Finite Group Databasebeta

← #13018262

Subgroups — #13018262

Order 1280.

462 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic5×#131C211yesmaximal, characteristic
2#10605001C212yesmaximal
3#10604694C211yesmaximal, characteristic, complemented
4C2×#64881C211yesmaximal, characteristic, complemented
5#10598793C212yesmaximal, complemented
6C2×C5×#131C411yescharacteristic
7#41×Dic5C2211yescharacteristic
8C2×#4094C411yescharacteristic
9#65748C2212yes—
10C2×C4⋊#170C2212yes—
11#65411—21no—
12#65411C411yescharacteristic
13M16×Dic5—21no—
14M16×Dic5C2211yescharacteristic
15#65390—21no—
16#65390C411yescharacteristic
17C2×C8×Dic5—21no—
18C2×C8×Dic5C2211yescharacteristic
19Q8⋊#170—22no—
20D4⋊#170—22no—
21#64882—21no—
22#64881—21no—
23#64881—21no—
24#64881—21no—
25#8604—51nomaximal, Sylow
26C2×C5×#41C2×C411yescharacteristic
27C22×#170—22no—
28C5×#131—22no—
29C5×#131C814yescomplemented
30C2×C5×M16—21no—
31C2×C5×M16C2×C411yescharacteristic
32C22×C5×C8—21no—
33C22×C5×C8C2×C411yescharacteristic
34#4094—22no—
35#4094—22no—
36Q8×Dic5D411yescharacteristic
37Q8×Dic5Q811yescharacteristic
38D4×Dic5—21no—
39D4×Dic5—21no—
40D4×Dic5D411yescharacteristic
41D4×Dic5Q811yescharacteristic
42#4072—21no—
43#4072C2×C411yescharacteristic
44C2×C4×Dic5—21no—
45C2×C4×Dic5C2311yescharacteristic
46C2×#681—21no—
47C2×#681C2×C411yescharacteristic
48C22×#168—21no—
49C22×#168C2×C411yescharacteristic
50C22⋊#170—22no—
51C4⋊#170—22no—
52C4⋊#170—22no—
53C4⋊#170—22no—
54C4×#170—22no—
55#3947—21no—
56#3947—21no—
57#3947—21no—
58C8×Dic5—21no—
59C8×Dic5—21no—
60C8×Dic5—21no—
61C8×Dic5D411yescharacteristic
62C8×Dic5D411yescharacteristic
63C8×Dic5D411yescharacteristic
64C8×Dic5D411yescharacteristic
65C4×#131—51no—
66#1564—51no—
67C2×#334—51no—
68#1477—52no—
69#1283—52no—
70C5×#41—21no—
71C5×#41—21no—
72C5×#41C2×C812yes—
73C5×#41M1612yes—
74C2×C5×Q8C4⋊C411yescharacteristic
75C2×C5×D4—21no—
76C2×C5×D4C4⋊C411yescharacteristic
77C22×C4×C5—21no—
78C22×C4×C5C22×C411yescharacteristic
79C22×Dic5—21no—
80C22×Dic5—21no—
81C22×Dic5#4111yescharacteristic
82C22×Dic5#4111yescharacteristic
83C2×#170—42no—
84C2×#170—42no—
85C2×#170—82no—
86C5×M16—21no—
87C5×M16—24no—
88C5×M16C2×C812yes—
89C2×C5×C8—21no—
90C2×C5×C8—24no—
91C2×C5×C8C22⋊C411yescharacteristic
92C2×C5×C8C22⋊C411yescharacteristic
93C2×C5×C8C2×C812yes—
94C2×C5×C8M1612yes—
95C22⋊Dic5—21no—
96C22⋊Dic5—21no—
97C22⋊Dic5—21no—
98C4⋊Dic5—21no—
99C4⋊Dic5—21no—
100C4⋊Dic5C4⋊C411yescharacteristic
101C4⋊Dic5C4⋊C411yescharacteristic
102C4×Dic5—21no—
103C4×Dic5—21no—
104C4×Dic5—21no—
105C4×Dic5C2×D411yescharacteristic
106C4×Dic5C2×D411yescharacteristic
107C4×Dic5C2×D411yescharacteristic
108C4×Dic5C2×Q811yescharacteristic
109#681—24no—
110#681—21no—
111#681M1612yes—
112C2×#168—24no—
113C2×#168—21no—
114C2×#168—21no—
115C2×#168—21no—
116C2×#168C22⋊C411yescharacteristic
117C2×#168C22⋊C411yescharacteristic
118C2×#131—51no—
119C2×#131AGL(1,𝔽5)11yescharacteristic
120C4×#41—51no—
121#431—52no—
122C2×C4⋊C8—52no—
123#405—51no—
124#405—51no—
125#405—101no—
126#405—101no—
127C4×M16—51no—
128C4×M16—101no—
129C2×C4×C8—51no—
130C2×C4×C8—101no—
131#335—101no—
132#334—101no—
133#334—101no—
134#334—101no—
135Q8⋊C8—102no—
136D4⋊C8—102no—
137C23×C5—21no—
138C23×C5#11711yescharacteristic
139C5×Q8—21no—
140C5×Q8C4⋊C812yes—
141C5×D4—22no—
142C5×D4—22no—
143C5×D4—21no—
144C5×D4C4⋊C812yes—
145C2×C4×C5—21no—
146C2×C4×C5—22no—
147C2×C4×C5—22no—
148C2×C4×C5C2×C22⋊C411yescharacteristic
149C2×C4×C5C2×C4⋊C411yescharacteristic
150C2×C4×C5C22×C811yescharacteristic
151C2×C4×C5C2×M1611yescharacteristic
152C2×C4×C5C2×M1611yescharacteristic
153C2×C4×C5C2×M1611yescharacteristic
154C2×Dic5—22no—
155C2×Dic5—21no—
156C2×Dic5—21no—
157C2×Dic5—41no—
158C2×Dic5—42no—
159C2×Dic5—42no—
160C2×Dic5#12111yescharacteristic
161C2×Dic5#12111yescharacteristic
162C2×Dic5C22⋊Q811yescharacteristic
163C2×Dic5C22⋊Q811yescharacteristic
164#170—82no—
165#170—82no—
166C5×C8—22no—
167C5×C8C22⋊C812yes—
168C5×C8C22⋊C812yes—
169#168—21no—
170#168—22no—
171#168—21no—
172C2×#41C2×AGL(1,𝔽5)11yescharacteristic
173#131—22no—
174#131—102no—
175#131—102no—
176#131#17014yescomplemented
177C2×M16—21no—
178C2×M16—51no—
179C2×M16—101no—
180C2×M16C2×AGL(1,𝔽5)11yescharacteristic
181C22×C8—21no—
182C22×C8—51no—
183C22×C8—101no—
184C22×C8—102no—
185C22×C8C2×AGL(1,𝔽5)11yescharacteristic
186C4×Q8—51no—
187C4×Q8—51no—
188C4×D4—51no—
189C4×D4—51no—
190C4×D4—101no—
191C4×D4—101no—
192#117—51no—
193#117—101no—
194C2×C42—51no—
195C2×C42—101no—
196C4⋊C8—102no—
197C4⋊C8—102no—
198C4⋊C8—102no—
199C22⋊C8—102no—
200#97—101no—
201#97—101no—
202#97—101no—
203C4×C8—51no—
204C4×C8—51no—
205C4×C8—51no—
206C4×C8—51no—
207C4×C8—101no—
208C4×C8—102no—
209C4×C8—101no—
210C4×C8—101no—
211C22×C5—21no—
212C22×C5—21no—
213C22×C5—22no—
214C22×C5—41no—
215C22×C5—41no—
216C22×C5#38011yescharacteristic
217C22×C5#43111yescharacteristic
218C22×C5#43211yescharacteristic
219C4×C5—22no—
220C4×C5C2×C22⋊C811yescharacteristic
221C4×C5#40711yescharacteristic
222C4×C5C2×C4⋊C811yescharacteristic
223C4×C5#42311yescharacteristic
224Dic5—21no—
225Dic5—21no—
226Dic5—21no—
227Dic5—41no—
228Dic5—41no—
229Dic5#47112yes—
230#41—21no—
231#41—21no—
232#41#70012yes—
233#41C2×#17012yes—
234C2×Q8C4⋊AGL(1,𝔽5)11yescharacteristic
235C2×D4—21no—
236C2×D4C4⋊AGL(1,𝔽5)11yescharacteristic
237C22×C4—21no—
238C22×C4—51no—
239C22×C4—51no—
240C22×C4—101no—
241C22×C4—101no—
242C22×C4C22×AGL(1,𝔽5)11yescharacteristic
243M16—21no—
244M16—24no—
245M16—52no—
246M16—104no—
247M16—101no—
248M16C2×#17012yes—
249C2×C8—21no—
250C2×C8—24no—
251C2×C8—51no—
252C2×C8—51no—
253C2×C8—104no—
254C2×C8—101no—
255C2×C8—101no—
256C2×C8—101no—
257C2×C8—202no—
258C2×C8—202no—
259C2×C8—402no—
260C2×C8C2×#17012yes—
261C2×C8#70412yes—
262C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
263C2×C8C22⋊AGL(1,𝔽5)11yescharacteristic
264C4⋊C4—51no—
265C4⋊C4—51no—
266C4⋊C4—101no—
267C4⋊C4—101no—
268C22⋊C4—101no—
269C22⋊C4—101no—
270C22⋊C4—101no—
271C42—51no—
272C42—51no—
273C42—51no—
274C42—51no—
275C42—101no—
276C42—101no—
277C42—101no—
278C2×C5—21no—
279C2×C5—21no—
280C2×C5—42no—
281C2×C5#179711yescharacteristic
282C2×C5#181411yescharacteristic
283C2×C5#181511yescharacteristic
284C23—21no—
285C23#413011yescharacteristic
286Q8—21no—
287Q8C4⋊#17012yes—
288D4—22no—
289D4—22no—
290D4—21no—
291D4C4⋊#17012yes—
292C2×C4—21no—
293C2×C4—22no—
294C2×C4—22no—
295C2×C4—51no—
296C2×C4—51no—
297C2×C4—51no—
298C2×C4—51no—
299C2×C4—102no—
300C2×C4—101no—
301C2×C4—101no—
302C2×C4—202no—
303C2×C4—201no—
304C2×C4—202no—
305C2×C4C2×#70011yescharacteristic
306C2×C4D5⋊M1611yescharacteristic
307C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
308C2×C4C22×#17011yescharacteristic
309C2×C4C2×#70411yescharacteristic
310C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
311C8—22no—
312C8—101no—
313C8—101no—
314C8—102no—
315C8—402no—
316C8—402no—
317C8C22⋊#17012yes—
318C8C22⋊#17012yes—
319C5#860411yescharacteristic, complemented, Sylow
320C22—21no—
321C22—21no—
322C22—22no—
323C22—41no—
324C22—41no—
325C22#6574811yescharacteristic
326C22#6575911yescharacteristic
327C22#6576511yescharacteristic
328C4—22no—
329C4—52no—
330C4—101no—
331C4—101no—
332C4—101no—
333C4—201no—
334C4—201no—
335C4C2×C4⋊#17011yescharacteristic
336C4#6575611yescharacteristic
337C4#6575811yescharacteristic
338C4C2×C22⋊#17011yescharacteristic
339C2—21no—
340C2—21no—
341C2—42no—
342C2#1060477911yescharacteristic
343C2#1060478111yescharacteristic
344C2#1060489911yescharacteristic
subgroupG/H
centerC22#65765
commutatorC2×C4×C5C22×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C5×#131C4
socleC22×C5#380
prime radicalC2×C5×#41C2×C4
cosocleC2×C4×Dic5C23
hypercenterC2×#131AGL(1,𝔽5)
hypocenterC5#8604
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
3. #10604694C2semidirect
4. C2×#64881C2semidirect
5. #10598793C2semidirect
29. C5×#131C8semidirect
176. #131#170semidirect
319. C5#8604semidirect

Maximal subgroups

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

subgroupindex
Dic5×#1312
#106050012
#106046942
C2×#648812
#105987932
#86045