Finite Group Databasebeta

← #11998550

Subgroups — #11998550

Order 1280.

522 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65359C211yesmaximal, characteristic
2C5×#1982C211yesmaximal, characteristic
3C2×#64764C211yesmaximal, characteristic
4C2×#64701C211yesmaximal, characteristic, complemented
5C2×#64700C211yesmaximal, characteristic, complemented
6#10600282C211yesmaximal, characteristic, complemented
7C4⋊C4×#168C211yesmaximal, characteristic, complemented
8C2×C5×#127C2211yescharacteristic
9C2×#4015C2211yescharacteristic
10C2×C5×C4⋊C8C2211yescharacteristic
11C2×C5×#102—22no—
12C4×C5×C4⋊C4C2211yescharacteristic
13C2×#3964—21no—
14C2×#3964—21no—
15#65359—22no—
16#65359C414yescomplemented
17C2×C4⋊#168C2211yescharacteristic
18C2×C4⋊#168C2211yescharacteristic
19C2×C4×#168—21no—
20C2×C4×#168C2211yescharacteristic
21#64764—22no—
22#64749—22no—
23#64744—21no—
24#64701—22no—
25#64700—22no—
26#9735—51nomaximal, Sylow
27C22×C5×D4—21no—
28C22×C5×D4—21no—
29C22×C5×D4—21no—
30C22×Dic10—21no—
31C22×C5×C8—21no—
32C5×#127—21no—
33C5×#127—21no—
34C5×#127—21no—
35C5×#127C2×C412yes—
36C2×C5×C4⋊C4D412yes—
37C2×C42×C5—21no—
38C2×C42×C5C2311yescharacteristic
39C2×C4⋊Dic5—21no—
40C2×C4⋊Dic5—21no—
41C22×#168—21no—
42C22×#168—21no—
43C22×#168D411yescharacteristic
44C22×#168D411yescharacteristic
45#4015—21no—
46#4015—21no—
47#4015—21no—
48#4015C2×C412yes—
49C5×C4⋊C8—21no—
50C5×C4⋊C8—21no—
51C5×#102—44no—
52C5×#95—21no—
53#3964—24no—
54#3964—24no—
55C4⋊#168—21no—
56C4⋊#168—21no—
57C4⋊#168—21no—
58C4⋊#168D412yes—
59C4×#168—42no—
60C4×#168C2×C412yes—
61C4×#168D412yes—
62C2×#486—51no—
63#1987—51no—
64#1982D511yescharacteristic
65C8×C4⋊C4—51no—
66C2×#334—51no—
67C2×#333—51no—
68C2×#331—51no—
69C24×C5—41no—
70C2×C5×D4—22no—
71C2×C5×D4—22no—
72C2×C5×D4—22no—
73C2×C5×D4—41no—
74C2×C5×D4—41no—
75C2×C5×D4—41no—
76C2×C5×D4—42no—
77C2×C5×D4—42no—
78C2×C5×D4—41no—
79C2×C5×D4—41no—
80C2×C5×D4—41no—
81C2×C5×D4—41no—
82C2×C5×D4—82no—
83C22×C4×C5—22no—
84C22×C4×C5C2×D411yescharacteristic
85C22×C4×C5C2×D411yescharacteristic
86C22×C4×C5#4111yescharacteristic
87C22×Dic5—41no—
88C2×Dic10—22no—
89C2×Dic10—41no—
90C2×Dic10—82no—
91C2×C5×C8—41no—
92C2×C5×C8—42no—
93C5×C4⋊C4—22no—
94C5×C4⋊C4SD1614yes—
95C42×C5—41no—
96C42×C5—41no—
97C42×C5C22×C411yescharacteristic
98C42×C5C2×D411yescharacteristic
99C42×C5C2×D411yescharacteristic
100C42×C5#4111yescharacteristic
101C4⋊Dic5—22no—
102C4⋊Dic5—22no—
103C4⋊Dic5—41no—
104C4⋊Dic5—41no—
105C2×#168—21no—
106C2×#168—21no—
107C2×#168—21no—
108C2×#168—21no—
109C2×#168—22no—
110C2×#168—41no—
111C2×#168—41no—
112C2×#168—41no—
113C2×#168—42no—
114C2×#168C22⋊C412yes—
115C2×#168C22⋊C412yes—
116C2×C4⋊Q8—51no—
117C2×#127C2×D511yescharacteristic
118#486—54no—
119#486—102no—
120C2×C4⋊C8—51no—
121C2×C4⋊C8—51no—
122C2×C4⋊C8C2×D511yescharacteristic
123C2×#102—22no—
124C2×#102—101no—
125C2×#102—101no—
126C2×C4×C8—51no—
127C2×C4×C8—101no—
128C4×C4⋊C4C2×D511yescharacteristic
129#340—102no—
130#336—101no—
131#334—102no—
132#333—102no—
133#331—102no—
134C23×C5—42no—
135C23×C5—81no—
136C23×C5—81no—
137C23×C5—82no—
138C23×C5—82no—
139C23×C5#12111yescharacteristic
140C5×D4—42no—
141C5×D4—42no—
142C5×D4—44no—
143C5×D4—82no—
144C5×D4—82no—
145C5×D4—81no—
146C5×D4—81no—
147C5×D4—81no—
148C5×D4—81no—
149C2×C4×C5—22no—
150C2×C4×C5—24no—
151C2×C4×C5—42no—
152C2×C4×C5—42no—
153C2×C4×C5C2×C22⋊C411yescharacteristic
154C2×C4×C5C4×D411yescharacteristic
155C2×C4×C5C4×D411yescharacteristic
156C2×C4×C5#12111yescharacteristic
157C2×C4×C5#12411yescharacteristic
158C2×C4×C5#12711yescharacteristic
159C2×C4×C5C2×SD1612yes—
160C2×C4×C5#13512yes—
161C2×C4×C5#13511yescharacteristic
162C2×C4×C5#13511yescharacteristic
163C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
164C2×C4×C5#13711yescharacteristic
165C2×Dic5—42no—
166C2×Dic5—82no—
167Dic10—82no—
168Dic10—82no—
169C5×C8—81no—
170#168—22no—
171#168—22no—
172#168—42no—
173#168—81no—
174C22×Q8—101no—
175C22×D4—21no—
176C22×D4—21no—
177C22×D4—21no—
178C22×C8—21no—
179C22×C8—51no—
180C22×C8—51no—
181C22×C8—101no—
182C22×C8—101no—
183C4⋊Q8—52no—
184C4⋊Q8—101no—
185C4⋊Q8—101no—
186C4⋊Q8—101no—
187#127—21no—
188#127—21no—
189#127—21no—
190#127C4×D512yes—
191C2×C4⋊C4—101no—
192C2×C4⋊C4—101no—
193C2×C4⋊C4C22⋊D512yes—
194C2×C42—21no—
195C2×C42C22×D511yescharacteristic
196C4⋊C8—21no—
197C4⋊C8—21no—
198C4⋊C8—52no—
199C4⋊C8—101no—
200C4⋊C8—101no—
201C4⋊C8—101no—
202#102—44no—
203#102—104no—
204#102—104no—
205C4×C8—52no—
206C4×C8—52no—
207C4×C8—202no—
208#95—21no—
209C22×C5—82no—
210C22×C5—82no—
211C22×C5—82no—
212C22×C5—162no—
213C22×C5—162no—
214C22×C5#39011yescharacteristic
215C22×C5#46311yescharacteristic
216C22×C5#46411yescharacteristic
217C22×C5#46512yes—
218C22×C5#47212yes—
219C4×C5—21no—
220C4×C5—21no—
221C4×C5—44no—
222C4×C5#41611yescharacteristic
223C4×C5#41711yescharacteristic
224C4×C5C4×SD1612yes—
225C4×C5#46311yescharacteristic
226C4×C5#46411yescharacteristic
227C4×C5#49211yescharacteristic
228C4×C5#49511yescharacteristic
229Dic5—82no—
230C24—41no—
231C2×Q8—102no—
232C2×Q8—201no—
233C2×Q8—402no—
234C2×D4—22no—
235C2×D4—22no—
236C2×D4—22no—
237C2×D4—42no—
238C2×D4—41no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4—42no—
245C2×D4—41no—
246C2×D4—82no—
247C22×C4—22no—
248C22×C4—201no—
249C22×C4D4×D511yescharacteristic
250C22×C4#71111yescharacteristic
251C22×C4C2×C22⋊D511yescharacteristic
252C2×C8—42no—
253C2×C8—41no—
254C2×C8—52no—
255C2×C8—52no—
256C2×C8—101no—
257C2×C8—101no—
258C2×C8—101no—
259C2×C8—101no—
260C2×C8—102no—
261C2×C8—201no—
262C2×C8—201no—
263C2×C8—202no—
264C2×C8—201no—
265C4⋊C4—22no—
266C4⋊C4—102no—
267C4⋊C4—102no—
268C4⋊C4—201no—
269C4⋊C4—201no—
270C4⋊C4#68714yes—
271C42—41no—
272C42—41no—
273C42C2×C4×D511yescharacteristic
274C42#70911yescharacteristic
275C42D4×D511yescharacteristic
276C42D4×D511yescharacteristic
277C2×C5—162no—
278C2×C5#167712yes—
279C2×C5#167812yes—
280C2×C5#196811yescharacteristic
281C2×C5#197811yescharacteristic
282C2×C5#198311yescharacteristic
283C23—42no—
284C23—82no—
285C23—81no—
286C23—81no—
287C23—82no—
288C23#408511yescharacteristic
289Q8—402no—
290Q8—402no—
291D4—44no—
292D4—42no—
293D4—42no—
294D4—82no—
295D4—82no—
296D4—81no—
297D4—81no—
298D4—81no—
299D4—81no—
300C2×C4—22no—
301C2×C4—24no—
302C2×C4—42no—
303C2×C4—42no—
304C2×C4—202no—
305C2×C4—402no—
306C2×C4D5×C22⋊C411yescharacteristic
307C2×C4#402711yescharacteristic
308C2×C4#403011yescharacteristic
309C2×C4#403111yescharacteristic
310C2×C4#405711yescharacteristic
311C2×C4#405811yescharacteristic
312C2×C4#406111yescharacteristic
313C2×C4#406211yescharacteristic
314C2×C4C4×C22⋊D511yescharacteristic
315C2×C4C2×#68712yes—
316C2×C4#408611yescharacteristic
317C2×C4#409612yes—
318C8—81no—
319C8—102no—
320C8—102no—
321C8—202no—
322C8—401no—
323C5#973511yescharacteristic, complemented, Sylow
324C22—82no—
325C22—82no—
326C22—82no—
327C22—162no—
328C22—162no—
329C22#6524611yescharacteristic
330C22#6533012yes—
331C22#6544211yescharacteristic
332C22#6545511yescharacteristic
333C22#6548812yes—
334C4—21no—
335C4—21no—
336C4—44no—
337C4—402no—
338C4#6505611yescharacteristic
339C4#6506011yescharacteristic
340C4#6506111yescharacteristic
341C4#6507611yescharacteristic
342C4C4×#68712yes—
343C4#6534811yescharacteristic
344C4#6536511yescharacteristic
345C2—162no—
346C2#1060043911yescharacteristic
347C2#1060095511yescharacteristic
348C2#1060110911yescharacteristic
349C2#1060179912yes—
350C2#1060181512yes—
subgroupG/H
centerC23#4085
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1982C2
socleC23×C5#121
prime radicalC2×C5×#127C22
cosocleC2×C42×C5C23
hypercenter#1982D5
hypocenterC5#9735
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
4. C2×#64701C2semidirect
5. C2×#64700C2semidirect
6. #10600282C2semidirect
7. C4⋊C4×#168C2semidirect
16. #65359C4semidirect
323. C5#9735semidirect

Maximal subgroups

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

subgroupindex
C2×#653592
C5×#19822
C2×#647642
C2×#647012
C2×#647002
#106002822
C4⋊C4×#1682
#97355