Finite Group Databasebeta

← #12017686

Subgroups — #12017686

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×#3960C211yesmaximal, characteristic
2C5×#1969C211yesmaximal, characteristic, complemented
3C2×#64784C211yesmaximal, characteristic, complemented
4C2×#64711C211yesmaximal, characteristic
5C2×#64709C211yesmaximal, characteristic, complemented
6#10600569C211yesmaximal, characteristic
7C2×#64681C211yesmaximal, characteristic, complemented
8C22×C5×Q16C2211yescharacteristic
9C22×D40C2211yescharacteristic
10C2×C5×#107C2211yescharacteristic
11C2×C5×#103—21no—
12C2×C4×C5×C8C2211yescharacteristic
13C5×#391—21no—
14C2×#3960—22no—
15C2×#3960—22no—
16C2×#3960C414yescomplemented
17C2×#3953—21no—
18C2×#3950C2211yescharacteristic
19C22×#672C2211yescharacteristic
20C22×#672C2211yescharacteristic
21#65228—21no—
22#64784—22no—
23#64711—22no—
24#64709—22no—
25#64681—22no—
26#13238—51nomaximal, Sylow
27C22×C5×Q8—21no—
28C22×D20—21no—
29C2×C5×Q16—21no—
30C2×C5×Q16—21no—
31C2×C5×Q16—21no—
32C2×C5×Q16—21no—
33C2×C5×Q16—21no—
34C2×C5×Q16C2×C412yes—
35C22×C5×C8D411yescharacteristic
36C22×C5×C8C2311yescharacteristic
37C2×C5×C4⋊C4—21no—
38C2×C42×C5D411yescharacteristic
39C2×#685—42no—
40C2×C4⋊Dic5—21no—
41C2×D40—21no—
42C2×D40—21no—
43C2×D40—21no—
44C2×D40—21no—
45C2×D40—21no—
46C2×D40C2×C412yes—
47C5×#107—21no—
48C5×#107—21no—
49C5×#103—42no—
50C4×C5×C8—21no—
51C4×C5×C8—21no—
52C5×#95—42no—
53#3960—28no—
54#3953—42no—
55#3950—21no—
56#3950—21no—
57C2×#672—21no—
58C2×#672—21no—
59C2×#672C2×C412yes—
60C2×#672D412yes—
61C2×#672D412yes—
62C2×#672D412yes—
63C22×SD32—51no—
64C2×#366—51no—
65C2×#358—51no—
66C2×#357—51no—
67C2×#346—51no—
68#1970—51no—
69#1969D511yescharacteristic, complemented
70C23×D5—41no—
71C2×C5×Q8—22no—
72C2×C5×Q8—41no—
73C2×C5×Q8—41no—
74C2×C5×Q8—41no—
75C2×C5×Q8—41no—
76C2×C5×Q8—41no—
77C22×C4×C5—41no—
78C22×C4×C5—41no—
79C22×C4×C5D812yes—
80C22×C4×C5C2×D411yescharacteristic
81C22×Dic5—41no—
82C2×D20—22no—
83C2×D20—41no—
84C2×D20—41no—
85C2×D20—41no—
86C2×D20—41no—
87C2×D20—41no—
88C5×Q16—22no—
89C5×Q16—22no—
90C5×Q16—41no—
91C5×Q16—41no—
92C2×C5×C8—21no—
93C2×C5×C8—21no—
94C2×C5×C8D812yes—
95C2×C5×C8C22×C411yescharacteristic
96C2×C5×C8C2×D411yescharacteristic
97C2×C5×C8C2×D411yescharacteristic
98C2×C5×C8C2×D411yescharacteristic
99C2×C5×C8#4111yescharacteristic
100C2×C5×C8#4111yescharacteristic
101C5×C4⋊C4—41no—
102C5×C4⋊C4—41no—
103C42×C5—21no—
104C42×C5—21no—
105#685—84no—
106C4⋊Dic5—41no—
107C4⋊Dic5—41no—
108D40—22no—
109D40—22no—
110D40—41no—
111D40—41no—
112#672—22no—
113#672C22⋊C414yescomplemented
114C22×Q16C2×D511yescharacteristic
115C22×D8—51no—
116C2×SD32—54no—
117C2×SD32—102no—
118C2×SD32—102no—
119C22×C16—51no—
120C22×C16—51no—
121C2×#107—51no—
122C2×#107C2×D511yescharacteristic
123C2×#103—21no—
124C2×#102—101no—
125C2×C4×C8C2×D511yescharacteristic
126#391—21no—
127#390—101no—
128#366—102no—
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—
138C5×Q8—42no—
139C5×Q8—42no—
140C5×Q8—81no—
141C5×Q8—81no—
142C2×C4×C5—22no—
143C2×C4×C5—22no—
144C2×C4×C5—22no—
145C2×C4×C5—42no—
146C2×C4×C5—81no—
147C2×C4×C5—81no—
148C2×C4×C5—81no—
149C2×C4×C5—82no—
150C2×C4×C5C4×D411yescharacteristic
151C2×C4×C5#12111yescharacteristic
152C2×C4×C5#12711yescharacteristic
153C2×C4×C5C2×D811yescharacteristic
154C2×C4×C5#13511yescharacteristic
155C2×C4×C5#13511yescharacteristic
156C2×Dic5—81no—
157C2×Dic5—82no—
158D20—42no—
159D20—42no—
160D20—81no—
161D20—81no—
162C5×C8—22no—
163C5×C8C2×C22⋊C411yescharacteristic
164C5×C8C4×D411yescharacteristic
165C5×C8#12111yescharacteristic
166C5×C8#12411yescharacteristic
167C22×Q8—21no—
168C22×D4—101no—
169C2×Q16—21no—
170C2×Q16—21no—
171C2×Q16—21no—
172C2×Q16—21no—
173C2×Q16—21no—
174C2×Q16C4×D512yes—
175C2×D8—52no—
176C2×D8—101no—
177C2×D8—101no—
178C2×D8—101no—
179C2×D8—101no—
180C2×D8—101no—
181C22×C8C22⋊D511yescharacteristic
182C22×C8C22×D511yescharacteristic
183C2×C4⋊C4—21no—
184C2×C4⋊C4—101no—
185C2×C22⋊C4—202no—
186C2×C42C22⋊D511yescharacteristic
187SD32—108no—
188C2×C16—52no—
189C2×C16—52no—
190C2×C16—52no—
191C2×C16—52no—
192C2×C16—101no—
193C2×C16—101no—
194#107—21no—
195#107—21no—
196#107—101no—
197#107—101no—
198#103—42no—
199#102—202no—
200C4×C8—21no—
201C4×C8—21no—
202#95—42no—
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—82no—
215C4×C5—161no—
216C4×C5#39011yescharacteristic
217C4×C5C4×D811yescharacteristic
218C4×C5#46611yescharacteristic
219C4×C5#49511yescharacteristic
220Dic5—161no—
221C24—201no—
222C2×Q8—22no—
223C2×Q8—41no—
224C2×Q8—41no—
225C2×Q8—41no—
226C2×Q8—41no—
227C2×Q8—41no—
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—201no—
237C22×C4#68612yes—
238C22×C4C2×C22⋊D511yescharacteristic
239Q16—22no—
240Q16—22no—
241Q16—41no—
242Q16—41no—
243D8—102no—
244D8—102no—
245D8—201no—
246D8—201no—
247C2×C8—21no—
248C2×C8—21no—
249C2×C8#68612yes—
250C2×C8C2×C4×D511yescharacteristic
251C2×C8#70911yescharacteristic
252C2×C8D4×D511yescharacteristic
253C2×C8D4×D511yescharacteristic
254C2×C8D4×D511yescharacteristic
255C2×C8#71111yescharacteristic
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—201no—
259C4⋊C4—201no—
260C22⋊C4—404no—
261C42—21no—
262C42—21no—
263C16—54no—
264C16—102no—
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—
276C23C2×#68611yescharacteristic
277Q8—42no—
278Q8—42no—
279Q8—81no—
280Q8—81no—
281D4—202no—
282D4—202no—
283D4—401no—
284D4—401no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—42no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—82no—
293C2×C4—401no—
294C2×C4—402no—
295C2×C4C4×C22⋊D511yescharacteristic
296C2×C4C2×#68611yescharacteristic
297C2×C4#408511yescharacteristic
298C2×C4#408611yescharacteristic
299C2×C4#409611yescharacteristic
300C2×C4#409611yescharacteristic
301C8—22no—
302C8D5×C22⋊C411yescharacteristic
303C8#402711yescharacteristic
304C8#403011yescharacteristic
305C8#403111yescharacteristic
306C5#1323811yescharacteristic, complemented, Sylow
307C22—404no—
308C22—402no—
309C22—801no—
310C22—801no—
311C22—802no—
312C22C4×#68611yescharacteristic
313C22#6532711yescharacteristic
314C22#6536211yescharacteristic
315C22#6546812yes—
316C22#6548212yes—
317C4—42no—
318C4—82no—
319C4—161no—
320C4—801no—
321C4#6524611yescharacteristic
322C4C4×#68611yescharacteristic
323C4#6532711yescharacteristic
324C4#6534811yescharacteristic
325C2—802no—
326C2#1060044011yescharacteristic
327C2#1060170612yes—
328C2#1060187712yes—
329C2#1060210711yescharacteristic
330C2#1060211411yescharacteristic
subgroupG/H
centerC23C2×#686
commutatorC2×C5×C8C22×C4
FrattiniC22×C8C22×D5
FittingC5×#1969C2
socleC23×C5C2×D8
prime radicalC22×D40C22
cosocleC22×C5×C8C23
hypercenter#1969D5
hypocenterC5#13238
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1969

Complements

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

NH ≅ G/Ntype
2. C5×#1969C2semidirect
3. C2×#64784C2semidirect
5. C2×#64709C2semidirect
7. C2×#64681C2semidirect
16. C2×#3960C4semidirect
69. #1969D5semidirect
113. #672C22⋊C4semidirect
306. C5#13238semidirect

Maximal subgroups

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

subgroupindex
C22×#39602
C5×#19692
C2×#647842
C2×#647112
C2×#647092
#106005692
C2×#646812
#132385