Finite Group Databasebeta

← #12017685

Subgroups — #12017685

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×#366C211yesmaximal, characteristic, complemented
3C2×#64722C211yesmaximal, characteristic, complemented
4#10601421C211yesmaximal, characteristic
5#10601420C211yesmaximal, characteristic, complemented
6C2×#64712C211yesmaximal, characteristic, complemented
7C2×#64711C211yesmaximal, characteristic
8C22×Dic20C2211yescharacteristic
9C22×D40C2211yescharacteristic
10C22×C5×C16C2211yescharacteristic
11C2×C5×#107C2211yescharacteristic
12C2×C5×#107C2211yescharacteristic
13C2×C8×Dic5C2211yescharacteristic
14C22×#672C2211yescharacteristic
15#65277—21no—
16#65263—21no—
17C2×#3942—21no—
18C2×#3941—21no—
19C2×#3932—22no—
20C2×#3932—22no—
21C2×#3932C414yescomplemented
22C5×#366—22no—
23#64722—22no—
24#64712—22no—
25#64711—22no—
26#13238—51nomaximal, Sylow
27C22×D20—21no—
28C22×Dic10—21no—
29C22×C5×C8C2311yescharacteristic
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—21no—
32C2×#685—42no—
33C2×C4×Dic5D411yescharacteristic
34C22×#168D411yescharacteristic
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×C16C2×C412yes—
48C2×C5×C16D412yes—
49C2×C5×C16D412yes—
50C5×#107—21no—
51C5×#107—21no—
52C5×#107—21no—
53C5×#107—21no—
54#3963—42no—
55C8×Dic5—21no—
56C8×Dic5—21no—
57C2×#672—21no—
58C2×#672—21no—
59C2×#672D412yes—
60#3942—42no—
61#3941—42no—
62#3932—28no—
63C22×SD32—51no—
64C2×#366D511yescharacteristic, complemented
65C2×#358—51no—
66C2×#357—51no—
67C2×#346—51no—
68#1970—51no—
69#1969—51no—
70C23×D5—41no—
71C22×C4×C5—41no—
72C22×C4×C5—41no—
73C22×C4×C5C2×D411yescharacteristic
74C22×Dic5—41no—
75C22×Dic5D812yes—
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×C8C22×C411yescharacteristic
89C2×C5×C8C2×D411yescharacteristic
90C2×C5×C8C2×D411yescharacteristic
91C2×C5×C8C2×D411yescharacteristic
92C2×C5×C8#4111yescharacteristic
93C2×C5×C8#4111yescharacteristic
94C5×C4⋊C4—41no—
95C5×C4⋊C4—41no—
96C5×C4⋊C4—41no—
97C5×C4⋊C4—41no—
98#685—84no—
99C4×Dic5—21no—
100C4×Dic5—21no—
101C2×#168—21no—
102C2×#168—21no—
103C2×#168D812yes—
104Dic20—22no—
105Dic20—22no—
106Dic20—41no—
107Dic20—41no—
108D40—22no—
109D40—22no—
110D40—41no—
111D40—41no—
112C5×C16C22⋊C414yescomplemented
113#672—22no—
114C22×Q16—51no—
115C22×D8—51no—
116C2×SD32—54no—
117C2×SD32—102no—
118C2×SD32—102no—
119C22×C16—51no—
120C22×C16C2×D511yescharacteristic
121C2×#107C2×D511yescharacteristic
122C2×#107C2×D511yescharacteristic
123C2×#103—101no—
124C2×#102—101no—
125C2×C4×C8—51no—
126#391—101no—
127#390—101no—
128#366—22no—
129#358—102no—
130#357—102no—
131#346—102no—
132C23×C5C2×D811yescharacteristic
133C22×D5—42no—
134C22×D5—81no—
135C22×D5—81no—
136C22×D5—82no—
137C22×D5—82no—
138C2×C4×C5—81no—
139C2×C4×C5—81no—
140C2×C4×C5—82no—
141C2×C4×C5—82no—
142C2×C4×C5C4×D411yescharacteristic
143C2×C4×C5#12111yescharacteristic
144C2×C4×C5#12711yescharacteristic
145C2×C4×C5C2×D811yescharacteristic
146C2×C4×C5#13511yescharacteristic
147C2×C4×C5#13511yescharacteristic
148C2×Dic5—22no—
149C2×Dic5—22no—
150C2×Dic5—22no—
151C2×Dic5—42no—
152C2×Dic5—81no—
153C2×Dic5—81no—
154D20—42no—
155D20—42no—
156D20—81no—
157D20—81no—
158Dic10—42no—
159Dic10—42no—
160Dic10—81no—
161Dic10—81no—
162C5×C8C2×C22⋊C411yescharacteristic
163C5×C8C4×D411yescharacteristic
164C5×C8#12111yescharacteristic
165C5×C8#12411yescharacteristic
166#168—22no—
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×C8—51no—
182C22×C8C22×D511yescharacteristic
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C22⋊C4—202no—
186C2×C42—51no—
187SD32—108no—
188C2×C16—52no—
189C2×C16—101no—
190C2×C16—101no—
191C2×C16C4×D512yes—
192C2×C16D2012yes—
193C2×C16C22⋊D512yes—
194#107—21no—
195#107—21no—
196#107—21no—
197#107—21no—
198#103—202no—
199#102—202no—
200C4×C8—101no—
201C4×C8—101no—
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—161no—
214C4×C5—161no—
215C4×C5#39011yescharacteristic
216C4×C5C4×D811yescharacteristic
217C4×C5#46611yescharacteristic
218C4×C5#49511yescharacteristic
219Dic5—42no—
220Dic5—82no—
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—41no—
235C22×C4—41no—
236C22×C4—52no—
237C22×C4—201no—
238C22×C4D4×D511yescharacteristic
239Q16—102no—
240Q16—102no—
241Q16—201no—
242Q16—201no—
243D8—102no—
244D8—102no—
245D8—201no—
246D8—201no—
247C2×C8—52no—
248C2×C8—101no—
249C2×C8—101no—
250C2×C8C2×C4×D511yescharacteristic
251C2×C8C2×D2011yescharacteristic
252C2×C8D4×D511yescharacteristic
253C2×C8#71311yescharacteristic
254C2×C8#71311yescharacteristic
255C2×C8C2×C22⋊D511yescharacteristic
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C22⋊C4—404no—
261C42—101no—
262C42—101no—
263C16—102no—
264C16#68514yescomplemented
265C2×C5#197011yescharacteristic
266C2×C5#217512yes—
267C2×C5#222012yes—
268C2×C5#225011yescharacteristic
269C2×C5#225111yescharacteristic
270D5—162no—
271C23—202no—
272C23—401no—
273C23—401no—
274C23—402no—
275C23—402no—
276C23D5×D811yescharacteristic
277Q8—202no—
278Q8—202no—
279Q8—401no—
280Q8—401no—
281D4—202no—
282D4—202no—
283D4—401no—
284D4—401no—
285C2×C4—81no—
286C2×C4—81no—
287C2×C4—82no—
288C2×C4—82no—
289C2×C4—102no—
290C2×C4—102no—
291C2×C4—102no—
292C2×C4—202no—
293C2×C4—401no—
294C2×C4—401no—
295C2×C4#403911yescharacteristic
296C2×C4#404111yescharacteristic
297C2×C4D5×D811yescharacteristic
298C2×C4#406511yescharacteristic
299C2×C4#406511yescharacteristic
300C2×C4#408611yescharacteristic
301C8—102no—
302C8#403911yescharacteristic
303C8#404111yescharacteristic
304C8C2×#68511yescharacteristic
305C8#409311yescharacteristic
306C5#1323811yescharacteristic, complemented, Sylow
307C22—404no—
308C22—402no—
309C22—801no—
310C22—801no—
311C22—802no—
312C22#6516111yescharacteristic
313C22#6517211yescharacteristic
314C22#6520012yes—
315C22#6520712yes—
316C22#6544011yescharacteristic
317C4—161no—
318C4—161no—
319C4—202no—
320C4—402no—
321C4#6516111yescharacteristic
322C4#6517211yescharacteristic
323C4#6527711yescharacteristic
324C4#6548011yescharacteristic
325C2—802no—
326C2#1060011212yes—
327C2#1060012212yes—
328C2#1060142111yescharacteristic
329C2#1060225911yescharacteristic
330C2#1060229411yescharacteristic
subgroupG/H
centerC23D5×D8
commutatorC2×C5×C8C22×C4
FrattiniC22×C8C22×D5
FittingC2×C5×#366C2
socleC23×C5C2×D8
prime radicalC22×D40C22
cosocleC22×C5×C8C23
hypercenterC2×#366D5
hypocenterC5#13238
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#366

Complements

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

NH ≅ G/Ntype
2. C2×C5×#366C2semidirect
3. C2×#64722C2semidirect
5. #10601420C2semidirect
6. C2×#64712C2semidirect
21. C2×#3932C4semidirect
64. C2×#366D5semidirect
112. 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×#3662
C2×#647222
#106014212
#106014202
C2×#647122
C2×#647112
#132385