Finite Group Databasebeta

← #11998538

Subgroups — #11998538

Order 1280.

518 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65381C211yesmaximal, characteristic
2C2×C5×#332C211yesmaximal, characteristic
3#10602573C211yesmaximal, characteristic
4#10601258C211yesmaximal, characteristic
5#10601253C211yesmaximal, characteristic
6C2×#64702C211yesmaximal, characteristic
7C2×#64699C211yesmaximal, characteristic
8C2×C5×C4⋊Q8C2211yescharacteristic
9C22×#689—21no—
10C22×#689—21no—
11C2×#4015C2211yescharacteristic
12C2×C5×C4⋊C8C2211yescharacteristic
13C2×C5×C4⋊C8C2211yescharacteristic
14C2×C8×Dic5—21no—
15#65381—22no—
16#65381C414yescomplemented
17C4×C4⋊Dic5C2211yescharacteristic
18C2×C4⋊#168C2211yescharacteristic
19C2×C4×#168C2211yescharacteristic
20C5×#332—22no—
21#64771—22no—
22#64770—21no—
23#64749—22no—
24#64702—22no—
25#64699—22no—
26#9733—51nomaximal, Sylow
27C22×C5×Q8—21no—
28C22×Dic10—21no—
29C22×C5×C8—21no—
30C22×C5×C8—21no—
31C5×C4⋊Q8—21no—
32C5×C4⋊Q8—21no—
33C5×C4⋊Q8—21no—
34C5×C4⋊Q8C2×C412yes—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4—21no—
37C2×C42×C5C2311yescharacteristic
38C2×#689—24no—
39C2×#689—24no—
40C2×#689—42no—
41C2×#689—42no—
42C2×#689—42no—
43C2×#689—42no—
44C2×C4⋊Dic5—21no—
45C2×C4⋊Dic5—21no—
46C2×C4⋊Dic5D412yes—
47C2×C4×Dic5—21no—
48C22×#168—21no—
49C22×#168D411yescharacteristic
50C22×#168D411yescharacteristic
51#4015—21no—
52#4015—21no—
53#4015—21no—
54#4015C2×C412yes—
55C5×C4⋊C8—21no—
56C5×C4⋊C8—21no—
57C5×C4⋊C8—21no—
58C5×C4⋊C8D412yes—
59#3963—21no—
60C8×Dic5—42no—
61C4⋊#168—21no—
62C4⋊#168—21no—
63C4×#168C2×C412yes—
64C4×#168D412yes—
65C2×#494—51no—
66#1988—51no—
67#1988—51no—
68C8×C4⋊C4—51no—
69C2×#335—51no—
70C2×#332—51no—
71C2×#332D511yescharacteristic
72C2×C5×Q8—22no—
73C2×C5×Q8—41no—
74C2×C5×Q8—41no—
75C2×C5×Q8—41no—
76C2×C5×Q8—41no—
77C2×C5×Q8—41no—
78C22×C4×C5—41no—
79C22×C4×C5C2×D411yescharacteristic
80C22×C4×C5C2×D411yescharacteristic
81C22×C4×C5#4111yescharacteristic
82C22×Dic5—22no—
83C22×Dic5—41no—
84C2×Dic10—22no—
85C2×Dic10—41no—
86C2×Dic10—41no—
87C2×Dic10—41no—
88C2×Dic10—41no—
89C2×Dic10—41no—
90C2×C5×C8—22no—
91C2×C5×C8—41no—
92C2×C5×C8—41no—
93C2×C5×C8—41no—
94C2×C5×C8—42no—
95C5×C4⋊C4—22no—
96C5×C4⋊C4—22no—
97C5×C4⋊C4—41no—
98C5×C4⋊C4—41no—
99C42×C5C22×C411yescharacteristic
100C42×C5C2×D411yescharacteristic
101C42×C5C2×D411yescharacteristic
102C42×C5#4111yescharacteristic
103#689—48no—
104#689—48no—
105C4⋊Dic5—22no—
106C4⋊Dic5—22no—
107C4⋊Dic5—22no—
108C4⋊Dic5—41no—
109C4⋊Dic5—41no—
110C4⋊Dic5Q1614yescomplemented
111C4×Dic5—41no—
112C4×Dic5—41no—
113C2×#168—21no—
114C2×#168—21no—
115C2×#168—41no—
116C2×#168—42no—
117C2×#168C22⋊C412yes—
118C2×#168C22⋊C412yes—
119C2×#168D812yes—
120C2×#168SD1612yes—
121C22×Q16—101no—
122C22×Q16—101no—
123C2×C4⋊Q8—51no—
124C2×C4⋊Q8C2×D511yescharacteristic
125#494—54no—
126#494—102no—
127C2×C4⋊C8—51no—
128C2×C4⋊C8C2×D511yescharacteristic
129C2×C4⋊C8C2×D511yescharacteristic
130C2×C4×C8—51no—
131C2×C4×C8—101no—
132C4×C4⋊C4—51no—
133#340—102no—
134#340—102no—
135#336—101no—
136#335—102no—
137#332—22no—
138#332—102no—
139C23×C5#12111yescharacteristic
140C5×Q8—42no—
141C5×Q8—42no—
142C5×Q8—81no—
143C5×Q8—81no—
144C2×C4×C5—22no—
145C2×C4×C5—42no—
146C2×C4×C5—81no—
147C2×C4×C5—81no—
148C2×C4×C5C2×C22⋊C411yescharacteristic
149C2×C4×C5C4×D411yescharacteristic
150C2×C4×C5C4×D411yescharacteristic
151C2×C4×C5#12111yescharacteristic
152C2×C4×C5#12411yescharacteristic
153C2×C4×C5#12711yescharacteristic
154C2×C4×C5C2×D811yescharacteristic
155C2×C4×C5C2×SD1611yescharacteristic
156C2×C4×C5C2×Q1612yes—
157C2×C4×C5#13512yes—
158C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
159C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
160C2×Dic5—24no—
161C2×Dic5—42no—
162C2×Dic5—42no—
163C2×Dic5—42no—
164C2×Dic5—81no—
165C2×Dic5—81no—
166Dic10—42no—
167Dic10—42no—
168Dic10—81no—
169Dic10—81no—
170C5×C8—42no—
171C5×C8—81no—
172#168—22no—
173#168—81no—
174#168#10214yes—
175C22×Q8—21no—
176C22×Q8—101no—
177C2×Q16—104no—
178C2×Q16—104no—
179C2×Q16—202no—
180C2×Q16—202no—
181C2×Q16—202no—
182C2×Q16—202no—
183C22×C8—21no—
184C22×C8—21no—
185C22×C8—51no—
186C22×C8—51no—
187C22×C8—101no—
188C4⋊Q8—21no—
189C4⋊Q8—21no—
190C4⋊Q8—21no—
191C4⋊Q8—52no—
192C4⋊Q8—101no—
193C4⋊Q8—101no—
194C4⋊Q8—101no—
195C4⋊Q8C4×D512yes—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—21no—
198C2×C4⋊C4—52no—
199C2×C4⋊C4—101no—
200C2×C4⋊C4—101no—
201C2×C42—101no—
202C2×C42C22×D511yescharacteristic
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8—101no—
207C4⋊C8—101no—
208C4⋊C8C22⋊D512yes—
209C4×C8—52no—
210C4×C8—52no—
211C4×C8—202no—
212#95—101no—
213C22×C5#39011yescharacteristic
214C22×C5#45911yescharacteristic
215C22×C5#46011yescharacteristic
216C22×C5#46712yes—
217C22×C5#47312yes—
218C4×C5—21no—
219C4×C5—21no—
220C4×C5—82no—
221C4×C5C2×#10211yescharacteristic
222C4×C5#41811yescharacteristic
223C4×C5C4×Q1612yes—
224C4×C5#45911yescharacteristic
225C4×C5#46011yescharacteristic
226C4×C5#49411yescharacteristic
227C4×C5#49511yescharacteristic
228Dic5—44no—
229Dic5—82no—
230C2×Q8—22no—
231C2×Q8—41no—
232C2×Q8—41no—
233C2×Q8—41no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—102no—
237C2×Q8—201no—
238C2×Q8—201no—
239C2×Q8—201no—
240C2×Q8—201no—
241C2×Q8—201no—
242C22×C4—41no—
243C22×C4—102no—
244C22×C4—201no—
245C22×C4#70911yescharacteristic
246C22×C4D4×D511yescharacteristic
247C22×C4D4×D511yescharacteristic
248Q16—208no—
249Q16—208no—
250C2×C8—22no—
251C2×C8—41no—
252C2×C8—41no—
253C2×C8—42no—
254C2×C8—41no—
255C2×C8—52no—
256C2×C8—52no—
257C2×C8—52no—
258C2×C8—52no—
259C2×C8—101no—
260C2×C8—101no—
261C2×C8—202no—
262C2×C8—201no—
263C4⋊C4—22no—
264C4⋊C4—22no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—54no—
268C4⋊C4—102no—
269C4⋊C4—102no—
270C4⋊C4—102no—
271C4⋊C4—201no—
272C4⋊C4—201no—
273C42—201no—
274C42—201no—
275C42C2×C4×D511yescharacteristic
276C42D4×D511yescharacteristic
277C42#71111yescharacteristic
278C42C2×C22⋊D511yescharacteristic
279C2×C5#166912yes—
280C2×C5#167012yes—
281C2×C5#196911yescharacteristic
282C2×C5#197911yescharacteristic
283C2×C5#198211yescharacteristic
284C23#403011yescharacteristic
285Q8—42no—
286Q8—42no—
287Q8—81no—
288Q8—81no—
289Q8—202no—
290Q8—202no—
291Q8—401no—
292Q8—401no—
293C2×C4—22no—
294C2×C4—42no—
295C2×C4—81no—
296C2×C4—81no—
297C2×C4—104no—
298C2×C4—202no—
299C2×C4—202no—
300C2×C4—202no—
301C2×C4—401no—
302C2×C4—401no—
303C2×C4D5×C22⋊C411yescharacteristic
304C2×C4#402711yescharacteristic
305C2×C4#403111yescharacteristic
306C2×C4D5×D811yescharacteristic
307C2×C4#405711yescharacteristic
308C2×C4D5×SD1611yescharacteristic
309C2×C4#406011yescharacteristic
310C2×C4#406212yes—
311C2×C4D5×Q1612yes—
312C2×C4C4×C22⋊D511yescharacteristic
313C2×C4#408511yescharacteristic
314C2×C4#408611yescharacteristic
315C8—42no—
316C8—54no—
317C8—81no—
318C8—102no—
319C8—401no—
320C5#973311yescharacteristic, complemented, Sylow
321C22#6504412yes—
322C22#6505111yescharacteristic
323C22#6507511yescharacteristic
324C22#6510212yes—
325C22#6524611yescharacteristic
326C4—21no—
327C4—21no—
328C4—82no—
329C4—204no—
330C4—402no—
331C4D5×#10211yescharacteristic
332C4#6505911yescharacteristic
333C4#6507912yes—
334C4#6543911yescharacteristic
335C4#6545211yescharacteristic
336C4#6545711yescharacteristic
337C4#6547011yescharacteristic
338C2#1059923412yes—
339C2#1059925812yes—
340C2#1060090111yescharacteristic
341C2#1060095411yescharacteristic
342C2#1060105111yescharacteristic
subgroupG/H
centerC23#4030
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC2×C5×#332C2
socle, prime radicalC23×C5#121
cosocleC2×C42×C5C23
hypercenterC2×#332D5
hypocenterC5#9733
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
16. #65381C4semidirect
110. C4⋊Dic5Q16semidirect
320. C5#9733semidirect

Maximal subgroups

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

subgroupindex
C2×#653812
C2×C5×#3322
#106025732
#106012582
#106012532
C2×#647022
C2×#646992
#97335