Finite Group Databasebeta

← #11997890

Subgroups — #11997890

Order 1280.

384 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
1#10601236C211yesmaximal, characteristic
2Dic5×C4⋊C8C211yesmaximal, characteristic
3C2×#64700C211yesmaximal, characteristic
4C4×#3946C211yesmaximal, characteristic
5C2×#64678C211yesmaximal, characteristic
6C5×#1277C211yesmaximal, characteristic
7#10598194C211yesmaximal, characteristic
8C2×C5×C4⋊C8C2211yescharacteristic
9C2×C5×C4⋊C8C2211yescharacteristic
10C2×C4×C5×C8C2211yescharacteristic
11C2×#3946C411yescharacteristic
12C2×#3946C411yescharacteristic
13C2×C8×Dic5—21no—
14C42×Dic5C2211yescharacteristic
15C2×C4⋊#168C2211yescharacteristic
16C2×C4⋊#168C2211yescharacteristic
17C2×C4×#168C2211yescharacteristic
18#64770—21no—
19#64770—21no—
20#64770—21no—
21#64770C411yescharacteristic
22#64770C411yescharacteristic
23#64700—22no—
24#64678—22no—
25#9603—51nomaximal, Sylow
26C22×C5×C8—21no—
27C22×C5×C8—21no—
28C22×C5×C8C2×C411yescharacteristic
29C22×C5×C8C2×C411yescharacteristic
30C2×C42×C5C2311yescharacteristic
31C2×C4×Dic5C2×C411yescharacteristic
32C2×C4×Dic5C2×C411yescharacteristic
33C2×C4×Dic5D411yescharacteristic
34C2×C4×Dic5D411yescharacteristic
35C2×C4×Dic5Q811yescharacteristic
36C2×C4×Dic5Q811yescharacteristic
37C22×#168—21no—
38C22×#168—21no—
39C22×#168C2×C411yescharacteristic
40C22×#168C2×C411yescharacteristic
41C5×C4⋊C8—21no—
42C5×C4⋊C8—21no—
43C5×C4⋊C8—21no—
44C5×C4⋊C8Q812yes—
45C4×C5×C8—21no—
46C4×C5×C8—21no—
47#3946—22no—
48#3946C814yescomplemented
49C8×Dic5—42no—
50C4⋊#168—21no—
51C4⋊#168—21no—
52C4⋊#168—21no—
53C4⋊#168D412yes—
54C4×#168—21no—
55C4×#168—21no—
56#1831—51no—
57C4×C4⋊C8—51no—
58C4×C4⋊C8—51no—
59C2×#335—51no—
60C2×#334—51no—
61#1277—51no—
62#1277D511yescharacteristic
63C22×C4×C5C22×C411yescharacteristic
64C22×C4×C5C2×D411yescharacteristic
65C22×C4×C5C2×Q811yescharacteristic
66C22×Dic5C4⋊C411yescharacteristic
67C22×Dic5C4⋊C411yescharacteristic
68C22×Dic5C4⋊C411yescharacteristic
69C22×Dic5C4⋊C411yescharacteristic
70C2×C5×C8—21no—
71C2×C5×C8—21no—
72C2×C5×C8—21no—
73C2×C5×C8—22no—
74C2×C5×C8—21no—
75C2×C5×C8—21no—
76C2×C5×C8—41no—
77C2×C5×C8—41no—
78C2×C5×C8—41no—
79C2×C5×C8—41no—
80C2×C5×C8—41no—
81C2×C5×C8C2×C812yes—
82C42×C5C2×D411yescharacteristic
83C42×C5C2×Q811yescharacteristic
84C42×C5#4111yescharacteristic
85C42×C5#4111yescharacteristic
86C4×Dic5—21no—
87C4×Dic5—21no—
88C4×Dic5—21no—
89C4×Dic5—21no—
90C4×Dic5—21no—
91C4×Dic5—21no—
92C4×Dic5—22no—
93C4×Dic5—41no—
94C4×Dic5C2×C812yes—
95C4×Dic5M1612yes—
96C2×#168—21no—
97C2×#168—21no—
98C2×#168—21no—
99C2×#168—22no—
100C2×#168—21no—
101C2×#168—21no—
102C2×#168—41no—
103C2×#168—41no—
104C2×#168—41no—
105C2×#168—41no—
106C2×#168—41no—
107C2×#168C2×C812yes—
108C2×C4⋊C8—51no—
109C2×C4⋊C8—51no—
110C2×C4⋊C8—51no—
111C2×C4⋊C8—51no—
112C2×C4⋊C8C2×D511yescharacteristic
113C2×C4⋊C8C2×D511yescharacteristic
114C2×C4×C8—51no—
115C2×C4×C8—101no—
116C2×C4×C8C2×D511yescharacteristic
117C43—51no—
118#336—51no—
119#336—51no—
120#336—101no—
121#336—101no—
122#336—101no—
123#335—102no—
124#334—102no—
125C23×C5C2×C4⋊C411yescharacteristic
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5C4×D411yescharacteristic
129C2×C4×C5C4×Q811yescharacteristic
130C2×C4×C5#12111yescharacteristic
131C2×C4×C5C22⋊Q811yescharacteristic
132C2×C4×C5#12511yescharacteristic
133C2×C4×C5C4⋊Q811yescharacteristic
134C2×C4×C5C22×C811yescharacteristic
135C2×C4×C5C2×M1611yescharacteristic
136C2×C4×C5#13111yescharacteristic
137C2×C4×C5#13111yescharacteristic
138C2×C4×C5#13511yescharacteristic
139C2×C4×C5#13511yescharacteristic
140C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C5#13711yescharacteristic
142C2×Dic5—21no—
143C2×Dic5—21no—
144C2×Dic5—21no—
145C2×Dic5—21no—
146C2×Dic5—21no—
147C2×Dic5—21no—
148C2×Dic5—21no—
149C2×Dic5—21no—
150C2×Dic5—21no—
151C2×Dic5C4⋊C812yes—
152C2×Dic5C4⋊C812yes—
153C2×Dic5#10812yes—
154C5×C8—22no—
155C5×C8—41no—
156C5×C8—42no—
157C5×C8—81no—
158#168—22no—
159#168—41no—
160#168—42no—
161#168—81no—
162C22×C8—21no—
163C22×C8—21no—
164C22×C8—51no—
165C22×C8—51no—
166C22×C8—101no—
167C22×C8—101no—
168C22×C8C4×D511yescharacteristic
169C22×C8C4×D511yescharacteristic
170C2×C42—51no—
171C2×C42—51no—
172C2×C42—51no—
173C2×C42—51no—
174C2×C42—51no—
175C2×C42—51no—
176C2×C42C22×D511yescharacteristic
177C4⋊C8—21no—
178C4⋊C8—21no—
179C4⋊C8—21no—
180C4⋊C8—54no—
181C4⋊C8—52no—
182C4⋊C8—102no—
183C4⋊C8—101no—
184C4⋊C8—101no—
185C4⋊C8—101no—
186C4⋊C8Dic1012yes—
187C4×C8—21no—
188C4×C8—21no—
189C4×C8—101no—
190C4×C8—101no—
191C4×C8—202no—
192C22×C5#38911yescharacteristic
193C22×C5C2×C4⋊C811yescharacteristic
194C22×C5#42411yescharacteristic
195C22×C5#42711yescharacteristic
196C22×C5#42811yescharacteristic
197C22×C5C2×#10811yescharacteristic
198C22×C5#43011yescharacteristic
199C4×C5—21no—
200C4×C5—21no—
201C4×C5C8×D411yescharacteristic
202C4×C5#43611yescharacteristic
203C4×C5C8×Q811yescharacteristic
204C4×C5#44611yescharacteristic
205C4×C5#46311yescharacteristic
206C4×C5#46411yescharacteristic
207C4×C5#47811yescharacteristic
208C4×C5#47911yescharacteristic
209Dic5—22no—
210Dic5—22no—
211Dic5—22no—
212Dic5—41no—
213C22×C4—51no—
214C22×C4—51no—
215C22×C4—51no—
216C22×C4—51no—
217C22×C4C2×C4×D511yescharacteristic
218C22×C4D4×D511yescharacteristic
219C22×C4Q8×D511yescharacteristic
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—22no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—52no—
232C2×C8—101no—
233C2×C8—101no—
234C2×C8—101no—
235C2×C8—102no—
236C2×C8—101no—
237C2×C8—101no—
238C2×C8—201no—
239C2×C8—201no—
240C2×C8—201no—
241C2×C8—201no—
242C2×C8—201no—
243C2×C8C8×D512yes—
244C42—52no—
245C42—52no—
246C42—102no—
247C42—101no—
248C42—101no—
249C42—101no—
250C42—101no—
251C42—101no—
252C42—101no—
253C42—201no—
254C42C2×Dic1011yescharacteristic
255C42#70911yescharacteristic
256C42D4×D511yescharacteristic
257C42#71111yescharacteristic
258C2×C5#156411yescharacteristic
259C2×C5#156511yescharacteristic
260C2×C5#157211yescharacteristic
261C2×C5#157311yescharacteristic
262C2×C5#193911yescharacteristic
263C2×C5#194911yescharacteristic
264C2×C5#195011yescharacteristic
265C23D5×C4⋊C411yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—52no—
269C2×C4—52no—
270C2×C4—52no—
271C2×C4—101no—
272C2×C4—101no—
273C2×C4—101no—
274C2×C4—101no—
275C2×C4—101no—
276C2×C4—101no—
277C2×C4—101no—
278C2×C4—101no—
279C2×C4—101no—
280C2×C4C4×Dic1011yescharacteristic
281C2×C4#402411yescharacteristic
282C2×C4#402711yescharacteristic
283C2×C4#403011yescharacteristic
284C2×C4#403411yescharacteristic
285C2×C4#403511yescharacteristic
286C2×C4C2×C8×D511yescharacteristic
287C2×C4#404711yescharacteristic
288C2×C4D5×M1611yescharacteristic
289C2×C4#405311yescharacteristic
290C2×C4#405811yescharacteristic
291C2×C4#406011yescharacteristic
292C2×C4#406111yescharacteristic
293C2×C4#406511yescharacteristic
294C8—22no—
295C8—42no—
296C8—41no—
297C8—81no—
298C8—102no—
299C8—202no—
300C8—201no—
301C8—401no—
302C5#960311yescharacteristic, complemented, Sylow
303C22#6493611yescharacteristic
304C22D5×C4⋊C811yescharacteristic
305C22#6512811yescharacteristic
306C22#6515011yescharacteristic
307C22#6516911yescharacteristic
308C22D5×#10811yescharacteristic
309C22#6518211yescharacteristic
310C4—21no—
311C4—21no—
312C4—102no—
313C4—102no—
314C4—102no—
315C4—201no—
316C4C8×Dic1011yescharacteristic
317C4#6499011yescharacteristic
318C4#6501411yescharacteristic
319C4#6501811yescharacteristic
320C4#6505511yescharacteristic
321C4#6505611yescharacteristic
322C4#6508511yescharacteristic
323C4#6510811yescharacteristic
324C2#1059932111yescharacteristic
325C2#1059932711yescharacteristic
326C2#1059936011yescharacteristic
327C2#1059936611yescharacteristic
328C2#1059941011yescharacteristic
329C2#1059959111yescharacteristic
330C2#1059971311yescharacteristic
subgroupG/H
centerC22×C4D4×D5
commutatorC2×C4×C5C22×C8
FrattiniC2×C42C22×D5
FittingC5×#1277C2
socle, prime radicalC23×C5C2×C4⋊C4
cosocleC2×C42×C5C23
hypercenter#1277D5
hypocenterC5#9603
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
48. #3946C8semidirect
302. C5#9603semidirect

Maximal subgroups

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

subgroupindex
#106012362
Dic5×C4⋊C82
C2×#647002
C4×#39462
C2×#646782
C5×#12772
#105981942
#96035