Finite Group Databasebeta

← #12017122

Subgroups — #12017122

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×#1974C211yesmaximal, characteristic
2C2×#64787C211yesmaximal, characteristic
3#10602870C211yesmaximal, characteristic
4C2×#64713C211yesmaximal, characteristic, complemented
5#10600572C211yesmaximal, characteristic, complemented
6#10598220C211yesmaximal, characteristic, complemented
7#10598148C211yesmaximal, characteristic, complemented
8C2×C5×#135C2211yescharacteristic
9C2×C5×#108C2211yescharacteristic
10C2×C5×#104—21no—
11C5×#408—21no—
12C2×C4×C5×C8C2211yescharacteristic
13C2×#3951C2211yescharacteristic
14#65395C2211yescharacteristic
15#65390—21no—
16C22×#672C2211yescharacteristic
17C22×#672C2211yescharacteristic
18#64787—22no—
19#64784C411yescharacteristic, complemented
20#64784C411yescharacteristic, complemented
21#64782C411yescharacteristic, complemented
22#64782C411yescharacteristic, complemented
23#64743—21no—
24#64713—22no—
25#13134—51nomaximal, Sylow
26C2×C5×#41—21no—
27C5×#135—21no—
28C5×#135—21no—
29C5×#135—21no—
30C5×#135—21no—
31C2×C5×Q16C2×C411yescharacteristic
32C2×C5×SD16—21no—
33C2×C5×D8C2×C411yescharacteristic
34C2×C5×M16—21no—
35C22×C5×C8D411yescharacteristic
36C22×C5×C8C2311yescharacteristic
37C2×C42×C5D411yescharacteristic
38#4072—21no—
39C2×#681—21no—
40C5×#108—21no—
41C5×#108—21no—
42C5×#104—42no—
43C5×C22⋊C8—41no—
44C5×C22⋊C8—41no—
45C4×C5×C8—21no—
46C4×C5×C8—21no—
47#3951—21no—
48#3951D412yes—
49#3950C2×C411yescharacteristic
50#3950C2×C411yescharacteristic
51#3949—21no—
52#3947—41no—
53C8×Dic5—41no—
54C2×#672—21no—
55C2×#672—21no—
56C2×#672—21no—
57C2×#672—21no—
58C2×#672—21no—
59C2×#672C2×C411yescharacteristic
60C2×#672C2×C411yescharacteristic
61C2×#368—51no—
62C2×#359—51no—
63#2138—51no—
64#1974D511yescharacteristic
65#1772—51no—
66#1382—51no—
67#1374—51no—
68C5×#41—41no—
69C5×#41—41no—
70C5×#41—41no—
71C5×#41—41no—
72C2×C5×Q8—21no—
73C2×C5×D4—21no—
74C2×C5×D4—41no—
75C22×C4×C5—21no—
76C22×C4×C5—41no—
77C22×C4×C5C2×D411yescharacteristic
78C5×Q16—21no—
79C5×Q16—21no—
80C5×SD16—41no—
81C5×SD16—41no—
82C5×D8—21no—
83C5×D8—21no—
84C5×M16—41no—
85C5×M16—41no—
86C2×C5×C8—21no—
87C2×C5×C8—21no—
88C2×C5×C8—41no—
89C2×C5×C8D811yescharacteristic
90C2×C5×C8D811yescharacteristic
91C2×C5×C8C22×C411yescharacteristic
92C2×C5×C8C2×D411yescharacteristic
93C2×C5×C8#4111yescharacteristic
94C2×C5×C8#4111yescharacteristic
95C2×C5×C8#4111yescharacteristic
96C2×C5×C8#4111yescharacteristic
97C42×C5—21no—
98C42×C5—21no—
99C22⋊Dic5—41no—
100C4⋊Dic5—21no—
101C4⋊Dic5—21no—
102C4×Dic5—41no—
103#681—22no—
104#681—41no—
105C2×#168—41no—
106#672—21no—
107#672—21no—
108#672—41no—
109C2×#135C2×D511yescharacteristic
110C22×C16—51no—
111C22×C16—51no—
112C2×#108—51no—
113C2×#108C2×D511yescharacteristic
114#427—51no—
115C2×#104—21no—
116#408—21no—
117#405—101no—
118C2×C4×C8C2×D511yescharacteristic
119#368—102no—
120#359—102no—
121#358—51no—
122#358—51no—
123#357—51no—
124#357—51no—
125#339—101no—
126C23×C5—41no—
127C23×C5#13511yescharacteristic
128C5×Q8—41no—
129C5×Q8—41no—
130C5×D4—41no—
131C5×D4—41no—
132C5×D4—81no—
133C5×D4—81no—
134C2×C4×C5—22no—
135C2×C4×C5—41no—
136C2×C4×C5—41no—
137C2×C4×C5—41no—
138C2×C4×C5—81no—
139C2×C4×C5—81no—
140C2×C4×C5C4×D411yescharacteristic
141C2×C4×C5#12111yescharacteristic
142C2×C4×C5#12311yescharacteristic
143C2×C4×C5C2×D811yescharacteristic
144C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C5#13711yescharacteristic
146C2×Dic5—41no—
147C2×Dic5—41no—
148C5×C8—21no—
149C5×C8—21no—
150C5×C8—81no—
151C5×C8#11711yescharacteristic
152C5×C8C4×D411yescharacteristic
153C5×C8#12411yescharacteristic
154C5×C8#12611yescharacteristic
155#168—42no—
156C2×#41—21no—
157#135—21no—
158#135—21no—
159#135—21no—
160#135—21no—
161C2×Q16C4×D511yescharacteristic
162C2×SD16—21no—
163C2×D8C4×D511yescharacteristic
164C2×M16—21no—
165C2×M16—101no—
166C22×C8C22⋊D511yescharacteristic
167C22×C8C22×D511yescharacteristic
168#117—101no—
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—21no—
179#108—52no—
180#108—101no—
181#107—51no—
182#107—51no—
183#106—101no—
184#104—42no—
185C22⋊C8—41no—
186C22⋊C8—41no—
187#97—201no—
188C4×C8—21no—
189C4×C8—21no—
190C4×C8—201no—
191C22×C5—21no—
192C22×C5—21no—
193C22×C5—81no—
194C22×C5—81no—
195C22×C5—81no—
196C22×C5C4×D811yescharacteristic
197C22×C5#46411yescharacteristic
198C22×C5#48211yescharacteristic
199C4×C5—42no—
200C4×C5—81no—
201C4×C5#38811yescharacteristic
202C4×C5#44011yescharacteristic
203C4×C5#45911yescharacteristic
204C4×C5#48011yescharacteristic
205Dic5—81no—
206Dic5—81no—
207#41—41no—
208#41—41no—
209#41—41no—
210#41—41no—
211C2×Q8—21no—
212C2×D4—21no—
213C2×D4—41no—
214C22×C4—21no—
215C22×C4—41no—
216C22×C4C2×C22⋊D511yescharacteristic
217Q16—21no—
218Q16—21no—
219SD16—41no—
220SD16—41no—
221D8—21no—
222D8—21no—
223M16—41no—
224M16—41no—
225M16—102no—
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×C8#70911yescharacteristic
235C2×C8D4×D511yescharacteristic
236C2×C8#71111yescharacteristic
237C2×C8#71111yescharacteristic
238C2×C8#71111yescharacteristic
239C4⋊C4—101no—
240C4⋊C4—101no—
241C22⋊C4—201no—
242C42—21no—
243C42—21no—
244C42—201no—
245C16—101no—
246C16—101no—
247C16—201no—
248C2×C5—21no—
249C2×C5—21no—
250C2×C5—161no—
251C2×C5#192511yescharacteristic
252C2×C5#217811yescharacteristic
253C2×C5#217911yescharacteristic
254C23—41no—
255C23#409611yescharacteristic
256Q8—41no—
257Q8—41no—
258D4—41no—
259D4—41no—
260D4—81no—
261D4—81no—
262C2×C4—22no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—81no—
267C2×C4—81no—
268C2×C4—201no—
269C2×C4—201no—
270C2×C4C4×C22⋊D511yescharacteristic
271C2×C4C2×#68611yescharacteristic
272C2×C4#407811yescharacteristic
273C2×C4#408111yescharacteristic
274C2×C4#408411yescharacteristic
275C2×C4#409711yescharacteristic
276C8—21no—
277C8—21no—
278C8—81no—
279C8—202no—
280C8#402311yescharacteristic
281C8#402511yescharacteristic
282C8#402711yescharacteristic
283C8#403111yescharacteristic
284C5#1313411yescharacteristic, complemented, Sylow
285C22—21no—
286C22—21no—
287C22—81no—
288C22—81no—
289C22—81no—
290C22C4×#68611yescharacteristic
291C22#6532411yescharacteristic
292C22#6534311yescharacteristic
293C4—42no—
294C4—81no—
295C4—401no—
296C4—401no—
297C4#6523311yescharacteristic
298C4#6530711yescharacteristic
299C4#6532211yescharacteristic
300C4#6536111yescharacteristic
301C2—21no—
302C2—21no—
303C2—161no—
304C2#1060042911yescharacteristic
305C2#1060171411yescharacteristic
306C2#1060171511yescharacteristic
subgroupG/H
centerC2×C4C2×#686
commutatorC2×C5×C8C22×C4
FrattiniC22×C8C22×D5
FittingC5×#1974C2
socleC22×C5C4×D8
prime radicalC2×C5×#135C22
cosocleC22×C5×C8C23
hypercenter#1974D5
hypocenterC5#13134
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4×C8 ◁ #1974

Complements

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

NH ≅ G/Ntype
4. C2×#64713C2semidirect
5. #10600572C2semidirect
6. #10598220C2semidirect
7. #10598148C2semidirect
19. #64784C4semidirect
20. #64784C4semidirect
21. #64782C4semidirect
22. #64782C4semidirect
284. C5#13134semidirect

Maximal subgroups

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

subgroupindex
C5×#19742
C2×#647872
#106028702
C2×#647132
#106005722
#105982202
#105981482
#131345