Finite Group Databasebeta

← C53×#3241 #20272178

Subgroups — C53×#3241 #20272178

Order 6784.

332 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
1C53×#544C211yesmaximal, characteristic, complemented
2C53×#540C211yesmaximal, characteristic
3C53×#501C211yesmaximal, characteristic, complemented
4C53×#499C211yesmaximal, characteristic, complemented
5C53×#490C211yesmaximal, characteristic, complemented
6C53×#486C211yesmaximal, characteristic, complemented
7C53×#482C211yesmaximal, characteristic, complemented
8C53×#482C211yesmaximal, characteristic, complemented
9C53×#481C211yesmaximal, characteristic, complemented
10C53×#480C211yesmaximal, characteristic, complemented
11C53×#478C211yesmaximal, characteristic, complemented
12C53×#478C211yesmaximal, characteristic, complemented
13C53×#476C211yesmaximal, characteristic, complemented
14C53×#474C211yesmaximal, characteristic, complemented
15C53×#433C211yesmaximal, characteristic, complemented
16C4⋊Q8×C53—21no—
17C4⋊Q8×C53C2211yescharacteristic
18C4⋊Q8×C53C2211yescharacteristic
19#127×C53C2211yescharacteristic
20#125×C53—21no—
21#125×C53C2211yescharacteristic
22#125×C53C2211yescharacteristic
23#125×C53C2211yescharacteristic
24#123×C53—21no—
25#123×C53—21no—
26C22⋊Q8×C53—21no—
27C22⋊Q8×C53—21no—
28#121×C53—21no—
29#121×C53—21no—
30#121×C53C2211yescharacteristic
31#121×C53C2211yescharacteristic
32C4×D4×C53C2211yescharacteristic
33C4×D4×C53C2211yescharacteristic
34#117×C53C2211yescharacteristic
35#117×C53C2211yescharacteristic
36C2×C4⋊C4×C53C2211yescharacteristic
37#107×C53C2211yescharacteristic
38#107×C53C2211yescharacteristic
39#107×C53C2211yescharacteristic
40#107×C53C2211yescharacteristic
41#106×C53C2211yescharacteristic
42#106×C53C2211yescharacteristic
43#106×C53C2211yescharacteristic
44#106×C53C2211yescharacteristic
45C4⋊C8×C53C2211yescharacteristic
46C4⋊C8×C53C2211yescharacteristic
47#102×C53C2211yescharacteristic
48#102×C53C2211yescharacteristic
49#102×C53C2211yescharacteristic
50#102×C53C2211yescharacteristic
51#102×C53C2211yescharacteristic
52#102×C53C2211yescharacteristic
53#102×C53C2211yescharacteristic
54#102×C53C2211yescharacteristic
55C22⋊C8×C53C2211yescharacteristic
56C22⋊C8×C53C2211yescharacteristic
57#97×C53C2211yescharacteristic
58C4×C8×C53C2211yescharacteristic
59C2×Q8×C53—21no—
60C2×Q8×C53—21no—
61C2×D4×C53—21no—
62C2×D4×C53—21no—
63C2×D4×C53—21no—
64C2×D4×C53—21no—
65C2×D4×C53C2311yescharacteristic
66C2×D4×C53C2311yescharacteristic
67C22×C4×C53—21no—
68C22×C4×C53—21no—
69C22×C4×C53—21no—
70C22×C4×C53C2311yescharacteristic
71C2×C8×C53C2311yescharacteristic
72C2×C8×C53C2311yescharacteristic
73C2×C8×C53C2311yescharacteristic
74C2×C8×C53C2311yescharacteristic
75C4⋊C4×C53—21no—
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×C53D411yescharacteristic
85C4⋊C4×C53D411yescharacteristic
86C4⋊C4×C53C2311yescharacteristic
87C4⋊C4×C53C2311yescharacteristic
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×C53D411yescharacteristic
98C22⋊C4×C53D411yescharacteristic
99C42×C53—21no—
100C42×C53C2311yescharacteristic
101C42×C53C2311yescharacteristic
102C23×C53—21no—
103C23×C53—21no—
104C23×C53C2×D411yescharacteristic
105Q8×C53—81no—
106Q8×C53—81no—
107D4×C53—21no—
108D4×C53—21no—
109D4×C53—21no—
110D4×C53—21no—
111D4×C53—81no—
112D4×C53—81no—
113D4×C53—81no—
114D4×C53—81no—
115C2×C4×C53—21no—
116C2×C4×C53—21no—
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—81no—
124C2×C4×C53—81no—
125C2×C4×C53—81no—
126C2×C4×C53C2×D411yescharacteristic
127C2×C4×C53C2×D411yescharacteristic
128C2×C4×C53C2×D411yescharacteristic
129C2×C4×C53C2×D411yescharacteristic
130C2×C4×C53C2×D411yescharacteristic
131C2×C4×C53C2411yescharacteristic
132C8×C53—21no—
133C8×C53—21no—
134C8×C53—21no—
135C8×C53—21no—
136C22×C53—21no—
137C22×C53—21no—
138C22×C53—21no—
139C22×C53—41no—
140C22×C53—41no—
141C22×C53—41no—
142C22×C53—41no—
143C22×C53—41no—
144C22×C53—41no—
145C22×C53C22×D411yescharacteristic
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×C532−1+411yescharacteristic
158C4×C532−1+411yescharacteristic
159#3241C5311yesmaximal, characteristic, direct product factor, Sylow
160C2×C53—41no—
161C2×C53—81no—
162C2×C53—81no—
163C2×C53#53611yescharacteristic
164C2×C53#57611yescharacteristic
165C2×C53#57711yescharacteristic
166#544C2×C5311yescharacteristic, complemented
167#540C2×C5311yescharacteristic
168#501C2×C5311yescharacteristic, complemented
169#499C2×C5311yescharacteristic, complemented
170#490C2×C5311yescharacteristic, complemented
171#486C2×C5311yescharacteristic, complemented
172#482C2×C5311yescharacteristic, complemented
173#482C2×C5311yescharacteristic, complemented
174#481C2×C5311yescharacteristic, complemented
175#480C2×C5311yescharacteristic, complemented
176#478C2×C5311yescharacteristic, complemented
177#478C2×C5311yescharacteristic, complemented
178#476C2×C5311yescharacteristic, complemented
179#474C2×C5311yescharacteristic, complemented
180#433C2×C5311yescharacteristic, complemented
181C53#324111yescharacteristic, direct product factor, Sylow
182C4⋊Q8—21no—
183C4⋊Q8C22×C5311yescharacteristic
184C4⋊Q8C22×C5311yescharacteristic
185#127C22×C5311yescharacteristic
186#125—21no—
187#125C22×C5311yescharacteristic
188#125C22×C5311yescharacteristic
189#125C22×C5311yescharacteristic
190#123—21no—
191#123—21no—
192C22⋊Q8—21no—
193C22⋊Q8—21no—
194#121—21no—
195#121—21no—
196#121C22×C5311yescharacteristic
197#121C22×C5311yescharacteristic
198C4×D4C22×C5311yescharacteristic
199C4×D4C22×C5311yescharacteristic
200#117C22×C5311yescharacteristic
201#117C22×C5311yescharacteristic
202C2×C4⋊C4C22×C5311yescharacteristic
203#107C22×C5311yescharacteristic
204#107C22×C5311yescharacteristic
205#107C22×C5311yescharacteristic
206#107C22×C5311yescharacteristic
207#106C22×C5311yescharacteristic
208#106C22×C5311yescharacteristic
209#106C22×C5311yescharacteristic
210#106C22×C5311yescharacteristic
211C4⋊C8C22×C5311yescharacteristic
212C4⋊C8C22×C5311yescharacteristic
213#102C22×C5311yescharacteristic
214#102C22×C5311yescharacteristic
215#102C22×C5311yescharacteristic
216#102C22×C5311yescharacteristic
217#102C22×C5311yescharacteristic
218#102C22×C5311yescharacteristic
219#102C22×C5311yescharacteristic
220#102C22×C5311yescharacteristic
221C22⋊C8C22×C5311yescharacteristic
222C22⋊C8C22×C5311yescharacteristic
223#97C22×C5311yescharacteristic
224C4×C8C22×C5311yescharacteristic
225C2×Q8—21no—
226C2×Q8—21no—
227C2×D4—21no—
228C2×D4—21no—
229C2×D4—21no—
230C2×D4—21no—
231C2×D4C23×C5311yescharacteristic
232C2×D4C23×C5311yescharacteristic
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4C23×C5311yescharacteristic
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⋊C4C23×C5311yescharacteristic
253C4⋊C4C23×C5311yescharacteristic
254C4⋊C4C23×C5311yescharacteristic
255C4⋊C4C23×C5311yescharacteristic
256C4⋊C4C23×C5311yescharacteristic
257C4⋊C4C23×C5311yescharacteristic
258C22⋊C4—21no—
259C22⋊C4—21no—
260C22⋊C4—21no—
261C22⋊C4—21no—
262C22⋊C4—21no—
263C22⋊C4D4×C5311yescharacteristic
264C22⋊C4D4×C5311yescharacteristic
265C42—21no—
266C42C23×C5311yescharacteristic
267C42C23×C5311yescharacteristic
268C23—21no—
269C23—21no—
270C23C2×D4×C5311yescharacteristic
271Q8—81no—
272Q8—81no—
273D4—21no—
274D4—21no—
275D4—21no—
276D4—21no—
277D4—81no—
278D4—81no—
279D4—81no—
280D4—81no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—81no—
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×C4C24×C5311yescharacteristic
298C8—21no—
299C8—21no—
300C8—21no—
301C8—21no—
302C22—21no—
303C22—21no—
304C22—21no—
305C22—41no—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—41no—
310C22—41no—
311C22C22×D4×C5311yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—21no—
317C4—41no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—41no—
323C42−1+4×C5311yescharacteristic
324C42−1+4×C5311yescharacteristic
325C2—41no—
326C2—81no—
327C2—81no—
328C2C53×#53611yescharacteristic
329C2C53×#57611yescharacteristic
330C2C53×#57711yescharacteristic
subgroupG/H
center, socleC22×C53C22×D4
commutator, Frattini, cosocleC2×C4C24×C53
prime radicalC53×#540C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C53 ◁ #117×C53 ◁ G

Complements

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

NH ≅ G/Ntype
1. C53×#544C2semidirect
3. C53×#501C2semidirect
4. C53×#499C2semidirect
5. C53×#490C2semidirect
6. C53×#486C2semidirect
7. C53×#482C2semidirect
8. C53×#482C2semidirect
9. C53×#481C2semidirect
10. C53×#480C2semidirect
11. C53×#478C2semidirect
12. C53×#478C2semidirect
13. C53×#476C2semidirect
14. C53×#474C2semidirect
15. C53×#433C2semidirect
159. #3241C53direct (N × H)
166. #544C2×C53semidirect
168. #501C2×C53semidirect
169. #499C2×C53semidirect
170. #490C2×C53semidirect
171. #486C2×C53semidirect
172. #482C2×C53semidirect
173. #482C2×C53semidirect
174. #481C2×C53semidirect
175. #480C2×C53semidirect
176. #478C2×C53semidirect
177. #478C2×C53semidirect
178. #476C2×C53semidirect
179. #474C2×C53semidirect
180. #433C2×C53semidirect
181. C53#3241direct (N × H)

Maximal subgroups

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

subgroupindex
C53×#5442
C53×#5402
C53×#5012
C53×#4992
C53×#4902
C53×#4862
C53×#4822
C53×#4812
C53×#4802
C53×#4782
C53×#4762
C53×#4742
C53×#4332
#324153