Finite Group Databasebeta

← C53×#3376 #20272313

Subgroups — C53×#3376 #20272313

Order 6784.

346 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#556C211yesmaximal, characteristic, complemented
2C53×#554C211yesmaximal, characteristic, complemented
3C53×#491C211yesmaximal, characteristic, complemented
4C53×#489C211yesmaximal, characteristic, complemented
5C53×#488C211yesmaximal, characteristic, complemented
6C53×#479C211yesmaximal, characteristic, complemented
7C53×#478C211yesmaximal, characteristic, complemented
8C53×#475C211yesmaximal, characteristic, complemented
9C53×#463C211yesmaximal, characteristic
10C53×#463C211yesmaximal, characteristic
11C53×#461C211yesmaximal, characteristic, complemented
12C53×#446C211yesmaximal, characteristic, complemented
13C53×#442C211yesmaximal, characteristic
14C53×#440C211yesmaximal, characteristic, complemented
15C4×SD16×C53C211yesmaximal, characteristic, complemented
16C2×SD16×C53C2211yescharacteristic
17C2×SD16×C53C2211yescharacteristic
18C2×D8×C53C2211yescharacteristic
19C4⋊Q8×C53C2211yescharacteristic
20C4⋊Q8×C53C2211yescharacteristic
21#126×C53—21no—
22#126×C53—21no—
23#125×C53C2211yescharacteristic
24#125×C53C2211yescharacteristic
25#124×C53C2211yescharacteristic
26#124×C53C2211yescharacteristic
27C22⋊Q8×C53—21no—
28C22⋊Q8×C53—21no—
29C22⋊Q8×C53—21no—
30C22⋊Q8×C53—21no—
31C4×Q8×C53C2211yescharacteristic
32C4×Q8×C53C2211yescharacteristic
33C4×Q8×C53C2211yescharacteristic
34C4×D4×C53C2211yescharacteristic
35C4×D4×C53C2211yescharacteristic
36C4×D4×C53C2211yescharacteristic
37C4×D4×C53C2211yescharacteristic
38#117×C53—21no—
39C2×C4⋊C4×C53—21no—
40#107×C53C2211yescharacteristic
41#106×C53C2211yescharacteristic
42#106×C53C2211yescharacteristic
43C4⋊C8×C53C2211yescharacteristic
44C4⋊C8×C53C2211yescharacteristic
45C4⋊C8×C53C2211yescharacteristic
46#103×C53C2211yescharacteristic
47#103×C53C2211yescharacteristic
48#103×C53C2211yescharacteristic
49#103×C53C2211yescharacteristic
50#103×C53C2211yescharacteristic
51#103×C53C2211yescharacteristic
52#102×C53C2211yescharacteristic
53#102×C53C2211yescharacteristic
54#102×C53C2211yescharacteristic
55#102×C53C2211yescharacteristic
56#97×C53C2211yescharacteristic
57#97×C53C2211yescharacteristic
58C4×C8×C53C2211yescharacteristic
59C2×Q8×C53—21no—
60C2×Q8×C53D411yescharacteristic
61C2×Q8×C53C2311yescharacteristic
62C2×Q8×C53C2311yescharacteristic
63C2×D4×C53C2311yescharacteristic
64C2×D4×C53C2311yescharacteristic
65C22×C4×C53—21no—
66C22×C4×C53—21no—
67C22×C4×C53—21no—
68C22×C4×C53—21no—
69SD16×C53—22no—
70SD16×C53—22no—
71D8×C53—22no—
72C2×C8×C53C2311yescharacteristic
73C2×C8×C53C2311yescharacteristic
74C2×C8×C53C2311yescharacteristic
75C2×C8×C53C2311yescharacteristic
76C4⋊C4×C53—21no—
77C4⋊C4×C53—21no—
78C4⋊C4×C53—21no—
79C4⋊C4×C53—21no—
80C4⋊C4×C53—21no—
81C4⋊C4×C53—21no—
82C4⋊C4×C53—21no—
83C4⋊C4×C53—21no—
84C4⋊C4×C53—21no—
85C4⋊C4×C53D411yescharacteristic
86C4⋊C4×C53D411yescharacteristic
87C4⋊C4×C53D411yescharacteristic
88C4⋊C4×C53C2311yescharacteristic
89C4⋊C4×C53C2311yescharacteristic
90C4⋊C4×C53C2311yescharacteristic
91C4⋊C4×C53C2311yescharacteristic
92C22⋊C4×C53—21no—
93C22⋊C4×C53—21no—
94C22⋊C4×C53—21no—
95C22⋊C4×C53—21no—
96C22⋊C4×C53—21no—
97C22⋊C4×C53—21no—
98C22⋊C4×C53—21no—
99C22⋊C4×C53—21no—
100C42×C53—21no—
101C42×C53—21no—
102C42×C53C2311yescharacteristic
103C42×C53C2311yescharacteristic
104C42×C53C2311yescharacteristic
105C23×C53—21no—
106C23×C53—21no—
107Q8×C53—21no—
108Q8×C53—21no—
109Q8×C53—21no—
110Q8×C53—21no—
111Q8×C53—41no—
112Q8×C53—81no—
113D4×C53—21no—
114D4×C53—21no—
115D4×C53—21no—
116D4×C53#4112yes—
117C2×C4×C53—21no—
118C2×C4×C53—21no—
119C2×C4×C53—21no—
120C2×C4×C53—21no—
121C2×C4×C53—21no—
122C2×C4×C53—21no—
123C2×C4×C53—42no—
124C2×C4×C53—42no—
125C2×C4×C53—81no—
126C2×C4×C53—81no—
127C2×C4×C53C2×D411yescharacteristic
128C2×C4×C53C2×D411yescharacteristic
129C2×C4×C53C2×D411yescharacteristic
130C2×C4×C53C2×D411yescharacteristic
131C2×C4×C53C2×D411yescharacteristic
132C2×C4×C53C2×D411yescharacteristic
133C2×C4×C53C2411yescharacteristic
134C8×C53—21no—
135C8×C53—21no—
136C8×C53—21no—
137C8×C53—21no—
138C22×C53—22no—
139C22×C53—41no—
140C22×C53—41no—
141C22×C53—41no—
142C22×C53—41no—
143C22×C53—41no—
144C22×C53C22×D411yescharacteristic
145C4×C53—21no—
146C4×C53—21no—
147C4×C53—21no—
148C4×C53—21no—
149C4×C53—21no—
150C4×C53—21no—
151C4×C53—41no—
152C4×C53—41no—
153C4×C53—41no—
154C4×C53—41no—
155C4×C53—41no—
156C4×C53—41no—
157C4×C53C2×#4111yescharacteristic
158C4×C532−1+411yescharacteristic
159#3376C5311yesmaximal, characteristic, direct product factor, Sylow
160C2×C53—42no—
161C2×C53—81no—
162C2×C53#54811yescharacteristic
163C2×C53#57511yescharacteristic
164C2×C53#57711yescharacteristic
165#556C2×C5311yescharacteristic, complemented
166#554C2×C5311yescharacteristic, complemented
167#491C2×C5311yescharacteristic, complemented
168#489C2×C5311yescharacteristic, complemented
169#488C2×C5311yescharacteristic, complemented
170#479C2×C5311yescharacteristic, complemented
171#478C2×C5311yescharacteristic, complemented
172#475C2×C5311yescharacteristic, complemented
173#463C2×C5311yescharacteristic
174#463C2×C5311yescharacteristic
175#461C2×C5311yescharacteristic, complemented
176#446C2×C5311yescharacteristic, complemented
177#442C2×C5311yescharacteristic
178#440C2×C5311yescharacteristic, complemented
179C4×SD16C2×C5311yescharacteristic, complemented
180C53#337611yescharacteristic, direct product factor, Sylow
181C2×SD16C22×C5311yescharacteristic
182C2×SD16C22×C5311yescharacteristic
183C2×D8C22×C5311yescharacteristic
184C4⋊Q8C22×C5311yescharacteristic
185C4⋊Q8C22×C5311yescharacteristic
186#126—21no—
187#126—21no—
188#125C22×C5311yescharacteristic
189#125C22×C5311yescharacteristic
190#124C22×C5311yescharacteristic
191#124C22×C5311yescharacteristic
192C22⋊Q8—21no—
193C22⋊Q8—21no—
194C22⋊Q8—21no—
195C22⋊Q8—21no—
196C4×Q8C22×C5311yescharacteristic
197C4×Q8C22×C5311yescharacteristic
198C4×Q8C22×C5311yescharacteristic
199C4×D4C22×C5311yescharacteristic
200C4×D4C22×C5311yescharacteristic
201C4×D4C22×C5311yescharacteristic
202C4×D4C22×C5311yescharacteristic
203#117—21no—
204C2×C4⋊C4—21no—
205#107C22×C5311yescharacteristic
206#106C22×C5311yescharacteristic
207#106C22×C5311yescharacteristic
208C4⋊C8C22×C5311yescharacteristic
209C4⋊C8C22×C5311yescharacteristic
210C4⋊C8C22×C5311yescharacteristic
211#103C22×C5311yescharacteristic
212#103C22×C5311yescharacteristic
213#103C22×C5311yescharacteristic
214#103C22×C5311yescharacteristic
215#103C22×C5311yescharacteristic
216#103C22×C5311yescharacteristic
217#102C22×C5311yescharacteristic
218#102C22×C5311yescharacteristic
219#102C22×C5311yescharacteristic
220#102C22×C5311yescharacteristic
221#97C22×C5311yescharacteristic
222#97C22×C5311yescharacteristic
223C4×C8C22×C5311yescharacteristic
224C2×Q8—21no—
225C2×Q8D4×C5311yescharacteristic
226C2×Q8C23×C5311yescharacteristic
227C2×Q8C23×C5311yescharacteristic
228C2×D4C23×C5311yescharacteristic
229C2×D4C23×C5311yescharacteristic
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234SD16—22no—
235SD16—22no—
236D8—22no—
237C2×C8C23×C5311yescharacteristic
238C2×C8C23×C5311yescharacteristic
239C2×C8C23×C5311yescharacteristic
240C2×C8C23×C5311yescharacteristic
241C4⋊C4—21no—
242C4⋊C4—21no—
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4D4×C5311yescharacteristic
251C4⋊C4D4×C5311yescharacteristic
252C4⋊C4D4×C5311yescharacteristic
253C4⋊C4C23×C5311yescharacteristic
254C4⋊C4C23×C5311yescharacteristic
255C4⋊C4C23×C5311yescharacteristic
256C4⋊C4C23×C5311yescharacteristic
257C22⋊C4—21no—
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—21no—
265C42—21no—
266C42—21no—
267C42C23×C5311yescharacteristic
268C42C23×C5311yescharacteristic
269C42C23×C5311yescharacteristic
270C23—21no—
271C23—21no—
272Q8—21no—
273Q8—21no—
274Q8—21no—
275Q8—21no—
276Q8—41no—
277Q8—81no—
278D4—21no—
279D4—21no—
280D4—21no—
281D4#41×C5312yes—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4C2×D4×C5311yescharacteristic
293C2×C4C2×D4×C5311yescharacteristic
294C2×C4C2×D4×C5311yescharacteristic
295C2×C4C2×D4×C5311yescharacteristic
296C2×C4C2×D4×C5311yescharacteristic
297C2×C4C2×D4×C5311yescharacteristic
298C2×C4C24×C5311yescharacteristic
299C8—21no—
300C8—21no—
301C8—21no—
302C8—21no—
303C22—22no—
304C22—41no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22C22×D4×C5311yescharacteristic
310C4—21no—
311C4—21no—
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—41no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4C2×#41×C5311yescharacteristic
323C42−1+4×C5311yescharacteristic
324C2—42no—
325C2—81no—
326C2C53×#54811yescharacteristic
327C2C53×#57511yescharacteristic
328C2C53×#57711yescharacteristic
subgroupG/H
center, socleC22×C53C22×D4
commutator, Frattini, cosocleC2×C4C24×C53
prime radicalC2×D8×C53C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C53 ◁ C4×Q8×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C53×#556C2semidirect
2. C53×#554C2semidirect
3. C53×#491C2semidirect
4. C53×#489C2semidirect
5. C53×#488C2semidirect
6. C53×#479C2semidirect
7. C53×#478C2semidirect
8. C53×#475C2semidirect
11. C53×#461C2semidirect
12. C53×#446C2semidirect
14. C53×#440C2semidirect
15. C4×SD16×C53C2semidirect
159. #3376C53direct (N × H)
165. #556C2×C53semidirect
166. #554C2×C53semidirect
167. #491C2×C53semidirect
168. #489C2×C53semidirect
169. #488C2×C53semidirect
170. #479C2×C53semidirect
171. #478C2×C53semidirect
172. #475C2×C53semidirect
175. #461C2×C53semidirect
176. #446C2×C53semidirect
178. #440C2×C53semidirect
179. C4×SD16C2×C53semidirect
180. C53#3376direct (N × H)

Maximal subgroups

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

subgroupindex
C53×#5562
C53×#5542
C53×#4912
C53×#4892
C53×#4882
C53×#4792
C53×#4782
C53×#4752
C53×#4632
C53×#4612
C53×#4462
C53×#4422
C53×#4402
C4×SD16×C532
#337653