—42no—
48C5×C4⋊C8—42no—
49C5×C22⋊C8—42no—
50#3963—21no—
51#3963—21no—
52#3963—21no—
53#3963—21no—
54#3963—21no—
55C22⋊#168—42no—
56C4×C22⋊Q8—51no—
57#1817—51no—
58#1797D511yescharacteristic
59#1272—52no—
60#1271—52no—
61C24×C5C22⋊C411yescharacteristic
62C22×C4×C5—22no—
63C22×C4×C5—21no—
64C22×C4×C5—21no—
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×C5SD1612yes—
75C22×C4×C5Q1612yes—
76C22×C4×C5C22×C411yescharacteristic
77C22×C4×C5C2×D411yescharacteristic
78C22×C4×C5C2×D411yescharacteristic
79C22×Dic5—21no—
80C22×Dic5—21no—
81C22×Dic5—21no—
82C22×Dic5—21no—
83C2×Dic10—21no—
84C2×Dic10—41no—
85C2×Dic10—41no—
86C2×Dic10M1612yes—
87C2×C5×C8—42no—
88C2×C5×C8—42no—
89C2×C5×C8—42no—
90C42×C5—22no—
91C42×C5—22no—
92C42×C5—41no—
93C42×C5—41no—
94C22⋊Dic5—24no—
95C22⋊Dic5—42no—
96C4⋊Dic5—21no—
97C4⋊Dic5—41no—
98C4⋊Dic5—41no—
99C4⋊Dic5M1612yes—
100#683—24no—
101#683—42no—
102#683—42no—
103C4×Dic5—42no—
104C4×Dic5—42no—
105C2×#168—42no—
106C2×#168—42no—
107C2×#168—42no—
108C2×C22⋊Q8—51no—
109C2×C4×Q8—51no—
110C22×C42C2×D511yescharacteristic
111C2×C4⋊C8—21no—
112C2×C22⋊C8—21no—
113C2×C22⋊C8—101no—
114#391—51no—
115#389—51no—
116#387—101no—
117#385—101no—
118#380—51no—
119C4×C4⋊C4—51no—
120C4×C4⋊C4—101no—
121C4×C22⋊C4—101no—
122#336—52no—
123#336—101no—
124#336C2×D512yes—
125C23×C5—21no—
126C23×C5—21no—
127C23×C5—21no—
128C23×C5—21no—
129C23×C5—21no—
130C23×C5—21no—
131C23×C5#10312yes—
132C23×C5C2×C22⋊C411yescharacteristic
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
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—42no—
147C2×C4×C5—42no—
148C2×C4×C5—44no—
149C2×C4×C5—42no—
150C2×C4×C5—42no—
151C2×C4×C5#9912yes—
152C2×C4×C5#10312yes—
153C2×C4×C5C2×M1611yescharacteristic
154C2×C4×C5C2×M1611yescharacteristic
155C2×C4×C5C2×SD1611yescharacteristic
156C2×C4×C5C2×Q1611yescharacteristic
157C2×C4×C5#13512yes—
158C2×Dic5—22no—
159C2×Dic5—22no—
160C2×Dic5—41no—
161C2×Dic5—41no—
162C2×Dic5—41no—
163C2×Dic5—41no—
164C2×Dic5—41no—
165C2×Dic5—41no—
166C2×Dic5—41no—
167C2×Dic5—41no—
168C2×Dic5—41no—
169C2×Dic5—41no—
170Dic10—42no—
171Dic10—42no—
172C5×C8—82no—
173#168—82no—
174C22×Q8—51no—
175C23×C4C4×D511yescharacteristic
176C23×C4D2011yescharacteristic
177C23×C4C22⋊D511yescharacteristic
178C22×C8—22no—
179C22×C8—102no—
180C22⋊Q8—102no—
181C22⋊Q8—102no—
182C4×Q8—202no—
183C2×C4⋊C4—51no—
184C2×C4⋊C4—51no—
185C2×C4⋊C4—51no—
186C2×C4⋊C4—101no—
187C2×C4⋊C4—101no—
188C2×C4⋊C4—101no—
189C2×C22⋊C4—101no—
190C2×C22⋊C4—101no—
191C2×C42—42no—
192C2×C42—101no—
193C2×C42—101no—
194C2×C42C4×D511yescharacteristic
195C2×C42D2011yescharacteristic
196C2×C42C22⋊D511yescharacteristic
197C2×C42C22×D511yescharacteristic
198C4⋊C8—42no—
199C22⋊C8—42no—
200C22⋊C8—202no—
201#95—101no—
202#95—101no—
203#95—101no—
204#95—101no—
205#95—101no—
206C22×C5—22no—
207C22×C5—22no—
208C22×C5—22no—
209C22×C5—41no—
210C22×C5—41no—
211C22×C5—41no—
212C22×C5—41no—
213C22×C5#40711yescharacteristic
214C22×C5C2×#9911yescharacteristic
215C22×C5#41311yescharacteristic
216C22×C5C2×#10311yescharacteristic
217C22×C5#41611yescharacteristic
218C22×C5#42111yescharacteristic
219C22×C5#42111yescharacteristic
220C4×C5—21no—
221C4×C5—21no—
222C4×C5—22no—
223C4×C5—22no—
224C4×C5—21no—
225C4×C5—22no—
226C4×C5—21no—
227C4×C5—41no—
228Dic5—42no—
229Dic5—42no—
230Dic5—81no—
231Dic5—81no—
232C24#68511yescharacteristic
233C2×Q8—52no—
234C2×Q8—101no—
235C2×Q8—201no—
236C2×Q8—201no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—101no—
247C22×C4—101no—
248C22×C4—101no—
249C22×C4—101no—
250C22×C4#68511yescharacteristic
251C22×C4#68511yescharacteristic
252C22×C4#68511yescharacteristic
253C22×C4#68712yes—
254C22×C4#68912yes—
255C22×C4C2×C4×D511yescharacteristic
256C22×C4C2×D2011yescharacteristic
257C22×C4C2×C22⋊D511yescharacteristic
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—202no—
262C2×C8—202no—
263C2×C8—202no—
264C4⋊C4—52no—
265C4⋊C4—104no—
266C4⋊C4—101no—
267C4⋊C4—201no—
268C4⋊C4—201no—
269C4⋊C4—202no—
270C4⋊C4—202no—
271C22⋊C4—104no—
272C22⋊C4—202no—
273C42—22no—
274C42—22no—
275C42—41no—
276C42—41no—
277C42—202no—
278C42—202no—
279C2×C5—42no—
280C2×C5#146511yescharacteristic
281C2×C5#148711yescharacteristic
282C2×C5#148811yescharacteristic
283C2×C5#151611yescharacteristic
284C2×C5#152011yescharacteristic
285C2×C5#153511yescharacteristic
286C2×C5#154211yescharacteristic
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23#394212yes—
294C23C2×#68511yescharacteristic
295Q8—202no—
296Q8—202no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—44no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—102no—
316C2×C4—102no—
317C2×C4—201no—
318C2×C4—201no—
319C2×C4—201no—
320C2×C4—201no—
321C2×C4—201no—
322C2×C4—201no—
323C2×C4—201no—
324C2×C4—201no—
325C2×C4—201no—
326C2×C4—201no—
327C2×C4#393812yes—
328C2×C4#394212yes—
329C2×C4#405012yes—
330C2×C4D5×M1611yescharacteristic
331C2×C4D5×M1611yescharacteristic
332C2×C4C2×#68711yescharacteristic
333C2×C4C2×#68911yescharacteristic
334C8—82no—
335C8—402no—
336C5#764811yescharacteristic, complemented, Sylow
337C22—22no—
338C22—22no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22C2×#393811yescharacteristic
345C22C2×#394211yescharacteristic
346C22#6529411yescharacteristic
347C22#6540211yescharacteristic
348C22#6541511yescharacteristic
349C22#6542111yescharacteristic
350C22#6542811yescharacteristic
351C4—22no—
352C4—22no—
353C4—21no—
354C4—21no—
355C4—21no—
356C4—22no—
357C4—21no—
358C4—41no—
359C4—202no—
360C4—202no—
361C4—401no—
362C4—401no—
363C2—42no—
364C2#1060030311yescharacteristic
365C2#1060073611yescharacteristic
366C2#1060076111yescharacteristic
367C2#1060123011yescharacteristic
368C2#1060129311yescharacteristic
369C2#1060155611yescharacteristic
370C2#1060160211yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1797C2
socleC23×C5C2×C22⋊C4
prime radicalC24×C5C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1797D5
hypocenterC5#7648
LCSG ▷ C22×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
336. C5#7648semidirect

Maximal subgroups

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

subgroupindex
C4×#40702
C5×#17972
#106023242
#105979712
#105979682
#76485