Finite Group Databasebeta

← #13033963

Subgroups — #13033963

Order 1280.

934 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65680C211yesmaximal, characteristic
2C2×D5⋊(C4⋊C8)C211yesmaximal, characteristic
3#10605878C211yesmaximal, characteristic
4#10604315C212yesmaximal, complemented
5C4⋊C4×#170C212yesmaximal, complemented
6#10603778C214yesmaximal, complemented
7#10603776C212yesmaximal
8#10603775C212yesmaximal
9C22×D5⋊C8C2212yes—
10C2×C42×D5C2211yescharacteristic
11C2×#4004C2212yes—
12C2×#4003C2211yescharacteristic
13C2×#4003C2211yescharacteristic
14C2×#4002C2214yes—
15C2×C4⋊#170C2212yes—
16C2×C4⋊#170C2211yescharacteristic
17C2×C4⋊#170C2211yescharacteristic
18C2×C4×#170C2214yes—
19C2×C4×#170C2212yes—
20#65680C418yescomplemented
21D5⋊(C4⋊C8)C418yescomplemented
22C5×#382C411yescharacteristic
23#65276C412yes—
24C4⋊C4×Dic5C2212yes—
25#65225C411yescharacteristic
26#64955C2212yes—
27#64953C412yes—
28#64940C412yes—
29#64937C2212yes—
30#64918C2214yes—
31#64918C2214yes—
32#20545—51nomaximal, Sylow
33C22×C4×D5C2×C411yescharacteristic
34C22×C4×D5C2×C411yescharacteristic
35C22×C4×D5C2311yescharacteristic
36C22×#170C2312yes—
37C22×#170C2312yes—
38C22×#170C2312yes—
39C22×#170C2312yes—
40C2×D5⋊C8—44no—
41C2×D5⋊C8C2×C418yes—
42C2×C5×C4⋊C4C2×C412yes—
43C2×C42×C5C2×C411yescharacteristic
44C2×#685C2×C414yes—
45C2×C4⋊Dic5C2×C412yes—
46C2×C4×Dic5C2×C411yescharacteristic
47C2×C4×Dic5C2314yes—
48C2×C4×Dic5C2311yescharacteristic
49C2×C4×Dic5C2311yescharacteristic
50C42×D5C2×C414yes—
51C42×D5C2×C414yes—
52#4004C2×C418yes—
53#4003C2×C414yes—
54#4003C2×C414yes—
55#4002—44no—
56C4⋊#170C2×C414yes—
57C4⋊#170C2×C414yes—
58C4⋊#170C2×C418yes—
59C4×#170—44no—
60C4×#170C2×C418yes—
61C5×#95C2×C412yes—
62C5×#95C2×C412yes—
63#3963C2×C414yes—
64#3963C2×C412yes—
65#3963C2×C414yes—
66#3963C2×C412yes—
67C2×#431—51no—
68C22×C4⋊C8—51no—
69#2283—51no—
70#1770—52no—
71C8×C4⋊C4—52no—
72#1768—54no—
73#1752—52no—
74C8×C22⋊C4—52no—
75C23×D5C22×C411yescharacteristic
76C22×C4×C5C22×C414yes—
77C22×C4×C5C22×C411yescharacteristic
78C22×C4×C5C22×C411yescharacteristic
79C22×C4×C5C22×C411yescharacteristic
80C22×Dic5C22×C414yes—
81C22×Dic5C22×C411yescharacteristic
82C22×Dic5C22×C411yescharacteristic
83C22×Dic5C2411yescharacteristic
84C2×C4×D5—24no—
85C2×C4×D5—22no—
86C2×C4×D5—22no—
87C2×C4×D5—22no—
88C2×C4×D5—22no—
89C2×C4×D5C4214yes—
90C2×C4×D5C4214yes—
91C2×C4×D5C22×C412yes—
92C2×C4×D5C22×C412yes—
93C2×#170—24no—
94C2×#170—24no—
95C2×#170—22no—
96C2×#170—22no—
97C2×#170—22no—
98C2×#170—22no—
99C2×#170C22×C414yes—
100C2×#170C22×C414yes—
101C2×#170C22×C414yes—
102C2×#170C22×C414yes—
103D5⋊C8—48no—
104C5×C4⋊C4—24no—
105C42×C5C4214yes—
106#685—28no—
107C4⋊Dic5—24no—
108C4×Dic5—24no—
109C4×Dic5—24no—
110C4×Dic5C4214yes—
111C4×Dic5C22×C412yes—
112C4×Dic5C22×C412yes—
113C4×Dic5C22×C412yes—
114C4×Dic5C22×C412yes—
115C23×C8—52no—
116C22×C42—51no—
117#431—58no—
118C2×C4⋊C8—58no—
119C2×C4⋊C8—51no—
120C2×C4⋊C8—51no—
121C2×C4⋊C8—52no—
122C2×C4⋊C8—52no—
123C2×C22⋊C8—51no—
124C2×C22⋊C8—51no—
125C2×#97—54no—
126C2×C4×C8—52no—
127C2×C4×C8—54no—
128#383—52no—
129#382—51no—
130#382AGL(1,𝔽5)11yescharacteristic
131#381—52no—
132#380—52no—
133C4×C4⋊C4—52no—
134C4×C22⋊C4—52no—
135#376—52no—
136#336—54no—
137#336—54no—
138C23×C5C23×C411yescharacteristic
139C22×D5—22no—
140C22×D5—21no—
141C22×D5—21no—
142C22×D5C2×C4212yes—
143C22×D5#13114yes—
144C2×C4×C5—22no—
145C2×C4×C5—22no—
146C2×C4×C5—24no—
147C2×C4×C5—24no—
148C2×C4×C5—24no—
149C2×C4×C5C2×C4212yes—
150C2×C4×C5C2×C4212yes—
151C2×C4×C5C2×C4212yes—
152C2×C4×C5#13112yes—
153C2×C4×C5#13112yes—
154C2×Dic5—21no—
155C2×Dic5—21no—
156C2×Dic5—22no—
157C2×Dic5—24no—
158C2×Dic5—24no—
159C2×Dic5—24no—
160C2×Dic5C2×C4212yes—
161C2×Dic5C2×C4212yes—
162C2×Dic5C23×C411yescharacteristic
163C2×Dic5C23×C411yescharacteristic
164C2×Dic5H(5,𝔽2)12yes—
165C2×Dic52−1+412yes—
166C4×D5—28no—
167C4×D5—28no—
168C4×D5—22no—
169C4×D5—22no—
170C4×D5—24no—
171#170—24no—
172#170—24no—
173#170—24no—
174#170—24no—
175C23×C4—51no—
176C23×C4—51no—
177C23×C4—51no—
178C22×C8—52no—
179C22×C8—52no—
180C22×C8—52no—
181C22×C8—52no—
182C22×C8—58no—
183C22×C8—204no—
184C2×C4⋊C4—52no—
185C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
186C2×C22⋊C4—54no—
187C2×C42—51no—
188C2×C42—51no—
189C2×C42—51no—
190C2×C42—54no—
191C2×C42—54no—
192C2×C42—54no—
193C2×C42C2×AGL(1,𝔽5)11yescharacteristic
194C4⋊C8—54no—
195C4⋊C8—54no—
196C4⋊C8—58no—
197C4⋊C8—58no—
198C22⋊C8—54no—
199C22⋊C8—54no—
200#97—204no—
201C4×C8—58no—
202C4×C8—204no—
203#95—54no—
204#95—52no—
205#95—52no—
206#95—54no—
207#95C2×AGL(1,𝔽5)12yes—
208#95C2×AGL(1,𝔽5)12yes—
209C22×C5C22×C4211yescharacteristic
210C22×C5#52012yes—
211C22×C5C2×#13111yescharacteristic
212C22×C5C2×#13111yescharacteristic
213C22×C5C2×#13112yes—
214C2×D5—22no—
215C2×D5—24no—
216C2×D5—24no—
217C2×D5—22no—
218C2×D5#40514yes—
219C4×C5—22no—
220C4×C5—22no—
221C4×C5—44no—
222C4×C5#40514yes—
223Dic5—22no—
224Dic5—22no—
225Dic5—44no—
226Dic5#51811yescharacteristic
227Dic5#51911yescharacteristic
228Dic5#52012yes—
229C24—51no—
230C22×C4—51no—
231C22×C4—51no—
232C22×C4—51no—
233C22×C4—52no—
234C22×C4—52no—
235C22×C4—54no—
236C22×C4—54no—
237C22×C4—54no—
238C22×C4—102no—
239C22×C4—102no—
240C22×C4—104no—
241C22×C4—102no—
242C22×C4—102no—
243C22×C4C22×AGL(1,𝔽5)14yes—
244C22×C4C22×AGL(1,𝔽5)11yescharacteristic
245C22×C4C22×AGL(1,𝔽5)11yescharacteristic
246C22×C4C22×AGL(1,𝔽5)11yescharacteristic
247C2×C8—54no—
248C2×C8—54no—
249C2×C8—54no—
250C2×C8—54no—
251C2×C8—102no—
252C2×C8—104no—
253C2×C8—102no—
254C2×C8—104no—
255C2×C8—102no—
256C2×C8—102no—
257C2×C8—208no—
258C4⋊C4—24no—
259C4⋊C4—104no—
260C22⋊C4—108no—
261C42—52no—
262C42—52no—
263C42—52no—
264C42—52no—
265C42—54no—
266C42—104no—
267C42—104no—
268C42C4×AGL(1,𝔽5)14yes—
269C2×C5#227411yescharacteristic
270C2×C5C2×#40511yescharacteristic
271C2×C5C2×#40511yescharacteristic
272C2×C5#299412yes—
273C2×C5#299412yes—
274D5—24no—
275C23—52no—
276C23—54no—
277C23—101no—
278C23—101no—
279C23—102no—
280C23C23×AGL(1,𝔽5)11yescharacteristic
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—24no—
284C2×C4—24no—
285C2×C4—24no—
286C2×C4—51no—
287C2×C4—51no—
288C2×C4—52no—
289C2×C4—52no—
290C2×C4—52no—
291C2×C4—52no—
292C2×C4—102no—
293C2×C4—104no—
294C2×C4—102no—
295C2×C4—108no—
296C2×C4—101no—
297C2×C4—101no—
298C2×C4—102no—
299C2×C4—108no—
300C2×C4—104no—
301C2×C4—104no—
302C2×C4—104no—
303C2×C4C2×C4×AGL(1,𝔽5)12yes—
304C2×C4C2×C4×AGL(1,𝔽5)12yes—
305C2×C4C2×C4×AGL(1,𝔽5)12yes—
306C2×C4#413112yes—
307C2×C4#413312yes—
308C8—104no—
309C8—104no—
310C8—104no—
311C8—104no—
312C5#2054511yescharacteristic, complemented, Sylow
313C22—54no—
314C22—102no—
315C22—104no—
316C22—102no—
317C22—104no—
318C22C22×C4×AGL(1,𝔽5)11yescharacteristic
319C22C2×#413111yescharacteristic
320C22C2×#413311yescharacteristic
321C22D5⋊#13112yes—
322C22#6626612yes—
323C4—22no—
324C4—22no—
325C4—44no—
326C4—51no—
327C4—52no—
328C4—51no—
329C4—102no—
330C4—102no—
331C4—204no—
332C4#6570114yes—
333C2—104no—
334C2C2×#6570111yescharacteristic
335C2#1061710511yescharacteristic
336C2#1061712711yescharacteristic
337C2#1061732112yes—
338C2#1061734112yes—
subgroupG/H
center, FrattiniC23C23×AGL(1,𝔽5)
commutatorC22×C5C22×C42
FittingC5×#382C4
socleC23×C5C23×C4
prime radicalC23×D5C22×C4
cosocleC22×Dic5C24
hypercenter#382AGL(1,𝔽5)
hypocenterC5#20545
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ #382

Complements

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

NH ≅ G/Ntype
4. #10604315C2semidirect
5. C4⋊C4×#170C2semidirect
6. #10603778C2semidirect
20. #65680C4semidirect
21. D5⋊(C4⋊C8)C4semidirect
312. C5#20545semidirect

Maximal subgroups

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

subgroupindex
C2×#656802
C2×D5⋊(C4⋊C8)2
#106058782
#106043152
C4⋊C4×#1702
#106037782
#106037762
#106037752
#205455