Finite Group Databasebeta

← #12017687

Subgroups — #12017687

Order 1280.

466 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3932C211yesmaximal, characteristic
2C2×C5×#346C211yesmaximal, characteristic, complemented
3C2×#64723C211yesmaximal, characteristic, complemented
4C2×#64729C211yesmaximal, characteristic
5C2×#64724C211yesmaximal, characteristic, complemented
6#10600569C211yesmaximal, characteristic
7#10600568C211yesmaximal, characteristic, complemented
8C22×Dic20C2211yescharacteristic
9C22×D40C2211yescharacteristic
10C22×C5×C16C2211yescharacteristic
11C22×C5×C16C2211yescharacteristic
12C2×C4×C5×C8C2211yescharacteristic
13C2×#3953—21no—
14C2×#3950C2211yescharacteristic
15C2×#3950C2211yescharacteristic
16C2×#3948—21no—
17#65228—21no—
18#65218—21no—
19C2×#3932—22no—
20C2×#3932—22no—
21C2×#3932C414yescomplemented
22C5×#346—22no—
23#64729—22no—
24#64724—22no—
25#64723—22no—
26#13238—51nomaximal, Sylow
27C22×D20—21no—
28C22×Dic10—21no—
29C22×C5×C8D411yescharacteristic
30C22×C5×C8C2311yescharacteristic
31C2×C42×C5D411yescharacteristic
32C2×#685—42no—
33C2×C4⋊Dic5—21no—
34C2×C4⋊Dic5—21no—
35C2×Dic20—21no—
36C2×Dic20—21no—
37C2×Dic20—21no—
38C2×Dic20—21no—
39C2×Dic20—21no—
40C2×Dic20C2×C412yes—
41C2×D40—21no—
42C2×D40—21no—
43C2×D40—21no—
44C2×D40—21no—
45C2×D40—21no—
46C2×D40C2×C412yes—
47C2×C5×C16—21no—
48C2×C5×C16—21no—
49C2×C5×C16C2×C412yes—
50C2×C5×C16D412yes—
51C2×C5×C16D412yes—
52C2×C5×C16D412yes—
53C4×C5×C8—21no—
54C4×C5×C8—21no—
55#3963—42no—
56#3953—42no—
57#3950—21no—
58#3950—21no—
59#3950—21no—
60#3950—21no—
61#3948—42no—
62#3932—28no—
63C22×SD32—51no—
64C2×#366—51no—
65C2×#358—51no—
66C2×#357—51no—
67C2×#346D511yescharacteristic, complemented
68#1970—51no—
69#1969—51no—
70C23×D5—41no—
71C22×C4×C5D812yes—
72C22×C4×C5C2×D411yescharacteristic
73C22×Dic5—41no—
74C22×Dic5—41no—
75C22×Dic5—41no—
76C2×D20—22no—
77C2×D20—41no—
78C2×D20—41no—
79C2×D20—41no—
80C2×D20—41no—
81C2×D20—41no—
82C2×Dic10—22no—
83C2×Dic10—41no—
84C2×Dic10—41no—
85C2×Dic10—41no—
86C2×Dic10—41no—
87C2×Dic10—41no—
88C2×C5×C8—21no—
89C2×C5×C8—21no—
90C2×C5×C8D812yes—
91C2×C5×C8C22×C411yescharacteristic
92C2×C5×C8C2×D411yescharacteristic
93C2×C5×C8C2×D411yescharacteristic
94C2×C5×C8C2×D411yescharacteristic
95C2×C5×C8#4111yescharacteristic
96C2×C5×C8#4111yescharacteristic
97C42×C5—21no—
98C42×C5—21no—
99#685—84no—
100C4⋊Dic5—41no—
101C4⋊Dic5—41no—
102C4⋊Dic5—41no—
103C4⋊Dic5—41no—
104Dic20—22no—
105Dic20—22no—
106Dic20—41no—
107Dic20—41no—
108D40—22no—
109D40—22no—
110D40—41no—
111D40—41no—
112C5×C16—22no—
113C5×C16C22⋊C414yescomplemented
114C22×Q16—51no—
115C22×D8—51no—
116C2×SD32—54no—
117C2×SD32—102no—
118C2×SD32—102no—
119C22×C16C2×D511yescharacteristic
120C22×C16C2×D511yescharacteristic
121C2×#107—51no—
122C2×#107—51no—
123C2×#103—101no—
124C2×#102—101no—
125C2×C4×C8C2×D511yescharacteristic
126#391—101no—
127#390—101no—
128#366—102no—
129#358—102no—
130#357—102no—
131#346—22no—
132C23×C5C2×D811yescharacteristic
133C22×D5—42no—
134C22×D5—81no—
135C22×D5—81no—
136C22×D5—82no—
137C22×D5—82no—
138C2×C4×C5—22no—
139C2×C4×C5—22no—
140C2×C4×C5—22no—
141C2×C4×C5C4×D411yescharacteristic
142C2×C4×C5#12111yescharacteristic
143C2×C4×C5#12711yescharacteristic
144C2×C4×C5C2×D811yescharacteristic
145C2×C4×C5#13511yescharacteristic
146C2×C4×C5#13511yescharacteristic
147C2×Dic5—42no—
148C2×Dic5—81no—
149C2×Dic5—81no—
150C2×Dic5—81no—
151C2×Dic5—81no—
152C2×Dic5—82no—
153C2×Dic5—82no—
154D20—42no—
155D20—42no—
156D20—81no—
157D20—81no—
158Dic10—42no—
159Dic10—42no—
160Dic10—81no—
161Dic10—81no—
162C5×C8—22no—
163C5×C8C2×C22⋊C411yescharacteristic
164C5×C8C4×D411yescharacteristic
165C5×C8#12111yescharacteristic
166C5×C8#12411yescharacteristic
167C22×Q8—101no—
168C22×D4—101no—
169C2×Q16—52no—
170C2×Q16—101no—
171C2×Q16—101no—
172C2×Q16—101no—
173C2×Q16—101no—
174C2×Q16—101no—
175C2×D8—52no—
176C2×D8—101no—
177C2×D8—101no—
178C2×D8—101no—
179C2×D8—101no—
180C2×D8—101no—
181C22×C8D2011yescharacteristic
182C22×C8C22×D511yescharacteristic
183C2×C4⋊C4—101no—
184C2×C4⋊C4—101no—
185C2×C22⋊C4—202no—
186C2×C42D2011yescharacteristic
187SD32—108no—
188C2×C16—21no—
189C2×C16—21no—
190C2×C16C4×D512yes—
191C2×C16D2012yes—
192C2×C16D2012yes—
193C2×C16C22⋊D512yes—
194#107—101no—
195#107—101no—
196#107—101no—
197#107—101no—
198#103—202no—
199#102—202no—
200C4×C8—21no—
201C4×C8—21no—
202#95—202no—
203C22×C5C4×D811yescharacteristic
204C22×C5#46611yescharacteristic
205C22×C5#49311yescharacteristic
206C22×C5#50912yes—
207C22×C5#51012yes—
208C2×D5—84no—
209C2×D5—82no—
210C2×D5—162no—
211C2×D5—161no—
212C2×D5—161no—
213C4×C5—42no—
214C4×C5#39011yescharacteristic
215C4×C5C4×D811yescharacteristic
216C4×C5#46611yescharacteristic
217C4×C5#49511yescharacteristic
218Dic5—82no—
219Dic5—161no—
220Dic5—161no—
221C24—201no—
222C2×Q8—102no—
223C2×Q8—201no—
224C2×Q8—201no—
225C2×Q8—201no—
226C2×Q8—201no—
227C2×Q8—201no—
228C2×D4—102no—
229C2×D4—201no—
230C2×D4—201no—
231C2×D4—201no—
232C2×D4—201no—
233C2×D4—201no—
234C22×C4—201no—
235C22×C4—201no—
236C22×C4—201no—
237C22×C4D4012yes—
238C22×C4C2×D2011yescharacteristic
239Q16—102no—
240Q16—102no—
241Q16—201no—
242Q16—201no—
243D8—102no—
244D8—102no—
245D8—201no—
246D8—201no—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8D4012yes—
250C2×C8C2×C4×D511yescharacteristic
251C2×C8C2×D2011yescharacteristic
252C2×C8C2×D2011yescharacteristic
253C2×C8#70911yescharacteristic
254C2×C8#70911yescharacteristic
255C2×C8C2×C22⋊D511yescharacteristic
256C4⋊C4—201no—
257C4⋊C4—201no—
258C4⋊C4—201no—
259C4⋊C4—201no—
260C22⋊C4—404no—
261C42—21no—
262C42—21no—
263C16—22no—
264C16#68514yescomplemented
265C2×C5#197011yescharacteristic
266C2×C5#217512yes—
267C2×C5#222012yes—
268C2×C5#225011yescharacteristic
269C2×C5#225111yescharacteristic
270D5—162no—
271C23—202no—
272C23—401no—
273C23—402no—
274C23—402no—
275C23—401no—
276C23C2×D4011yescharacteristic
277Q8—202no—
278Q8—202no—
279Q8—401no—
280Q8—401no—
281D4—202no—
282D4—202no—
283D4—401no—
284D4—401no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—202no—
289C2×C4—401no—
290C2×C4—401no—
291C2×C4—402no—
292C2×C4—402no—
293C2×C4—401no—
294C2×C4—401no—
295C2×C4C4×D2011yescharacteristic
296C2×C4#402011yescharacteristic
297C2×C4C2×D4011yescharacteristic
298C2×C4#405011yescharacteristic
299C2×C4#405011yescharacteristic
300C2×C4#407611yescharacteristic
301C8—22no—
302C8C4×D2011yescharacteristic
303C8#402111yescharacteristic
304C8C2×#68511yescharacteristic
305C8#407611yescharacteristic
306C5#1323811yescharacteristic, complemented, Sylow
307C22—402no—
308C22—404no—
309C22—801no—
310C22—801no—
311C22—802no—
312C22C4×D4011yescharacteristic
313C22#6498411yescharacteristic
314C22#6519712yes—
315C22#6519812yes—
316C22#6540411yescharacteristic
317C4—42no—
318C4—402no—
319C4—801no—
320C4—801no—
321C4C4×D4011yescharacteristic
322C4#6498511yescharacteristic
323C4#6522811yescharacteristic
324C4#6540411yescharacteristic
325C2—802no—
326C2#1059987012yes—
327C2#1059987411yescharacteristic
328C2#1059987711yescharacteristic
329C2#1060056911yescharacteristic
330C2#1060223712yes—
subgroupG/H
centerC23C2×D40
commutatorC2×C5×C8C22×C4
FrattiniC22×C8C22×D5
FittingC2×C5×#346C2
socleC23×C5C2×D8
prime radicalC22×D40C22
cosocleC22×C5×C8C23
hypercenterC2×#346D5
hypocenterC5#13238
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×#346

Complements

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

NH ≅ G/Ntype
2. C2×C5×#346C2semidirect
3. C2×#64723C2semidirect
5. C2×#64724C2semidirect
7. #10600568C2semidirect
21. C2×#3932C4semidirect
67. C2×#346D5semidirect
113. C5×C16C22⋊C4semidirect
264. C16#685semidirect
306. C5#13238semidirect

Maximal subgroups

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

subgroupindex
C22×#39322
C2×C5×#3462
C2×#647232
C2×#647292
C2×#647242
#106005692
#106005682
#132385