Finite Group Databasebeta

← #11992745

Subgroups — #11992745

Order 1280.

522 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Dic5×#117C211yesmaximal, characteristic
2C5×#1458C211yesmaximal, characteristic
3#10602364C211yesmaximal, characteristic
4#10598228C212yesmaximal, complemented
5#10598227C212yesmaximal, complemented
6C2×C5×#117C2211yescharacteristic
7C2×#4072C411yescharacteristic
8C22×C4×Dic5C411yescharacteristic
9C5×#431C2212yes—
10C4⋊C4×Dic5—21no—
11C4⋊C4×Dic5—21no—
12C22⋊C4×Dic5—21no—
13C22⋊C4×Dic5—21no—
14#65221C411yescharacteristic
15#65221C2211yescharacteristic
16C42×Dic5C411yescharacteristic
17C42×Dic5C2211yescharacteristic
18#65214C2212yes—
19C5×#324—21no—
20C5×#323—21no—
21#64748—21no—
22#64745—21no—
23#8731—51nomaximal, Sylow
24C23×C4×C5C2×C411yescharacteristic
25C23×Dic5—21no—
26C5×#117—22no—
27C5×#117—22no—
28C2×C5×C4⋊C4D411yescharacteristic
29C2×C5×C4⋊C4D411yescharacteristic
30C2×C5×C22⋊C4D411yescharacteristic
31C2×C5×C22⋊C4D411yescharacteristic
32C2×C42×C5C2×C411yescharacteristic
33C2×C42×C5C2311yescharacteristic
34C2×C22⋊Dic5—21no—
35#4072—22no—
36#4072C814yescomplemented
37C2×C4⋊Dic5—21no—
38C2×C4×Dic5—21no—
39C2×C4×Dic5—22no—
40C2×C4×Dic5—22no—
41C2×C4×Dic5—21no—
42C2×C4×Dic5—21no—
43C2×C4×Dic5—21no—
44C2×C4×Dic5—21no—
45C2×C4×Dic5C2×C411yescharacteristic
46C2×C4×Dic5C2×C411yescharacteristic
47C2×C4×Dic5C2×C411yescharacteristic
48C2×C4×Dic5C2×C411yescharacteristic
49C5×C4⋊C8—22no—
50C5×C22⋊C8—22no—
51C4×C5×C8—22no—
52#3963—21no—
53#3963—21no—
54#3963—21no—
55#3963—21no—
56C22⋊#168—22no—
57C4⋊#168—22no—
58C4×#168—22no—
59C4×#117—51no—
60#1458—51no—
61#1458D511yescharacteristic
62#1276—52no—
63#1274—52no—
64C24×C5C22⋊C411yescharacteristic
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5—21no—
69C22×C4×C5C22⋊C411yescharacteristic
70C22×C4×C5C22⋊C411yescharacteristic
71C22×C4×C5C22⋊C411yescharacteristic
72C22×C4×C5C2×C812yes—
73C22×C4×C5M1612yes—
74C22×C4×C5C22×C411yescharacteristic
75C22×C4×C5C2×D411yescharacteristic
76C22×C4×C5C2×D411yescharacteristic
77C22×Dic5—21no—
78C22×Dic5—24no—
79C22×Dic5—21no—
80C22×Dic5—21no—
81C22×Dic5—21no—
82C22×Dic5—42no—
83C22×Dic5—42no—
84C2×C5×C8—42no—
85C5×C4⋊C4—22no—
86C5×C4⋊C4—22no—
87C5×C22⋊C4—22no—
88C5×C22⋊C4—22no—
89C42×C5—21no—
90C42×C5—21no—
91C42×C5#4112yes—
92C42×C5#4112yes—
93C22⋊Dic5—24no—
94C4⋊Dic5—24no—
95C4×Dic5—24no—
96C4×Dic5—21no—
97C4×Dic5—21no—
98C4×Dic5—21no—
99C4×Dic5—21no—
100C4×Dic5—42no—
101C4×Dic5—42no—
102C4×Dic5—42no—
103C4×Dic5—42no—
104C4×Dic5C2×C812yes—
105C4×Dic5C2×C812yes—
106C4×Dic5M1612yes—
107C4×Dic5M1612yes—
108C2×#168—42no—
109C2×#117—51no—
110C2×#117C2×D511yescharacteristic
111C22×C42—51no—
112#431—52no—
113#431C2×D512yes—
114C4×C4⋊C4—101no—
115C4×C4⋊C4—101no—
116C4×C22⋊C4—101no—
117C4×C22⋊C4—101no—
118#376—51no—
119#376—51no—
120C43—51no—
121C43—51no—
122#324—21no—
123#324—101no—
124#323—21no—
125#323—101no—
126C23×C5—21no—
127C23×C5—21no—
128C23×C5—41no—
129C23×C5—41no—
130C23×C5C22⋊C812yes—
131C23×C5C2×C22⋊C411yescharacteristic
132C2×C4×C5—21no—
133C2×C4×C5—21no—
134C2×C4×C5—22no—
135C2×C4×C5—22no—
136C2×C4×C5—22no—
137C2×C4×C5—22no—
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5—41no—
141C2×C4×C5—41no—
142C2×C4×C5—41no—
143C2×C4×C5—41no—
144C2×C4×C5C22⋊C812yes—
145C2×C4×C5#11711yescharacteristic
146C2×C4×C5#11711yescharacteristic
147C2×C4×C5#12312yes—
148C2×C4×C5#12312yes—
149C2×C4×C5C22×C811yescharacteristic
150C2×C4×C5C2×M1611yescharacteristic
151C2×C4×C5C2×M1611yescharacteristic
152C2×C4×C5C2×M1611yescharacteristic
153C2×Dic5—22no—
154C2×Dic5—22no—
155C2×Dic5—22no—
156C2×Dic5—22no—
157C2×Dic5—22no—
158C2×Dic5—22no—
159C2×Dic5—48no—
160C2×Dic5—41no—
161C2×Dic5—41no—
162C2×Dic5—41no—
163C2×Dic5—41no—
164C2×Dic5—41no—
165C2×Dic5—41no—
166C5×C8—82no—
167#168—82no—
168C23×C4—101no—
169C23×C4C4×D511yescharacteristic
170#117—22no—
171#117—22no—
172#117—54no—
173#117—102no—
174C2×C4⋊C4—101no—
175C2×C4⋊C4D2011yescharacteristic
176C2×C4⋊C4C22⋊D511yescharacteristic
177C2×C22⋊C4—101no—
178C2×C22⋊C4D2011yescharacteristic
179C2×C22⋊C4C22⋊D511yescharacteristic
180C2×C42—51no—
181C2×C42—51no—
182C2×C42—51no—
183C2×C42—51no—
184C2×C42—102no—
185C2×C42—102no—
186C2×C42—101no—
187C2×C42—101no—
188C2×C42—101no—
189C2×C42—101no—
190C2×C42—101no—
191C2×C42C4×D511yescharacteristic
192C2×C42C22×D511yescharacteristic
193C4⋊C8—22no—
194C4⋊C8—102no—
195C22⋊C8—22no—
196C22⋊C8—102no—
197C4×C8—22no—
198C4×C8—102no—
199#95—101no—
200#95—101no—
201#95—101no—
202#95—101no—
203C22×C5—21no—
204C22×C5—21no—
205C22×C5—22no—
206C22×C5—42no—
207C22×C5—42no—
208C22×C5—41no—
209C22×C5—41no—
210C22×C5#38111yescharacteristic
211C22×C5C2×C22⋊C811yescharacteristic
212C22×C5#40711yescharacteristic
213C4×C5—22no—
214C4×C5—22no—
215C4×C5—22no—
216C4×C5—41no—
217C4×C5—41no—
218C4×C5#43111yescharacteristic
219C4×C5#43111yescharacteristic
220C4×C5#43211yescharacteristic
221C4×C5#43211yescharacteristic
222Dic5—24no—
223Dic5—42no—
224Dic5—42no—
225Dic5—42no—
226C24#68511yescharacteristic
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—101no—
232C22×C4—104no—
233C22×C4—101no—
234C22×C4—101no—
235C22×C4—101no—
236C22×C4—202no—
237C22×C4—202no—
238C22×C4C8×D512yes—
239C22×C4#67612yes—
240C22×C4#68511yescharacteristic
241C22×C4#68511yescharacteristic
242C22×C4#68511yescharacteristic
243C22×C4C2×C4×D511yescharacteristic
244C22×C4C2×D2011yescharacteristic
245C22×C4C2×C22⋊D511yescharacteristic
246C2×C8—42no—
247C2×C8—202no—
248C4⋊C4—22no—
249C4⋊C4—22no—
250C4⋊C4—104no—
251C22⋊C4—22no—
252C22⋊C4—22no—
253C22⋊C4—104no—
254C42—21no—
255C42—21no—
256C42—52no—
257C42—52no—
258C42—52no—
259C42—52no—
260C42—104no—
261C42—101no—
262C42—101no—
263C42—101no—
264C42—101no—
265C42—202no—
266C42—202no—
267C42—202no—
268C42—202no—
269C42#71112yes—
270C42#71112yes—
271C2×C5—21no—
272C2×C5—21no—
273C2×C5—42no—
274C2×C5#181711yescharacteristic
275C2×C5#182711yescharacteristic
276C2×C5#182711yescharacteristic
277C23—21no—
278C23—21no—
279C23—41no—
280C23—41no—
281C23#395212yes—
282C23C2×#68511yescharacteristic
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—22no—
288C2×C4—22no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—102no—
296C2×C4—102no—
297C2×C4—102no—
298C2×C4—102no—
299C2×C4—102no—
300C2×C4—102no—
301C2×C4—208no—
302C2×C4—201no—
303C2×C4—201no—
304C2×C4—201no—
305C2×C4—201no—
306C2×C4—201no—
307C2×C4—201no—
308C2×C4#395212yes—
309C2×C4#402311yescharacteristic
310C2×C4#402311yescharacteristic
311C2×C4#403212yes—
312C2×C4C2×C8×D511yescharacteristic
313C2×C4C2×#67611yescharacteristic
314C2×C4D5×M1611yescharacteristic
315C2×C4D5×M1611yescharacteristic
316C2×C4#408112yes—
317C8—82no—
318C8—402no—
319C5#873111yescharacteristic, complemented, Sylow
320C22—21no—
321C22—21no—
322C22—22no—
323C22—42no—
324C22—42no—
325C22—41no—
326C22—41no—
327C22#6523211yescharacteristic
328C22C2×#395211yescharacteristic
329C22#6541511yescharacteristic
330C4—22no—
331C4—22no—
332C4—22no—
333C4—41no—
334C4—41no—
335C4—104no—
336C4—202no—
337C4—202no—
338C4—202no—
339C4#6500711yescharacteristic
340C4#6500711yescharacteristic
341C4#6500811yescharacteristic
342C4#6500811yescharacteristic
343C2—21no—
344C2—21no—
345C2—42no—
346C2#1060070311yescharacteristic
347C2#1060083211yescharacteristic
348C2#1060092411yescharacteristic
subgroupG/H
centerC2×C4#4023
commutatorC2×C4×C5C22×C8
FrattiniC2×C42C22×D5
FittingC5×#1458C2
socleC22×C5#381
prime radicalC24×C5C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1458D5
hypocenterC5#8731
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1458

Complements

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

NH ≅ G/Ntype
4. #10598228C2semidirect
5. #10598227C2semidirect
36. #4072C8semidirect
319. C5#8731semidirect

Maximal subgroups

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

subgroupindex
Dic5×#1172
C5×#14582
#106023642
#105982282
#105982272
#87315