Finite Group Databasebeta

← #13016191

Subgroups — #13016191

Order 1280.

706 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65678C211yesmaximal, characteristic
2C2×D5⋊(C4⋊C8)C211yesmaximal, characteristic
3#10605484C211yesmaximal, characteristic
4#10598725C214yesmaximal, complemented
5C22×D5⋊C8—21no—
6C2×#4018—21no—
7C2×C42×D5C2211yescharacteristic
8C2×#4004C2212yes—
9C2×#4004C2212yes—
10C2×#4003—21no—
11C2×C4⋊#170—21no—
12C2×C4×#170—21no—
13D5⋊(C4⋊C8)—22no—
14D5⋊(C4⋊C8)C414yescomplemented
15#65678—22no—
16#65678C414yescomplemented
17C4×C5×C4⋊C4C411yescharacteristic
18#65276C412yes—
19#65265C2212yes—
20C4×C4⋊Dic5C411yescharacteristic
21C4×#683—21no—
22#64956—21no—
23#64939—21no—
24#8039—51nomaximal, Sylow
25C22×C4×D5C2×C411yescharacteristic
26C22×C4×D5D411yescharacteristic
27C22×C4×D5D411yescharacteristic
28C22×#170—22no—
29C22×#170—22no—
30C2×D5⋊C8—24no—
31C2×D5⋊C8—42no—
32C2×D5⋊C8—42no—
33C2×C5×C4⋊C4C2×C412yes—
34C2×C42×C5—21no—
35C2×C42×C5C2×C411yescharacteristic
36C2×#685—22no—
37C2×C4⋊Dic5C2×C412yes—
38C2×#683—22no—
39C2×#683—22no—
40C2×C4×Dic5—21no—
41C2×C4×Dic5D411yescharacteristic
42C2×C4×Dic5D411yescharacteristic
43C2×C4×Dic5C2311yescharacteristic
44#4018—42no—
45#4018—42no—
46C42×D5C2×C412yes—
47C42×D5C2×C412yes—
48C42×D5D412yes—
49C42×D5Q812yes—
50#4004—22no—
51#4004—22no—
52#4004C2×C414yes—
53#4004C2×C414yes—
54#4003—24no—
55C4⋊#170—24no—
56C4×#170—24no—
57C5×#95—21no—
58#3963—21no—
59#3963—22no—
60C2×#431—51no—
61C22×C4⋊C8—51no—
62#2285—51no—
63#1296—54no—
64C23×D5C22⋊C411yescharacteristic
65C22×C4×C5—22no—
66C22×C4×C5C22⋊C411yescharacteristic
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22×C411yescharacteristic
69C22×Dic5—22no—
70C22×Dic5C22⋊C411yescharacteristic
71C22×Dic5C2×D411yescharacteristic
72C22×Dic5C2×D411yescharacteristic
73C2×C4×D5—24no—
74C2×C4×D5—42no—
75C2×C4×D5C4212yes—
76C2×C4×D5C22⋊C412yes—
77C2×C4×D5C22⋊C412yes—
78C2×C4×D5C4⋊C412yes—
79C2×C4×D5C4⋊C412yes—
80C2×C4×D5C4⋊C412yes—
81C2×C4×D5D812yes—
82C2×C4×D5SD1612yes—
83C2×C4×D5SD1612yes—
84C2×C4×D5Q1612yes—
85C2×#170—24no—
86C2×#170—24no—
87C2×#170—42no—
88C2×#170—42no—
89C2×#170—44no—
90D5⋊C8—48no—
91C5×C4⋊C4—42no—
92C42×C5—42no—
93C42×C5C4212yes—
94C42×C5C4⋊C412yes—
95#685—44no—
96C4⋊Dic5—42no—
97#683—42no—
98#683—42no—
99#683—44no—
100C4×Dic5—42no—
101C4×Dic5C22⋊C412yes—
102C4×Dic5C22⋊C412yes—
103C4×Dic5C4⋊C412yes—
104C4×Dic5C4⋊C412yes—
105C4×Dic5C22×C411yescharacteristic
106C4×Dic5C22×C411yescharacteristic
107C4×Dic5C2×D411yescharacteristic
108C4×Dic5C2×Q811yescharacteristic
109C23×C8—101no—
110C2×#117—101no—
111C22×C42—51no—
112#431—54no—
113#431—102no—
114C2×C4⋊C8—52no—
115C2×C4⋊C8—52no—
116C2×C4⋊C8—54no—
117C2×C4⋊C8—102no—
118C2×C4⋊C8—101no—
119C2×C22⋊C8—101no—
120C2×C4×C8—101no—
121#384—52no—
122#382—101no—
123#380—52no—
124#380—101no—
125C4×C4⋊C4—51no—
126C4×C4⋊C4—101no—
127C4×C4⋊C4AGL(1,𝔽5)11yescharacteristic
128C23×C5C2×C22⋊C411yescharacteristic
129C22×D5—22no—
130C22×D5—22no—
131C22×D5#9512yes—
132C22×D5#10212yes—
133C22×D5#10312yes—
134C2×C4×C5—22no—
135C2×C4×C5—22no—
136C2×C4×C5—42no—
137C2×C4×C5—42no—
138C2×C4×C5—42no—
139C2×C4×C5#9512yes—
140C2×C4×C5#9512yes—
141C2×C4×C5#10212yes—
142C2×C4×C5#10312yes—
143C2×C4×C5C2×C4211yescharacteristic
144C2×C4×C5C2×C4⋊C411yescharacteristic
145C2×Dic5—22no—
146C2×Dic5—42no—
147C2×Dic5—42no—
148C2×Dic5—42no—
149C2×Dic5#9512yes—
150C2×Dic5C2×C22⋊C411yescharacteristic
151C2×Dic5C2×C22⋊C411yescharacteristic
152C2×Dic5C2×C4⋊C411yescharacteristic
153C2×Dic5C2×C4⋊C411yescharacteristic
154C2×Dic5C2×D811yescharacteristic
155C2×Dic5C2×SD1611yescharacteristic
156C2×Dic5C2×SD1611yescharacteristic
157C2×Dic5C2×Q1611yescharacteristic
158C2×Dic5#13514yes—
159C4×D5—24no—
160C4×D5—24no—
161C4×D5—42no—
162C4×D5—42no—
163C4×D5#10214yes—
164C4×D5#10314yes—
165C4×D5#10614yes—
166C4×D5#10714yes—
167#170—44no—
168#170—44no—
169C23×C4—51no—
170C23×C4—51no—
171C23×C4—51no—
172C22×C8—104no—
173C22×C8—102no—
174C22×C8—102no—
175C22×C8—202no—
176C22×C8—202no—
177#117—202no—
178#117—202no—
179C2×C4⋊C4—52no—
180C2×C4⋊C4—102no—
181C2×C4⋊C4—102no—
182C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
183C2×C22⋊C4—102no—
184C2×C42—21no—
185C2×C42—51no—
186C2×C42—51no—
187C2×C42—51no—
188C2×C42—52no—
189C2×C42—52no—
190C2×C42—52no—
191C2×C42—52no—
192C2×C42—101no—
193C2×C42C2×AGL(1,𝔽5)11yescharacteristic
194C4⋊C8—54no—
195C4⋊C8—54no—
196C4⋊C8—104no—
197C4⋊C8—102no—
198C4⋊C8—102no—
199C22⋊C8—104no—
200C4×C8—104no—
201#95—21no—
202#95—102no—
203#95—101no—
204C22×C5C2×#9511yescharacteristic
205C22×C5#41312yes—
206C22×C5C2×#10211yescharacteristic
207C22×C5C2×#10311yescharacteristic
208C22×C5#41612yes—
209C2×D5—24no—
210C2×D5—24no—
211C2×D5—22no—
212C2×D5—22no—
213C2×D5#34014yes—
214C4×C5—22no—
215C4×C5—21no—
216C4×C5—21no—
217C4×C5—82no—
218C4×C5#34014yes—
219Dic5—22no—
220Dic5—82no—
221Dic5C2×#10211yescharacteristic
222Dic5C2×#10311yescharacteristic
223Dic5#41612yes—
224Dic5C2×#10611yescharacteristic
225Dic5C2×#10711yescharacteristic
226Dic5#42712yes—
227C24—51no—
228C22×C4—22no—
229C22×C4—51no—
230C22×C4—51no—
231C22×C4—52no—
232C22×C4—52no—
233C22×C4—52no—
234C22×C4—52no—
235C22×C4—52no—
236C22×C4—52no—
237C22×C4—51no—
238C22×C4—52no—
239C22×C4—52no—
240C22×C4—52no—
241C22×C4—52no—
242C22×C4—104no—
243C22×C4—102no—
244C22×C4—202no—
245C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
246C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
247C22×C4C22×AGL(1,𝔽5)11yescharacteristic
248C2×C8—104no—
249C2×C8—104no—
250C2×C8—208no—
251C2×C8—202no—
252C2×C8—202no—
253C2×C8—204no—
254C4⋊C4—42no—
255C4⋊C4—202no—
256C4⋊C4—202no—
257C4⋊C4—202no—
258C4⋊C4—204no—
259C22⋊C4—204no—
260C42—42no—
261C42—51no—
262C42—51no—
263C42—51no—
264C42—51no—
265C42—52no—
266C42—52no—
267C42—52no—
268C42—52no—
269C42—202no—
270C42C4×AGL(1,𝔽5)12yes—
271C42C4⋊AGL(1,𝔽5)12yes—
272C2×C5#154012yes—
273C2×C5#154212yes—
274C2×C5C2×#34011yescharacteristic
275C2×C5#173511yescharacteristic
276C2×C5#174211yescharacteristic
277D5—24no—
278C23—52no—
279C23—52no—
280C23—52no—
281C23—102no—
282C23—102no—
283C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—54no—
290C2×C4—51no—
291C2×C4—51no—
292C2×C4—51no—
293C2×C4—51no—
294C2×C4—51no—
295C2×C4—51no—
296C2×C4—51no—
297C2×C4—51no—
298C2×C4—54no—
299C2×C4—54no—
300C2×C4—54no—
301C2×C4—54no—
302C2×C4—52no—
303C2×C4—104no—
304C2×C4—104no—
305C2×C4—102no—
306C2×C4—202no—
307C2×C4—202no—
308C2×C4—202no—
309C2×C4—202no—
310C2×C4—202no—
311C2×C4(C2×AGL(1,𝔽5))⋊C412yes—
312C2×C4(C2×AGL(1,𝔽5))⋊C412yes—
313C2×C4#400712yes—
314C2×C4#400912yes—
315C2×C4C2×C4×AGL(1,𝔽5)11yescharacteristic
316C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
317C8—204no—
318C8—204no—
319C5#803911yescharacteristic, complemented, Sylow
320C22—54no—
321C22—102no—
322C22—104no—
323C22—104no—
324C22—102no—
325C22#6576112yes—
326C22C2×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
327C22C2×#400711yescharacteristic
328C22C2×#400911yescharacteristic
329C22#6579412yes—
330C4—22no—
331C4—21no—
332C4—21no—
333C4—52no—
334C4—52no—
335C4—51no—
336C4—51no—
337C4—51no—
338C4—51no—
339C4—82no—
340C4—102no—
341C4—402no—
342C4#6487414yes—
343C2—104no—
344C2#1060419211yescharacteristic
345C2C2×#6487411yescharacteristic
346C2#1060437811yescharacteristic
347C2#1060440812yes—
348C2#1060444312yes—
subgroupG/H
centerC22×C4C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C2×C42
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC4×C5×C4⋊C4C4
socleC23×C5C2×C22⋊C4
prime radicalC23×D5C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC4×C4⋊C4AGL(1,𝔽5)
hypocenterC5#8039
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #10598725C2semidirect
14. D5⋊(C4⋊C8)C4semidirect
16. #65678C4semidirect
319. C5#8039semidirect

Maximal subgroups

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

subgroupindex
C2×#656782
C2×D5⋊(C4⋊C8)2
#106054842
#105987252
#80395