Finite Group Databasebeta

← C53×#3179 #20272116

Subgroups — C53×#3179 #20272116

Order 6784.

374 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C53×#542C211yesmaximal, characteristic, complemented
2C53×#540C211yesmaximal, characteristic, complemented
3C53×#501C211yesmaximal, characteristic, complemented
4C53×#496C211yesmaximal, characteristic, complemented
5C53×#488C211yesmaximal, characteristic, complemented
6C53×#486C211yesmaximal, characteristic, complemented
7C53×#469C211yesmaximal, characteristic, complemented
8C53×#468C211yesmaximal, characteristic, complemented
9C53×#466C211yesmaximal, characteristic, complemented
10C53×#465C211yesmaximal, characteristic, complemented
11C53×#442C211yesmaximal, characteristic, complemented
12C53×#440C211yesmaximal, characteristic, complemented
13C4×SD16×C53C211yesmaximal, characteristic, complemented
14C4×D8×C53C211yesmaximal, characteristic, complemented
15C53×#405C211yesmaximal, characteristic, complemented
16C2×SD16×C53C2211yescharacteristic
17C2×SD16×C53C2211yescharacteristic
18C2×D8×C53C2211yescharacteristic
19C2×D8×C53C2211yescharacteristic
20C2×M16×C53C2211yescharacteristic
21C22×C8×C53C2211yescharacteristic
22C4⋊Q8×C53C2211yescharacteristic
23#127×C53C2211yescharacteristic
24#126×C53—21no—
25#125×C53C2211yescharacteristic
26#124×C53—21no—
27#124×C53C2211yescharacteristic
28#123×C53—21no—
29#123×C53—21no—
30#123×C53—21no—
31C22⋊Q8×C53—21no—
32C22⋊Q8×C53C2211yescharacteristic
33#121×C53—21no—
34#121×C53—21no—
35#121×C53C2211yescharacteristic
36#121×C53C2211yescharacteristic
37#121×C53C2211yescharacteristic
38C4×Q8×C53C2211yescharacteristic
39C4×D4×C53C2211yescharacteristic
40C4×D4×C53C2211yescharacteristic
41C4×D4×C53C2211yescharacteristic
42#117×C53C2211yescharacteristic
43#107×C53C2211yescharacteristic
44#107×C53C2211yescharacteristic
45#106×C53C2211yescharacteristic
46#106×C53C2211yescharacteristic
47#103×C53C2211yescharacteristic
48#103×C53C2211yescharacteristic
49#102×C53C2211yescharacteristic
50#102×C53C2211yescharacteristic
51#102×C53C2211yescharacteristic
52#102×C53C2211yescharacteristic
53#102×C53C2211yescharacteristic
54#102×C53C2211yescharacteristic
55#97×C53C2211yescharacteristic
56#97×C53C2211yescharacteristic
57C4×C8×C53C2211yescharacteristic
58C4×C8×C53C2211yescharacteristic
59C2×Q8×C53—21no—
60C2×Q8×C53C2311yescharacteristic
61C2×D4×C53—21no—
62C2×D4×C53—21no—
63C2×D4×C53—21no—
64C2×D4×C53—21no—
65C2×D4×C53—21no—
66C2×D4×C53C2311yescharacteristic
67C2×D4×C53C2311yescharacteristic
68C2×D4×C53C2311yescharacteristic
69C22×C4×C53—21no—
70C22×C4×C53—21no—
71C22×C4×C53—21no—
72C22×C4×C53C2311yescharacteristic
73SD16×C53—22no—
74SD16×C53—22no—
75D8×C53—22no—
76D8×C53—22no—
77M16×C53—22no—
78C2×C8×C53—22no—
79C2×C8×C53C2311yescharacteristic
80C2×C8×C53C2311yescharacteristic
81C2×C8×C53C2311yescharacteristic
82C2×C8×C53C2311yescharacteristic
83C4⋊C4×C53—21no—
84C4⋊C4×C53—21no—
85C4⋊C4×C53—21no—
86C4⋊C4×C53—21no—
87C4⋊C4×C53—21no—
88C4⋊C4×C53D411yescharacteristic
89C4⋊C4×C53D411yescharacteristic
90C4⋊C4×C53C2311yescharacteristic
91C4⋊C4×C53C2311yescharacteristic
92C4⋊C4×C53C2311yescharacteristic
93C4⋊C4×C53C2311yescharacteristic
94C22⋊C4×C53—21no—
95C22⋊C4×C53—21no—
96C22⋊C4×C53—21no—
97C22⋊C4×C53—21no—
98C22⋊C4×C53—21no—
99C22⋊C4×C53—21no—
100C22⋊C4×C53—21no—
101C22⋊C4×C53—21no—
102C22⋊C4×C53—21no—
103C22⋊C4×C53D411yescharacteristic
104C22⋊C4×C53D411yescharacteristic
105C42×C53—21no—
106C42×C53C2311yescharacteristic
107C42×C53C2311yescharacteristic
108C23×C53—21no—
109C23×C53—21no—
110C23×C53—21no—
111C23×C53C2×D411yescharacteristic
112Q8×C53—21no—
113Q8×C53—21no—
114Q8×C53—81no—
115D4×C53—21no—
116D4×C53—21no—
117D4×C53—21no—
118D4×C53—21no—
119D4×C53—21no—
120D4×C53—21no—
121D4×C53—81no—
122D4×C53—81no—
123D4×C53—81no—
124D4×C53—81no—
125D4×C53—81no—
126C2×C4×C53—21no—
127C2×C4×C53—21no—
128C2×C4×C53—21no—
129C2×C4×C53—21no—
130C2×C4×C53—21no—
131C2×C4×C53—21no—
132C2×C4×C53—21no—
133C2×C4×C53—81no—
134C2×C4×C53—81no—
135C2×C4×C53—81no—
136C2×C4×C53C2×D411yescharacteristic
137C2×C4×C53C2×D411yescharacteristic
138C2×C4×C53C2×D411yescharacteristic
139C2×C4×C53C2×D411yescharacteristic
140C2×C4×C53C2×D411yescharacteristic
141C2×C4×C53C2411yescharacteristic
142C8×C53—21no—
143C8×C53—21no—
144C8×C53#4112yes—
145C8×C53#4112yes—
146C22×C53—21no—
147C22×C53—21no—
148C22×C53—21no—
149C22×C53—41no—
150C22×C53—41no—
151C22×C53—41no—
152C22×C53—41no—
153C22×C53—41no—
154C22×C53—41no—
155C22×C53—41no—
156C22×C53—41no—
157C22×C53—41no—
158C22×C53C22×D411yescharacteristic
159C4×C53—21no—
160C4×C53—21no—
161C4×C53—21no—
162C4×C53—21no—
163C4×C53—21no—
164C4×C53—41no—
165C4×C53—41no—
166C4×C53—41no—
167C4×C53—41no—
168C4×C53—41no—
169C4×C53C2×#4111yescharacteristic
170C4×C53C2×#4111yescharacteristic
171#3179C5311yesmaximal, characteristic, direct product factor, Sylow
172C2×C53—41no—
173C2×C53—81no—
174C2×C53—81no—
175C2×C53—81no—
176C2×C53#53211yescharacteristic
177C2×C53#57611yescharacteristic
178C2×C53#57711yescharacteristic
179#542C2×C5311yescharacteristic, complemented
180#540C2×C5311yescharacteristic, complemented
181#501C2×C5311yescharacteristic, complemented
182#496C2×C5311yescharacteristic, complemented
183#488C2×C5311yescharacteristic, complemented
184#486C2×C5311yescharacteristic, complemented
185#469C2×C5311yescharacteristic, complemented
186#468C2×C5311yescharacteristic, complemented
187#466C2×C5311yescharacteristic, complemented
188#465C2×C5311yescharacteristic, complemented
189#442C2×C5311yescharacteristic, complemented
190#440C2×C5311yescharacteristic, complemented
191C4×SD16C2×C5311yescharacteristic, complemented
192C4×D8C2×C5311yescharacteristic, complemented
193#405C2×C5311yescharacteristic, complemented
194C53#317911yescharacteristic, direct product factor, Sylow
195C2×SD16C22×C5311yescharacteristic
196C2×SD16C22×C5311yescharacteristic
197C2×D8C22×C5311yescharacteristic
198C2×D8C22×C5311yescharacteristic
199C2×M16C22×C5311yescharacteristic
200C22×C8C22×C5311yescharacteristic
201C4⋊Q8C22×C5311yescharacteristic
202#127C22×C5311yescharacteristic
203#126—21no—
204#125C22×C5311yescharacteristic
205#124—21no—
206#124C22×C5311yescharacteristic
207#123—21no—
208#123—21no—
209#123—21no—
210C22⋊Q8—21no—
211C22⋊Q8C22×C5311yescharacteristic
212#121—21no—
213#121—21no—
214#121C22×C5311yescharacteristic
215#121C22×C5311yescharacteristic
216#121C22×C5311yescharacteristic
217C4×Q8C22×C5311yescharacteristic
218C4×D4C22×C5311yescharacteristic
219C4×D4C22×C5311yescharacteristic
220C4×D4C22×C5311yescharacteristic
221#117C22×C5311yescharacteristic
222#107C22×C5311yescharacteristic
223#107C22×C5311yescharacteristic
224#106C22×C5311yescharacteristic
225#106C22×C5311yescharacteristic
226#103C22×C5311yescharacteristic
227#103C22×C5311yescharacteristic
228#102C22×C5311yescharacteristic
229#102C22×C5311yescharacteristic
230#102C22×C5311yescharacteristic
231#102C22×C5311yescharacteristic
232#102C22×C5311yescharacteristic
233#102C22×C5311yescharacteristic
234#97C22×C5311yescharacteristic
235#97C22×C5311yescharacteristic
236C4×C8C22×C5311yescharacteristic
237C4×C8C22×C5311yescharacteristic
238C2×Q8—21no—
239C2×Q8C23×C5311yescharacteristic
240C2×D4—21no—
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—21no—
245C2×D4C23×C5311yescharacteristic
246C2×D4C23×C5311yescharacteristic
247C2×D4C23×C5311yescharacteristic
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4C23×C5311yescharacteristic
252SD16—22no—
253SD16—22no—
254D8—22no—
255D8—22no—
256M16—22no—
257C2×C8—22no—
258C2×C8C23×C5311yescharacteristic
259C2×C8C23×C5311yescharacteristic
260C2×C8C23×C5311yescharacteristic
261C2×C8C23×C5311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4D4×C5311yescharacteristic
268C4⋊C4D4×C5311yescharacteristic
269C4⋊C4C23×C5311yescharacteristic
270C4⋊C4C23×C5311yescharacteristic
271C4⋊C4C23×C5311yescharacteristic
272C4⋊C4C23×C5311yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4D4×C5311yescharacteristic
283C22⋊C4D4×C5311yescharacteristic
284C42—21no—
285C42C23×C5311yescharacteristic
286C42C23×C5311yescharacteristic
287C23—21no—
288C23—21no—
289C23—21no—
290C23C2×D4×C5311yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—81no—
294D4—21no—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—21no—
300D4—81no—
301D4—81no—
302D4—81no—
303D4—81no—
304D4—81no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4C2×D4×C5311yescharacteristic
316C2×C4C2×D4×C5311yescharacteristic
317C2×C4C2×D4×C5311yescharacteristic
318C2×C4C2×D4×C5311yescharacteristic
319C2×C4C2×D4×C5311yescharacteristic
320C2×C4C24×C5311yescharacteristic
321C8—21no—
322C8—21no—
323C8#41×C5312yes—
324C8#41×C5312yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22C22×D4×C5311yescharacteristic
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—41no—
347C4—41no—
348C4C2×#41×C5311yescharacteristic
349C4C2×#41×C5311yescharacteristic
350C2—41no—
351C2—81no—
352C2—81no—
353C2—81no—
354C2C53×#53211yescharacteristic
355C2C53×#57611yescharacteristic
356C2C53×#57711yescharacteristic
subgroupG/H
center, socleC22×C53C22×D4
commutator, Frattini, cosocleC2×C4C24×C53
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×#542C2semidirect
2. C53×#540C2semidirect
3. C53×#501C2semidirect
4. C53×#496C2semidirect
5. C53×#488C2semidirect
6. C53×#486C2semidirect
7. C53×#469C2semidirect
8. C53×#468C2semidirect
9. C53×#466C2semidirect
10. C53×#465C2semidirect
11. C53×#442C2semidirect
12. C53×#440C2semidirect
13. C4×SD16×C53C2semidirect
14. C4×D8×C53C2semidirect
15. C53×#405C2semidirect
171. #3179C53direct (N × H)
179. #542C2×C53semidirect
180. #540C2×C53semidirect
181. #501C2×C53semidirect
182. #496C2×C53semidirect
183. #488C2×C53semidirect
184. #486C2×C53semidirect
185. #469C2×C53semidirect
186. #468C2×C53semidirect
187. #466C2×C53semidirect
188. #465C2×C53semidirect
189. #442C2×C53semidirect
190. #440C2×C53semidirect
191. C4×SD16C2×C53semidirect
192. C4×D8C2×C53semidirect
193. #405C2×C53semidirect
194. C53#3179direct (N × H)

Maximal subgroups

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

subgroupindex
C53×#5422
C53×#5402
C53×#5012
C53×#4962
C53×#4882
C53×#4862
C53×#4692
C53×#4682
C53×#4662
C53×#4652
C53×#4422
C53×#4402
C4×SD16×C532
C4×D8×C532
C53×#4052
#317953