Finite Group Databasebeta

← #12019066

Subgroups — #12019066

Order 1280.

382 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×C4⋊C16C211yesmaximal, characteristic, complemented
2C2×#64729C211yesmaximal, characteristic
3C2×#64729C211yesmaximal, characteristic
4C2×#64725C211yesmaximal, characteristic, complemented
5#10600569C211yesmaximal, characteristic
6#10600563C211yesmaximal, characteristic, complemented
7#10598297C211yesmaximal, characteristic, complemented
8C22×D40C2211yescharacteristic
9C22×C5×C16C2211yescharacteristic
10C22×C5×C16C2211yescharacteristic
11C2×C4×C5×C8C2211yescharacteristic
12C2×#3953—21no—
13C2×#3950C2211yescharacteristic
14C2×#3950C2211yescharacteristic
15C2×#3950C2211yescharacteristic
16#65228—21no—
17#65217—21no—
18C5×C4⋊C16—22no—
19#64771—21no—
20#64729—22no—
21#64729—22no—
22#64725—22no—
23#13476—51nomaximal, Sylow
24C22×D20—21no—
25C22×C5×C8D411yescharacteristic
26C22×C5×C8C2311yescharacteristic
27C2×C42×C5D411yescharacteristic
28C2×#685—41no—
29C2×#685—41no—
30C2×C4⋊Dic5—21no—
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5—21no—
33C2×#683—41no—
34C2×D40—21no—
35C2×D40—21no—
36C2×D40—21no—
37C2×D40—21no—
38C2×D40—21no—
39C2×D40Q812yes—
40C2×C5×C16—21no—
41C2×C5×C16—21no—
42C2×C5×C16—21no—
43C2×C5×C16—21no—
44C2×C5×C16—21no—
45C2×C5×C16D412yes—
46C4×C5×C8—21no—
47C4×C5×C8—21no—
48#3963—41no—
49#3953—42no—
50#3950—21no—
51#3950—21no—
52#3950—21no—
53#3950—21no—
54#3950—21no—
55#3950D412yes—
56C2×#367—51no—
57C2×C4⋊C16D511yescharacteristic, complemented
58C2×#357—51no—
59C2×#357—51no—
60#1970—51no—
61#1942—51no—
62#1380—51no—
63C23×D5—41no—
64C22×C4×C5D811yescharacteristic
65C22×C4×C5D811yescharacteristic
66C22×C4×C5C2×D411yescharacteristic
67C22×Dic5—41no—
68C22×Dic5—41no—
69C22×Dic5—41no—
70C2×D20—22no—
71C2×D20—41no—
72C2×D20—41no—
73C2×D20—41no—
74C2×D20—41no—
75C2×D20—41no—
76C2×C5×C8—21no—
77C2×C5×C8—21no—
78C2×C5×C8—21no—
79C2×C5×C8C2×D411yescharacteristic
80C2×C5×C8C2×D411yescharacteristic
81C2×C5×C8C2×Q811yescharacteristic
82C2×C5×C8#4111yescharacteristic
83C2×C5×C8#4111yescharacteristic
84C2×C5×C8#4111yescharacteristic
85C42×C5—21no—
86C42×C5—21no—
87#685—82no—
88#685—82no—
89C4⋊Dic5—22no—
90C4⋊Dic5—41no—
91C4⋊Dic5—41no—
92C4⋊Dic5—41no—
93C4⋊Dic5—41no—
94C4⋊Dic5—41no—
95#683—82no—
96D40—22no—
97D40—22no—
98D40—41no—
99D40—41no—
100C5×C16—22no—
101C5×C16—41no—
102C22×D8—51no—
103C22×C16C2×D511yescharacteristic
104C22×C16C2×D511yescharacteristic
105C2×#107—51no—
106C2×#107—51no—
107C2×#107—51no—
108C2×#102—101no—
109C2×C4×C8C2×D511yescharacteristic
110#390—101no—
111#389—101no—
112#367—102no—
113C4⋊C16—22no—
114#357—102no—
115#357—102no—
116#340—101no—
117C23×C5C2×D811yescharacteristic
118C22×D5—42no—
119C22×D5—81no—
120C22×D5—81no—
121C22×D5—81no—
122C22×D5—81no—
123C22×D5—81no—
124C22×D5—81no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5SD3212yes—
131C2×C4×C5#12111yescharacteristic
132C2×C4×C5#12111yescharacteristic
133C2×C4×C5C22⋊Q811yescharacteristic
134C2×C4×C5#13511yescharacteristic
135C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C5#13711yescharacteristic
137C2×Dic5—42no—
138C2×Dic5—81no—
139C2×Dic5—81no—
140C2×Dic5—81no—
141C2×Dic5—81no—
142C2×Dic5—81no—
143C2×Dic5—81no—
144C2×Dic5—81no—
145C2×Dic5—81no—
146D20—42no—
147D20—42no—
148D20—81no—
149D20—81no—
150C5×C8—41no—
151C5×C8#12111yescharacteristic
152C5×C8C22⋊Q811yescharacteristic
153C5×C8C22⋊Q811yescharacteristic
154C5×C8#12611yescharacteristic
155C22×D4—101no—
156C2×D8—52no—
157C2×D8—101no—
158C2×D8—101no—
159C2×D8—101no—
160C2×D8—101no—
161C2×D8—101no—
162C22×C8D2011yescharacteristic
163C22×C8C22×D511yescharacteristic
164C2×C4⋊C4—101no—
165C2×C4⋊C4—101no—
166C2×C4⋊C4—101no—
167C2×C4⋊C4—201no—
168C2×C22⋊C4—201no—
169C2×C22⋊C4—201no—
170C2×C42D2011yescharacteristic
171C2×C16—21no—
172C2×C16—21no—
173C2×C16—21no—
174C2×C16—21no—
175C2×C16—21no—
176C2×C16C22⋊D512yes—
177#107—52no—
178#107—101no—
179#107—101no—
180#107—101no—
181#107—101no—
182#107—101no—
183#102—202no—
184C4×C8—21no—
185C4×C8—21no—
186#95—201no—
187C22×C5#45911yescharacteristic
188C22×C5#46611yescharacteristic
189C22×C5#47411yescharacteristic
190C22×C5C2×SD3211yescharacteristic
191C22×C5#50811yescharacteristic
192C22×C5#50911yescharacteristic
193C22×C5#50911yescharacteristic
194C2×D5—82no—
195C2×D5—82no—
196C2×D5—82no—
197C2×D5—161no—
198C2×D5—161no—
199C2×D5—161no—
200C2×D5—161no—
201C4×C5—22no—
202C4×C5—41no—
203C4×C5#39611yescharacteristic
204C4×C5#46411yescharacteristic
205C4×C5#46811yescharacteristic
206C4×C5#47811yescharacteristic
207Dic5—82no—
208Dic5—161no—
209Dic5—161no—
210C24—201no—
211C2×D4—102no—
212C2×D4—201no—
213C2×D4—201no—
214C2×D4—201no—
215C2×D4—201no—
216C2×D4—201no—
217C22×C4—201no—
218C22×C4—201no—
219C22×C4—201no—
220C22×C4D4011yescharacteristic
221C22×C4D4011yescharacteristic
222C22×C4C2×D2011yescharacteristic
223D8—102no—
224D8—102no—
225D8—201no—
226D8—201no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8#70911yescharacteristic
231C2×C8D4×D511yescharacteristic
232C2×C8#71111yescharacteristic
233C2×C8Q8×D511yescharacteristic
234C2×C8#71311yescharacteristic
235C2×C8C2×C22⋊D511yescharacteristic
236C4⋊C4—102no—
237C4⋊C4—201no—
238C4⋊C4—201no—
239C4⋊C4—201no—
240C4⋊C4—201no—
241C4⋊C4—201no—
242C4⋊C4—402no—
243C22⋊C4—402no—
244C22⋊C4—402no—
245C42—21no—
246C42—21no—
247C16—22no—
248C16—41no—
249C2×C5#206711yescharacteristic
250C2×C5#220711yescharacteristic
251C2×C5#221011yescharacteristic
252C2×C5#221711yescharacteristic
253C2×C5#221811yescharacteristic
254C2×C5#222611yescharacteristic
255C2×C5#222811yescharacteristic
256D5—162no—
257C23—202no—
258C23—401no—
259C23—401no—
260C23—401no—
261C23—401no—
262C23—401no—
263C23—401no—
264C23C2×D4011yescharacteristic
265D4—202no—
266D4—202no—
267D4—401no—
268D4—401no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—202no—
275C2×C4—401no—
276C2×C4—401no—
277C2×C4—401no—
278C2×C4—401no—
279C2×C4—401no—
280C2×C4—401no—
281C2×C4—401no—
282C2×C4—401no—
283C2×C4#393212yes—
284C2×C4#404111yescharacteristic
285C2×C4#404311yescharacteristic
286C2×C4#405011yescharacteristic
287C2×C4#405411yescharacteristic
288C2×C4#405511yescharacteristic
289C2×C4#407611yescharacteristic
290C8—41no—
291C8#404211yescharacteristic
292C8#404411yescharacteristic
293C8#408511yescharacteristic
294C8#409211yescharacteristic
295C5#1347611yescharacteristic, complemented, Sylow
296C22—402no—
297C22—402no—
298C22—402no—
299C22—801no—
300C22—801no—
301C22—801no—
302C22—801no—
303C22#6513211yescharacteristic
304C22#6513511yescharacteristic
305C22C2×#393211yescharacteristic
306C22#6519311yescharacteristic
307C22#6519711yescharacteristic
308C22#6519711yescharacteristic
309C22#6540411yescharacteristic
310C4—22no—
311C4—41no—
312C4—402no—
313C4—801no—
314C4—801no—
315C4#6513411yescharacteristic
316C4#6513611yescharacteristic
317C4#6528311yescharacteristic
318C4#6542311yescharacteristic
319C2—802no—
320C2#1060008111yescharacteristic
321C2#1060008311yescharacteristic
322C2#1060008411yescharacteristic
323C2#1060008511yescharacteristic
324C2#1060127711yescharacteristic
325C2#1060220711yescharacteristic
326C2#1060223611yescharacteristic
subgroupG/H
centerC23C2×D40
commutator, cosocleC22×C5×C8C23
FrattiniC22×C8C22×D5
FittingC2×C5×C4⋊C16C2
socleC23×C5C2×D8
prime radicalC22×D40C22
hypercenterC2×C4⋊C16D5
hypocenterC5#13476
LCSG ▷ C22×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4⋊C16

Complements

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

NH ≅ G/Ntype
1. C2×C5×C4⋊C16C2semidirect
4. C2×#64725C2semidirect
6. #10600563C2semidirect
7. #10598297C2semidirect
57. C2×C4⋊C16D5semidirect
295. C5#13476semidirect

Maximal subgroups

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

subgroupindex
C2×C5×C4⋊C162
C2×#647292
C2×#647252
#106005692
#106005632
#105982972
#134765