Finite Group Databasebeta

← #12017125

Subgroups — #12017125

Order 1280.

324 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#1772C211yesmaximal, characteristic, complemented
2C2×#64717C211yesmaximal, characteristic
3C2×#64713C211yesmaximal, characteristic, complemented
4#10601444C211yesmaximal, characteristic
5#10600588C211yesmaximal, characteristic
6#10598215C211yesmaximal, characteristic, complemented
7#10598148C211yesmaximal, characteristic, complemented
8C2×#4050C2211yescharacteristic
9C2×C5×#108C2211yescharacteristic
10C5×#427C2211yescharacteristic
11C5×#405—21no—
12C2×C4×C5×C8C2211yescharacteristic
13#65399—21no—
14C2×#3951C2211yescharacteristic
15C22×#672C2211yescharacteristic
16C22×#672C2211yescharacteristic
17C2×#3937—21no—
18C5×#339—21no—
19#64717—22no—
20#64713—22no—
21#64712C411yescharacteristic, complemented
22#64712C411yescharacteristic, complemented
23#64711C411yescharacteristic, complemented
24#64711C411yescharacteristic, complemented
25#13134—51nomaximal, Sylow
26C2×#709—21no—
27C2×C5×M16—21no—
28C22×C5×C8D411yescharacteristic
29C22×C5×C8C2311yescharacteristic
30C5×#117—21no—
31C2×C42×C5D411yescharacteristic
32C2×#681—21no—
33C2×Dic20C2×C411yescharacteristic
34#4050—21no—
35#4050—21no—
36#4050—21no—
37#4050—21no—
38C2×D40C2×C411yescharacteristic
39C2×#677—21no—
40C5×#108—21no—
41C5×#108D412yes—
42C5×#107C2×C411yescharacteristic
43C5×#107C2×C411yescharacteristic
44C5×#106—21no—
45C5×#97—41no—
46C4×C5×C8—21no—
47C4×C5×C8—21no—
48C4×C5×C8—41no—
49#3952—41no—
50#3952—41no—
51#3951—21no—
52#3951—21no—
53C2×#672—21no—
54C2×#672—21no—
55C2×#672—21no—
56C2×#672—21no—
57C2×#672—21no—
58C2×#672C2×C411yescharacteristic
59C2×#672C2×C411yescharacteristic
60#3937—42no—
61C2×#368—51no—
62C2×#359—51no—
63#2138—51no—
64#1974—51no—
65#1772D511yescharacteristic, complemented
66#1382—51no—
67#1374—51no—
68C22×C4×C5—21no—
69C22×C4×C5C2×D411yescharacteristic
70C2×C22⋊D5—41no—
71#709—41no—
72#709—41no—
73#709—41no—
74#709—41no—
75C2×D20—21no—
76C2×C4×D5—41no—
77C2×Dic10—21no—
78C5×M16—22no—
79C5×M16—41no—
80C2×C5×C8—21no—
81C2×C5×C8—21no—
82C2×C5×C8—41no—
83C2×C5×C8D811yescharacteristic
84C2×C5×C8D811yescharacteristic
85C2×C5×C8C22×C411yescharacteristic
86C2×C5×C8C2×D411yescharacteristic
87C2×C5×C8#4111yescharacteristic
88C2×C5×C8#4111yescharacteristic
89C2×C5×C8#4111yescharacteristic
90C2×C5×C8#4111yescharacteristic
91C5×C4⋊C4—21no—
92C5×C4⋊C4—21no—
93C5×C22⋊C4—41no—
94C42×C5—21no—
95C42×C5—21no—
96C42×C5—41no—
97#681—41no—
98#681—41no—
99C2×#168—41no—
100Dic20—21no—
101Dic20—21no—
102D40—21no—
103D40—21no—
104#677—41no—
105#677—41no—
106#672—21no—
107#672—21no—
108#672—41no—
109C2×#135—51no—
110C22×C16—51no—
111C22×C16—51no—
112C2×#108—51no—
113C2×#108C2×D511yescharacteristic
114#427C2×D511yescharacteristic
115C2×#104—101no—
116#408—101no—
117#405—21no—
118C2×C4×C8C2×D511yescharacteristic
119#368—102no—
120#359—102no—
121#358—51no—
122#358—51no—
123#357—51no—
124#357—51no—
125#339—21no—
126C23×C5#13511yescharacteristic
127C22×D5—41no—
128C2×C4×C5—22no—
129C2×C4×C5—41no—
130C2×C4×C5—41no—
131C2×C4×C5—41no—
132C2×C4×C5—41no—
133C2×C4×C5C4×D411yescharacteristic
134C2×C4×C5#12111yescharacteristic
135C2×C4×C5#12311yescharacteristic
136C2×C4×C5C2×D811yescharacteristic
137C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C5#13711yescharacteristic
139C22⋊D5—81no—
140C22⋊D5—81no—
141C2×Dic5—41no—
142D20—41no—
143D20—41no—
144C4×D5—81no—
145C4×D5—81no—
146Dic10—41no—
147Dic10—41no—
148C5×C8—21no—
149C5×C8—21no—
150C5×C8—42no—
151C5×C8#11711yescharacteristic
152C5×C8C4×D411yescharacteristic
153C5×C8#12411yescharacteristic
154C5×C8#12611yescharacteristic
155#168—81no—
156C2×#41—101no—
157#135—101no—
158#135—101no—
159#135—101no—
160#135—101no—
161C2×Q16—51no—
162C2×SD16—101no—
163C2×D8—51no—
164C2×M16—21no—
165C2×M16—101no—
166C22×C8C22⋊D511yescharacteristic
167C22×C8C22×D511yescharacteristic
168#117—21no—
169C2×C42C22⋊D511yescharacteristic
170C2×C16—51no—
171C2×C16—51no—
172C2×C16—101no—
173C2×C16—101no—
174C2×C16—101no—
175C2×C16—101no—
176C2×C16—101no—
177#108—21no—
178#108—101no—
179#108—101no—
180#108D2012yes—
181#107C4×D511yescharacteristic
182#107C4×D511yescharacteristic
183#106—21no—
184#104—202no—
185C22⋊C8—201no—
186C22⋊C8—201no—
187#97—41no—
188C4×C8—21no—
189C4×C8—21no—
190C4×C8—41no—
191C22×C5—21no—
192C22×C5—21no—
193C22×C5C4×D811yescharacteristic
194C22×C5#46411yescharacteristic
195C22×C5#48211yescharacteristic
196C2×D5—81no—
197C2×D5—81no—
198C2×D5—81no—
199C4×C5—42no—
200C4×C5—81no—
201C4×C5—81no—
202C4×C5#38811yescharacteristic
203C4×C5#44011yescharacteristic
204C4×C5#45911yescharacteristic
205C4×C5#48011yescharacteristic
206Dic5—81no—
207#41—201no—
208#41—201no—
209#41—201no—
210#41—201no—
211C2×Q8—101no—
212C2×D4—101no—
213C2×D4—201no—
214C22×C4—21no—
215C22×C4—201no—
216C22×C4C2×C22⋊D511yescharacteristic
217Q16—101no—
218Q16—101no—
219SD16—201no—
220SD16—201no—
221D8—101no—
222D8—101no—
223M16—22no—
224M16—41no—
225M16—201no—
226M16—201no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—41no—
230C2×C8—201no—
231C2×C8#68611yescharacteristic
232C2×C8#68611yescharacteristic
233C2×C8C2×C4×D511yescharacteristic
234C2×C8C2×D2011yescharacteristic
235C2×C8#70911yescharacteristic
236C2×C8#70911yescharacteristic
237C2×C8#70911yescharacteristic
238C2×C8#70911yescharacteristic
239C4⋊C4—21no—
240C4⋊C4—21no—
241C22⋊C4—41no—
242C42—21no—
243C42—21no—
244C42—41no—
245C16—101no—
246C16—101no—
247C16—201no—
248C2×C5—21no—
249C2×C5—21no—
250C2×C5#192511yescharacteristic
251C2×C5#217811yescharacteristic
252C2×C5#217911yescharacteristic
253D5—161no—
254C23—201no—
255C23#409611yescharacteristic
256Q8—201no—
257Q8—201no—
258D4—201no—
259D4—201no—
260D4—401no—
261D4—401no—
262C2×C4—22no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—201no—
268C2×C4—401no—
269C2×C4—401no—
270C2×C4C4×C22⋊D511yescharacteristic
271C2×C4#407511yescharacteristic
272C2×C4#407611yescharacteristic
273C2×C4C2×#68611yescharacteristic
274C2×C4#408811yescharacteristic
275C2×C4#409511yescharacteristic
276C8—21no—
277C8—21no—
278C8—42no—
279C8—401no—
280C8#401811yescharacteristic
281C8C4×D2011yescharacteristic
282C8#402111yescharacteristic
283C8#402211yescharacteristic
284C5#1313411yescharacteristic, complemented, Sylow
285C22—21no—
286C22—21no—
287C22—401no—
288C22—401no—
289C22—401no—
290C22#6529211yescharacteristic
291C22C4×#68611yescharacteristic
292C22#6531711yescharacteristic
293C4—42no—
294C4—81no—
295C4—81no—
296C4—401no—
297C4#6522911yescharacteristic
298C4#6525611yescharacteristic
299C4#6530411yescharacteristic
300C4#6531511yescharacteristic
301C2—21no—
302C2—21no—
303C2—801no—
304C2#1060025511yescharacteristic
305C2#1060171411yescharacteristic
306C2#1060171511yescharacteristic
subgroupG/H
centerC2×C4C2×#686
commutatorC2×C5×C8C22×C4
FrattiniC22×C8C22×D5
FittingC5×#1772C2
socleC22×C5C4×D8
prime radicalC2×#4050C22
cosocleC22×C5×C8C23
hypercenter#1772D5
hypocenterC5#13134
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4×C8 ◁ #1772

Complements

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

NH ≅ G/Ntype
1. C5×#1772C2semidirect
3. C2×#64713C2semidirect
6. #10598215C2semidirect
7. #10598148C2semidirect
21. #64712C4semidirect
22. #64712C4semidirect
23. #64711C4semidirect
24. #64711C4semidirect
65. #1772D5semidirect
284. C5#13134semidirect

Maximal subgroups

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

subgroupindex
C5×#17722
C2×#647172
C2×#647132
#106014442
#106005882
#105982152
#105981482
#131345